342 lines
13 KiB
Python
342 lines
13 KiB
Python
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"""Simple, minimal implementation of Mamba in one file of PyTorch.
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Suggest reading the following before/while reading the code:
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[1] Mamba: Linear-Time Sequence Modeling with Selective State Spaces (Albert Gu and Tri Dao)
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https://arxiv.org/abs/2312.00752
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[2] The Annotated S4 (Sasha Rush and Sidd Karamcheti)
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https://srush.github.io/annotated-s4
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Glossary:
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b: batch size (`B` in Mamba paper [1] Algorithm 2)
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l: sequence length (`L` in [1] Algorithm 2)
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d or d_model: hidden dim
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n or d_state: latent state dim (`N` in [1] Algorithm 2)
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expand: expansion factor (`E` in [1] Section 3.4)
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d_in or d_inner: d * expand (`D` in [1] Algorithm 2)
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A, B, C, D: state space parameters (See any state space representation formula)
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(B, C are input-dependent (aka selective, a key innovation in Mamba); A, D are not)
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Δ or delta: input-dependent step size
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dt_rank: rank of Δ (See [1] Section 3.6 "Parameterization of ∆")
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"""
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from __future__ import annotations
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import math
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import json
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import torch
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import torch.nn as nn
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import torch.nn.functional as F
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from dataclasses import dataclass
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from einops import rearrange, repeat, einsum
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@dataclass
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class ModelArgs:
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d_model: int
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n_layer: int
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vocab_size: int
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d_state: int = 16
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expand: int = 2
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dt_rank: Union[int, str] = 'auto'
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d_conv: int = 4
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pad_vocab_size_multiple: int = 8
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conv_bias: bool = True
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bias: bool = False
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def __post_init__(self):
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self.d_inner = int(self.expand * self.d_model)
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if self.dt_rank == 'auto':
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self.dt_rank = math.ceil(self.d_model / 16)
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if self.vocab_size % self.pad_vocab_size_multiple != 0:
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self.vocab_size += (self.pad_vocab_size_multiple
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- self.vocab_size % self.pad_vocab_size_multiple)
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class Mamba(nn.Module):
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def __init__(self, args: ModelArgs):
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"""Full Mamba model."""
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super().__init__()
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self.args = args
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self.embedding = nn.Embedding(args.vocab_size, args.d_model)
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self.layers = nn.ModuleList([ResidualBlock(args) for _ in range(args.n_layer)])
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self.norm_f = RMSNorm(args.d_model)
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self.lm_head = nn.Linear(args.d_model, args.vocab_size, bias=False)
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self.lm_head.weight = self.embedding.weight # Tie output projection to embedding weights.
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# See "Weight Tying" paper
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def forward(self, input_ids):
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"""
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Args:
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input_ids (long tensor): shape (b, l) (See Glossary at top for definitions of b, l, d_in, n...)
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Returns:
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logits: shape (b, l, vocab_size)
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Official Implementation:
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class MambaLMHeadModel, https://github.com/state-spaces/mamba/blob/main/mamba_ssm/models/mixer_seq_simple.py#L173
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"""
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x = self.embedding(input_ids)
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for layer in self.layers:
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x = layer(x)
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x = self.norm_f(x)
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logits = self.lm_head(x)
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return logits
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@staticmethod
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def from_pretrained(pretrained_model_name: str):
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"""Load pretrained weights from HuggingFace into model.
