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import math
from dataclasses import dataclass
from typing import Union
import torch
import torch.nn as nn
import torch.nn.functional as F
from pscan import pscan
"""
This file closely follows the mamba_simple.py from the official Mamba implementation, and the mamba-minimal by @johnma2006.
The major differences are :
-the convolution is done with torch.nn.Conv1d
-the selective scan is done in PyTorch
A sequential version of the selective scan is also available for comparison.
- A Mamba model is composed of several layers, which are ResidualBlock.
- A ResidualBlock is composed of a MambaBlock, a normalization, and a residual connection : ResidualBlock(x) = mamba(norm(x)) + x
- This leaves us with the MambaBlock : its input x is (B, L, D) and its outputs y is also (B, L, D) (B=batch size, L=seq len, D=model dim).
First, we expand x into (B, L, 2*ED) (where E is usually 2) and split it into x and z, each (B, L, ED).
Then, we apply the short 1d conv to x, followed by an activation function (silu), then the SSM.
We then multiply it by silu(z).
See Figure 3 of the paper (page 8) for a visual representation of a MambaBlock.
"""
@dataclass
class MambaConfig:
d_model: int # D
n_layers: int
dt_rank: Union[int, str] = 'auto'
d_state: int = 16 # N in paper/comments
expand_factor: int = 2 # E in paper/comments
d_conv: int = 4
dt_min: float = 0.001
dt_max: float = 0.1
dt_init: str = "random" # "random" or "constant"
dt_scale: float = 1.0
dt_init_floor = 1e-4
bias: bool = False
conv_bias: bool = True
pscan: bool = True # use parallel scan mode or sequential mode when training
def __post_init__(self):
self.d_inner = self.expand_factor * self.d_model # E*D = ED in comments
if self.dt_rank == 'auto':
self.dt_rank = math.ceil(self.d_model / 16)
class Mamba(nn.Module):
def __init__(self, config: MambaConfig):
super().__init__()
self.config = config
self.layers = nn.ModuleList([ResidualBlock(config) for _ in range(config.n_layers)])
#self.norm_f = RMSNorm(config.d_model)
def forward(self, x):
# x : (B, L, D)
# y : (B, L, D)
for layer in self.layers:
x = layer(x)
#x = self.norm_f(x)
return x
def step(self, x, caches):
# x : (B, L, D)
# caches : [cache(layer) for all layers], cache : (h, inputs)
# y : (B, L, D)
# caches : [cache(layer) for all layers], cache : (h, inputs)
for i, layer in enumerate(self.layers):
x, caches[i] = layer.step(x, caches[i])
return x, caches
class ResidualBlock(nn.Module):
def __init__(self, config: MambaConfig):
super().__init__()
self.mixer = MambaBlock(config)
self.norm = RMSNorm(config.d_model)
def forward(self, x):
# x : (B, L, D)
# output : (B, L, D)
output = self.mixer(self.norm(x)) + x
return output
def step(self, x, cache):
# x : (B, D)
# cache : (h, inputs)
# h : (B, ED, N)
# inputs: (B, ED, d_conv-1)
# output : (B, D)
# cache : (h, inputs)
output, cache = self.mixer.step(self.norm(x), cache)
output = output + x
return output, cache
class MambaBlock(nn.Module):
def __init__(self, config: MambaConfig):
super().__init__()
self.config = config
# projects block input from D to 2*ED (two branches)
self.in_proj = nn.Linear(config.d_model, 2 * config.d_inner, bias=config.bias)
self.conv1d = nn.Conv1d(in_channels=config.d_inner, out_channels=config.d_inner,
kernel_size=config.d_conv, bias=config.conv_bias,
groups=config.d_inner,
padding=config.d_conv - 1)
nn.init.kaiming_normal_(self.conv1d.weight, mode='fan_out', nonlinearity='leaky_relu')
# projects x to input-dependent Δ, B, C
self.x_proj = nn.Linear(config.d_inner, config.dt_rank + 2 * config.d_state, bias=False)
# projects Δ from dt_rank to d_inner
self.dt_proj = nn.Linear(config.dt_rank, config.d_inner, bias=True)
# dt initialization
# dt weights
dt_init_std = config.dt_rank**-0.5 * config.dt_scale
if config.dt_init == "constant":
nn.init.constant_(self.dt_proj.weight, dt_init_std)
