Daily Papers

Vector quantization is common in deep models, yet its hard assignments block gradients and hinder end-to-end training. We propose DiVeQ, which treats quantization as adding an error vector that mimics the quantization distortion, keeping the forward pass hard while letting gradients flow. We also present a space-filling variant (SF-DiVeQ) that assigns to a curve constructed by the lines connecting codewords, resulting in less quantization error and full codebook usage. Both methods train end-to-end without requiring auxiliary losses or temperature schedules. In VQ-VAE image compression, VQGAN image generation, and DAC speech coding tasks across various data sets, our proposed methods improve reconstruction and sample quality over alternative quantization approaches.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A common workaround is to replace the discrete distribution with a continuous relaxation, yielding a smooth surrogate that admits reparameterized gradient estimates via the reparameterization trick. Building on this idea, we introduce ReDGE, a novel and efficient diffusion-based soft reparameterization method for categorical distributions. Our approach defines a flexible class of gradient estimators that includes the Straight-Through estimator as a special case. Experiments spanning latent variable models and inference-time reward guidance in discrete diffusion models demonstrate that ReDGE consistently matches or outperforms existing gradient-based methods. The code will be made available at https://github.com/samsongourevitch/redge.

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.

Convolutional Neural Networks (CNNs) have exhibited great performance in discriminative feature learning for complex visual tasks. Besides discrimination power, interpretability is another important yet under-explored property for CNNs. One difficulty in the CNN interpretability is that filters and image classes are entangled. In this paper, we introduce a novel pathway to alleviate the entanglement between filters and image classes. The proposed pathway groups the filters in a late conv-layer of CNN into class-specific clusters. Clusters and classes are in a one-to-one relationship. Specifically, we use the Bernoulli sampling to generate the filter-cluster assignment matrix from a learnable filter-class correspondence matrix. To enable end-to-end optimization, we develop a novel reparameterization trick for handling the non-differentiable Bernoulli sampling. We evaluate the effectiveness of our method on ten widely used network architectures (including nine CNNs and a ViT) and five benchmark datasets. Experimental results have demonstrated that our method PICNN (the combination of standard CNNs with our proposed pathway) exhibits greater interpretability than standard CNNs while achieving higher or comparable discrimination power.

We present a variational approximation to the information bottleneck of Tishby et al. (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method "Deep Variational Information Bottleneck", or Deep VIB. We show that models trained with the VIB objective outperform those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.

The soft-thinking paradigm for Large Language Model (LLM) reasoning can outperform the conventional discrete-token Chain-of-Thought (CoT) reasoning in some scenarios, underscoring its research and application value. However, while the discrete-token CoT reasoning pattern can be reinforced through policy optimization algorithms such as group relative policy optimization (GRPO), extending the soft-thinking pattern with Reinforcement Learning (RL) remains challenging. This difficulty stems from the complexities of injecting stochasticity into soft-thinking tokens and updating soft-thinking policies accordingly. As a result, previous attempts to combine soft-thinking with GRPO typically underperform their discrete-token GRPO counterparts. To fully unlock the potential of soft-thinking, this paper presents a novel policy optimization algorithm, SofT-GRPO, to reinforce LLMs under the soft-thinking reasoning pattern. SofT-GRPO injects the Gumbel noise into logits, employs the Gumbel-Softmax technique to avoid soft-thinking tokens outside the pre-trained embedding space, and leverages the reparameterization trick in policy gradient. We conduct experiments across base LLMs ranging from 1.5B to 7B parameters, and results demonstrate that SofT-GRPO enables soft-thinking LLMs to slightly outperform discrete-token GRPO on Pass@1 (+0.13% on average accuracy), while exhibiting a substantial uplift on Pass@32 (+2.19% on average accuracy). Codes and weights are available on https://github.com/zz1358m/SofT-GRPO-master

The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the Unscented Transform (UT) -- a well-known distribution approximation used in the Unscented Kalman Filter (UKF) from the field of filtering. A finite set of statistics called sigma points, sampled deterministically, provides a more informative and lower-variance posterior representation than the ubiquitous noise-scaling of the reparameterization trick, while ensuring higher-quality reconstruction. We further boost the performance by replacing the Kullback-Leibler (KL) divergence with the Wasserstein distribution metric that allows for a sharper posterior. Inspired by the two components, we derive a novel, deterministic-sampling flavor of the VAE, the Unscented Autoencoder (UAE), trained purely with regularization-like terms on the per-sample posterior. We empirically show competitive performance in Fr\'echet Inception Distance (FID) scores over closely-related models, in addition to a lower training variance than the VAE.

We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.

We introduce Reprompting, an iterative sampling algorithm that searches for the Chain-of-Thought (CoT) recipes for a given task without human intervention. Through Gibbs sampling, we infer CoT recipes that work consistently well for a set of training samples. Our method iteratively samples new recipes using previously sampled solutions as parent prompts to solve other training problems. On five Big-Bench Hard tasks that require multi-step reasoning, Reprompting achieves consistently better performance than the zero-shot, few-shot, and human-written CoT baselines. Reprompting can also facilitate transfer of knowledge from a stronger model to a weaker model leading to substantially improved performance of the weaker model. Overall, Reprompting brings up to +17 point improvements over the previous state-of-the-art method that uses human-written CoT prompts.

Large language models (LLMs) have shown impressive performance on language tasks but face challenges when deployed on resource-constrained devices due to their extensive parameters and reliance on dense multiplications, resulting in high memory demands and latency bottlenecks. Shift-and-add reparameterization offers a promising solution by replacing costly multiplications with hardware-friendly primitives in both the attention and multi-layer perceptron (MLP) layers of an LLM. However, current reparameterization techniques require training from scratch or full parameter fine-tuning to restore accuracy, which is resource-intensive for LLMs. To address this, we propose accelerating pretrained LLMs through post-training shift-and-add reparameterization, creating efficient multiplication-free models, dubbed ShiftAddLLM. Specifically, we quantize each weight matrix into binary matrices paired with group-wise scaling factors. The associated multiplications are reparameterized into (1) shifts between activations and scaling factors and (2) queries and adds according to the binary matrices. To reduce accuracy loss, we present a multi-objective optimization method to minimize both weight and output activation reparameterization errors. Additionally, based on varying sensitivity across layers to reparameterization, we develop an automated bit allocation strategy to further reduce memory usage and latency. Experiments on five LLM families and eight tasks consistently validate the effectiveness of ShiftAddLLM, achieving average perplexity improvements of 5.6 and 22.7 points at comparable or lower latency compared to the most competitive quantized LLMs at 3 and 2 bits, respectively, and more than 80% memory and energy reductions over the original LLMs. Codes and models are available at https://github.com/GATECH-EIC/ShiftAddLLM.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and attention speedup. This leaves an underexplored research question: can we reduce the number of stacked transformer layers while maintaining comparable representational capacity? To answer this, we propose a branch-based structural reparameterization technique that operates during the training phase. Our approach leverages parallel branches within transformer blocks that can be systematically consolidated into streamlined single-path models suitable for inference deployment. The consolidation mechanism works by gradually merging branches at the entry points of nonlinear components, enabling both feed-forward networks (FFN) and multi-head self-attention (MHSA) modules to undergo exact mathematical reparameterization without inducing approximation errors at test time. When applied to ViT-Tiny, the framework successfully reduces the original 12-layer architecture to 6, 4, or as few as 3 layers while maintaining classification accuracy on ImageNet-1K. The resulting compressed models achieve inference speedups of up to 37% on mobile CPU platforms. Our findings suggest that the conventional wisdom favoring extremely deep transformer stacks may be unnecessarily restrictive, and point toward new opportunities for constructing efficient vision transformers.

Deep reinforcement learning (DRL) has successfully solved various problems recently, typically with a unimodal policy representation. However, grasping distinguishable skills for some tasks with non-unique optima can be essential for further improving its learning efficiency and performance, which may lead to a multimodal policy represented as a mixture-of-experts (MOE). To our best knowledge, present DRL algorithms for general utility do not deploy this method as policy function approximators due to the potential challenge in its differentiability for policy learning. In this work, we propose a probabilistic mixture-of-experts (PMOE) implemented with a Gaussian mixture model (GMM) for multimodal policy, together with a novel gradient estimator for the indifferentiability problem, which can be applied in generic off-policy and on-policy DRL algorithms using stochastic policies, e.g., Soft Actor-Critic (SAC) and Proximal Policy Optimisation (PPO). Experimental results testify the advantage of our method over unimodal polices and two different MOE methods, as well as a method of option frameworks, based on the above two types of DRL algorithms, on six MuJoCo tasks. Different gradient estimations for GMM like the reparameterisation trick (Gumbel-Softmax) and the score-ratio trick are also compared with our method. We further empirically demonstrate the distinguishable primitives learned with PMOE and show the benefits of our method in terms of exploration.

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.

We reveal that feedforward network (FFN) layers, rather than attention layers, are the primary contributors to Vision Transformer (ViT) inference latency, with their impact signifying as model size increases. This finding highlights a critical opportunity for optimizing the efficiency of large-scale ViTs by focusing on FFN layers. In this work, we propose a novel channel idle mechanism that facilitates post-training structural reparameterization for efficient FFN layers during testing. Specifically, a set of feature channels remains idle and bypasses the nonlinear activation function in each FFN layer, thereby forming a linear pathway that enables structural reparameterization during inference. This mechanism results in a family of ReParameterizable Vision Transformers (RePaViTs), which achieve remarkable latency reductions with acceptable sacrifices (sometimes gains) in accuracy across various ViTs. The benefits of our method scale consistently with model sizes, demonstrating greater speed improvements and progressively narrowing accuracy gaps or even higher accuracies on larger models. In particular, RePa-ViT-Large and RePa-ViT-Huge enjoy 66.8% and 68.7% speed-ups with +1.7% and +1.1% higher top-1 accuracies under the same training strategy, respectively. RePaViT is the first to employ structural reparameterization on FFN layers to expedite ViTs to our best knowledge, and we believe that it represents an auspicious direction for efficient ViTs. Source code is available at https://github.com/Ackesnal/RePaViT.

Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression setting, showing that verifier-guided retraining can yield near-term improvements, but ultimately drives the parameter estimate to the verifier's "knowledge center" in the long run. Our theory further predicts that, unless the verifier is perfectly reliable, these early gains will plateau and may even reverse. Indeed, our experiments across linear regression, Variational Autoencoders (VAEs) trained on MNIST, and fining-tuning SmolLM2-135M on the XSUM task confirm these theoretical insights.

While Large Language Models (LLMs) have demonstrated impressive performance in various domains and tasks, concerns about their safety are becoming increasingly severe. In particular, since models may store unsafe knowledge internally, machine unlearning has emerged as a representative paradigm to ensure model safety. Existing approaches employ various training techniques, such as gradient ascent and negative preference optimization, in attempts to eliminate the influence of undesired data on target models. However, these methods merely suppress the activation of undesired data through parametric training without completely eradicating its informational traces within the model. This fundamental limitation makes it difficult to achieve effective continuous unlearning, rendering these methods vulnerable to relearning attacks. To overcome these challenges, we propose a Metamorphosis Representation Projection (MRP) approach that pioneers the application of irreversible projection properties to machine unlearning. By implementing projective transformations in the hidden state space of specific network layers, our method effectively eliminates harmful information while preserving useful knowledge. Experimental results demonstrate that our approach enables effective continuous unlearning and successfully defends against relearning attacks, achieving state-of-the-art performance in unlearning effectiveness while preserving natural performance. Our code is available in https://github.com/ChengcanWu/MRP.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. But both attention and multi-layer perceptions (MLPs) in ViTs are not efficient enough due to dense multiplications, resulting in costly training and inference. To this end, we propose to reparameterize the pre-trained ViT with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed ShiftAddViT, which aims for end-to-end inference speedups on GPUs without the need of training from scratch. Specifically, all MatMuls among queries, keys, and values are reparameterized by additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized by shift kernels. We utilize TVM to implement and optimize those customized kernels for practical hardware deployment on GPUs. We find that such a reparameterization on (quadratic or linear) attention maintains model accuracy, while inevitably leading to accuracy drops when being applied to MLPs. To marry the best of both worlds, we further propose a new mixture of experts (MoE) framework to reparameterize MLPs by taking multiplication or its primitives as experts, e.g., multiplication and shift, and designing a new latency-aware load-balancing loss. Such a loss helps to train a generic router for assigning a dynamic amount of input tokens to different experts according to their latency. In principle, the faster experts run, the larger amount of input tokens are assigned. Extensive experiments consistently validate the effectiveness of our proposed ShiftAddViT, achieving up to 5.18\times$ latency reductions on GPUs and 42.9%$ energy savings, while maintaining comparable accuracy as original or efficient ViTs.

