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# -*- coding: utf-8 -*-
from __future__ import annotations
import math
from typing import Optional
import torch
import torch.nn.functional as F
from torch import nn
from fla.modules.activations import fast_gelu_impl, sigmoid, sqrelu, swish
from fla.modules.layernorm import layer_norm
from fla.utils import checkpoint
@checkpoint
def flatten_diag_outer_product(x, y):
z = torch.einsum("...i,...j->...ij", x, y)
N = z.size(-1)
indicies = torch.triu_indices(N, N)
return z[..., indicies[0], indicies[1]]
@checkpoint
def flatten_diag_outer_product_off1(x, y):
z = torch.einsum("...i,...j->...ij", x, y)
N = z.size(-1)
indicies = torch.triu_indices(N, N, 1)
indices2 = torch.arange(0, N)
return z[..., indicies[0], indicies[1]], z[..., indices2, indices2]
def is_power_of_2(n):
return (n & (n - 1) == 0) and n != 0
class HedgehogFeatureMap(nn.Module):
r"""
Hedgehog feature map as introduced in
`The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry <https://arxiv.org/abs/2402.04347>`_
"""
def __init__(
self,
head_dim: int
) -> HedgehogFeatureMap:
super().__init__()
# Trainable map
self.layer = nn.Linear(head_dim, head_dim)
self.init_weights_()
def init_weights_(self):
"""Initialize trainable map as identity"""
with torch.no_grad():
identity = torch.eye(*self.layer.weight.shape[-2:], dtype=torch.float)
self.layer.weight.copy_(identity.to(self.layer.weight))
nn.init.zeros_(self.layer.bias)
def forward(self, x: torch.Tensor):
x = self.layer(x) # shape b, h, l, d
return torch.cat([2*x, -2*x], dim=-1).softmax(-1)
class T2RFeatureMap(nn.Module):
r"""
Simple linear mapping feature map as in
`Finetuning Pretrained Transformers into RNNs <https://arxiv.org/abs/2103.13076>`_
"""
def __init__(
self,
head_dim: int,
dot_dim: int = None,
bias: Optional[bool] = False
) -> T2RFeatureMap:
super().__init__()
# Trainable map
if dot_dim is None:
dot_dim = head_dim
self.head_dim = head_dim
self.dot_dim = dot_dim
self.bias = bias
self.layer = nn.Linear(head_dim, dot_dim, bias=bias)
def __repr__(self) -> str:
return f"{self.__class__.__name__}(head_dim={self.head_dim}, dot_dim={self.dot_dim}, bias={self.bias})"
def forward(self, x: torch.Tensor):
return self.layer(x).relu()
class DPFPFeatureMap(nn.Module):
r"""
Deterministic Parameter-Free Projection (DPFP) feature map in
`Linear Transformers Are Secretly Fast Weight Programmers <https://arxiv.org/abs/2102.11174>`_
"""
def __init__(
self,
head_dim: int,
nu: int = 4
) -> DPFPFeatureMap:
super().__init__()
self.nu = nu
def forward(self, x: torch.Tensor):
x = torch.cat([x.relu(), -x.relu()], dim=-1)
x_rolled = torch.cat([x.roll(shifts=j, dims=-1) for j in range(1, self.nu+1)], dim=-1)
x_repeat = torch.cat([x] * self.nu, dim=-1)
return x_repeat * x_rolled
class HadamardFeatureMap(nn.Module):
def __init__(
self,
head_dim: int
) -> HadamardFeatureMap:
super().__init__()
# Trainable map
self.layer1 = nn.Linear(head_dim, head_dim)
self.layer2 = nn.Linear(head_dim, head_dim)
def forward(self, x: torch.Tensor):
return self.layer1(x) * self.layer2(x)
class LearnableOuterProductFeatureMap(nn.Module):
def __init__(
self,
head_dim: int,
feature_dim: int
) -> LearnableOuterProductFeatureMap:
super().__init__()
# Trainable map
self.layer1 = nn.Linear(head_dim, feature_dim, bias=False)
self.layer2 = nn.Linear(head_dim, feature_dim, bias=False)
self.normalizer = feature_dim ** -0.5
def forward(self, x: torch.Tensor):
return flatten_diag_outer_product(self.layer1(x), self.layer2(x))
class LearnablePolySketchNonNegativeFeatureMap(nn.Module):
def __init__(
self,
head_dim: int,