elif config.dt_init == "random":
nn.init.uniform_(self.dt_proj.weight, -dt_init_std, dt_init_std)
else:
raise NotImplementedError
# dt bias
dt = torch.exp(
torch.rand(config.d_inner) * (math.log(config.dt_max) - math.log(config.dt_min)) + math.log(config.dt_min)
).clamp(min=config.dt_init_floor)
inv_dt = dt + torch.log(-torch.expm1(-dt)) # inverse of softplus: https://github.com/pytorch/pytorch/issues/72759
with torch.no_grad():
self.dt_proj.bias.copy_(inv_dt)
#self.dt_proj.bias._no_reinit = True # initialization would set all Linear.bias to zero, need to mark this one as _no_reinit
# todo : explain why removed
# S4D real initialization
A = torch.arange(1, config.d_state + 1, dtype=torch.float32).repeat(config.d_inner, 1)
self.A_log = nn.Parameter(torch.log(A)) # why store A in log ? to keep A < 0 (cf -torch.exp(...)) ? for gradient stability ?
self.D = nn.Parameter(torch.ones(config.d_inner))
# projects block output from ED back to D
self.out_proj = nn.Linear(config.d_inner, config.d_model, bias=config.bias)
def forward(self, x):
# x : (B, L, D)
# y : (B, L, D)
_, L, _ = x.shape
xz = self.in_proj(x) # (B, L, 2*ED)
x, z = xz.chunk(2, dim=-1) # (B, L, ED), (B, L, ED)
# x branch
x = x.transpose(1, 2) # (B, ED, L)
x = self.conv1d(x)[:, :, :L] # depthwise convolution over time, with a short filter
x = x.transpose(1, 2) # (B, L, ED)
x = F.silu(x)
y = self.ssm(x)
# z branch
z = F.silu(z)
output = y * z
output = self.out_proj(output) # (B, L, D)
return output
def ssm(self, x):
# x : (B, L, ED)
# y : (B, L, ED)
A = -torch.exp(self.A_log.float()) # (ED, N)
D = self.D.float()
# TODO remove .float()
deltaBC = self.x_proj(x) # (B, L, dt_rank+2*N)
delta, B, C = torch.split(deltaBC, [self.config.dt_rank, self.config.d_state, self.config.d_state], dim=-1) # (B, L, dt_rank), (B, L, N), (B, L, N)
delta = F.softplus(self.dt_proj(delta)) # (B, L, ED)
if self.config.pscan:
y = self.selective_scan(x, delta, A, B, C, D)
else:
y = self.selective_scan_seq(x, delta, A, B, C, D)
return y
def selective_scan(self, x, delta, A, B, C, D):
# x : (B, L, ED)
# Δ : (B, L, ED)
# A : (ED, N)
# B : (B, L, N)
# C : (B, L, N)
# D : (ED)
# y : (B, L, ED)
deltaA = torch.exp(delta.unsqueeze(-1) * A) # (B, L, ED, N)
deltaB = delta.unsqueeze(-1) * B.unsqueeze(2) # (B, L, ED, N)
BX = deltaB * (x.unsqueeze(-1)) # (B, L, ED, N)
hs = pscan(deltaA, BX)
y = (hs @ C.unsqueeze(-1)).squeeze(3) # (B, L, ED, N) @ (B, L, N, 1) -> (B, L, ED, 1)
y = y + D * x
return y
def selective_scan_seq(self, x, delta, A, B, C, D):
# x : (B, L, ED)
# Δ : (B, L, ED)
# A : (ED, N)
# B : (B, L, N)
# C : (B, L, N)
# D : (ED)
# y : (B, L, ED)
_, L, _ = x.shape
deltaA = torch.exp(delta.unsqueeze(-1) * A) # (B, L, ED, N)
deltaB = delta.unsqueeze(-1) * B.unsqueeze(2) # (B, L, ED, N)
BX = deltaB * (x.unsqueeze(-1)) # (B, L, ED, N)
h = torch.zeros(x.size(0), self.config.d_inner, self.config.d_state, device=deltaA.device) # (B, ED, N)
hs = []
for t in range(0, L):
h = deltaA[:, t] * h + BX[:, t]
hs.append(h)
hs = torch.stack(hs, dim=1) # (B, L, ED, N)
y = (hs @ C.unsqueeze(-1)).squeeze(3) # (B, L, ED, N) @ (B, L, N, 1) -> (B, L, ED, 1)
y = y + D * x
return y
# -------------------------- inference -------------------------- #
"""
Concerning auto-regressive inference
The cool part of using Mamba : inference is constant wrt to sequence length
We just have to keep in cache, for each layer, two things :
- the hidden state h (which is (B, ED, N)), as you typically would when doing inference with a RNN
- the last d_conv-1 inputs of the layer, to be able to compute the 1D conv which is a convolution over the time dimension
(d_conv is fixed so this doesn't incur a growing cache as we progress on generating the sequence)
(and d_conv is usually very small, like 4, so we just have to "remember" the last 3 inputs)
Concretely, these two quantities are put inside a cache tuple, and are named h and inputs respectively.