Machine unlearning for large language models often faces a privacy dilemma in which strict constraints prohibit sharing either the server's parameters or the client's forget set. To address this dual non-disclosure constraint, we propose MPU, an algorithm-agnostic privacy-preserving Multiple Perturbed Copies Unlearning framework that primarily introduces two server-side modules: Pre-Process for randomized copy generation and Post-Process for update aggregation. In Pre-Process, the server distributes multiple perturbed and reparameterized model instances, allowing the client to execute unlearning locally on its private forget set without accessing the server's exact original parameters. After local unlearning, the server performs Post-Process by inverting the reparameterization and aggregating updates with a harmonic denoising procedure to alleviate the impact of perturbation. Experiments with seven unlearning algorithms show that MPU achieves comparable unlearning performance to noise-free baselines, with most algorithms' average degradation well below 1% under 10% noise, and can even outperform the noise-free baseline for some algorithms under 1% noise. Code is available at https://github.com/Tristan-SHU/MPU.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

Large Language Models memorize vast amounts of training data, raising concerns regarding privacy, copyright infringement, and safety. Machine unlearning seeks to remove the influence of a targeted forget set while preserving model performance, ideally approximating a model retrained from scratch without the forget set. Existing approaches aim to achieve this by updating model parameters via gradient-based methods. However, these updates are computationally expensive, lead to irreversible weight changes, and degrade when the model is quantized for deployment. A recent alternative to changing model weights is activation engineering, where activations are changed during inference to steer model behavior. Despite circumventing weight editing, naive activation steering introduces its own failure modes, as a single global steering vector applies the same intervention to every input, leading to unintended changes in model behavior. We introduce Inference-Time Unlearning via Gated Activation Redirection (GUARD-IT), a training- and gradient-free method that unlearns via input-dependent activation steering at inference time. The resulting intervention is applied as a norm-preserving rotation in the residual stream, leaving model weights untouched. Experiments on TOFU and MUSE show that GUARD-IT matches or exceeds 12 gradient-based baselines across three model scales, while being the only method to simultaneously preserve utility, suppress memorization, and avoid catastrophic collapse across all settings. GUARD-IT further supports continual unlearning without retraining, and remains effective under quantization, a scenario in which parameter-editing methods degrade.

In this paper, we introduce Selective-distillation for Class and Architecture-agnostic unleaRning (SCAR), a novel approximate unlearning method. SCAR efficiently eliminates specific information while preserving the model's test accuracy without using a retain set, which is a key component in state-of-the-art approximate unlearning algorithms. Our approach utilizes a modified Mahalanobis distance to guide the unlearning of the feature vectors of the instances to be forgotten, aligning them to the nearest wrong class distribution. Moreover, we propose a distillation-trick mechanism that distills the knowledge of the original model into the unlearning model with out-of-distribution images for retaining the original model's test performance without using any retain set. Importantly, we propose a self-forget version of SCAR that unlearns without having access to the forget set. We experimentally verified the effectiveness of our method, on three public datasets, comparing it with state-of-the-art methods. Our method obtains performance higher than methods that operate without the retain set and comparable w.r.t the best methods that rely on the retain set.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

Class-Incremental Learning (CIL) requires models to continually acquire knowledge of new classes without forgetting old ones. Despite Pre-trained Models (PTMs) have shown excellent performance in CIL, catastrophic forgetting still occurs as the model learns new concepts. Existing work seeks to utilize lightweight components to adjust the PTM, while the forgetting phenomenon still comes from {\em parameter and retrieval} levels. Specifically, iterative updates of the model result in parameter drift, while mistakenly retrieving irrelevant modules leads to the mismatch during inference. To this end, we propose MOdel Surgery (MOS) to rescue the model from forgetting previous knowledge. By training task-specific adapters, we continually adjust the PTM to downstream tasks. To mitigate parameter-level forgetting, we present an adapter merging approach to learn task-specific adapters, which aims to bridge the gap between different components while reserve task-specific information. Besides, to address retrieval-level forgetting, we introduce a training-free self-refined adapter retrieval mechanism during inference, which leverages the model's inherent ability for better adapter retrieval. By jointly rectifying the model with those steps, MOS can robustly resist catastrophic forgetting in the learning process. Extensive experiments on seven benchmark datasets validate MOS's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/AAAI25-MOS

We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in https://github.com/radarFudan/Curse-of-memory

Large language models trained on web-scale corpora can memorize undesirable data containing misinformation, copyrighted material, or private or sensitive information. Recently, several machine unlearning algorithms have been proposed to eliminate the effect of such datapoints from trained models -- that is, to approximate a model that had never been trained on these datapoints in the first place. However, evaluating the effectiveness of unlearning algorithms remains an open challenge. Previous work has relied on heuristics -- such as verifying that the model can no longer reproduce the specific information targeted for removal while maintaining accuracy on unrelated test data. These approaches inadequately capture the complete effect of reversing the influence of datapoints on a trained model. In this work, we propose the RESTOR framework for machine unlearning evaluation, which assesses the ability of unlearning algorithms for targeted data erasure, by evaluating the ability of models to forget the knowledge introduced in these datapoints, while simultaneously recovering the model's knowledge state had it never encountered these datapoints. RESTOR helps uncover several novel insights about popular unlearning algorithms, and the mechanisms through which they operate -- for instance, identifying that some algorithms merely emphasize forgetting but not recovering knowledge, and that localizing unlearning targets can enhance unlearning performance.

This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling. The code is available at https://github.com/checkcrab/SDSB.

Neural Networks can be efficiently compressed through pruning, significantly reducing storage and computational demands while maintaining predictive performance. Simple yet effective methods like Iterative Magnitude Pruning (IMP, Han et al., 2015) remove less important parameters and require a costly retraining procedure to recover performance after pruning. However, with the rise of Large Language Models (LLMs), full retraining has become infeasible due to memory and compute constraints. In this study, we challenge the practice of retraining all parameters by demonstrating that updating only a small subset of highly expressive parameters is often sufficient to recover or even improve performance compared to full retraining. Surprisingly, retraining as little as 0.27%-0.35% of the parameters of GPT-architectures (OPT-2.7B/6.7B/13B/30B) achieves comparable performance to One Shot IMP across various sparsity levels. Our method, Parameter-Efficient Retraining after Pruning (PERP), drastically reduces compute and memory demands, enabling pruning and retraining of up to 30 billion parameter models on a single NVIDIA A100 GPU within minutes. Despite magnitude pruning being considered as unsuited for pruning LLMs, our findings show that PERP positions it as a strong contender against state-of-the-art retraining-free approaches such as Wanda (Sun et al., 2023) and SparseGPT (Frantar & Alistarh, 2023), opening up a promising alternative to avoiding retraining.

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by straightening generation trajectories. However, ReFlow is an iterative procedure, typically requiring training on simulated data, and results in reduced sample quality. To mitigate sample deterioration, we examine the design space of ReFlow and highlight potential pitfalls in prior heuristic practices. We then propose seven improvements for training dynamics, learning and inference, which are verified with thorough ablation studies on CIFAR10 32 times 32, AFHQv2 64 times 64, and FFHQ 64 times 64. Combining all our techniques, we achieve state-of-the-art FID scores (without / with guidance, resp.) for fast generation via neural ODEs: 2.23 / 1.98 on CIFAR10, 2.30 / 1.91 on AFHQv2, 2.84 / 2.67 on FFHQ, and 3.49 / 1.74 on ImageNet-64, all with merely 9 neural function evaluations.

Recent studies suggest that with sufficiently wide models, most SGD solutions can, up to permutation, converge into the same basin. This phenomenon, known as the model re-basin regime, has significant implications for model averaging by ensuring the linear mode connectivity. However, current re-basin strategies are ineffective in many scenarios due to a lack of comprehensive understanding of underlying mechanisms. Addressing this gap, this paper provides novel insights into understanding and improving the standard practice. Firstly, we decompose re-normalization into rescaling and reshift, uncovering that rescaling plays a crucial role in re-normalization while re-basin performance is sensitive to shifts in model activation. The finding calls for a more nuanced handling of the activation shift. Secondly, we identify that the merged model suffers from the issue of activation collapse and magnitude collapse. Varying the learning rate, weight decay, and initialization method can mitigate the issues and improve model performance. Lastly, we propose a new perspective to unify the re-basin and pruning, under which a lightweight yet effective post-pruning technique is derived, which can significantly improve the model performance after pruning. Our implementation is available at https://github.com/XingyuQu/rethink-re-basin.

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation, which approximates the pruned blocks. The estimated linear mapping can be seamlessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25\% pruning while retaining approximately 90\% of the original model's performance on open benchmarks - without any training or healing steps, resulting in minimal computational overhead. We provide an open-source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at https://github.com/mts-ai/ReplaceMe

Previous studies have found that an adversary attacker can often infer unintended input information from intermediate-layer features. We study the possibility of preventing such adversarial inference, yet without too much accuracy degradation. We propose a generic method to revise the neural network to boost the challenge of inferring input attributes from features, while maintaining highly accurate outputs. In particular, the method transforms real-valued features into complex-valued ones, in which the input is hidden in a randomized phase of the transformed features. The knowledge of the phase acts like a key, with which any party can easily recover the output from the processing result, but without which the party can neither recover the output nor distinguish the original input. Preliminary experiments on various datasets and network structures have shown that our method significantly diminishes the adversary's ability in inferring about the input while largely preserves the resulting accuracy.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

We introduce RE-Adapt, an approach to fine-tuning large language models on new domains without degrading any pre-existing instruction-tuning. We reverse engineer an adapter which isolates what an instruction-tuned model has learned beyond its corresponding pretrained base model. Importantly, this requires no additional data or training. We can then fine-tune the base model on a new domain and readapt it to instruction following with the reverse engineered adapter. RE-Adapt and our low-rank variant LoRE-Adapt both outperform other methods of fine-tuning, across multiple popular LLMs and datasets, even when the models are used in conjunction with retrieval-augmented generation.

Current LLM unlearning methods are not robust. A few steps of finetuning can revert their effects. We begin by showing that this is true even for an idealized form of unlearning: training to imitate a model that was never trained on unwanted information. This shows that training a model can drastically modify its input-output behavior while leaving its underlying capabilities intact. In light of this dynamic, we show our main result. Training a randomly initialized student on the outputs of an unlearned model transfers behaviors while leaving latent capabilities behind. In short, distillation robustifies unlearning. Based on this result, we propose Unlearn-Noise-Distill-on-Outputs (UNDO), a scalable method that distills an unlearned model into a noised copy of itself. UNDO introduces a tunable tradeoff between compute cost and robustness, establishing a new Pareto frontier on synthetic language and arithmetic tasks. At its strongest setting, UNDO matches the robustness of a model retrained from scratch with perfect data filtering while using only 60-80% of the compute and requiring only 0.01% of the pretraining data to be labeled. We also show that UNDO robustifies unlearning on the more realistic Weapons of Mass Destruction Proxy (WMDP) benchmark. Since distillation is widely used in practice, incorporating an unlearning step beforehand offers a convenient path to robust capability removal.

