fla/models/mamba2/modeling_mamba2.py

# Copyright 2024 state-spaces/mamba2 org and HuggingFace Inc. team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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"""PyTorch MAMBA2 model."""

import math
import warnings
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch
import torch.utils.checkpoint
from torch import nn
from transformers.activations import ACT2FN
from transformers.generation import GenerationMixin
from transformers.modeling_utils import PreTrainedModel
from transformers.utils import ModelOutput, logging

from fla.models.mamba2.configuration_mamba2 import Mamba2Config
from fla.modules import (FusedCrossEntropyLoss, FusedLinearCrossEntropyLoss,
                         RMSNorm)
from fla.modules.layernorm_gated import RMSNormGated

logger = logging.get_logger(__name__)

with warnings.catch_warnings():
    warnings.simplefilter('ignore')
    try:
        from mamba_ssm.ops.triton.selective_state_update import \
            selective_state_update
        from mamba_ssm.ops.triton.ssd_combined import (
            mamba_chunk_scan_combined, mamba_split_conv1d_scan_combined)
    except ImportError:
        (
            selective_state_update,
            mamba_chunk_scan_combined,
            mamba_split_conv1d_scan_combined,
        ) = (None, None, None)
    try:
        from causal_conv1d import causal_conv1d_fn, causal_conv1d_update
    except ImportError:
        causal_conv1d_update, causal_conv1d_fn = None, None
    is_fast_path_available = all((
        selective_state_update,
        causal_conv1d_fn,
        causal_conv1d_update
    ))


def pad_tensor_by_size(input_tensor: torch.Tensor, pad_size: int):
    """
    Padding x tensor with `pad_size` on the seq_len dim (dim=1)

    Assumes that we only have tensors of either size 4 or 3
    """
    pad_shape = (0, 0, 0, 0, 0, pad_size, 0, 0) if len(input_tensor.shape) == 4 else (0, 0, 0, pad_size, 0, 0)

    return torch.nn.functional.pad(input_tensor, pad_shape, mode="constant", value=0)


def reshape_into_chunks(input_tensor, pad_size, chunk_size):
    """
    Padding input_tensor with `pad_size` on the seq_len dim (dim=1) and
    simultaneously splitting it into chunk sequences.

    Assumes that we only have tensors of either size 4 or 3
    """
    # [bsz, seq_len, ...] -> [bsz, seq_len multiple of chunk_size, ...]
    input_tensor = pad_tensor_by_size(input_tensor, pad_size)

    if len(input_tensor.shape) == 3:
        # [bsz, seq_len multiple of chunk_size, num_heads] -> [bsz, -1, chunk_size, num_heads]
        return input_tensor.reshape(input_tensor.shape[0], -1, chunk_size, input_tensor.shape[2])
    else:
        # [bsz, seq_len multiple of chunk_size, num_heads, head_dim or state_size] ->
        # [bsz, -1, chunk_size, num_heads, head_dim or state_size]
        return input_tensor.reshape(
            input_tensor.shape[0], -1, chunk_size, input_tensor.shape[2], input_tensor.shape[3]
        )


def segment_sum(input_tensor):
    """
    More stable segment sum calculation. Uses cumulative sums and masking instead of direct subtractions.
    """
    chunk_size = input_tensor.size(-1)
    # 1. expand input tensor to have an additional dimension and repeat along that dimension
    # [..., chunk_size] -> [..., chunk_size, chunk_size]
    input_tensor = input_tensor[..., None].expand(*input_tensor.size(), chunk_size)
    # 2. create a lower triangular mask with the diagonal set to 0 to 0 out elements above diag
    mask = torch.tril(torch.ones(chunk_size, chunk_size, device=input_tensor.device, dtype=torch.bool), diagonal=-1)
    input_tensor = input_tensor.masked_fill(~mask, 0)
    # 3. compute actual cumsum
    tensor_segsum = torch.cumsum(input_tensor, dim=-2)

    # 4. apply mask to keep only the lower triangular part of the cumulative sum result (incl diagonal this time)
    mask = torch.tril(torch.ones(chunk_size, chunk_size, device=input_tensor.device, dtype=torch.bool), diagonal=0)
    tensor_segsum = tensor_segsum.masked_fill(~mask, -torch.inf)
    return tensor_segsum


class Mamba2Cache:
    """
    Arguments:
        config: Mamba2Config
        batch_size: int
        dtype: torch.dtype
        device: torch.device

    Attributes:
        seqlen_offset: int
        dtype: torch.dtype
        conv_states: Dict[int, torch.Tensor] # layer_idx -> [batch_size, intermediate_size, conv_kernel_size]
        ssm_states: Dict[int, torch.Tensor] # layer_idx -> [batch_size, intermediate_size, ssm_state_size]
    """

    def __init__(
        self,
        config: Mamba2Config,
        batch_size: int,
        dtype: torch.dtype = torch.float16,
        device: Optional[str] = None,
    ):
        self.seqlen_offset = 0
        self.dtype = dtype
        self.conv_kernel_size = config.conv_kernel
        self.intermediate_size = int(config.expand * config.hidden_size)

        self.conv_states = {
            i: torch.zeros(
                batch_size,
                self.intermediate_size + 2 * config.n_groups * config.state_size,
                self.conv_kernel_size,
                device=device,
                dtype=dtype,
            )
            for i in range(config.num_hidden_layers)
        }
        self.ssm_states = {
            i: torch.zeros(
                batch_size,
                config.num_heads,
                config.head_dim,
                config.state_size,
                device=device,
                dtype=dtype,
            )
            for i in range(config.num_hidden_layers)
        }
        self.activation = config.hidden_act
        self.act = ACT2FN[config.hidden_act]