h is (B, ED, N), and inputs is (B, ED, d_conv-1)
The MambaBlock.step() receives this cache, and, along with outputing the output, alos outputs the updated cache for the next call.
The cache object is initialized as follows : (None, torch.zeros()).
When h is None, the selective scan function detects it and start with h=0.
The torch.zeros() isn't a problem (it's same as just feeding the input, because the conv1d is padded)
As we need one such cache variable per layer, we store a caches object, which is simply a list of cache object. (See mamba_lm.py)
"""
def step(self, x, cache):
# x : (B, D)
# cache : (h, inputs)
# h : (B, ED, N)
# inputs : (B, ED, d_conv-1)
# y : (B, D)
# cache : (h, inputs)
h, inputs = cache
xz = self.in_proj(x) # (B, 2*ED)
x, z = xz.chunk(2, dim=1) # (B, ED), (B, ED)
# x branch
x_cache = x.unsqueeze(2)
x = self.conv1d(torch.cat([inputs, x_cache], dim=2))[:, :, self.config.d_conv-1] # (B, ED)
x = F.silu(x)
y, h = self.ssm_step(x, h)
# z branch
z = F.silu(z)
output = y * z
output = self.out_proj(output) # (B, D)
# prepare cache for next call
inputs = torch.cat([inputs[:, :, 1:], x_cache], dim=2) # (B, ED, d_conv-1)
cache = (h, inputs)
return output, cache
def ssm_step(self, x, h):
# x : (B, ED)
# h : (B, ED, N)
# y : (B, ED)
# h : (B, ED, N)
A = -torch.exp(self.A_log.float()) # (ED, N) # todo : ne pas le faire tout le temps, puisque c'est indépendant de la timestep
D = self.D.float()
# TODO remove .float()
deltaBC = self.x_proj(x) # (B, dt_rank+2*N)
delta, B, C = torch.split(deltaBC, [self.config.dt_rank, self.config.d_state, self.config.d_state], dim=-1) # (B, dt_rank), (B, N), (B, N)
delta = F.softplus(self.dt_proj(delta)) # (B, ED)
deltaA = torch.exp(delta.unsqueeze(-1) * A) # (B, ED, N)
deltaB = delta.unsqueeze(-1) * B.unsqueeze(1) # (B, ED, N)
BX = deltaB * (x.unsqueeze(-1)) # (B, ED, N)
if h is None:
h = torch.zeros(x.size(0), self.config.d_inner, self.config.d_state, device=deltaA.device) # (B, ED, N)
h = deltaA * h + BX # (B, ED, N)
y = (h @ C.unsqueeze(-1)).squeeze(2) # (B, ED, N) @ (B, N, 1) -> (B, ED, 1)
y = y + D * x
# todo : pq h.squeeze(1) ??
return y, h.squeeze(1)
# taken straight from https://github.com/johnma2006/mamba-minimal/blob/master/model.py
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
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