With the success of flow matching in visual generation, sampling efficiency remains a critical bottleneck for its practical application. Among flow models' accelerating methods, ReFlow has been somehow overlooked although it has theoretical consistency with flow matching. This is primarily due to its suboptimal performance in practical scenarios compared to consistency distillation and score distillation. In this work, we investigate this issue within the ReFlow framework and propose FlowSteer, a method unlocks the potential of ReFlow-based distillation by guiding the student along teacher's authentic generation trajectories. We first identify that Piecewised ReFlow's performance is hampered by a critical distribution mismatch during the training and propose Online Trajectory Alignment(OTA) to resolve it. Then, we introduce a adversarial distillation objective applied directly on the ODE trajectory, improving the student's adherence to the teacher's generation trajectory. Furthermore, we find and fix a previously undiscovered flaw in the widely-used FlowMatchEulerDiscreteScheduler that largely degrades few-step inference quality. Our experiment result on SD3 demonstrates our method's efficacy.

In this paper, we introduce agentic unlearning which removes specified information from both model parameters and persistent memory in agents with closed-loop interaction. Existing unlearning methods target parameters alone, leaving two critical gaps: (i) parameter-memory backflow, where retrieval reactivates parametric remnants or memory artifacts reintroduce sensitive content, and (ii) the absence of a unified strategy that covers both parameter and memory pathways. We present Synchronized Backflow Unlearning (SBU), a framework that unlearns jointly across parameter and memory pathways. The memory pathway performs dependency closure-based unlearning that prunes isolated entities while logically invalidating shared artifacts. The parameter pathway employs stochastic reference alignment to guide model outputs toward a high-entropy prior. These pathways are integrated via a synchronized dual-update protocol, forming a closed-loop mechanism where memory unlearning and parametric suppression reinforce each other to prevent cross-pathway recontamination. Experiments on medical QA benchmarks show that SBU reduces traces of targeted private information across both pathways with limited degradation on retained data.

Repeated Sampling (RS) is a simple inference-time algorithm that has been shown to improve model performance on complex tasks. Although it is an effective way of scaling inference time, it often struggles to generate diverse solution candidates, frequently relying on the same underlying approach to solve the problem and thus producing redundant samples. To address this limitation, we propose a new inference algorithm, GuidedSampling, which decouples the exploration and generation phases during inference, increasing diversity of generated candidate solutions. The exploration phase identifies multiple concepts that can be utilized to solve the problem, while the generation phase applies a specific concept to provide final solution candidates. We first define the theoretical bounds of GuidedSampling and then empirically demonstrate that it improves the performance of base model at pass@50 by on an average ~21.6% across various benchmarks compared to RS. Furthermore, models trained on trajectories of GuidedSampling exhibit substantial performance improvements at pass@5 by on an average ~9.7%, compared to models trained on traditional RS. Additionally, models trained with GuidedSampling increases the average number of concepts per instance (1.67 -> 3.03), yielding a diverse set of candidates than traditional RS.

Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for each task, it largely overlooks scenarios where models are compressed into low-rank representations, either through low-rank adaptation (LoRA) or post-training singular value decomposition (SVD). We first demonstrate that applying conventional merging methods to low-rank weights leads to severe performance degradation in the merged model. Motivated by this phenomenon, we propose a fundamentally different approach: instead of collapsing all adapters into one set of weights, we construct a compact basis (e.g., an equivalent of holding two or more models) from which original task-specific models can be recovered via linear combination. This reframes merging as generating a reconstruction-capable model space rather than producing a single merged model. Crucially, this allows us to ``revert'' to each individual model when needed, recognizing that no merged model can consistently outperform one specialized for its task. Building on this insight, we introduce our method, Reversible Model Merging (RMM), an efficient, data-free, and flexible method that provides a closed-form solution for selecting the optimal basis of model weights and task-specific coefficients for linear combination. Extensive experiments across diverse datasets and model scales demonstrate that RMM consistently outperforms existing merging approaches, preserving the performance of low-rank compressed models by a significant margin.

Inspired by the principle of deliberate practice in human learning, we propose Deliberate Practice for Synthetic Data Generation (DP), a novel framework that improves sample efficiency through dynamic synthetic data generation. Prior work has shown that scaling synthetic data is inherently challenging, as naively adding new data leads to diminishing returns. To address this, pruning has been identified as a key mechanism for improving scaling, enabling models to focus on the most informative synthetic samples. Rather than generating a large dataset and pruning it afterward, DP efficiently approximates the direct generation of informative samples. We theoretically show how training on challenging, informative examples improves scaling laws and empirically validate that DP achieves better scaling performance with significantly fewer training samples and iterations. On ImageNet-100, DP generates 3.4x fewer samples and requires six times fewer iterations, while on ImageNet-1k, it generates 8x fewer samples with a 30 percent reduction in iterations, all while achieving superior performance compared to prior work.

Recent advances in Reinforcement Learning with Verified Reward (RLVR) have driven the emergence of more sophisticated cognitive behaviors in large language models (LLMs), thereby enhancing their reasoning capabilities. However, in prior RLVR pipelines, the repeated use of static initial-state sampling drawn exactly from the dataset distribution during each sampling phase produced overly deterministic, low diversity model behavior, which manifested as rapid entropy collapse and hindered sustained performance gains during prolonged training. To address this issue, we introduce CURE (Critical-token-gUided Re concatenation for Entropy-collapse prevention), a two-stage framework that balances exploration and exploitation. Specifically, in the first stage, to deliberately steer the model toward novel yet coherent contexts, we re-generate at high-entropy critical tokens and jointly optimize the original and the branched trajectories. The further comparison with vanilla DAPO shows that the regeneration process achieves a better performance on math reasoning tasks while sustaining a high-level entropy degree for exploration. In the second stage, we continue training with static initial-state sampling by DAPO, intentionally placing the model in a familiar state to gradually strengthen exploitation. Extensive experiments on Qwen-2.5-Math-7B show that, compared to other RLVR methods, CURE achieves a 5% performance gain across six math benchmarks, establishing state-of-the-art performance in both entropy and accuracy. A series of experiments further validate the effectiveness of our approach. Code is available at https://github.com/bytedance/CURE.

Large transformer models have demonstrated remarkable success. Post-training quantization (PTQ), which requires only a small dataset for calibration and avoids end-to-end retraining, is a promising solution for compressing these large models. Regrettably, existing PTQ methods typically exhibit non-trivial performance loss. We find that the performance bottleneck stems from over-consideration of hardware compatibility in the quantization process, compelling them to reluctantly employ simple quantizers, albeit at the expense of accuracy. With the above insights, we propose RepQuant, a novel PTQ framework with quantization-inference decoupling paradigm to address the above issues. RepQuant employs complex quantizers in the quantization process and simplified quantizers in the inference process, and performs mathematically equivalent transformations between the two through quantization scale reparameterization, thus ensuring both accurate quantization and efficient inference. More specifically, we focus on two components with extreme distributions: LayerNorm activations and Softmax activations. Initially, we apply channel-wise quantization and log2 quantization, respectively, which are tailored to their distributions. In particular, for the former, we introduce a learnable per-channel dual clipping scheme, which is designed to efficiently identify outliers in the unbalanced activations with fine granularity. Then, we reparameterize the scales to hardware-friendly layer-wise quantization and log2 quantization for inference. Moreover, quantized weight reconstruction is seamlessly integrated into the above procedure to further push the performance limits. Extensive experiments are performed on different large-scale transformer variants on multiple tasks, including vision, language, and multi-modal transformers, and RepQuant encouragingly demonstrates significant performance advantages.

A central challenge in sequence modeling is efficiently handling tasks with extended contexts. While recent state-space models (SSMs) have made significant progress in this area, they often lack input-dependent filtering or require substantial increases in model complexity to handle input variability. We address this gap by introducing S7, a simplified yet powerful SSM that can handle input dependence while incorporating stable reparameterization and specific design choices to dynamically adjust state transitions based on input content, maintaining efficiency and performance. We prove that this reparameterization ensures stability in long-sequence modeling by keeping state transitions well-behaved over time. Additionally, it controls the gradient norm, enabling efficient training and preventing issues like exploding or vanishing gradients. S7 significantly outperforms baselines across various sequence modeling tasks, including neuromorphic event-based datasets, Long Range Arena benchmarks, and various physical and biological time series. Overall, S7 offers a more straightforward approach to sequence modeling without relying on complex, domain-specific inductive biases, achieving significant improvements across key benchmarks.

Flow-based generative models have recently demonstrated strong performance, yet sampling typically relies on expensive numerical integration of ordinary differential equations (ODEs). Rectified Flow enables one-step sampling by learning nearly straight probability paths, but achieving such straightness requires multiple computationally intensive reflow iterations. MeanFlow achieves one-step generation by directly modeling the average velocity over time; however, when trained on highly curved flows, it suffers from slow convergence and noisy supervision. To address these limitations, we propose Rectified MeanFlow, a framework that models the mean velocity field along the rectified trajectory using only a single reflow step. This eliminates the need for perfectly straightened trajectories while enabling efficient training. Furthermore, we introduce a simple yet effective truncation heuristic that aims to reduce residual curvature and further improve performance. Extensive experiments on ImageNet at 64, 256, and 512 resolutions show that Re-MeanFlow consistently outperforms prior one-step flow distillation and Rectified Flow methods in both sample quality and training efficiency. Code is available at https://github.com/Xinxi-Zhang/Re-MeanFlow.

Multimodal language models (MLLMs) require large parameter capacity to align high-dimensional visual features with linguistic representations, making them computationally heavy and difficult to deploy efficiently. We introduce a progressive reparameterization strategy that compresses these models by gradually replacing dense feed-forward network blocks with compact Parameterized Hypercomplex Multiplication (PHM) layers. A residual interpolation schedule, together with lightweight reconstruction and knowledge distillation losses, ensures that the PHM modules inherit the functional behavior of their dense counterparts during training. This transition yields substantial parameter and FLOP reductions while preserving strong multimodal alignment, enabling faster inference without degrading output quality. We evaluate the approach on multiple vision-language models (VLMs). Our method maintains performance comparable to the base models while delivering significant reductions in model size and inference latency. Progressive PHM substitution thus offers an architecture-compatible path toward more efficient multimodal reasoning and complements existing low-bit quantization techniques.

Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data doubles the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by 8 times. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.

If we cannot inspect the training data of a large language model (LLM), how can we ever know what it has seen? We believe the most compelling evidence arises when the model itself freely reproduces the target content. As such, we propose RECAP, an agentic pipeline designed to elicit and verify memorized training data from LLM outputs. At the heart of RECAP is a feedback-driven loop, where an initial extraction attempt is evaluated by a secondary language model, which compares the output against a reference passage and identifies discrepancies. These are then translated into minimal correction hints, which are fed back into the target model to guide subsequent generations. In addition, to address alignment-induced refusals, RECAP includes a jailbreaking module that detects and overcomes such barriers. We evaluate RECAP on EchoTrace, a new benchmark spanning over 30 full books, and the results show that RECAP leads to substantial gains over single-iteration approaches. For instance, with GPT-4.1, the average ROUGE-L score for the copyrighted text extraction improved from 0.38 to 0.47 - a nearly 24% increase.