    def update_conv_state(
        self,
        layer_idx: int,
        new_conv_state: torch.Tensor,
        cache_position: torch.LongTensor,
    ) -> torch.Tensor:
        conv_state = self.conv_states[layer_idx]
        cache_position = cache_position.clamp(0, self.conv_kernel_size - 1)

        conv_state = conv_state.roll(shifts=-1, dims=-1)
        conv_state[:, :, cache_position] = new_conv_state.to(conv_state.device)
        self.conv_states[layer_idx].zero_()
        self.conv_states[layer_idx] += conv_state
        return self.conv_states[layer_idx]

    def reset(self):
        self.conv_states.zero_()
        self.ssm_states.zero_()


class Mamba2Mixer(nn.Module):
    """
    Compute ∆, A, B, C, and D the state space parameters and compute the `contextualized_states`.
    A, D are input independent (see Mamba paper [1] Section 3.5.2 "Interpretation of A" for why A isn't selective)
    ∆, B, C are input-dependent (this is a key difference between Mamba and the linear time invariant S4,
    and is why Mamba is called **selective** state spaces)
    """

    def __init__(self, config: Mamba2Config, layer_idx: int):
        super().__init__()
        self.num_heads = config.num_heads
        self.hidden_size = config.hidden_size
        self.ssm_state_size = config.state_size
        self.conv_kernel_size = config.conv_kernel
        self.intermediate_size = int(config.expand * self.hidden_size)
        self.time_step_rank = int(config.time_step_rank)
        self.layer_idx = layer_idx
        self.use_conv_bias = config.use_conv_bias
        self.activation = config.hidden_act
        self.act = ACT2FN[config.hidden_act]

        self.layer_norm_epsilon = config.layer_norm_epsilon
        self.rms_norm = config.rms_norm

        self.n_groups = config.n_groups
        self.head_dim = config.head_dim
        self.chunk_size = config.chunk_size

        self.time_step_limit = config.time_step_limit
        self.time_step_min = config.time_step_min
        self.time_step_max = config.time_step_max

        self.conv_dim = self.intermediate_size + 2 * self.n_groups * self.ssm_state_size
        self.conv1d = nn.Conv1d(
            in_channels=self.conv_dim,
            out_channels=self.conv_dim,
            bias=config.use_conv_bias,
            kernel_size=config.conv_kernel,
            groups=self.conv_dim,
            padding=config.conv_kernel - 1,
        )

        # projection of the input hidden states
        projection_size = self.intermediate_size + self.conv_dim + self.num_heads
        self.in_proj = nn.Linear(
            self.hidden_size,
            projection_size,
            bias=config.use_bias,
        )
        # selective projection used to make dt, B and C input dependant

        # time step projection (discretization)
        # instantiate once and copy inv_dt in init_weights of PretrainedModel
        self.dt_bias = nn.Parameter(torch.ones(self.num_heads))

        # S4D real initialization. These are not discretized!
        # The core is to load them, compute the discrete states, then write the updated state. Keeps the memory bounded
        A = torch.arange(1, self.num_heads + 1)
        self.A_log = nn.Parameter(torch.log(A))
        self.A_log._no_weight_decay = True
        self.norm = RMSNormGated(
            self.intermediate_size, eps=self.layer_norm_epsilon, norm_before_gate=False
        )
        self.D = nn.Parameter(torch.ones(self.num_heads))
        self.D._no_weight_decay = True

        self.out_proj = nn.Linear(self.intermediate_size, self.hidden_size, bias=config.use_bias)
        self.use_bias = config.use_bias

        if not is_fast_path_available:
            logger.warning_once(
                "The fast path is not available because one of "
                "`(selective_state_update, causal_conv1d_fn, causal_conv1d_update)` is None. "
                "Falling back to the naive implementation. "
                "To install follow https://github.com/state-spaces/mamba/#installation and"
                "https://github.com/Dao-AILab/causal-conv1d"
            )

    def cuda_kernels_forward(
        self,
        hidden_states: torch.Tensor,
        cache_params: Optional[Mamba2Cache] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
    ):
        # set up dimensions for reshapes later
        batch_size, seq_len, _ = hidden_states.shape
        groups_time_state_size = self.n_groups * self.ssm_state_size
        d_to_remove = 2 * self.intermediate_size + 2 * self.n_groups * self.ssm_state_size + self.num_heads

        # getting projected states from cache if it exists
        if cache_params is not None and cache_params.seqlen_offset > 0:
            in_projected_states = self.in_proj(hidden_states.squeeze(1))  # (B 2D)
            d_mlp = (in_projected_states.shape[-1] - d_to_remove) // 2
            split_projection_dim = [d_mlp, d_mlp, self.intermediate_size, self.conv_dim, self.num_heads]
            _, _, gate, hidden_states_B_C, dt = torch.split(in_projected_states, split_projection_dim, dim=-1)

            hidden_states_B_C = causal_conv1d_update(
                hidden_states_B_C,
                cache_params.conv_states[self.layer_idx],
                self.conv1d.weight.squeeze(1),
                self.conv1d.bias,
                self.activation,
            )

            hidden_states, B, C = torch.split(
                hidden_states_B_C,
                [
                    self.intermediate_size,
                    groups_time_state_size,
                    groups_time_state_size,
                ],
                dim=-1,
            )
            A = -torch.exp(self.A_log.float())  # (nheads,)

