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# -*- coding: utf-8 -*-
# from https://github.com/HazyResearch/zoology/blob/main/zoology/mixers/convolution.py
import math
import warnings
from typing import Optional, Tuple
import torch
import torch.nn as nn
import torch.nn.functional as F
from einops import rearrange
from fla.modules.activations import ACT2FN
from fla.utils import checkpoint
try:
from causal_conv1d import causal_conv1d_fn, causal_conv1d_update
except ImportError:
causal_conv1d_fn = None
causal_conv1d_update = None
def fft_conv(u, k, dropout_mask, gelu=True, k_rev=None):
seqlen = u.shape[-1]
fft_size = 2 * seqlen
k_f = torch.fft.rfft(k, n=fft_size) / fft_size
if k_rev is not None:
k_rev_f = torch.fft.rfft(k_rev, n=fft_size) / fft_size
k_f = k_f + k_rev_f.conj()
u_f = torch.fft.rfft(u.to(dtype=k.dtype), n=fft_size)
if len(u.shape) > 3:
k_f = k_f.unsqueeze(1)
y = torch.fft.irfft(u_f * k_f, n=fft_size, norm="forward")[..., :seqlen]
out = y + u
if gelu:
out = F.gelu(out)
if dropout_mask is not None:
return (out * rearrange(dropout_mask, "b H -> b H 1")).to(dtype=u.dtype)
else:
return out.to(dtype=u.dtype)
@checkpoint
def proj_then_conv1d(
x: torch.Tensor,
proj_weight: torch.Tensor,
conv1d_weight: torch.Tensor,
conv1d_bias: Optional[torch.Tensor] = None,
cache: Optional[torch.Tensor] = None
) -> torch.Tensor:
# We do matmul and transpose BLH -> HBL at the same time
x = rearrange(proj_weight @ rearrange(x, "b t d -> d (b t)"), "d (b t) -> b d t", t=x.shape[-2])
if causal_conv1d_fn is None:
raise ImportError("`causal_conv1d_fn` is not available. Please install `causal-conv1d` first.")
if cache is None:
x = causal_conv1d_fn(
x=x,
weight=rearrange(conv1d_weight, "d 1 w -> d w"),
bias=conv1d_bias,
activation="silu",
).transpose(1, 2)
else:
assert x.shape[-1] == 1, "Only support decoding with 1 token at a time for now"
x = x.squeeze(-1)
x = causal_conv1d_update(
x=x,
weight=rearrange(conv1d_weight, "d 1 w -> d w"),
bias=conv1d_bias,
cache=cache,
activation="silu",
)
return x
class ShortConvolution(nn.Conv1d):
"""
Simple wrapper around `nn.Conv1d` that accepts dimension last.
"""
def __init__(
self,
hidden_size: int,
kernel_size: int,
bias: bool = False,
activation: Optional[str] = 'silu',
use_fast_conv1d: Optional[bool] = True
):
super().__init__(
in_channels=hidden_size,
out_channels=hidden_size,
kernel_size=kernel_size,
groups=hidden_size,
bias=bias,
padding=kernel_size - 1
)
self.hidden_size = hidden_size
self.activation = None
if activation is not None:
assert activation in ['silu', 'swish'], f"Activation `{activation}` not supported yet."
self.activation = activation
if causal_conv1d_fn is None:
if use_fast_conv1d:
raise RuntimeError(
"Please either install `causal-conv1d>=1.4.0` to enable fast causal short convolution CUDA kernel "
"or set `use_fast_conv1d` to False"
)
else:
warnings.warn(
"The naive Pytorch verison is very slow in practice, "
"please run `pip install causal-conv1d>=1.4.0` to install fast causal short convolution CUDA kernel",
category=ImportWarning
)
self.use_fast_conv1d = use_fast_conv1d
def extra_repr(self):
s = ('{in_channels}, {out_channels}, kernel_size={kernel_size}'
', stride={stride}')
if self.padding != (0,) * len(self.padding):
s += ', padding={padding}'
if self.dilation != (1,) * len(self.dilation):
s += ', dilation={dilation}'
if self.output_padding != (0,) * len(self.output_padding):
s += ', output_padding={output_padding}'
if self.groups != 1:
s += ', groups={groups}'
if self.bias is None:
s += ', bias=False'
if self.padding_mode != 'zeros':
s += ', padding_mode={padding_mode}'
if self.activation is not None:
s += ', activation={activation}'
if not self.use_fast_conv1d:
s += ', use_fast_conv1d={use_fast_conv1d}'
return s.format(**self.__dict__)
def forward(
self,
x: torch.Tensor,
mask: Optional[torch.Tensor] = None,
cache: Optional[torch.Tensor] = None,
output_final_state: bool = False
) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Args:
x (`torch.Tensor`):
Tensor of shape `[batch_size, seq_len, hidden_size]`
mask (`Optional[torch.Tensor]`):
Attention mask dealing with padded positions.
cache (`Optional[torch.Tensor]`):
Previous cache tensor of shape `[batch_size, hidden_size, kernel_size]`.
If provided, the cache is updated **inplace**.
output_final_state (Optional[bool]):
Whether to output the final state of shape `[batch_size, hidden_size, kernel_size]`. Default: `False`.
Returns:
Tensor of shape `[batch_size, seq_len, hidden_size]`.