Works on lottery ticket hypothesis (LTH) and single-shot network pruning (SNIP) have raised a lot of attention currently on post-training pruning (iterative magnitude pruning), and before-training pruning (pruning at initialization). The former method suffers from an extremely large computation cost and the latter usually struggles with insufficient performance. In comparison, during-training pruning, a class of pruning methods that simultaneously enjoys the training/inference efficiency and the comparable performance, temporarily, has been less explored. To better understand during-training pruning, we quantitatively study the effect of pruning throughout training from the perspective of pruning plasticity (the ability of the pruned networks to recover the original performance). Pruning plasticity can help explain several other empirical observations about neural network pruning in literature. We further find that pruning plasticity can be substantially improved by injecting a brain-inspired mechanism called neuroregeneration, i.e., to regenerate the same number of connections as pruned. We design a novel gradual magnitude pruning (GMP) method, named gradual pruning with zero-cost neuroregeneration (GraNet), that advances state of the art. Perhaps most impressively, its sparse-to-sparse version for the first time boosts the sparse-to-sparse training performance over various dense-to-sparse methods with ResNet-50 on ImageNet without extending the training time. We release all codes in https://github.com/Shiweiliuiiiiiii/GraNet.

Large Reasoning Models possess remarkable capabilities for self-correction in general domain; however, they frequently struggle to recover from unsafe reasoning trajectories under adversarial attacks. Existing alignment methods attempt to mitigate this vulnerability by fine-tuning the model on expert data including reflection traces or adversarial prefixes. Crucially, these approaches are often hindered by static training data which inevitably deviate from model's dynamic, on-policy reasoning traces, resulting in model hardly covering its vast generation space and learning to recover from its own failures. To bridge this gap, we propose Self-ReSET, a pure reinforcement learning framework designed to equip LRMs with the intrinsic capacity to recover from their own safety error trajectories, which are subsequently reused as an initial state for reinforcement learning. Extensive experiments across various LRMs and benchmarks demonstrate that Self-ReSET significantly enhances robustness against adversarial attacks especially out-of-distribution (OOD) jailbreak prompts while maintaining general utility, along with efficient data utilization. Further analysis reveals that our method effectively fosters self-recovery patterns, enabling models to better identify and recover from unsafe intermediate error states back to benign paths. Our codes and data are available at https://github.com/Ing1024/Self-ReSET.

Text-to-image models encounter safety issues, including concerns related to copyright and Not-Safe-For-Work (NSFW) content. Despite several methods have been proposed for erasing inappropriate concepts from diffusion models, they often exhibit incomplete erasure, consume a lot of computing resources, and inadvertently damage generation ability. In this work, we introduce Reliable and Efficient Concept Erasure (RECE), a novel approach that modifies the model in 3 seconds without necessitating additional fine-tuning. Specifically, RECE efficiently leverages a closed-form solution to derive new target embeddings, which are capable of regenerating erased concepts within the unlearned model. To mitigate inappropriate content potentially represented by derived embeddings, RECE further aligns them with harmless concepts in cross-attention layers. The derivation and erasure of new representation embeddings are conducted iteratively to achieve a thorough erasure of inappropriate concepts. Besides, to preserve the model's generation ability, RECE introduces an additional regularization term during the derivation process, resulting in minimizing the impact on unrelated concepts during the erasure process. All the processes above are in closed-form, guaranteeing extremely efficient erasure in only 3 seconds. Benchmarking against previous approaches, our method achieves more efficient and thorough erasure with minor damage to original generation ability and demonstrates enhanced robustness against red-teaming tools. Code is available at https://github.com/CharlesGong12/RECE.

While diffusion models effectively generate remarkable synthetic images, a key limitation is the inference inefficiency, requiring numerous sampling steps. To accelerate inference and maintain high-quality synthesis, teacher-student distillation is applied to compress the diffusion models in a progressive and binary manner by retraining, e.g., reducing the 1024-step model to a 128-step model in 3 folds. In this paper, we propose a single-fold distillation algorithm, SFDDM, which can flexibly compress the teacher diffusion model into a student model of any desired step, based on reparameterization of the intermediate inputs from the teacher model. To train the student diffusion, we minimize not only the output distance but also the distribution of the hidden variables between the teacher and student model. Extensive experiments on four datasets demonstrate that our student model trained by the proposed SFDDM is able to sample high-quality data with steps reduced to as little as approximately 1%, thus, trading off inference time. Our remarkable performance highlights that SFDDM effectively transfers knowledge in single-fold distillation, achieving semantic consistency and meaningful image interpolation.

As neural networks grow in size and complexity, inference speeds decline. To combat this, one of the most effective compression techniques -- channel pruning -- removes channels from weights. However, for multi-branch segments of a model, channel removal can introduce inference-time memory copies. In turn, these copies increase inference latency -- so much so that the pruned model can be slower than the unpruned model. As a workaround, pruners conventionally constrain certain channels to be pruned together. This fully eliminates memory copies but, as we show, significantly impairs accuracy. We now have a dilemma: Remove constraints but increase latency, or add constraints and impair accuracy. In response, our insight is to reorder channels at export time, (1) reducing latency by reducing memory copies and (2) improving accuracy by removing constraints. Using this insight, we design a generic algorithm UPSCALE to prune models with any pruning pattern. By removing constraints from existing pruners, we improve ImageNet accuracy for post-training pruned models by 2.1 points on average -- benefiting DenseNet (+16.9), EfficientNetV2 (+7.9), and ResNet (+6.2). Furthermore, by reordering channels, UPSCALE improves inference speeds by up to 2x over a baseline export.

Language models trained on web-scale corpora risk memorizing and exposing sensitive information, prompting the need for effective machine unlearning. Prior methods mainly focus on input queries to suppress sensitive outputs, yet this often fails to eliminate the underlying knowledge and limits scalability. To address this, we propose Corrective Unlearning with Retrieved Exclusions (CURE), a novel unlearning framework that verifies model outputs for leakage and revises them into safe responses. Specifically, CURE employs a lightweight corrector that is applied to the original model to verify whether outputs contain target knowledge and to rewrite them if any leakage is detected. To efficiently handle large-scale unlearning requests, CURE retrieves unlearning targets that are relevant to the initial response and provides them as in-context references to the corrector for detection and conditional revision. By leveraging this retrieval augmentation, the corrector can adapt to new unlearning requests without additional training. Extensive evaluations demonstrate that CURE substantially reduces information leakage, even from indirect queries where prior works fall short, while maintaining response quality and general utility. Moreover, it demonstrates robustness under continual unlearning scenarios, making it practical for real-world applications.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

High-quality pretraining data is the fossil fuel of large language models (LLMs), yet its reserves are running low for frontier models. In this paper, we introduce RePro, a novel web recycling method that trains a relatively small LM with reinforcement learning to generate effective and faithful rephrasings of pretraining data. Specifically, we design one quality reward and three faithfulness rewards, optimizing the LM rephraser to convert organic data into high-quality rephrasings while maintaining its core semantics and structure. In our experiment, we train a 4B rephraser to recycle 72B tokens sampled from DCLM-RefinedWeb. Pretraining results on 400M and 1.4B models demonstrate that RePro delivers 4.7%-14.0% relative accuracy gains over organic-only baseline on 22 downstream tasks. RePro also outperforms ReWire, the state-of-the-art web recycling method that prompts a 70B rephraser, as well as the organic baseline with a 4x larger data pool. Experiments with different amounts of recycled data highlight that RePro improves organic data efficiency by 2-3x. Individual and distributional analyses validate that RePro preserves more critical information and faithfully reflects the characteristics of organic data compared to prompting-based methods. Together, these results show that RePro provides an efficient and controllable path to effectively harness the fossil fuel of LLM pretraining. We open-source our code, rephraser, and recycled data at https://github.com/cxcscmu/RePro.

As large language models evolve, Machine Unlearning has emerged to address growing concerns around user privacy, copyright infringement, and overall safety. Yet state-of-the-art (SOTA) unlearning methods often suffer from catastrophic forgetting and metric imbalance, for example, by over-optimizing one objective (e.g., unlearning effectiveness, utility preservation, or privacy protection) at the expense of others. In addition, small perturbations in the representation or parameter space can be exploited by relearn and jailbreak attacks. To address these challenges, we propose PRISM, a unified framework that enforces dual-space smoothness in representation and parameter spaces to improve robustness and balance unlearning metrics. PRISM consists of two smoothness optimization stages: (i) a representation space stage that employs a robustly trained probe to defend against jailbreak attacks, and (ii) a parameter-space stage that decouples retain-forget gradient conflicts, reduces imbalance, and smooths the parameter space to mitigate relearning attacks. Extensive experiments on WMDP and MUSE, across conversational-dialogue and continuous-text settings, show that PRISM outperforms SOTA baselines under multiple attacks while achieving a better balance among key metrics.

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

Unlearning in large language models (LLMs) aims to remove harmful training data while preserving overall utility. However, we find that existing methods often hallucinate, generate abnormal token sequences, or behave inconsistently, raising safety and trust concerns. According to prior literature on LLM honesty, such behaviors are often associated with dishonesty. This motivates us to investigate the notion of honesty in the context of model unlearning. We propose a formal definition of unlearning honesty, which includes: (1) preserving both utility and honesty on retained knowledge, and (2) ensuring effective forgetting while encouraging the model to acknowledge its limitations and respond consistently to questions related to forgotten knowledge. To systematically evaluate the honesty of unlearning, we introduce a suite of metrics that cover utility, honesty on the retained set, effectiveness of forgetting, rejection rate and refusal stability in Q&A and MCQ settings. Evaluating 9 methods across 3 mainstream families shows that all current methods fail to meet these standards. After experimental and theoretical analyses, we present ReVa, a representation-alignment procedure that fine-tunes feature-randomized unlearned models to better acknowledge forgotten knowledge. On Q&A tasks from the forget set, ReVa achieves the highest rejection rate after two rounds of interaction, nearly doubling the performance of the second-best method. Remarkably, It also improves honesty on the retained set. We release our data and code at https://github.com/renjiegu.

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

Neural models are usually adapted through changes in parameters shared among model components via fine-tuning, alignment-based training, and reinforcement learning. These changes have been found effective in short-term optimization. However, they result in long-term alterations in the model's base behavior. In this study, we introduce the concept of structural irreversibility as a characteristic of shared-parameter model adaptation. This concept refers to the intertwining of task-specific objectives with the representational identity of the model. We show that when parameters are directly mutated, the resulting model behaves divergently from the original model. This divergence cannot be reversed deterministically without an explicit parameter snapshot. We introduce reversible behavioral learning, in which model behaviors are structurally dissociated from identity parameters and can be deterministically unloaded through an explicit unload process. We also introduce the Recoverability Factor as a normalized measure of behavioral recoverability and provide additional diagnostics based on model divergence. Experiments show that reversible model adaptation achieves rollback within numerical precision, whereas shared-parameter mutation exhibits persistent post-reset divergence.