            A = A[:, None, ...][:, :, None].expand(-1, self.head_dim, self.ssm_state_size).to(dtype=torch.float32)
            dt = dt[:, :, None].expand(-1, -1, self.head_dim)
            dt_bias = self.dt_bias[:, None, ...].expand(-1, self.head_dim)
            D = self.D[:, None, ...].expand(-1, self.head_dim)
            B = B.view(batch_size, self.n_groups, B.shape[1] // self.n_groups)
            C = C.view(batch_size, self.n_groups, C.shape[1] // self.n_groups)
            hidden_states_reshaped = hidden_states.view(batch_size, self.num_heads, self.head_dim)

            hidden_states = selective_state_update(
                cache_params.ssm_states[self.layer_idx],
                hidden_states_reshaped,
                dt,
                A,
                B,
                C,
                D,
                z=None,
                dt_bias=dt_bias,
                dt_softplus=True,
            )
            hidden_states = hidden_states.view(batch_size, self.num_heads * self.head_dim)
            hidden_states = self.norm(hidden_states, gate)
            out = self.out_proj(hidden_states)[:, None, ...]
        # if no cache is found, calling the kernel
        else:
            if attention_mask is not None and attention_mask.shape[1] > 1 and attention_mask.shape[0] > 1:
                # tune out hidden states for pad tokens, see https://github.com/state-spaces/mamba/issues/66
                dtype = hidden_states.dtype
                hidden_states = (hidden_states * attention_mask[:, :, None]).to(dtype)
            # 1. Gated MLP's linear projection
            projected_states = self.in_proj(hidden_states)
            A = -torch.exp(self.A_log.float())  # (num_heads) or (intermediate_size, state_size)
            dt_limit_kwargs = {} if self.time_step_limit == (0.0, float("inf")) else {"dt_limit": self.time_step_limit}

            if self.training and cache_params is None:
                out, ssm_state = mamba_split_conv1d_scan_combined(
                    projected_states,
                    self.conv1d.weight.squeeze(1),
                    self.conv1d.bias,
                    self.dt_bias,
                    A,
                    D=self.D,
                    chunk_size=self.chunk_size,
                    seq_idx=None,  # was seq_idx
                    activation=self.activation,
                    rmsnorm_weight=self.norm.weight,
                    rmsnorm_eps=self.norm.eps,
                    outproj_weight=self.out_proj.weight,
                    outproj_bias=self.out_proj.bias,
                    headdim=self.head_dim,
                    ngroups=self.n_groups,
                    norm_before_gate=False,
                    return_final_states=True,
                    **dt_limit_kwargs,
                )

            else:
                gate, hidden_states_B_C, time_step = torch.split(
                    projected_states,
                    [self.intermediate_size, self.conv_dim, self.num_heads],
                    dim=-1,
                )

                # 1D Convolution
                if causal_conv1d_fn is None or self.activation not in ["silu", "swish"]:
                    hidden_states_B_C = self.act(
                        self.conv1d(hidden_states_B_C.transpose(1, 2)).transpose(1, 2)[:, :seq_len]
                    )  # (B, L, self.d_inner + 2 * ngroups * d_state)
                else:
                    hidden_states_B_C = causal_conv1d_fn(
                        x=hidden_states_B_C.transpose(1, 2),
                        weight=self.conv1d.weight.squeeze(1),
                        bias=self.conv1d.bias,
                        activation=self.activation,
                    ).transpose(1, 2)[:, :seq_len]
                hidden_states, B, C = torch.split(
                    hidden_states_B_C,
                    [self.intermediate_size, groups_time_state_size, groups_time_state_size],
                    dim=-1,
                )
                if attention_mask is not None and attention_mask.shape[1] > 1 and attention_mask.shape[0] > 1:
                    # tune out hidden states for pad tokens, see https://github.com/state-spaces/mamba/issues/66
                    dtype = hidden_states.dtype
                    hidden_states = (hidden_states * attention_mask[:, :, None]).to(dtype)
                scan_output, ssm_state = mamba_chunk_scan_combined(
                    hidden_states.view(batch_size, seq_len, -1, self.head_dim),
                    time_step,
                    A,
                    B.view(batch_size, seq_len, self.n_groups, -1),
                    C.view(batch_size, seq_len, self.n_groups, -1),
                    chunk_size=self.chunk_size,
                    D=self.D,
                    z=None,
                    seq_idx=None,
                    return_final_states=True,
                    dt_bias=self.dt_bias,
                    dt_softplus=True,
                    **dt_limit_kwargs,
                )
                if ssm_state is not None and cache_params is not None:
                    cache_params.ssm_states[self.layer_idx].copy_(ssm_state)
                scan_output = scan_output.view(batch_size, seq_len, -1)
                # Multiply "gate" branch and apply extra normalization layer
                scan_output = self.norm(scan_output, gate)
                out = self.out_proj(scan_output)
        return out

    # fmt: off
    def torch_forward(
        self,
        input_states,
        cache_params: Optional[Mamba2Cache] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None
    ):
        batch_size, seq_len, _ = input_states.shape
        dtype = input_states.dtype
        # Gated MLP's linear projection
        projected_states = self.in_proj(input_states.squeeze(1))
        d_mlp = (projected_states.shape[-1] - 2 * self.intermediate_size -
                 2 * self.n_groups * self.ssm_state_size - self.num_heads) // 2
        _, _, gate, hidden_states, dt = projected_states.split(
                [d_mlp, d_mlp, self.intermediate_size,  self.conv_dim, self.num_heads], dim=-1
        )