"""
batch_size, _, hidden_size = x.shape
if mask is not None:
x = x.mul_(mask.unsqueeze(-1))
if output_final_state and cache is None:
cache = x.new_zeros(batch_size, hidden_size, self.kernel_size[0])
if cache is not None and x.shape[1] == 1:
return self.step(x, cache)
x = rearrange(x, "b t d -> b d t")
# Update state (B D W)
if cache is not None:
cache.copy_(F.pad(x, (self.kernel_size[0] - x.shape[-1], 0)))
if self.use_fast_conv1d:
x = causal_conv1d_fn(
x=x,
weight=rearrange(self.weight, "d 1 w -> d w"),
bias=self.bias,
activation=self.activation,
)
else:
x = self._conv_forward(x, self.weight, self.bias)[..., :x.shape[-1]]
if self.activation is not None:
x = ACT2FN[self.activation](x)
return rearrange(x, "b d t -> b t d"), cache
def step(
self,
x: torch.Tensor,
cache: torch.Tensor
):
assert x.shape[1] == 1, "Only support decoding with 1 token at a time for now"
x = x.squeeze(1)
if self.use_fast_conv1d:
x = causal_conv1d_update(
x=x,
conv_state=cache,
weight=rearrange(self.weight, "d 1 w -> d w"),
bias=self.bias,
activation=self.activation,
)
else:
dtype = x.dtype
cache.copy_(torch.roll(cache, shifts=-1, dims=-1))
cache[:, :, -1] = x
x = torch.sum(cache * rearrange(self.weight, "d 1 w -> d w"), dim=-1)
if self.bias is not None:
x = x + self.bias
if self.activation is not None:
x = ACT2FN[self.activation](x).to(dtype=dtype)
return x.unsqueeze(1), cache
@property
def state_size(self) -> int:
return self.hidden_size * self.kernel_size
class LongConvolution(nn.Module):
"""
LongConvolution applies a convolution operation on the input tensor using a fixed
filter of length max_len.
The filter is learned during training and is applied using FFT convolution.
Args:
hidden_size (int): The number of expected features in the input and output.
max_len (int): The maximum sequence length.
Returns:
y: [batch_size, seq_len, hidden_size] tensor
"""
def __init__(
self,
hidden_size: int,
max_len: int,
**kwargs,
):
"""
Initializes the LongConvolution module.
Args:
hidden_size (int): The number of expected features in the input and output.
max_len (int): The maximum sequence length.
"""
super().__init__()
self.hidden_size = hidden_size
self.filter = nn.Parameter(torch.randn(self.hidden_size, max_len), requires_grad=True)
def forward(self, x: torch.Tensor, *args, **kwargs):
"""
Applies the LongConvolution operation on the input tensor.
Args:
x: [batch_size, seq_len, hidden_size] tensor
Returns:
y: [batch_size, seq_len, hidden_size] tensor
"""
x = x.transpose(1, 2)
y = fft_conv(x, self.filter, dropout_mask=None, gelu=False)
y = y.transpose(1, 2)
return y.to(dtype=x.dtype)
class PositionalEmbedding(nn.Module):
def __init__(self, emb_dim: int, seq_len: int, **kwargs):
"""Complex exponential positional embeddings for implicit long convolution filters."""
super().__init__()
self.seq_len = seq_len
# The time embedding fed to the filteres is normalized so that t_f = 1
t = torch.linspace(0, 1, self.seq_len)[None, :, None] # 1, L, 1
if emb_dim > 1:
bands = (emb_dim - 1) // 2
# To compute the right embeddings we use the "proper" linspace
t_rescaled = torch.linspace(0, seq_len - 1, seq_len)[None, :, None]
w = 2 * math.pi * t_rescaled / seq_len # 1, L, 1
f = torch.linspace(1e-4, bands - 1, bands)[None, None]
z = torch.exp(-1j * f * w)
z = torch.cat([t, z.real, z.imag], dim=-1)
self.z = nn.Parameter(z, requires_grad=False)
def forward(self, L):
return self.z[:, :L]
class ImplicitLongConvolution(nn.Module):
"""
Long convolution with implicit filter parameterized by an MLP.
Args:
hidden_size (int):
The number of expected features in the input and output.
max_len (int):
The maximum sequence length.
d_emb (Optional[int]):
The dimension of the positional embeddings. Must be odd and greater or equal to 3 (time, sine and cosine).
Defaults to 3.
d_hidden (Optional[int]):
The number of features in the hidden layer of the MLP. Defaults to 16.
Attributes:
pos_emb (`PositionalEmbedding`): The positional embedding layer.
mlp (`nn.Sequential`): The MLP that parameterizes the implicit filter.
"""
def __init__(
self,
hidden_size: int,
max_len: int,
d_emb: int = 3,
d_hidden: int = 16,
**kwargs,
):
"""
Long convolution with implicit filter parameterized by an MLP.
"""
super().__init__()
self.hidden_size = hidden_size
self.d_emb = d_emb
assert (
d_emb % 2 != 0 and d_emb >= 3
), "d_emb must be odd and greater or equal to 3 (time, sine and cosine)"
self.pos_emb = PositionalEmbedding(d_emb, max_len)
# final linear layer
self.mlp = nn.Sequential(
nn.Linear(d_emb, d_hidden),
torch.nn.ReLU(),
nn.Linear(d_hidden, hidden_size),
)
def filter(self, seq_len: int, *args, **kwargs):
k = self.mlp(self.pos_emb(seq_len))
return k.transpose(1, 2)
def forward(self, x: torch.Tensor, *args, **kwargs):
"""
Args:
x: [batch_size, seq_len, hidden_size] tensor
Returns:
y: [batch_size, seq_len, hidden_size] tensor
"""
x = x.transpose(1, 2)
k = self.filter(x.shape[-1])
y = fft_conv(x, k, dropout_mask=None, gelu=False)
y = y.transpose(1, 2)
return y.to(dtype=x.dtype)
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