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import math
import json
import torch
import torch.nn as nn
import torch.nn.functional as F
from dataclasses import dataclass
from einops import rearrange, repeat, einsum
from typing import Union
@dataclass
class ModelArgs:
d_model: int
n_layer: int
vocab_size: int
d_state: int = 16
expand: int = 2
dt_rank: Union[int, str] = 'auto'
d_conv: int = 4
pad_vocab_size_multiple: int = 8
conv_bias: bool = True
bias: bool = False
def __post_init__(self):
self.d_inner = int(self.expand * self.d_model)
if self.dt_rank == 'auto':
self.dt_rank = math.ceil(self.d_model / 16)
if self.vocab_size % self.pad_vocab_size_multiple != 0:
self.vocab_size += (self.pad_vocab_size_multiple
- self.vocab_size % self.pad_vocab_size_multiple)
class MambaBlock_CD(nn.Module):
def __init__(self, d_model,d_conv, d_state, bias = True, conv_bias = True):
"""A single Mamba block, as described in Figure 3 in Section 3.4 in the Mamba paper [1]."""
super().__init__()
# self.args = args
self.norm = RMSNorm(d_model=d_model)
self.d_inner = 2 * d_model
self.dt_rank = math.ceil(d_model / 16)
self.in_proj = nn.Linear(d_model, self.d_inner * 2, bias=bias)
self.mlp_1 = nn.Linear(self.d_inner, d_model)
self.mlp_2 = nn.Linear(self.d_inner, d_model)
self.conv1d = nn.Conv1d(
in_channels=self.d_inner,
out_channels=self.d_inner,
bias=conv_bias,
kernel_size=d_conv,
groups=self.d_inner,
padding=d_conv - 1,
)
# x_proj takes in `x` and outputs the input-specific Δ, B, C
self.x_proj = nn.Linear(self.d_inner, self.dt_rank + d_state * 2, bias=False)
# dt_proj projects Δ from dt_rank to d_in
self.dt_proj = nn.Linear(self.dt_rank, self.d_inner, bias=True)
A = repeat(torch.arange(1, d_state + 1), 'n -> d n', d=self.d_inner)
self.A_log = nn.Parameter(torch.log(A))
self.D = nn.Parameter(torch.ones(self.d_inner))
self.D_p = nn.Parameter(torch.ones(self.d_inner))
self.out_proj = nn.Linear(self.d_inner, d_model, bias=bias)
def forward(self, t1,t2):
ee1 = t1
ee2 = t2
(b, l, d) = t1.shape
t1 = self.norm(t1)
t1_and_res = self.in_proj(t1) # shape (b, l, 2 * d_in)
(t1, res1) = t1_and_res.split(split_size=[self.d_inner, self.d_inner], dim=-1)
t1 = rearrange(t1, 'b l d_in -> b d_in l')
t1 = self.conv1d(t1)[:, :, :l]
t1 = rearrange(t1, 'b d_in l -> b l d_in')
t1 = F.silu(t1)
(b, l, d) = t2.shape
t2 = self.norm(t2)
t2_and_res = self.in_proj(t2) # shape (b, l, 2 * d_in)
(t2, res2) = t2_and_res.split(split_size=[self.d_inner, self.d_inner], dim=-1)
t2 = rearrange(t2, 'b l d_in -> b d_in l')
t2 = self.conv1d(t2)[:, :, :l]
t2 = rearrange(t2, 'b d_in l -> b l d_in')
t2 = F.silu(t2)
y1,y2 = self.cssm(t1,t2)
y1 = y1 * F.silu(res1)
y2 = y2 * F.silu(res2)
output1 = self.out_proj(y1)
output2 = self.out_proj(y2)
return output1 + ee1, output2 + ee2
def cssm(self, t1, t2):
(d_in, n) = self.A_log.shape
A = -torch.exp(self.A_log.float()) # shape (d_in, n)
D = self.D.float()
t1_dbl = self.x_proj(t1) # (b, l, dt_rank + 2*n)
(delta, B, C) = t1_dbl.split(split_size=[self.dt_rank, n, n], dim=-1) # delta: (b, l, dt_rank). B, C: (b, l, n)
delta = F.softplus(self.dt_proj(delta)) # (b, l, d_in)