        # Convolution sequence transformation
        if cache_params is not None:
            ssm_state = cache_params.ssm_states[self.layer_idx].clone()
            ssm_state = ssm_state.to(hidden_states.device)
            if cache_params.seqlen_offset > 0:
                # [batch, intermediate_size, conv_kernel_size]
                conv_state = cache_params.conv_states[self.layer_idx]
                conv_state = torch.roll(conv_state, shifts=-1, dims=-1)
                # handle batched generation - states are copied through
                conv_state[:, :, -1] = hidden_states[:, 0, :] if hidden_states.ndim == 3 else hidden_states
                cache_params.conv_states[self.layer_idx].copy_(conv_state)
                hidden_states = torch.sum(conv_state.to(projected_states.device) * self.conv1d.weight[:, 0, :], dim=-1)
                if self.use_conv_bias:
                    hidden_states += self.conv1d.bias
                # [batch, 1, intermediate_size] : decoding
                hidden_states = self.act(hidden_states).to(dtype)[:, None, ...]
            else:
                hidden_states = hidden_states.transpose(1, 2)
                conv_state = nn.functional.pad(
                    hidden_states,
                    (self.conv_kernel_size - hidden_states.shape[-1], 0)
                )
                cache_params.conv_states[self.layer_idx].copy_(conv_state)
                # [batch, intermediate_size, seq_len]
                hidden_states = self.act(self.conv1d(hidden_states).transpose(1, 2))[:, :seq_len, :]
                if attention_mask is not None and attention_mask.shape[1] > 1 and attention_mask.shape[0] > 1:
                    dtype = hidden_states.dtype
                    # tune out hidden states for pad tokens, see https://github.com/state-spaces/mamba/issues/66
                    hidden_states = (hidden_states * attention_mask[:, :, None]).to(dtype)
        else:
            ssm_state = torch.zeros(
                (batch_size, self.num_heads, self.head_dim, self.ssm_state_size),
                device=hidden_states.device, dtype=dtype
            )
            hidden_states = self.act(self.conv1d(hidden_states.transpose(1, 2))[..., :seq_len].transpose(1, 2))
        hidden_states, B, C = torch.split(
            hidden_states,
            [self.intermediate_size, self.n_groups * self.ssm_state_size, self.n_groups * self.ssm_state_size],
            dim=-1
        )
        A = -torch.exp(self.A_log.float())                            # [num_heads]
        if cache_params is not None and cache_params.seqlen_offset > 0:
            # Note: there is no need to pad parameter matrices here, as there is just one new token
            # for batched generation
            dt = dt[:, None, ...] if dt.ndim == 2 else dt[:, 0, :][:, None, ...]
            dt = dt.transpose(1, 2).expand(batch_size, dt.shape[-1], self.head_dim)
            # [num_heads] -> [num_heads, head_dim]
            dt_bias = self.dt_bias[..., None].expand(self.dt_bias.shape[0], self.head_dim)

            dt = torch.nn.functional.softplus(dt + dt_bias.to(dt.dtype))
            dt = torch.clamp(dt, self.time_step_min)
            A = A[..., None, None].expand(self.num_heads, self.head_dim, self.ssm_state_size).to(dtype=torch.float32)
            # [bsz, num_heads, head_dim, state_size]
            dA = torch.exp(dt[..., None] * A)

            # Discretize B
            # [bsz, n_groups * state_size] -> [bsz, n_groups, 1, state_size] ->
            # -> [bsz, n_groups, group to head repetition factor, state_size] -> [bsz, num_heads, state_size]
            B = B.reshape(batch_size, self.n_groups, -1)[..., None, :]
            B = B.expand(batch_size, self.n_groups, self.num_heads // self.n_groups, B.shape[-1]).contiguous()
            B = B.reshape(batch_size, -1, B.shape[-1])
            # [bsz, num_heads, head_dim, state_size]
            dB = dt[..., None] * B[..., None, :]

            # Discretize x into dB
            # [bsz, intermediate_size] -> [bsz, num_heads, head_dim]
            hidden_states = hidden_states.reshape(batch_size, -1, self.head_dim)
            dBx = dB * hidden_states[..., None]

            # State calculation
            cache_params.ssm_states[self.layer_idx].copy_(
                cache_params.ssm_states[self.layer_idx] * dA + dBx
            )

            # Subsequent output
            # [bsz, n_groups * state_size] -> [bsz, num_heads, state_size]
            C = C.reshape(batch_size, self.n_groups, -1)[..., None, :]
            C = C.expand(batch_size, self.n_groups, self.num_heads // self.n_groups, C.shape[-1]).contiguous()
            C = C.reshape(batch_size, -1, C.shape[-1])
            # [bsz, num_heads, head_dim]

            ssm_states = cache_params.ssm_states[self.layer_idx].to(C.dtype)  # Shape: [b, h, d, n]
            # Reshape ssm_states to merge the first two dimensions
            # Shape: [b*h, d, n]
            ssm_states_reshaped = ssm_states.view(batch_size * self.num_heads, self.head_dim, self.ssm_state_size)
            C_reshaped = C.view(batch_size * self.num_heads, self.ssm_state_size, 1)  # Shape: [b*h, n, 1]
            y = torch.bmm(ssm_states_reshaped, C_reshaped)
            y = y.view(batch_size, self.num_heads, self.head_dim)