Fine-tuning multi-turn dialogue systems requires high-quality supervision but often suffers from degraded performance when exposed to low-quality data. Supervision errors in early turns can propagate across subsequent turns, undermining coherence and response quality. Existing methods typically address data quality via static prefiltering, which decouples quality control from training and fails to mitigate turn-level error propagation. In this context, we propose ReSURE (Regularizing Supervision UnREliability), an adaptive learning method that dynamically down-weights unreliable supervision without explicit filtering. ReSURE estimates per-turn loss distributions using Welford's online statistics and reweights sample losses on the fly accordingly. Experiments on both single-source and mixed-quality datasets show improved stability and response quality. Notably, ReSURE enjoys positive Spearman correlations (0.21 ~ 1.0 across multiple benchmarks) between response scores and number of samples regardless of data quality, which potentially paves the way for utilizing large-scale data effectively. Code is publicly available at https://github.com/Elvin-Yiming-Du/ReSURE_Multi_Turn_Training.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work shows that existing machine unlearning techniques do not hold up to thorough evaluation in non-convex settings. In this work, we introduce a new machine unlearning technique that exhibits strong empirical performance even in such challenging settings. Our starting point is the perspective that the goal of unlearning is to produce a model whose outputs are statistically indistinguishable from those of a model re-trained on all but the forget set. This perspective naturally suggests a reduction from the unlearning problem to that of data attribution, where the goal is to predict the effect of changing the training set on a model's outputs. Thus motivated, we propose the following meta-algorithm, which we call Datamodel Matching (DMM): given a trained model, we (a) use data attribution to predict the output of the model if it were re-trained on all but the forget set points; then (b) fine-tune the pre-trained model to match these predicted outputs. In a simple convex setting, we show how this approach provably outperforms a variety of iterative unlearning algorithms. Empirically, we use a combination of existing evaluations and a new metric based on the KL-divergence to show that even in non-convex settings, DMM achieves strong unlearning performance relative to existing algorithms. An added benefit of DMM is that it is a meta-algorithm, in the sense that future advances in data attribution translate directly into better unlearning algorithms, pointing to a clear direction for future progress in unlearning.

Large language models are finetuned to refuse questions about hazardous knowledge, but these protections can often be bypassed. Unlearning methods aim at completely removing hazardous capabilities from models and make them inaccessible to adversaries. This work challenges the fundamental differences between unlearning and traditional safety post-training from an adversarial perspective. We demonstrate that existing jailbreak methods, previously reported as ineffective against unlearning, can be successful when applied carefully. Furthermore, we develop a variety of adaptive methods that recover most supposedly unlearned capabilities. For instance, we show that finetuning on 10 unrelated examples or removing specific directions in the activation space can recover most hazardous capabilities for models edited with RMU, a state-of-the-art unlearning method. Our findings challenge the robustness of current unlearning approaches and question their advantages over safety training.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

As backdoor attacks become more stealthy and robust, they reveal critical weaknesses in current defense strategies: detection methods often rely on coarse-grained feature statistics, and purification methods typically require full retraining or additional clean models. To address these challenges, we propose DUP (Detection-guided Unlearning for Purification), a unified framework that integrates backdoor detection with unlearning-based purification. The detector captures feature-level anomalies by jointly leveraging class-agnostic distances and inter-layer transitions. These deviations are integrated through a weighted scheme to identify poisoned inputs, enabling more fine-grained analysis. Based on the detection results, we purify the model through a parameter-efficient unlearning mechanism that avoids full retraining and does not require any external clean model. Specifically, we innovatively repurpose knowledge distillation to guide the student model toward increasing its output divergence from the teacher on detected poisoned samples, effectively forcing it to unlearn the backdoor behavior. Extensive experiments across diverse attack methods and language model architectures demonstrate that DUP achieves superior defense performance in detection accuracy and purification efficacy. Our code is available at https://github.com/ManHu2025/DUP.

Language models (LMs) can "memorize" information, i.e., encode training data in their weights in such a way that inference-time queries can lead to verbatim regurgitation of that data. This ability to extract training data can be problematic, for example, when data are private or sensitive. In this work, we investigate methods to mitigate memorization: three regularizer-based, three finetuning-based, and eleven machine unlearning-based methods, with five of the latter being new methods that we introduce. We also introduce TinyMem, a suite of small, computationally-efficient LMs for the rapid development and evaluation of memorization-mitigation methods. We demonstrate that the mitigation methods that we develop using TinyMem can successfully be applied to production-grade LMs, and we determine via experiment that: regularizer-based mitigation methods are slow and ineffective at curbing memorization; fine-tuning-based methods are effective at curbing memorization, but overly expensive, especially for retaining higher accuracies; and unlearning-based methods are faster and more effective, allowing for the precise localization and removal of memorized information from LM weights prior to inference. We show, in particular, that our proposed unlearning method BalancedSubnet outperforms other mitigation methods at removing memorized information while preserving performance on target tasks.

The task of "unlearning" certain concepts in large language models (LLMs) has attracted immense attention recently, due to its importance for mitigating undesirable model behaviours, such as the generation of harmful, private, or incorrect information. Current protocols to evaluate unlearning methods largely rely on behavioral tests, without monitoring the presence of unlearned knowledge within the model's parameters. This residual knowledge can be adversarially exploited to recover the erased information post-unlearning. We argue that unlearning should also be evaluated internally, by considering changes in the parametric knowledge traces of the unlearned concepts. To this end, we propose a general methodology for eliciting directions in the parameter space (termed "concept vectors") that encode concrete concepts, and construct ConceptVectors, a benchmark dataset containing hundreds of common concepts and their parametric knowledge traces within two open-source LLMs. Evaluation on ConceptVectors shows that existing unlearning methods minimally impact concept vectors, while directly ablating these vectors demonstrably removes the associated knowledge from the LLMs and significantly reduces their susceptibility to adversarial manipulation. Our results highlight limitations in behavioral-based unlearning evaluations and call for future work to include parametric-based evaluations. To support this, we release our code and benchmark at https://github.com/yihuaihong/ConceptVectors.

Unlearning in large language models (LLMs) is critical for regulatory compliance and for building ethical generative AI systems that avoid producing private, toxic, illegal, or copyrighted content. Despite rapid progress, in this work we show that almost all existing unlearning methods fail to achieve true forgetting in practice. Specifically, while evaluations of these `unlearned' models under deterministic (greedy) decoding often suggest successful knowledge removal using standard benchmarks (as has been done in the literature), we show that sensitive information reliably resurfaces when models are sampled with standard probabilistic decoding. To rigorously capture this vulnerability, we introduce leak@k, a new meta-evaluation metric that quantifies the likelihood of forgotten knowledge reappearing when generating k samples from the model under realistic decoding strategies. Using three widely adopted benchmarks, TOFU, MUSE, and WMDP, we conduct the first large-scale, systematic study of unlearning reliability using our newly defined leak@k metric. Our findings demonstrate that knowledge leakage persists across methods and tasks, underscoring that current state-of-the-art unlearning techniques provide only limited forgetting and highlighting the urgent need for more robust approaches to LLM unlearning.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Machine unlearning, the removal of a training subset's influence from a deployed model, is critical for privacy preservation and model reliability, yet gradient ascent on forget samples often harms retained knowledge. Existing approaches face a persistent tradeoff between effective forgetting and preservation on the retain set. While previous methods provide useful heuristics, they often lack a formal analysis on how exactly forgetting updates harm retained knowledge, and whether the side effects can be removed with theoretical guarantees. To explore a theoretically sound and simple solution, we start from the first principle on how performance on the retain set is actually affected: a first-order analysis of the local change of the retain loss under small parameter updates during model training. We start from a crisp equivalence: the retain loss is unchanged to first order iff the update direction is orthogonal to the subspace spanned by retain gradients ("retain-invariant"). This identifies the entangled component as the tangential part of forget update within the retain-gradient subspace, and characterizes disentanglement as orthogonality. Guided by this, we propose the Geometric-disentanglement Unlearning (GU) that decomposes any candidate forget gradient update into tangential and normal components to retain space and executes only the normal component. Under a standard trust-region budget, the projected direction aligned with the raw forget gradient is optimal among all first-order retain-invariant moves, and we also derive the optimal projected direction for joint forget-retain updating objectives. Our method is plug-and-play and can be attached to existing gradient-based unlearning procedures to mitigate side effects. GU achieves consistent improvement on various methods across three benchmarks TOFU, MUSE, and WMDP.

Hyperparameter optimization (HPO) is a core problem for the machine learning community and remains largely unsolved due to the significant computational resources required to evaluate hyperparameter configurations. As a result, a series of recent related works have focused on the direction of transfer learning for quickly fine-tuning hyperparameters on a dataset. Unfortunately, the community does not have a common large-scale benchmark for comparing HPO algorithms. Instead, the de facto practice consists of empirical protocols on arbitrary small-scale meta-datasets that vary inconsistently across publications, making reproducibility a challenge. To resolve this major bottleneck and enable a fair and fast comparison of black-box HPO methods on a level playing field, we propose HPO-B, a new large-scale benchmark in the form of a collection of meta-datasets. Our benchmark is assembled and preprocessed from the OpenML repository and consists of 176 search spaces (algorithms) evaluated sparsely on 196 datasets with a total of 6.4 million hyperparameter evaluations. For ensuring reproducibility on our benchmark, we detail explicit experimental protocols, splits, and evaluation measures for comparing methods for both non-transfer, as well as, transfer learning HPO.

Multimodal LLMs are powerful but prone to object hallucinations, which describe non-existent entities and harm reliability. While recent unlearning methods attempt to mitigate this, we identify a critical flaw: structural fragility. We empirically demonstrate that standard erasure achieves only superficial suppression, trapping the model in sharp minima where hallucinations catastrophically resurge after lightweight relearning. To ensure geometric stability, we propose SARE, which casts unlearning as a targeted min-max optimization problem and uses a Targeted-SAM mechanism to explicitly flatten the loss landscape around hallucinated concepts. By suppressing hallucinations under simulated worst-case parameter perturbations, our framework ensures robust removal stable against weight shifts. Extensive experiments demonstrate that SARE significantly outperforms baselines in erasure efficacy while preserving general generation quality. Crucially, it maintains persistent hallucination suppression against relearning and parameter updates, validating the effectiveness of geometric stabilization.

Large language models (LLMs) inherently absorb harmful knowledge, misinformation, and personal data during pretraining on large-scale web corpora, with no native mechanism for selective removal. While machine unlearning offers a principled solution, existing approaches are provider-centric, requiring retraining pipelines, curated retain datasets, and direct intervention by model service providers (MSPs), thereby excluding end users from controlling their own data. We introduce Interactive Machine Unlearning (IMU), a new paradigm in which users can instruct LLMs to forget targeted knowledge through natural language at inference time. To realize IMU, we propose RePAIR, a prompt-aware model repair framework comprising (i) a watchdog model for unlearning intent detection, (ii) a surgeon model for generating repair procedures, and (iii) a patient model whose parameters are updated autonomously. At the core of RePAIR, we develop Steering Through Activation Manipulation with PseudoInverse (STAMP), a training-free, single-sample unlearning method that redirects MLP activations toward a refusal subspace via closed-form pseudoinverse updates. Its low-rank variant reduces computational complexity from O(d^3) to O(r^3 + r^2 * d), enabling efficient on-device unlearning with up to ~3x speedup over training-based baselines. Extensive experiments across harmful knowledge suppression, misinformation correction, and personal data erasure demonstrate that RePAIR achieves near-zero forget scores (Acc_f = 0.00, F-RL = 0.00) while preserving model utility (Acc_r up to 84.47, R-RL up to 0.88), outperforming six state-of-the-art baselines. These results establish RePAIR as an effective and practical framework for user-driven model editing, advancing transparent and on-device control over learned knowledge, with potential extensions to multimodal foundation models.

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

Reinforcement learning with verifiable rewards (RLVR) has delivered impressive gains in mathematical and multimodal reasoning and has become a standard post-training paradigm for contemporary language and vision-language models. However, the RLVR recipe introduces a significant risk of capability regression, where models forget foundational skills after prolonged training without employing regularization strategies. We empirically confirm this concern, observing that open-source reasoning models suffer performance degradation on core capabilities such as perception and faithfulness. While imposing regularization terms like KL divergence can help prevent deviation from the base model, these terms are calculated on the current task, thus they do not guarantee broader knowledge. Meanwhile, commonly used experience replay across heterogeneous domains makes it nontrivial to decide how much training focus each objective should receive. To address this, we propose RECAP-a replay strategy with dynamic objective reweighting for general knowledge preservation. Our reweighting mechanism adapts in an online manner using short-horizon signals of convergence and instability, shifting the post-training focus away from saturated objectives and toward underperforming or volatile ones. Our method is end-to-end and readily applicable to existing RLVR pipelines without training additional models or heavy tuning. Extensive experiments on benchmarks based on Qwen2.5-VL-3B and Qwen2.5-VL-7B demonstrate the effectiveness of our method, which not only preserves general capabilities but also improves reasoning by enabling more flexible trade-offs among in-task rewards.

