# BERT-tiny model finetuned with M-FAC

This model is finetuned on SQuAD version 2 dataset with state-of-the-art second-order optimizer M-FAC.
Check NeurIPS 2021 paper for more details on M-FAC: [https://arxiv.org/pdf/2107.03356.pdf](https://arxiv.org/pdf/2107.03356.pdf).

## Finetuning setup

For fair comparison against default Adam baseline, we finetune the model in the same framework as described here [https://github.com/huggingface/transformers/tree/master/examples/pytorch/question-answering](https://github.com/huggingface/transformers/tree/master/examples/pytorch/question-answering) and just swap Adam optimizer with M-FAC.
Hyperparameters used by M-FAC optimizer:

```bash
learning rate = 1e-4
number of gradients = 1024
dampening = 1e-6
```

## Results

We share the best model out of 5 runs with the following score on SQuAD version 2 validation set:

```bash
exact_match = 50.29
f1 = 52.43
```

Mean and standard deviation for 5 runs on SQuAD version 2 validation set:

| | Exact Match | F1  |
|:----:|:-----------:|:----:|
| Adam | 48.41 ± 0.57 | 49.99 ± 0.54 |
| M-FAC | 49.80 ± 0.43 | 52.18 ± 0.20 |

Results can be reproduced by adding M-FAC optimizer code in [https://github.com/huggingface/transformers/blob/master/examples/pytorch/question-answering/run_qa.py](https://github.com/huggingface/transformers/blob/master/examples/pytorch/question-answering/run_qa.py) and running the following bash script:

```bash
CUDA_VISIBLE_DEVICES=0 python run_qa.py \
    --seed 42 \
    --model_name_or_path prajjwal1/bert-tiny \
    --dataset_name squad_v2 \
    --version_2_with_negative \
    --do_train \
    --do_eval \
    --per_device_train_batch_size 12 \
    --learning_rate 1e-4 \
    --num_train_epochs 2 \
    --max_seq_length 384 \
    --doc_stride 128 \
    --output_dir out_dir/ \
    --optim MFAC \
    --optim_args '{"lr": 1e-4, "num_grads": 1024, "damp": 1e-6}'
```

We believe these results could be improved with modest tuning of hyperparameters: `per_device_train_batch_size`, `learning_rate`, `num_train_epochs`, `num_grads` and `damp`. For the sake of fair comparison  and a robust default setup we use the same hyperparameters across all models (`bert-tiny`, `bert-mini`) and all datasets (SQuAD version 2 and GLUE).

## BibTeX entry and citation info

```bibtex
@article{DBLP:journals/corr/abs-2107-03356,
  author    = {Elias Frantar and
               Eldar Kurtic and
               Dan Alistarh},
  title     = {Efficient Matrix-Free Approximations of Second-Order Information,
               with Applications to Pruning and Optimization},
  journal   = {CoRR},
  volume    = {abs/2107.03356},
  year      = {2021},
  url       = {https://arxiv.org/abs/2107.03356},
  eprinttype = {arXiv},
  eprint    = {2107.03356},
  timestamp = {Tue, 20 Jul 2021 15:08:33 +0200},
  biburl    = {https://dblp.org/rec/journals/corr/abs-2107-03356.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

```