            # D skip connection
            # [num_heads] -> [num_heads, head_dim]
            D = self.D[..., None].expand(self.D.shape[0], self.head_dim)
            y = (y + hidden_states * D).to(y.dtype)

            # [bsz, num_heads, head_dim] -> [bsz, 1, intermediate_size]
            y = y.reshape(batch_size, -1)[:, None, ...]
        else:
            # begin ssd naive implementation without einsums
            dt = nn.functional.softplus(dt + self.dt_bias)
            dt = torch.clamp(dt, self.time_step_min)
            hidden_states = hidden_states.reshape(batch_size, seq_len, -1, self.head_dim).float()
            B = B.reshape(batch_size, seq_len,  -1, self.ssm_state_size).float()
            C = C.reshape(batch_size, seq_len, -1, self.ssm_state_size).float()
            B = B.repeat(1, 1, self.num_heads // self.n_groups, 1)
            C = C.repeat(1, 1, self.num_heads // self.n_groups, 1)
            pad_size = (self.chunk_size - seq_len % self.chunk_size) % self.chunk_size

            D_residual = self.D[..., None] * pad_tensor_by_size(hidden_states, pad_size)

            # Discretize x and A
            hidden_states = hidden_states * dt[..., None]
            A = A.to(hidden_states.dtype) * dt

            # Rearrange into blocks/chunks
            hidden_states, A, B, C = [reshape_into_chunks(t, pad_size, self.chunk_size) for t in (hidden_states, A, B, C)]

            # [bsz, -1, chunk_size, num_heads] -> [bsz, num_heads, -1, chunk_size]
            A = A.permute(0, 3, 1, 2)
            A_cumsum = torch.cumsum(A, dim=-1)

            # 1. Compute the output for each intra-chunk (diagonal blocks)
            # This is the analog of a causal mask
            L = torch.exp(segment_sum(A))

            # Contraction of C and B to get G (attention-weights like)
            # shape: (b, c, l, s, h, n)
            G_intermediate = C[:, :, :, None, :, :] * B[:, :, None, :, :, :]
            G = G_intermediate.sum(dim=-1)  # shape: (b, c, l, s, h)

            # Compute M, equivalent to applying attention mask to weights
            M_intermediate = G[..., None] * L.permute(0, 2, 3, 4, 1)[..., None]
            M = M_intermediate.sum(dim=-1)

            # Compute Y_diag (apply to values)
            Y_diag = (M[..., None] * hidden_states[:, :, None]).sum(dim=3)

            # 2. Compute the state for each intra-chunk
            # (right term of low-rank factorization of off-diagonal blocks; B terms)
            decay_states = torch.exp((A_cumsum[:, :, :, -1:] - A_cumsum))
            B_decay = B * decay_states.permute(0, -2, -1, 1)[..., None]
            states = (B_decay[..., None, :] * hidden_states[..., None]).sum(dim=2)

            # 3. Compute the inter-chunk SSM recurrence; produces correct SSM states at chunk boundaries
            # (middle term of factorization of off-diag blocks; A terms)
            if cache_params is not None and cache_params.seqlen_offset > 0:
                previous_states = cache_params.ssm_states[self.layer_idx][:, None, ...]
            else:
                previous_states = torch.zeros_like(states[:, :1])
            states = torch.cat([previous_states, states], dim=1)
            decay_chunk = torch.exp(segment_sum(nn.functional.pad(A_cumsum[:, :, :, -1], (1, 0))))
            decay_chunk = decay_chunk.transpose(1, 3)
            new_states = (decay_chunk[..., None, None] * states[:, :, None, ...]).sum(dim=1)
            states, ssm_state = new_states[:, :-1], new_states[:, -1]

            # 4. Compute state -> output conversion per chunk
            # (left term of low-rank factorization of off-diagonal blocks; C terms)
            state_decay_out = torch.exp(A_cumsum)
            C_times_states = (C[..., None, :] * states[:, :, None, ...])
            state_decay_out_permuted = state_decay_out.permute(0, 2, 3, 1)
            Y_off = (C_times_states.sum(-1) * state_decay_out_permuted[..., None])

            # Add output of intra-chunk and inter-chunk terms (diagonal and off-diagonal blocks)
            y = Y_diag + Y_off
            # [bsz, -1, self.chunk_size, num_heads, head_dim] -> [bsz, (padded) seq_len, num_heads, head_dim]
            y = y.reshape(batch_size, -1, self.num_heads, self.head_dim)

            y = y + D_residual
            # Cutting off padded chunks
            if pad_size > 0:
                y = y[:, :seq_len, :, :]
            y = y.reshape(batch_size, seq_len, -1)
            if ssm_state is not None and cache_params is not None:
                cache_params.ssm_states[self.layer_idx].copy_(ssm_state)

        scan_output = self.norm(y, gate)
        # end ssd naive

        # 4. Final linear projection
        contextualized_states = self.out_proj(scan_output.to(dtype))  # [batch, seq_len, hidden_size]
        return contextualized_states
    # fmt: on

    def forward(
        self,
        hidden_states,
        cache_params: Optional[Mamba2Cache] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
    ):
        if is_fast_path_available and "cuda" in self.in_proj.weight.device.type:
            return self.cuda_kernels_forward(hidden_states, cache_params, cache_position, attention_mask)
        dtype = hidden_states.dtype
        if attention_mask is not None and attention_mask.shape[1] > 1 and attention_mask.shape[0] > 1:
            # tune out hidden states for pad tokens, see https://github.com/state-spaces/mamba/issues/66
            hidden_states = (hidden_states * attention_mask[:, :, None]).to(dtype)