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially, even in scenarios where they are explicitly told that they are making a mistake. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a single-turn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation learning and reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on math reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models. Our analysis shows that RISE makes meaningful improvements to responses to arrive at the correct solution for challenging prompts, without disrupting one-turn abilities as a result of expressing more complex distributions.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

Reinforcement learning (RL) has achieved remarkable success in LLM reasoning, but whether it can also improve direct recall of parametric knowledge remains an open question. We study this question in a controlled zero-shot, one-hop, closed-book QA setting with no chain-of-thought, training only on binary correctness rewards and applying fact-level train-test deduplication to ensure gains reflect improved recall rather than reasoning or memorization. Across three model families and multiple factual QA benchmarks, RL yields ~27% average relative gains, surpassing both training- and inference-time baselines alike. Mechanistically, RL primarily redistributes probability mass over existing knowledge rather than acquiring new facts, moving correct answers from the low-probability tail into reliable greedy generations. Our data-attribution study reveals that the hardest examples are the most informative: those whose answers never appear in 128 pre-RL samples (only ~18% of training data) drive ~83% of the gain, since rare correct rollouts still emerge during training and get reinforced. Together, these findings broaden the role of RL beyond reasoning, repositioning it as a tool for unlocking rather than acquiring latent parametric knowledge.

Large reasoning models (LRMs) "think" by generating structured chain-of-thought (CoT) before producing a final answer, yet they still lack the ability to reason critically about safety alignment and are easily biased when a flawed premise is injected into their thought process. We propose RECAP (Robust Safety Alignment via Counter-Aligned Prefilling), a principled reinforcement learning (RL) method for post-training that explicitly teaches models to override flawed reasoning trajectories and reroute to safe and helpful responses. RECAP trains on a mixture of synthetically generated counter-aligned CoT prefills and standard prompts, requires no additional training cost or modifications beyond vanilla reinforcement learning from human feedback (RLHF), and substantially improves safety and jailbreak robustness, reduces overrefusal, and preserves core reasoning capability -- all while maintaining inference token budget. Extensive analysis shows that RECAP-trained models engage in self-reflection more frequently and remain robust under adaptive attacks, preserving safety even after repeated attempts to override their reasoning.

Machine unlearning seeks to remove the influence of particular data or class from trained models to meet privacy, legal, or ethical requirements. Existing unlearning methods tend to forget shallowly: phenomenon of an unlearned model pretend to forget by adjusting only the model response, while its internal representations retain information sufficiently to restore the forgotten data or behavior. We empirically confirm the widespread shallowness by reverting the forgetting effect of various unlearning methods via training-free performance recovery attack and gradient-inversion-based data reconstruction attack. To address this vulnerability fundamentally, we define a theoretical criterion of ``deep forgetting'' based on one-point-contraction of feature representations of data to forget. We also propose an efficient approximation algorithm, and use it to construct a novel general-purpose unlearning algorithm: One-Point-Contraction (OPC). Empirical evaluations on image classification unlearning benchmarks show that OPC achieves not only effective unlearning performance but also superior resilience against both performance recovery attack and gradient-inversion attack. The distinctive unlearning performance of OPC arises from the deep feature forgetting enforced by its theoretical foundation, and recaps the need for improved robustness of machine unlearning methods.

Post-training quantization (PTQ), which only requires a tiny dataset for calibration without end-to-end retraining, is a light and practical model compression technique. Recently, several PTQ schemes for vision transformers (ViTs) have been presented; unfortunately, they typically suffer from non-trivial accuracy degradation, especially in low-bit cases. In this paper, we propose RepQ-ViT, a novel PTQ framework for ViTs based on quantization scale reparameterization, to address the above issues. RepQ-ViT decouples the quantization and inference processes, where the former employs complex quantizers and the latter employs scale-reparameterized simplified quantizers. This ensures both accurate quantization and efficient inference, which distinguishes it from existing approaches that sacrifice quantization performance to meet the target hardware. More specifically, we focus on two components with extreme distributions: post-LayerNorm activations with severe inter-channel variation and post-Softmax activations with power-law features, and initially apply channel-wise quantization and log2 quantization, respectively. Then, we reparameterize the scales to hardware-friendly layer-wise quantization and log2 quantization for inference, with only slight accuracy or computational costs. Extensive experiments are conducted on multiple vision tasks with different model variants, proving that RepQ-ViT, without hyperparameters and expensive reconstruction procedures, can outperform existing strong baselines and encouragingly improve the accuracy of 4-bit PTQ of ViTs to a usable level. Code is available at https://github.com/zkkli/RepQ-ViT.

Large language models (LLMs) are routinely pre-trained on billions of tokens, only to start the process over again once new data becomes available. A much more efficient solution is to continually pre-train these models, saving significant compute compared to re-training. However, the distribution shift induced by new data typically results in degraded performance on previous data or poor adaptation to the new data. In this work, we show that a simple and scalable combination of learning rate (LR) re-warming, LR re-decaying, and replay of previous data is sufficient to match the performance of fully re-training from scratch on all available data, as measured by final loss and language model (LM) evaluation benchmarks. Specifically, we show this for a weak but realistic distribution shift between two commonly used LLM pre-training datasets (EnglishrightarrowEnglish) and a stronger distribution shift (EnglishrightarrowGerman) at the 405M parameter model scale with large dataset sizes (hundreds of billions of tokens). Selecting the weak but realistic shift for larger-scale experiments, we also find that our continual learning strategies match the re-training baseline for a 10B parameter LLM. Our results demonstrate that LLMs can be successfully updated via simple and scalable continual learning strategies, matching the re-training baseline using only a fraction of the compute. Finally, inspired by previous work, we propose alternatives to the cosine learning rate schedule that help circumvent forgetting induced by LR re-warming and that are not bound to a fixed token budget.

With the proliferation of domain-specific models, model merging has emerged as a set of techniques that combine the capabilities of multiple models into one that can multitask without the cost of additional training. In this paper, we propose a new model merging technique, Drop and rEscaLe via sampLing with mAgnitude (DELLA-Merging), that employs a novel pruning technique, MAGPRUNE, which shows significant advantages over DARE and TIES. MAGPRUNE first ranks the parameters in order of their magnitude and assigns higher dropout probabilities (p) to parameters with lower ranks corresponding to lower magnitudes. To approximate the original embeddings, MAGPRUNE employs a rescaling operation on the parameters that survive the random dropping by 1/(1 - p). On three different expert models considered for merging (LM, Math, Code) and corresponding benchmark datasets (AlpacaEval, GSM8K, MBPP), DELLA shows an average improvement of 2.4 points over baseline methods employing delta parameter pruning (an improvement of 3.6 points over TIES, 1.2 points over DARE), and 11.1 points over the no-pruning baseline (TA). We release the source code at: https://github.com/declare-lab/della.

Language models can retain dangerous knowledge and skills even after extensive safety fine-tuning, posing both misuse and misalignment risks. Recent studies show that even specialized unlearning methods can be easily reversed. To address this, we systematically evaluate many existing and novel components of unlearning methods and identify ones crucial for irreversible unlearning. We introduce Disruption Masking, a technique in which we only allow updating weights, where the signs of the unlearning gradient and the retaining gradient are the same. This ensures all updates are non-disruptive. Additionally, we identify the need for normalizing the unlearning gradients, and also confirm the usefulness of meta-learning. We combine these insights into MUDMAN (Meta-Unlearning with Disruption Masking and Normalization) and validate its effectiveness at preventing the recovery of dangerous capabilities. MUDMAN outperforms the prior TAR method by 40%, setting a new state-of-the-art for robust unlearning.

Large language models (LLMs) have recently revolutionized language processing tasks but have also brought ethical and legal issues. LLMs have a tendency to memorize potentially private or copyrighted information present in the training data, which might then be delivered to end users at inference time. When this happens, a naive solution is to retrain the model from scratch after excluding the undesired data. Although this guarantees that the target data have been forgotten, it is also prohibitively expensive for LLMs. Approximate unlearning offers a more efficient alternative, as it consists of ex post modifications of the trained model itself to prevent undesirable results, but it lacks forgetting guarantees because it relies solely on empirical evidence. In this work, we present DP2Unlearning, a novel LLM unlearning framework that offers formal forgetting guarantees at a significantly lower cost than retraining from scratch on the data to be retained. DP2Unlearning involves training LLMs on textual data protected using {\epsilon}-differential privacy (DP), which later enables efficient unlearning with the guarantees against disclosure associated with the chosen {\epsilon}. Our experiments demonstrate that DP2Unlearning achieves similar model performance post-unlearning, compared to an LLM retraining from scratch on retained data -- the gold standard exact unlearning -- but at approximately half the unlearning cost. In addition, with a reasonable computational cost, it outperforms approximate unlearning methods at both preserving the utility of the model post-unlearning and effectively forgetting the targeted information.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

Machine unlearning, the ability for a machine learning model to forget, is becoming increasingly important to comply with data privacy regulations, as well as to remove harmful, manipulated, or outdated information. The key challenge lies in forgetting specific information while protecting model performance on the remaining data. While current state-of-the-art methods perform well, they typically require some level of retraining over the retained data, in order to protect or restore model performance. This adds computational overhead and mandates that the training data remain available and accessible, which may not be feasible. In contrast, other methods employ a retrain-free paradigm, however, these approaches are prohibitively computationally expensive and do not perform on par with their retrain-based counterparts. We present Selective Synaptic Dampening (SSD), a novel two-step, post hoc, retrain-free approach to machine unlearning which is fast, performant, and does not require long-term storage of the training data. First, SSD uses the Fisher information matrix of the training and forgetting data to select parameters that are disproportionately important to the forget set. Second, SSD induces forgetting by dampening these parameters proportional to their relative importance to the forget set with respect to the wider training data. We evaluate our method against several existing unlearning methods in a range of experiments using ResNet18 and Vision Transformer. Results show that the performance of SSD is competitive with retrain-based post hoc methods, demonstrating the viability of retrain-free post hoc unlearning approaches.

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting. Our main insight is that under realistic settings, a single iteration of the Reflow algorithm for training rectified flows is sufficient to learn nearly straight trajectories; hence, the current practice of using multiple Reflow iterations is unnecessary. We thus propose techniques to improve one-round training of rectified flows, including a U-shaped timestep distribution and LPIPS-Huber premetric. With these techniques, we improve the FID of the previous 2-rectified flow by up to 72% in the 1 NFE setting on CIFAR-10. On ImageNet 64times64, our improved rectified flow outperforms the state-of-the-art distillation methods such as consistency distillation and progressive distillation in both one-step and two-step settings and rivals the performance of improved consistency training (iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.