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Args:
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pretrained_model_name: One of
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* 'state-spaces/mamba-2.8b-slimpj'
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* 'state-spaces/mamba-2.8b'
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* 'state-spaces/mamba-1.4b'
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* 'state-spaces/mamba-790m'
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* 'state-spaces/mamba-370m'
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* 'state-spaces/mamba-130m'
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Returns:
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model: Mamba model with weights loaded
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"""
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from transformers.utils import WEIGHTS_NAME, CONFIG_NAME
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from transformers.utils.hub import cached_file
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def load_config_hf(model_name):
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resolved_archive_file = cached_file(model_name, CONFIG_NAME,
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_raise_exceptions_for_missing_entries=False)
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return json.load(open(resolved_archive_file))
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def load_state_dict_hf(model_name, device=None, dtype=None):
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resolved_archive_file = cached_file(model_name, WEIGHTS_NAME,
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_raise_exceptions_for_missing_entries=False)
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return torch.load(resolved_archive_file, weights_only=True, map_location='cpu', mmap=True)
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config_data = load_config_hf(pretrained_model_name)
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args = ModelArgs(
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d_model=config_data['d_model'],
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n_layer=config_data['n_layer'],
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vocab_size=config_data['vocab_size']
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)
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model = Mamba(args)
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state_dict = load_state_dict_hf(pretrained_model_name)
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new_state_dict = {}
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for key in state_dict:
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new_key = key.replace('backbone.', '')
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new_state_dict[new_key] = state_dict[key]
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model.load_state_dict(new_state_dict)
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return model
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class ResidualBlock(nn.Module):
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def __init__(self, args: ModelArgs):
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"""Simple block wrapping Mamba block with normalization and residual connection."""
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super().__init__()
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self.args = args
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self.mixer = MambaBlock(args)
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self.norm = RMSNorm(args.d_model)
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def forward(self, x):
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"""
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Args:
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x: shape (b, l, d) (See Glossary at top for definitions of b, l, d_in, n...)
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Returns:
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output: shape (b, l, d)
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Official Implementation:
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Block.forward(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/modules/mamba_simple.py#L297
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Note: the official repo chains residual blocks that look like
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[Add -> Norm -> Mamba] -> [Add -> Norm -> Mamba] -> [Add -> Norm -> Mamba] -> ...
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where the first Add is a no-op. This is purely for performance reasons as this
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allows them to fuse the Add->Norm.
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We instead implement our blocks as the more familiar, simpler, and numerically equivalent
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[Norm -> Mamba -> Add] -> [Norm -> Mamba -> Add] -> [Norm -> Mamba -> Add] -> ....
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"""
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output = self.mixer(self.norm(x)) + x
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return output
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class MambaBlock(nn.Module):
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def __init__(self, args: ModelArgs):
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"""A single Mamba block, as described in Figure 3 in Section 3.4 in the Mamba paper [1]."""
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super().__init__()
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self.args = args
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self.in_proj = nn.Linear(args.d_model, args.d_inner * 2, bias=args.bias)
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self.conv1d = nn.Conv1d(
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in_channels=args.d_inner,
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out_channels=args.d_inner,
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bias=args.conv_bias,
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kernel_size=args.d_conv,
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groups=args.d_inner,
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padding=args.d_conv - 1,
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)
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# x_proj takes in `x` and outputs the input-specific Δ, B, C
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self.x_proj = nn.Linear(args.d_inner, args.dt_rank + args.d_state * 2, bias=False)
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# dt_proj projects Δ from dt_rank to d_in
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self.dt_proj = nn.Linear(args.dt_rank, args.d_inner, bias=True)
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A = repeat(torch.arange(1, args.d_state + 1), 'n -> d n', d=args.d_inner)
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self.A_log = nn.Parameter(torch.log(A))
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self.D = nn.Parameter(torch.ones(args.d_inner))
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self.out_proj = nn.Linear(args.d_inner, args.d_model, bias=args.bias)
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def forward(self, x):
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"""Mamba block forward. This looks the same as Figure 3 in Section 3.4 in the Mamba paper [1].
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Args:
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x: shape (b, l, d) (See Glossary at top for definitions of b, l, d_in, n...)
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Returns:
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output: shape (b, l, d)
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Official Implementation:
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class Mamba, https://github.com/state-spaces/mamba/blob/main/mamba_ssm/modules/mamba_simple.py#L119
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mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
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"""
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(b, l, d) = x.shape
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x_and_res = self.in_proj(x) # shape (b, l, 2 * d_in)
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(x, res) = x_and_res.split(split_size=[self.args.d_inner, self.args.d_inner], dim=-1)
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x = rearrange(x, 'b l d_in -> b d_in l')
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x = self.conv1d(x)[:, :, :l]
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x = rearrange(x, 'b d_in l -> b l d_in')
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x = F.silu(x)
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y = self.ssm(x)
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y = y * F.silu(res)
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output = self.out_proj(y)
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return output
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def ssm(self, x):
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"""Runs the SSM. See:
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- Algorithm 2 in Section 3.2 in the Mamba paper [1]
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- run_SSM(A, B, C, u) in The Annotated S4 [2]
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Args:
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x: shape (b, l, d_in) (See Glossary at top for definitions of b, l, d_in, n...)