A_prim = -torch.exp(self.A_log.float()) # shape (d_in, n)
D_prim = self.D_p.float()
t2_dbl = self.x_proj(t2) # (b, l, dt_rank + 2*n)
(delta, B_prim, C_prim) = t2_dbl.split(split_size=[self.dt_rank, n, n], dim=-1) # delta: (b, l, dt_rank). B, C: (b, l, n)
delta = F.softplus(self.dt_proj(delta)) # (b, l, d_in)
y = self.selective_scan(t1,t2, delta, A, B, C, D, A_prim, B_prim, C_prim, D_prim) # This is similar to run_SSM(A, B, C, u) in The Annotated S4 [2]
return y
def selective_scan(self, t1,t2, delta, A, B, C, D, A_prim, B_prim, C_prim, D_prim):
(b, l, d_in) = t1.shape
n = A.shape[1]
deltaA = torch.exp(einsum(delta, A, 'b l d_in, d_in n -> b l d_in n'))
deltaB_u = einsum(delta, B, t1, 'b l d_in, b l n, b l d_in -> b l d_in n')
deltaB_u_prim = einsum(delta, B_prim, t2, 'b l d_in, b l n, b l d_in -> b l d_in n')
x = torch.zeros((b, d_in, n), device=deltaA.device)
ys = []
for i in range(l):
x = deltaA[:, i] * x + torch.abs(deltaB_u[:, i] - deltaB_u_prim[:,i])
y1 = einsum(x, C[:, i, :], 'b d_in n, b n -> b d_in')
ys.append(y1)
y1 = torch.stack(ys, dim=1) # shape (b, l, d_in)
y1 = y1 + t1 * D
(b, l, d_in) = t2.shape
n = A_prim.shape[1]
deltaA_prim = torch.exp(einsum(delta, A_prim, 'b l d_in, d_in n -> b l d_in n'))
# deltaB_u = einsum(delta, B, u, 'b l d_in, b l n, b l d_in -> b l d_in n')
x = torch.zeros((b, d_in, n), device=deltaA.device)
ys = []
for i in range(l):
x = deltaA_prim[:, i] * x + torch.abs(deltaB_u[:, i] - deltaB_u_prim[:,i])
y2 = einsum(x, C_prim[:, i, :], 'b d_in n, b n -> b d_in')
ys.append(y2)
y2 = torch.stack(ys, dim=1) # shape (b, l, d_in)
y2 = y2 + t2 * D_prim
return y1 ,y2
class MambaCSSM(nn.Module):
def __init__(self, num_layers, d_model,d_conv, d_state, bias = True, conv_bias = True ):
super().__init__()
self.layers = nn.ModuleList([MambaBlock_CD(d_model,d_conv, d_state, bias = True, conv_bias = True) for _ in range(num_layers)])
def forward(self, t1,t2):
for layer in self.layers:
t1,t2 = layer(t1,t2)
return t1,t2
class MambaBlock(nn.Module):
def __init__(self, d_model,d_conv, d_state, bias = True, conv_bias = True):
"""A single Mamba block, as described in Figure 3 in Section 3.4 in the Mamba paper [1]."""
super().__init__()
# self.args = args
self.d_inner = 2 * d_model
self.dt_rank = math.ceil(d_model / 16)
self.in_proj = nn.Linear(d_model, self.d_inner * 2, bias=bias)
self.conv1d = nn.Conv1d(
in_channels=self.d_inner,
out_channels=self.d_inner,
bias=conv_bias,
kernel_size=d_conv,
groups=self.d_inner,
padding=d_conv - 1,
)
# x_proj takes in `x` and outputs the input-specific Δ, B, C
self.x_proj = nn.Linear(self.d_inner, self.dt_rank + d_state * 2, bias=False)
# dt_proj projects Δ from dt_rank to d_in
self.dt_proj = nn.Linear(self.dt_rank, self.d_inner, bias=True)
A = repeat(torch.arange(1, d_state + 1), 'n -> d n', d=self.d_inner)
self.A_log = nn.Parameter(torch.log(A))
self.D = nn.Parameter(torch.ones(self.d_inner))
self.out_proj = nn.Linear(self.d_inner, d_model, bias=bias)
def forward(self, x):
"""Mamba block forward. This looks the same as Figure 3 in Section 3.4 in the Mamba paper [1].