Standard large language model training can create models that produce outputs their trainer deems unacceptable in deployment. The probability of these outputs can be reduced using methods such as LLM unlearning. However, unlearning a set of data (called the forget set) can degrade model performance on other distributions where the trainer wants to retain the model's behavior. To improve this trade-off, we demonstrate that using the forget set to compute only a few uphill Gauss-Newton steps provides a conceptually simple, state-of-the-art unlearning approach for LLMs. While Gauss-Newton steps adapt Newton's method to non-linear models, it is non-trivial to efficiently and accurately compute such steps for LLMs. Hence, our approach crucially relies on parametric Hessian approximations such as Kronecker-Factored Approximate Curvature (K-FAC). We call this combined approach K-FADE (K-FAC for Distribution Erasure). Our evaluation on the WMDP and ToFU benchmarks demonstrates that K-FADE suppresses outputs from the forget set and approximates, in output space, the results of retraining without the forget set. Critically, our method does this while altering the outputs on the retain set less than previous methods. This is because K-FADE transforms a constraint on the model's outputs across the entire retain set into a constraint on the model's weights, allowing the algorithm to minimally change the model's behavior on the retain set at each step. Moreover, the unlearning updates computed by K-FADE can be reapplied later if the model undergoes further training, allowing unlearning to be cheaply maintained.

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities are unmodified, we are able to explore the graph more efficiently, improving the concentration of statistical estimators whilst leaving them unbiased. The mechanism has a trivial drop-in implementation. We showcase the effectiveness of repelling random walks in a range of settings including estimation of graph kernels, the PageRank vector and graphlet concentrations. We provide detailed experimental evaluation and robust theoretical guarantees. To our knowledge, repelling random walks constitute the first rigorously studied quasi-Monte Carlo scheme correlating the directions of walkers on a graph, inviting new research in this exciting nascent domain.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Test-Time Scaling enhances the reasoning capabilities of Large Language Models by allocating additional inference compute to broaden the exploration of the solution space. However, existing search strategies typically treat rollouts as disposable samples, where valuable intermediate insights are effectively discarded after each trial. This systemic memorylessness leads to massive computational redundancy, as models repeatedly re-derive discovered conclusions and revisit known dead ends across extensive attempts. To bridge this gap, we propose Recycling Search Experience (RSE), a self-guided, training-free strategy that turns test-time search from a series of isolated trials into a cumulative process. By actively distilling raw trajectories into a shared experience bank, RSE enables positive recycling of intermediate conclusions to shortcut redundant derivations and negative recycling of failure patterns to prune encountered dead ends. Theoretically, we provide an analysis that formalizes the efficiency gains of RSE, validating its advantage over independent sampling in solving complex reasoning tasks. Empirically, extensive experiments on HMMT24, HMMT25, IMO-Bench, and HLE show that RSE consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art scaling efficiency.

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates "self-consuming loops" which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made exponentially more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

In the pursuit of reducing the number of trainable parameters in deep transformer networks, we employ Reinforcement Learning to dynamically select layers during training and tie them together. Every few iterations, the RL agent is asked whether to train each layer i independently or to copy the weights of a previous layer j<i. This facilitates weight sharing, reduces the number of trainable parameters, and also serves as an effective regularization technique. Experimental evaluations validate that our model modestly outperforms the baseline transformer model with regard to perplexity and drastically reduces the number of trainable parameters. In particular, the memory consumption during training is up to one order of magnitude less than the conventional training method.

Representation alignment (REPA) guides generative training by distilling representations from a strong, pretrained vision encoder to intermediate diffusion features. We investigate a fundamental question: what aspect of the target representation matters for generation, its global semantic information (e.g., measured by ImageNet-1K accuracy) or its spatial structure (i.e. pairwise cosine similarity between patch tokens)? Prevalent wisdom holds that stronger global semantic performance leads to better generation as a target representation. To study this, we first perform a large-scale empirical analysis across 27 different vision encoders and different model scales. The results are surprising; spatial structure, rather than global performance, drives the generation performance of a target representation. To further study this, we introduce two straightforward modifications, which specifically accentuate the transfer of spatial information. We replace the standard MLP projection layer in REPA with a simple convolution layer and introduce a spatial normalization layer for the external representation. Surprisingly, our simple method (implemented in <4 lines of code), termed iREPA, consistently improves convergence speed of REPA, across a diverse set of vision encoders, model sizes, and training variants (such as REPA, REPA-E, Meanflow, JiT etc). %, etc. Our work motivates revisiting the fundamental working mechanism of representational alignment and how it can be leveraged for improved training of generative models. The code and project page are available at https://end2end-diffusion.github.io/irepa

Normalization layers have recently experienced a renaissance in the deep reinforcement learning and continual learning literature, with several works highlighting diverse benefits such as improving loss landscape conditioning and combatting overestimation bias. However, normalization brings with it a subtle but important side effect: an equivalence between growth in the norm of the network parameters and decay in the effective learning rate. This becomes problematic in continual learning settings, where the resulting effective learning rate schedule may decay to near zero too quickly relative to the timescale of the learning problem. We propose to make the learning rate schedule explicit with a simple re-parameterization which we call Normalize-and-Project (NaP), which couples the insertion of normalization layers with weight projection, ensuring that the effective learning rate remains constant throughout training. This technique reveals itself as a powerful analytical tool to better understand learning rate schedules in deep reinforcement learning, and as a means of improving robustness to nonstationarity in synthetic plasticity loss benchmarks along with both the single-task and sequential variants of the Arcade Learning Environment. We also show that our approach can be easily applied to popular architectures such as ResNets and transformers while recovering and in some cases even slightly improving the performance of the base model in common stationary benchmarks.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their specialized capabilities across different tasks and domains. Current model merging techniques focus on merging all available models simultaneously, with weight interpolation-based methods being the predominant approaches. However, these conventional approaches are not well-suited for scenarios where models become available sequentially, and they often suffer from high memory requirements and potential interference between tasks. In this study, we propose a training-free projection-based continual merging method that processes models sequentially through orthogonal projections of weight matrices and adaptive scaling mechanisms. Our method operates by projecting new parameter updates onto subspaces orthogonal to existing merged parameter updates while using an adaptive scaling mechanism to maintain stable parameter distances, enabling efficient sequential integration of task-specific knowledge. Our approach maintains constant memory complexity to the number of models, minimizes interference between tasks through orthogonal projections, and retains the performance of previously merged models through adaptive task vector scaling. Extensive experiments on CLIP-ViT models demonstrate that our method achieves a 5-8% average accuracy improvement while maintaining robust performance in different task orderings.

In response to recent data regulation requirements, machine unlearning (MU) has emerged as a critical process to remove the influence of specific examples from a given model. Although exact unlearning can be achieved through complete model retraining using the remaining dataset, the associated computational costs have driven the development of efficient, approximate unlearning techniques. Moving beyond data-centric MU approaches, our study introduces a novel model-based perspective: model sparsification via weight pruning, which is capable of reducing the gap between exact unlearning and approximate unlearning. We show in both theory and practice that model sparsity can boost the multi-criteria unlearning performance of an approximate unlearner, closing the approximation gap, while continuing to be efficient. This leads to a new MU paradigm, termed prune first, then unlearn, which infuses a sparse model prior into the unlearning process. Building on this insight, we also develop a sparsity-aware unlearning method that utilizes sparsity regularization to enhance the training process of approximate unlearning. Extensive experiments show that our proposals consistently benefit MU in various unlearning scenarios. A notable highlight is the 77% unlearning efficacy gain of fine-tuning (one of the simplest unlearning methods) when using sparsity-aware unlearning. Furthermore, we demonstrate the practical impact of our proposed MU methods in addressing other machine learning challenges, such as defending against backdoor attacks and enhancing transfer learning. Codes are available at https://github.com/OPTML-Group/Unlearn-Sparse.

Model merging leverages multiple finetuned expert models to construct a multi-task model with low cost, and is gaining increasing attention. However, as a growing number of finetuned models become publicly available, concerns about the safety of model merging have emerged. Unauthorized merging may infringe on developers' rights and risk leaking sensitive personal information. Most existing methods focus on detecting whether a merged model originates from a specific source model, but fail to effectively prevent illegal merging. In this paper, we propose MergeLock, an active protection mechanism that disrupts model parameters to render them unmergeable, thereby directly preventing unauthorized model merging. Specifically, leveraging the inherent symmetry of the attention mechanism in Transformer-based models, we randomly sample two pairs of invertible matrices and apply them to the Query-Key (QK) and Value-Output (VO) branches. This transformation keeps the model's output unchanged while pushing it away from the shared parameter space of other finetuned models. Extensive experiments across both vision and language tasks demonstrate that MergeLock can degrade the performance of merged models by over 95% when a protected model is involved in most cases, demonstrating its effectiveness. Moreover, we further demonstrate that merged models protected by MergeLock cannot be effectively recovered using low-cost restoration methods, further enhancing robustness against unauthorized merging. The code is available at https://github.com/hetailang/Merge-Lock.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

Standard unlearning evaluations measure behavioral suppression in full precision, immediately after training, despite every deployed language model being quantized first. Recent work has shown that 4-bit post-training quantization can reverse machine unlearning; we show this is not a tuning artefact but a systematic dual failure: gradient-based methods that achieve meaningful forgetting lose it under compression, while methods that survive quantization barely change the model. Both failures trace to the same root cause: across all baselines, per-parameter updates lie 47-828x below the NF4 quantization bin width; updates diffused across billions of parameters cannot clear quantization bin boundaries, a consequence we formalize as a sparsity-permanence tradeoff. We present MANSU (Mechanistic-Aligned Null-Space Unlearning), which resolves both modes by combining causal circuit attribution to isolate the minimal forget-set subgraph, circuit-restricted null-space projection with a diagonal-Fisher retain bound, and a per-parameter magnitude floor guaranteeing quantization survival by construction. We additionally introduce Circuit Attribution Divergence (CAD), a mechanistic verification metric distinguishing structural erasure from behavioral suppression, a distinction existing metrics cannot make. Across multiple model families and hazard benchmarks, MANSU is the first method to jointly satisfy all four properties with margin on each (meaningful forgetting, retain preservation, non-positive PTQ gap, and structural erasure), while gradient-based baselines recover up to +0.05 accuracy under compression.

Growing concerns over data privacy and security highlight the importance of machine unlearning--removing specific data influences from trained models without full retraining. Techniques like Membership Inference Attacks (MIAs) are widely used to externally assess successful unlearning. However, existing methods face two key limitations: (1) maximizing MIA effectiveness (e.g., via online attacks) requires prohibitive computational resources, often exceeding retraining costs; (2) MIAs, designed for binary inclusion tests, struggle to capture granular changes in approximate unlearning. To address these challenges, we propose the Interpolated Approximate Measurement (IAM), a framework natively designed for unlearning inference. IAM quantifies sample-level unlearning completeness by interpolating the model's generalization-fitting behavior gap on queried samples. IAM achieves strong performance in binary inclusion tests for exact unlearning and high correlation for approximate unlearning--scalable to LLMs using just one pre-trained shadow model. We theoretically analyze how IAM's scoring mechanism maintains performance efficiently. We then apply IAM to recent approximate unlearning algorithms, revealing general risks of both over-unlearning and under-unlearning, underscoring the need for stronger safeguards in approximate unlearning systems. The code is available at https://github.com/Happy2Git/Unlearning_Inference_IAM.

Large language models (LLMs) demonstrate impressive capabilities across diverse tasks but raise concerns about privacy, copyright, and harmful materials. Existing LLM unlearning methods rarely consider the continual and high-volume nature of real-world deletion requests, which can cause utility degradation and catastrophic forgetting as requests accumulate. To address this challenge, we introduce \fit, a framework for continual unlearning that handles large numbers of deletion requests while maintaining robustness against both catastrophic forgetting and post-unlearning recovery. \fit mitigates degradation through rigorous data Filtering, Importance-aware updates, and Targeted layer attribution, enabling stable performance across long sequences of unlearning operations and achieving a favorable balance between forgetting effectiveness and utility retention. To support realistic evaluation, we present PCH, a benchmark covering Personal information, Copyright, and Harmful content in sequential deletion scenarios, along with two symmetric metrics, Forget Degree (F.D.) and Retain Utility (R.U.), which jointly assess forgetting quality and utility preservation. Extensive experiments on four open-source LLMs with hundreds of deletion requests show that \fit achieves the strongest trade-off between F.D. and R.U., surpasses existing methods on MMLU, CommonsenseQA, and GSM8K, and remains resistant against both relearning and quantization recovery attacks.