        return self.torch_forward(hidden_states, cache_params, cache_position, attention_mask)


class Mamba2Block(nn.Module):
    def __init__(self, config, layer_idx):
        super().__init__()
        self.config = config
        self.layer_idx = layer_idx
        self.residual_in_fp32 = config.residual_in_fp32
        self.norm = RMSNorm(config.hidden_size, eps=config.layer_norm_epsilon)
        self.mixer = Mamba2Mixer(config, layer_idx=layer_idx)

    def forward(
        self,
        hidden_states,
        cache_params: Optional[Mamba2Cache] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
    ):
        residual = hidden_states
        hidden_states = self.norm(hidden_states.to(dtype=self.norm.weight.dtype))
        if self.residual_in_fp32:
            residual = residual.to(torch.float32)

        hidden_states = self.mixer(
            hidden_states,
            cache_params=cache_params,
            cache_position=cache_position,
            attention_mask=attention_mask,
        )
        hidden_states = residual + hidden_states
        return hidden_states


class Mamba2PreTrainedModel(PreTrainedModel, GenerationMixin):
    """
    An abstract class to handle weights initialization and a simple interface for downloading and loading pretrained
    models.
    """

    config_class = Mamba2Config
    base_model_prefix = "backbone"
    _no_split_modules = ["Mamba2Block"]
    supports_gradient_checkpointing = True
    _is_stateful = True

    def _init_weights(self, module):
        """Initialize the weights."""
        if isinstance(module, Mamba2Mixer):
            module.A_log._no_weight_decay = True
            module.D._no_weight_decay = True

            dt = torch.exp(
                torch.rand(self.config.num_heads)
                * (math.log(self.config.time_step_max) - math.log(self.config.time_step_min))
                + math.log(self.config.time_step_min)
            ).clamp(min=self.config.time_step_floor)

            # # Inverse of softplus: https://github.com/pytorch/pytorch/issues/72759
            inv_dt = dt + torch.log(-torch.expm1(-dt))
            with torch.no_grad():
                module.dt_bias.copy_(inv_dt)
            module.dt_bias._no_reinit = True

        if isinstance(module, nn.Linear):
            if module.bias is not None:
                if not getattr(module.bias, "_no_reinit", False):
                    nn.init.zeros_(module.bias)
        elif isinstance(module, nn.Embedding):
            nn.init.normal_(module.weight, std=self.config.initializer_range)

        if self.config.rescale_prenorm_residual:
            # Reinitialize selected weights subject to the OpenAI GPT-2 Paper Scheme:
            #   > A modified initialization which accounts for the accumulation on the residual path with model depth. Scale
            #   > the weights of residual layers at initialization by a factor of 1/√N where N is the # of residual layers.
            #   >   -- GPT-2 :: https://openai.com/blog/better-language-models/
            #
            # Reference (Megatron-LM): https://github.com/NVIDIA/Megatron-LM/blob/main/megatron/model/gpt_model.py
            for name, p in module.named_parameters():
                if name in ["out_proj.weight"]:
                    # Special Scaled Initialization --> There are 2 Layer Norms per Transformer Block
                    # Following Pytorch init, except scale by 1/sqrt(2 * n_layer)
                    # We need to reinit p since this code could be called multiple times
                    # Having just p *= scale would repeatedly scale it down
                    nn.init.kaiming_uniform_(p, a=math.sqrt(5))
                    with torch.no_grad():
                        p /= math.sqrt(self.config.num_hidden_layers)


@dataclass
# Copied from transformers.models.mamba.modeling_mamba.MambaOutput with MAMBA->MAMBA2,Mamba->Mamba2
class Mamba2Output(ModelOutput):
    """
    Class for the MAMBA2 model outputs.

    Args:
        last_hidden_state (`torch.FloatTensor` of shape `(batch_size, sequence_length, hidden_size)`):
            Sequence of hidden-states at the output of the last layer of the model.
        cache_params (`Mamba2Cache`):
            The state of the model at the last time step. Can be used in a forward method with the next `input_ids` to
            avoid providing the old `input_ids`.

            Includes both the State space model state matrices after the selective scan, and the Convolutional states
        hidden_states (`tuple(torch.FloatTensor)`, *optional*,
            returned when `output_hidden_states=True` is passed or when `config.output_hidden_states=True`):
            Tuple of `torch.FloatTensor` (one for the output of the embeddings, if the model has an embedding layer, +
            one for the output of each layer) of shape `(batch_size, sequence_length, hidden_size)`.

            Hidden-states of the model at the output of each layer plus the optional initial embedding outputs.
    """

    last_hidden_state: Optional[torch.FloatTensor] = None
    cache_params: Optional[Mamba2Cache] = None
    hidden_states: Optional[Tuple[torch.FloatTensor]] = None


@dataclass
# Copied from transformers.models.mamba.modeling_mamba.MambaCausalLMOutput with Mamba->Mamba2
class Mamba2CausalLMOutput(ModelOutput):
    """
    Base class for causal language model (or autoregressive) outputs.

    Args:
        loss (`torch.FloatTensor` of shape `(1,)`, *optional*, returned when `labels` is provided):
            Language modeling loss (for next-token prediction).
        logits (`torch.FloatTensor` of shape `(batch_size, sequence_length, config.vocab_size)`):
            Prediction scores of the language modeling head (scores for each vocabulary token before SoftMax).
        cache_params (`Mamba2Cache`):
            The state of the model at the last time step. Can be used in a forward method with the next `input_ids` to
            avoid providing the old `input_ids`.