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Returns:
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output: shape (b, l, d_in)
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Official Implementation:
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mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
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"""
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(d_in, n) = self.A_log.shape
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# Compute ∆ A B C D, the state space parameters.
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# A, D are input independent (see Mamba paper [1] Section 3.5.2 "Interpretation of A" for why A isn't selective)
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# ∆, B, C are input-dependent (this is a key difference between Mamba and the linear time invariant S4,
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# and is why Mamba is called **selective** state spaces)
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A = -torch.exp(self.A_log.float()) # shape (d_in, n)
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D = self.D.float()
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x_dbl = self.x_proj(x) # (b, l, dt_rank + 2*n)
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(delta, B, C) = x_dbl.split(split_size=[self.args.dt_rank, n, n], dim=-1) # delta: (b, l, dt_rank). B, C: (b, l, n)
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delta = F.softplus(self.dt_proj(delta)) # (b, l, d_in)
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y = self.selective_scan(x, delta, A, B, C, D) # This is similar to run_SSM(A, B, C, u) in The Annotated S4 [2]
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return y
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def selective_scan(self, u, delta, A, B, C, D):
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"""Does selective scan algorithm. See:
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- Section 2 State Space Models in the Mamba paper [1]
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- Algorithm 2 in Section 3.2 in the Mamba paper [1]
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- run_SSM(A, B, C, u) in The Annotated S4 [2]
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This is the classic discrete state space formula:
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x(t + 1) = Ax(t) + Bu(t)
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y(t) = Cx(t) + Du(t)
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except B and C (and the step size delta, which is used for discretization) are dependent on the input x(t).
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Args:
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u: shape (b, l, d_in) (See Glossary at top for definitions of b, l, d_in, n...)
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delta: shape (b, l, d_in)
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A: shape (d_in, n)
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B: shape (b, l, n)
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C: shape (b, l, n)
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D: shape (d_in,)
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Returns:
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output: shape (b, l, d_in)
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Official Implementation:
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selective_scan_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L86
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Note: I refactored some parts out of `selective_scan_ref` out, so the functionality doesn't match exactly.
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"""
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(b, l, d_in) = u.shape
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n = A.shape[1]
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# Discretize continuous parameters (A, B)
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# - A is discretized using zero-order hold (ZOH) discretization (see Section 2 Equation 4 in the Mamba paper [1])
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# - B is discretized using a simplified Euler discretization instead of ZOH. From a discussion with authors:
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# "A is the more important term and the performance doesn't change much with the simplification on B"
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deltaA = torch.exp(einsum(delta, A, 'b l d_in, d_in n -> b l d_in n'))
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deltaB_u = einsum(delta, B, u, 'b l d_in, b l n, b l d_in -> b l d_in n')
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# Perform selective scan (see scan_SSM() in The Annotated S4 [2])
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# Note that the below is sequential, while the official implementation does a much faster parallel scan that
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# is additionally hardware-aware (like FlashAttention).
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x = torch.zeros((b, d_in, n), device=deltaA.device)
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ys = []
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for i in range(l):
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x = deltaA[:, i] * x + deltaB_u[:, i]
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y = einsum(x, C[:, i, :], 'b d_in n, b n -> b d_in')
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ys.append(y)
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y = torch.stack(ys, dim=1) # shape (b, l, d_in)
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y = y + u * D
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return y
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class RMSNorm(nn.Module):
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def __init__(self,
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d_model: int,
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eps: float = 1e-5):
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super().__init__()
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self.eps = eps
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self.weight = nn.Parameter(torch.ones(d_model))
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def forward(self, x):
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output = x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps) * self.weight
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return output
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