R1-style Reinforcement Learning (RL) significantly enhances Large Language Models' reasoning capabilities, yet the mechanism behind rule-based RL remains unclear. We found that small-scale SFT has significant influence on RL but shows poor efficiency. To explain our observations, we propose an analytical framework and compare the efficiency of SFT and RL by measuring sample effect. Hypothetical analysis show that SFT efficiency is limited by training data. Guided by our analysis, we propose Re-distillation, a technique that fine-tunes pretrain model through small-scale distillation from the RL-trained policy. Experiments on Knight & Knave and MATH datasets demonstrate re-distillation's surprising efficiency: re-distilled models match RL performance with far fewer samples and less computation. Empirical verification shows that sample effect is a good indicator of performance improvements. As a result, on K&K dataset, our re-distilled Qwen2.5-1.5B model surpasses DeepSeek-V3-0324 with only 1K SFT samples. On MATH, Qwen2.5-1.5B fine-tuned with re-distilled 500 samples matches its instruct-tuned variant without RL. Our work explains several interesting phenomena in R1-style RL, shedding light on the mechanisms behind its empirical success. Code is available at: https://github.com/on1262/deep-reasoning

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this work, we demonstrate that RLVR weight trajectories are extremely low-rank and highly predictable. Specifically, we find that the majority of downstream performance gains are captured by a rank-1 approximation of the parameter deltas, where the magnitude of this projection evolves near-linearly with training steps. Motivated by this, we propose a simple and compute-efficient method RELEX (REinforcement Learning EXtrapolation), which estimates the rank-1 subspace from a short observation window and extrapolates future checkpoints via linear regression, with no learned model required. Across three models (i.e., Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base), RELEX produces checkpoints that match or exceed RLVR performance on both in-domain and out-of-domain benchmarks, requiring as few as 15% steps of full RLVR training. Remarkably, RELEX is able to extrapolate far beyond the observation window at no training cost, predicting checkpoints up to 10-20times beyond the observed prefix with continued improvement (e.g., observe only the first 50 steps and extrapolate to 1000 steps). Our ablation analysis confirms the minimalist sufficiency of RELEX: neither increasing the subspace rank nor employing non-linear modeling yields further gains in extrapolation. Finally, we show that RELEX's success stems from a "denoising" effect: by projecting updates onto the rank-1 subspace, the model discards stochastic optimization noise that would otherwise degrade performance during extrapolation. Our code is available at https://github.com/weizhepei/RELEX.

In the realm of resource-constrained mobile vision tasks, the pursuit of efficiency and performance consistently drives innovation in lightweight Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs). While ViTs excel at capturing global context through self-attention mechanisms, their deployment in resource-limited environments is hindered by computational complexity and latency. Conversely, lightweight CNNs are favored for their parameter efficiency and low latency. This study investigates the complementary advantages of CNNs and ViTs to develop a versatile vision backbone tailored for resource-constrained applications. We introduce RepNeXt, a novel model series integrates multi-scale feature representations and incorporates both serial and parallel structural reparameterization (SRP) to enhance network depth and width without compromising inference speed. Extensive experiments demonstrate RepNeXt's superiority over current leading lightweight CNNs and ViTs, providing advantageous latency across various vision benchmarks. RepNeXt-M4 matches RepViT-M1.5's 82.3\% accuracy on ImageNet within 1.5ms on an iPhone 12, outperforms its AP^{box} by 1.3 on MS-COCO, and reduces parameters by 0.7M. Codes and models are available at https://github.com/suous/RepNeXt.

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50% post-unlearning to nearly 100% with fine-tuning on just the retain set -- i.e., zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, L_2-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

In the era of large-scale training, model merging has evolved into a tool for creating multitasking models efficiently. It enables the knowledge of models to be fused, without the need for heavy computation as required in traditional multitask learning. Existing merging methods often assume that entries at identical positions in weight matrices serve the same function, enabling straightforward entry-wise comparison and merging. However, this assumption overlooks the complexity of finetuned neural networks, where neurons may develop distinct feature compositions, making direct entry-wise merging problematic. We present Decom-Renorm-Merge (DRM), a simple yet effective approach that leverages Singular Value Decomposition to decompose and coordinate weight matrices into an aligned joint space, where entry-wise merging becomes possible. We showcase the effectiveness of DRM across various settings ranging from smaller encoder-based such as ViT and DeBERTa, encoder-decoder-based such as T5, and larger decoder-based such as Llama3.1-8B. Our experimental results show that DRM outperforms several state-of-the-art merging techniques across full finetuning and low-rank adaptation settings. Moreover, our analysis reveals renormalization as the crucial component for creating a robust and even joint space for merging, significantly contributing to the method's performance.

Aligned language models face a significant limitation as their fine-tuning often results in compromised safety. To tackle this, we propose a simple method RESTA that performs LLM safety realignment. RESTA stands for REstoring Safety through Task Arithmetic. At its core, it involves a simple arithmetic addition of a safety vector to the weights of the compromised model. We demonstrate the effectiveness of RESTA in both parameter-efficient and full fine-tuning, covering a wide range of downstream tasks, including instruction following in Chinese, English, and Hindi, as well as problem-solving capabilities in Code and Math. We also showcase the generalizability of RESTA on three existing safety evaluation benchmarks and a multilingual benchmark dataset proposed as a part of this work, consisting of 550 harmful questions covering 11 categories, each with 5 sub-categories of harm. Overall, RESTA decreases the harmfulness of the compromised model from 18.6% to 5.1% and from 9.2% to 1.5% in parameter-efficient and full fine-tuning, respectively, while maintaining most of the model's performance on the task. We release the source codes at: https://github.com/declare-lab/resta.

We characterize how memorization is represented in transformer models and show that it can be disentangled in the weights of both language models (LMs) and vision transformers (ViTs) using a decomposition based on the loss landscape curvature. This insight is based on prior theoretical and empirical work showing that the curvature for memorized training points is much sharper than non memorized, meaning ordering weight components from high to low curvature can reveal a distinction without explicit labels. This motivates a weight editing procedure that suppresses far more recitation of untargeted memorized data more effectively than a recent unlearning method (BalancedSubnet), while maintaining lower perplexity. Since the basis of curvature has a natural interpretation for shared structure in model weights, we analyze the editing procedure extensively on its effect on downstream tasks in LMs, and find that fact retrieval and arithmetic are specifically and consistently negatively affected, even though open book fact retrieval and general logical reasoning is conserved. We posit these tasks rely heavily on specialized directions in weight space rather than general purpose mechanisms, regardless of whether those individual datapoints are memorized. We support this by showing a correspondence between task data's activation strength with low curvature components that we edit out, and the drop in task performance after the edit. Our work enhances the understanding of memorization in neural networks with practical applications towards removing it, and provides evidence for idiosyncratic, narrowly-used structures involved in solving tasks like math and fact retrieval.

Fine-tuning large pre-trained models has become the de facto strategy for developing both task-specific and general-purpose machine learning systems, including developing models that are safe to deploy. Despite its clear importance, there has been minimal work that explains how fine-tuning alters the underlying capabilities learned by a model during pretraining: does fine-tuning yield entirely novel capabilities or does it just modulate existing ones? We address this question empirically in synthetic, controlled settings where we can use mechanistic interpretability tools (e.g., network pruning and probing) to understand how the model's underlying capabilities are changing. We perform an extensive analysis of the effects of fine-tuning in these settings, and show that: (i) fine-tuning rarely alters the underlying model capabilities; (ii) a minimal transformation, which we call a 'wrapper', is typically learned on top of the underlying model capabilities, creating the illusion that they have been modified; and (iii) further fine-tuning on a task where such hidden capabilities are relevant leads to sample-efficient 'revival' of the capability, i.e., the model begins reusing these capability after only a few gradient steps. This indicates that practitioners can unintentionally remove a model's safety wrapper merely by fine-tuning it on a, e.g., superficially unrelated, downstream task. We additionally perform analysis on language models trained on the TinyStories dataset to support our claims in a more realistic setup.

The LLM unlearning technique has recently been introduced to comply with data regulations and address the safety and ethical concerns of LLMs by removing the undesired data-model influence. However, state-of-the-art unlearning methods face a critical vulnerability: they are susceptible to ``relearning'' the removed information from a small number of forget data points, known as relearning attacks. In this paper, we systematically investigate how to make unlearned models robust against such attacks. For the first time, we establish a connection between robust unlearning and sharpness-aware minimization (SAM) through a unified robust optimization framework, in an analogy to adversarial training designed to defend against adversarial attacks. Our analysis for SAM reveals that smoothness optimization plays a pivotal role in mitigating relearning attacks. Thus, we further explore diverse smoothing strategies to enhance unlearning robustness. Extensive experiments on benchmark datasets, including WMDP and MUSE, demonstrate that SAM and other smoothness optimization approaches consistently improve the resistance of LLM unlearning to relearning attacks. Notably, smoothness-enhanced unlearning also helps defend against (input-level) jailbreaking attacks, broadening our proposal's impact in robustifying LLM unlearning. Codes are available at https://github.com/OPTML-Group/Unlearn-Smooth.

Data teams at frontier AI companies routinely train small proxy models to make critical decisions about pretraining data recipes for full-scale training runs. However, the community has a limited understanding of whether and when conclusions drawn from small-scale experiments reliably transfer to full-scale model training. In this work, we uncover a subtle yet critical issue in the standard experimental protocol for data recipe assessment: the use of identical small-scale model training configurations across all data recipes in the name of "fair" comparison. We show that the experiment conclusions about data quality can flip with even minor adjustments to training hyperparameters, as the optimal training configuration is inherently data-dependent. Moreover, this fixed-configuration protocol diverges from full-scale model development pipelines, where hyperparameter optimization is a standard step. Consequently, we posit that the objective of data recipe assessment should be to identify the recipe that yields the best performance under data-specific tuning. To mitigate the high cost of hyperparameter tuning, we introduce a simple patch to the evaluation protocol: using reduced learning rates for proxy model training. We show that this approach yields relative performance that strongly correlates with that of fully tuned large-scale LLM pretraining runs. Theoretically, we prove that for random-feature models, this approach preserves the ordering of datasets according to their optimal achievable loss. Empirically, we validate this approach across 23 data recipes covering four critical dimensions of data curation, demonstrating dramatic improvements in the reliability of small-scale experiments.

Scaling Large Language Models (LLMs) typically relies on increasing the number of parameters or test-time computations to boost performance. However, these strategies are impractical for edge device deployment due to limited RAM and NPU resources. Despite hardware constraints, deploying performant LLM on edge devices such as smartphone remains crucial for user experience. To address this, we propose MeKi (Memory-based Expert Knowledge Injection), a novel system that scales LLM capacity via storage space rather than FLOPs. MeKi equips each Transformer layer with token-level memory experts that injects pre-stored semantic knowledge into the generation process. To bridge the gap between training capacity and inference efficiency, we employ a re-parameterization strategy to fold parameter matrices used during training into a compact static lookup table. By offloading the knowledge to ROM, MeKi decouples model capacity from computational cost, introducing zero inference latency overhead. Extensive experiments demonstrate that MeKi significantly outperforms dense LLM baselines with identical inference speed, validating the effectiveness of memory-based scaling paradigm for on-device LLMs. Project homepage is at https://github.com/ningding-o/MeKi.