            Includes both the State space model state matrices after the selective scan, and the Convolutional states
        hidden_states (`tuple(torch.FloatTensor)`, *optional*,
            returned when `output_hidden_states=True` is passed or when `config.output_hidden_states=True`):
            Tuple of `torch.FloatTensor` (one for the output of the embeddings, if the model has an embedding layer, +
            one for the output of each layer) of shape `(batch_size, sequence_length, hidden_size)`.

            Hidden-states of the model at the output of each layer plus the optional initial embedding outputs.
    """

    loss: Optional[torch.FloatTensor] = None
    logits: Optional[torch.FloatTensor] = None
    cache_params: Optional[Mamba2Cache] = None
    hidden_states: Optional[Tuple[torch.FloatTensor]] = None


class Mamba2Model(Mamba2PreTrainedModel):
    def __init__(self, config):
        super().__init__(config)

        self.embeddings = nn.Embedding(config.vocab_size, config.hidden_size)
        self.layers = nn.ModuleList([Mamba2Block(config, layer_idx=idx) for idx in range(config.num_hidden_layers)])

        self.gradient_checkpointing = False
        self.norm_f = RMSNorm(config.hidden_size, eps=config.layer_norm_epsilon)
        # Initialize weights and apply final processing
        self._register_load_state_dict_pre_hook(self.load_hook)
        self.post_init()

    def load_hook(self, state_dict, prefix, *args):
        for k in state_dict:
            if "embedding." in k:
                state_dict[k.replace("embedding.", "embeddings.")] = state_dict.pop(k)
                break

    def get_input_embeddings(self):
        return self.embeddings

    def set_input_embeddings(self, new_embeddings):
        self.embeddings = new_embeddings

    def forward(
        self,
        input_ids: Optional[torch.LongTensor] = None,
        inputs_embeds: Optional[torch.LongTensor] = None,
        cache_params: Optional[Mamba2Cache] = None,
        use_cache: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        **kwargs,
    ) -> Union[Tuple, Mamba2Output]:
        output_hidden_states = (
            output_hidden_states if output_hidden_states is not None else self.config.output_hidden_states
        )
        use_cache = use_cache if use_cache is not None else (self.config.use_cache if not self.training else False)
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        if (input_ids is None) ^ (inputs_embeds is not None):  # ^ is python for xor
            raise ValueError("You must specify exactly one of input_ids or inputs_embeds")

        if inputs_embeds is None:
            inputs_embeds = self.embeddings(input_ids)

        if self.gradient_checkpointing and self.training and use_cache:
            use_cache = False

        if use_cache:
            if cache_params is None:
                cache_params = Mamba2Cache(
                    self.config, inputs_embeds.size(0), device=inputs_embeds.device, dtype=inputs_embeds.dtype
                )
                cache_position = torch.arange(0, self.config.conv_kernel, device=inputs_embeds.device)
            elif cache_position is None:
                # cases when we do manual forward instead of using `model.generate` which will initiate
                # `cache_position` and makes sure it is not None, throw error here instead of doing some
                # hack to conjecture the current cache position
                raise ValueError(
                    "You have to specify the `cache_position` manually when `use_cache=True` and `cache_params` is passed, "
                    "you don't have to pass a `cache_params` if you are in prefilling stage because in that case it will "
                    "be initialized for you automatically"
                )
        else:
            cache_params = None

        hidden_states = inputs_embeds
        all_hidden_states = () if output_hidden_states else None
        for mixer_block in self.layers:
            if self.gradient_checkpointing and self.training:
                hidden_states = self._gradient_checkpointing_func(
                    mixer_block.__call__,
                    hidden_states,
                    cache_params,
                    cache_position,
                    attention_mask,
                )
            else:
                hidden_states = mixer_block(
                    hidden_states,
                    cache_params=cache_params,
                    cache_position=cache_position,
                    attention_mask=attention_mask,
                )

            if output_hidden_states:
                all_hidden_states = all_hidden_states + (hidden_states,)

        if use_cache:
            cache_params.seqlen_offset += inputs_embeds.shape[1]

        hidden_states = self.norm_f(hidden_states)

        if output_hidden_states:
            all_hidden_states = all_hidden_states + (hidden_states,)

        if not return_dict:
            return tuple(v for v in [hidden_states, cache_params, all_hidden_states] if v is not None)

        return Mamba2Output(
            last_hidden_state=hidden_states,
            cache_params=cache_params if use_cache else None,
            hidden_states=all_hidden_states,
        )


class Mamba2ForCausalLM(Mamba2PreTrainedModel):
    _tied_weights_keys = []

    def __init__(self, config):
        super().__init__(config)
        self.backbone = Mamba2Model(config)
        self.lm_head = nn.Linear(config.hidden_size, config.vocab_size, bias=False)
        # Initialize weights and apply final processing
        self.post_init()

    def get_output_embeddings(self):
        return self.lm_head

    def set_output_embeddings(self, new_embeddings):
        self.lm_head = new_embeddings

    def get_input_embeddings(self):
        return self.backbone.get_input_embeddings()

    def set_input_embeddings(self, new_embeddings):
        return self.backbone.set_input_embeddings(new_embeddings)