Args:
x: shape (b, l, d) (See Glossary at top for definitions of b, l, d_in, n...)
Returns:
output: shape (b, l, d)
Official Implementation:
class Mamba, https://github.com/state-spaces/mamba/blob/main/mamba_ssm/modules/mamba_simple.py#L119
mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
"""
(b, l, d) = x.shape
x_and_res = self.in_proj(x) # shape (b, l, 2 * d_in)
(x, res) = x_and_res.split(split_size=[self.d_inner, self.d_inner], dim=-1)
x = rearrange(x, 'b l d_in -> b d_in l')
x = self.conv1d(x)[:, :, :l]
x = rearrange(x, 'b d_in l -> b l d_in')
x = F.silu(x)
y = self.ssm(x)
y = y * F.silu(res)
output = self.out_proj(y)
return output
def ssm(self, x):
"""Runs the SSM. See:
- Algorithm 2 in Section 3.2 in the Mamba paper [1]
- run_SSM(A, B, C, u) in The Annotated S4 [2]
Args:
x: shape (b, l, d_in) (See Glossary at top for definitions of b, l, d_in, n...)
Returns:
output: shape (b, l, d_in)
Official Implementation:
mamba_inner_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L311
"""
(d_in, n) = self.A_log.shape
# Compute ∆ A B C D, the state space parameters.
# 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)
A = -torch.exp(self.A_log.float()) # shape (d_in, n)
D = self.D.float()
x_dbl = self.x_proj(x) # (b, l, dt_rank + 2*n)
(delta, B, C) = x_dbl.split(split_size=[self.dt_rank, n, n], dim=-1) # delta: (b, l, dt_rank). B, C: (b, l, n)
delta = F.softplus(self.dt_proj(delta)) # (b, l, d_in)
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]
return y
def selective_scan(self, u, delta, A, B, C, D):
"""Does selective scan algorithm. See:
- Section 2 State Space Models in the Mamba paper [1]
- Algorithm 2 in Section 3.2 in the Mamba paper [1]
- run_SSM(A, B, C, u) in The Annotated S4 [2]
This is the classic discrete state space formula:
x(t + 1) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)
except B and C (and the step size delta, which is used for discretization) are dependent on the input x(t).
Args:
u: shape (b, l, d_in) (See Glossary at top for definitions of b, l, d_in, n...)
delta: shape (b, l, d_in)
A: shape (d_in, n)
B: shape (b, l, n)
C: shape (b, l, n)
D: shape (d_in,)
Returns:
output: shape (b, l, d_in)
Official Implementation:
selective_scan_ref(), https://github.com/state-spaces/mamba/blob/main/mamba_ssm/ops/selective_scan_interface.py#L86
Note: I refactored some parts out of `selective_scan_ref` out, so the functionality doesn't match exactly.
"""
(b, l, d_in) = u.shape
n = A.shape[1]
# Discretize continuous parameters (A, B)
# - A is discretized using zero-order hold (ZOH) discretization (see Section 2 Equation 4 in the Mamba paper [1])
# - B is discretized using a simplified Euler discretization instead of ZOH. From a discussion with authors:
# "A is the more important term and the performance doesn't change much with the simplification on B"
deltaA = torch.exp(einsum(delta, A, 'b l d_in, d_in n -> b l d_in n'))
deltaB_u = einsum(delta, B, u, 'b l d_in, b l n, b l d_in -> b l d_in n')
# Perform selective scan (see scan_SSM() in The Annotated S4 [2])
# Note that the below is sequential, while the official implementation does a much faster parallel scan that
# is additionally hardware-aware (like FlashAttention).
x = torch.zeros((b, d_in, n), device=deltaA.device)
ys = []
for i in range(l):
x = deltaA[:, i] * x + deltaB_u[:, i]
y = einsum(x, C[:, i, :], 'b d_in n, b n -> b d_in')
ys.append(y)
y = torch.stack(ys, dim=1) # shape (b, l, d_in)
y = y + u * D
return y
class RMSNorm(nn.Module):
def __init__(self,
d_model: int,
eps: float = 1e-5):
super().__init__()
self.eps = eps
self.weight = nn.Parameter(torch.ones(d_model))
def forward(self, x):
output = x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps) * self.weight
return output |