    def prepare_inputs_for_generation(
        self,
        input_ids,
        inputs_embeds=None,
        use_cache=None,
        cache_params: Optional[Mamba2Cache] = None,
        cache_position: Optional[torch.LongTensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        num_logits_to_keep: Optional[int] = None,
        **kwargs,
    ):
        if inputs_embeds is not None:
            past_len = inputs_embeds.shape[1] + input_ids.shape[1]
        else:
            past_len = input_ids.shape[1]
        if use_cache:
            # `cache_position` should have been initialized in `generate`
            if cache_position is None:
                raise ValueError(
                    "`cache_position` should not be None as it should have been initialized in "
                    "`model.generate`, you are responsible for passing in a valid `cache_position` if "
                    "you are calling `prepare_inputs_for_generation` directly with `use_cache=True`"
                )
            # how do we detect that we are in decoding without cache?
            if cache_position[0] > 0:
                input_ids = input_ids[:, -1][..., None]
                attention_mask = attention_mask[:, -1][..., None]
            else:
                # we initialize the `cache_position` to full size of `conv_states` at prefill stage
                # considering padding will be applied when input length is shorter, and truncation
                # will be applied when it is longer, so it will be equivalent to always have it match
                # the length of `cache_params.conv_states`, which is `config.conv_kernel`
                cache_position = torch.arange(0, past_len, device=input_ids.device)
                # if the cache is not used, we also do have to extend the attention mask here
                # TODO there is likely a cleverer way to do this
                extended_mask = torch.ones(
                    attention_mask.size(0), past_len - attention_mask.shape[1], device=attention_mask.device
                )
                attention_mask = torch.cat([attention_mask, extended_mask], dim=1)
                cache_params = None

        if attention_mask.shape[1] < past_len:
            # we have to update manually the attention mask if
            # we are in decoding without cache
            # and we don't have position_ids here
            # TODO but we should be able to use cache_position though at a later time
            extended_mask = torch.ones(
                attention_mask.size(0), past_len - attention_mask.shape[1], device=attention_mask.device
            )
            attention_mask = torch.cat([attention_mask, extended_mask], dim=1)
        if inputs_embeds is not None and cache_params is None:
            model_inputs = {"inputs_embeds": inputs_embeds}
        else:
            model_inputs = {"input_ids": input_ids}

        if num_logits_to_keep is not None:
            model_inputs['num_logits_to_keep'] = num_logits_to_keep

        model_inputs.update({
            'attention_mask': attention_mask,
            'cache_params': cache_params,
            'use_cache': use_cache,
            'cache_position': cache_position,
            'num_logits_to_keep': num_logits_to_keep
        })
        return model_inputs

    def forward(
        self,
        input_ids: Optional[torch.LongTensor] = None,
        inputs_embeds: Optional[torch.FloatTensor] = None,
        cache_params: Optional[Mamba2Cache] = None,
        labels: Optional[torch.LongTensor] = None,
        output_hidden_states: Optional[bool] = None,
        return_dict: Optional[bool] = None,
        use_cache: Optional[bool] = None,
        cache_position: Optional[torch.Tensor] = None,
        attention_mask: Optional[torch.Tensor] = None,
        num_logits_to_keep: Optional[int] = 0,
        **kwargs,  # for now we need this for generation
    ) -> Union[Tuple, Mamba2CausalLMOutput]:
        r"""
        labels (`torch.LongTensor` of shape `(batch_size, sequence_length)`, *optional*):
            Labels for language modeling. Note that the labels **are shifted** inside the model, i.e. you can set
            `labels = input_ids` Indices are selected in `[-100, 0, ..., config.vocab_size]` All labels set to `-100`
            are ignored (masked), the loss is only computed for labels in `[0, ..., config.vocab_size]`
        """
        return_dict = return_dict if return_dict is not None else self.config.use_return_dict

        outputs = self.backbone(
            input_ids,
            cache_params=cache_params,
            inputs_embeds=inputs_embeds,
            output_hidden_states=output_hidden_states,
            return_dict=return_dict,
            use_cache=use_cache,
            cache_position=cache_position,
            attention_mask=attention_mask,
        )
        hidden_states = outputs[0]
        fuse_linear_and_cross_entropy = self.config.fuse_cross_entropy and self.training
        logits = None if fuse_linear_and_cross_entropy else self.lm_head(hidden_states[:, -num_logits_to_keep:])

        loss = None
        if labels is not None:
            if self.config.fuse_cross_entropy:
                if fuse_linear_and_cross_entropy:
                    loss_fct = FusedLinearCrossEntropyLoss()
                else:
                    loss_fct = FusedCrossEntropyLoss(inplace_backward=True)
            else:
                loss_fct = nn.CrossEntropyLoss()
            # Enable model parallelism
            labels = labels.to(hidden_states.device)
            labels = torch.cat((labels[..., 1:], torch.full_like(labels[:, :1], loss_fct.ignore_index)), 1)
            if fuse_linear_and_cross_entropy:
                loss = loss_fct(hidden_states.view(-1, self.config.hidden_size),
                                labels.view(-1),
                                self.lm_head.weight,
                                self.lm_head.bias)
            else:
                loss = loss_fct(logits.view(-1, self.config.vocab_size), labels.view(-1))

        if not return_dict:
            output = (logits,) + outputs[1:]
            return (loss,) + output if loss is not None else output

        return Mamba2CausalLMOutput(
            loss=loss,
            logits=logits,
            cache_params=outputs.cache_params,
            hidden_states=outputs.hidden_states,
        )