sketch_size: Optional[int] = None,
degree: Optional[int] = 2
) -> LearnablePolySketchNonNegativeFeatureMap:
super().__init__()
assert is_power_of_2(degree) and degree >= 2, f"The degree {degree} must be a power of 2"
self.head_dim = head_dim
self.sketch_size = sketch_size if sketch_size is not None else head_dim
self.degree = degree
self.gamma = nn.Parameter(torch.ones(head_dim))
self.beta = nn.Parameter(torch.zeros(head_dim))
# NOTE: the sketch layers defined here are quite different from the original paper
# currently we simply use linear layers without any non-linear activations
self.sketches1 = nn.ModuleList([
nn.Linear(head_dim, sketch_size, bias=False),
*[nn.Linear(sketch_size, sketch_size, bias=False) for _ in range(int(math.log2(self.degree)) - 2)]
])
self.sketches2 = nn.ModuleList([
nn.Linear(head_dim, sketch_size, bias=False),
*[nn.Linear(sketch_size, sketch_size, bias=False) for _ in range(int(math.log2(self.degree)) - 2)]
])
def forward(self, x: torch.Tensor):
# Section 2.1
x = layer_norm(x, self.gamma, self.beta)
# first map the input to sketch size with learnable parameters
x = self.sketches1[0](x) * self.sketches2[0](x) * self.head_dim ** -0.5
for i in range(1, int(math.log2(self.degree)) - 1):
x = self.sketches1[i](x) * self.sketches2[i](x) * self.head_dim ** -0.5
# do sketch mapping for log2(p) - 1 times in total
# do p=2 mapping to ensure non-negativity
return flatten_diag_outer_product(x, x)
class TaylorFeatureMap(nn.Module):
def __init__(
self,
head_dim: int
) -> TaylorFeatureMap:
super().__init__()
self.head_dim = head_dim
self.r2 = math.sqrt(2)
self.rd = math.sqrt(self.head_dim)
self.rrd = math.sqrt(self.rd)
def forward(self, x: torch.Tensor):
x2_1, x2_2 = flatten_diag_outer_product_off1(x, x)
return torch.cat([torch.ones_like(x[..., 0:1]), x / self.rrd, x2_2 / (self.rd * self.r2), x2_1 / self.rd], dim=-1)
class RebasedFeatureMap(nn.Module):
def __init__(
self,
head_dim: int,
use_gamma: Optional[bool] = True,
use_beta: Optional[bool] = True,
normalize: Optional[bool] = True
) -> RebasedFeatureMap:
super().__init__()
self.head_dim = head_dim
self.use_gamma = use_gamma
self.use_beta = use_beta
self.normalize = normalize
self.gamma = None
self.beta = None
if use_gamma:
self.gamma = nn.Parameter(torch.ones(head_dim))
if use_beta:
self.beta = nn.Parameter(torch.zeros(head_dim))
def forward(self, x: torch.Tensor, flatten: Optional[bool] = True):
if self.use_beta and self.use_gamma and self.normalize:
x = layer_norm(x, self.gamma, self.beta)
elif self.normalize:
x = F.layer_norm(x, (self.head_dim,), self.gamma, self.beta)
elif self.use_gamma and self.use_beta:
x = torch.addcmul(self.beta, x, self.gamma)
elif self.use_gamma:
x = x.mul(self.gamma)
else:
raise RuntimeError(f"Not supported combination of `use_gamma`, `use_beta` and `normalize`, "
f"which is currentlt set as (`{self.use_gamma}`, `{self.use_beta}`, `{self.normalize}`)")
if not flatten:
return x
x2_1, x2_2 = flatten_diag_outer_product_off1(x, x)
# rebased use learnable parameters to approximate any quadratic function
return torch.cat([x2_2 * self.head_dim ** -0.5, x2_1 * (2 / self.head_dim) ** 0.5], dim=-1)
class ReLUFeatureMap(nn.Module):
def __init__(
self,
) -> ReLUFeatureMap:
super().__init__()
def forward(self, x: torch.Tensor):
return F.relu(x)
class SquaredReLUFeatureMap(nn.Module):
def __init__(
self,
) -> SquaredReLUFeatureMap:
super().__init__()
def forward(self, x: torch.Tensor):
return sqrelu(x)
class GELUFeatureMap(nn.Module):
def __init__(
self,
) -> GELUFeatureMap:
super().__init__()
def forward(self, x: torch.Tensor):
return fast_gelu_impl(x)
class SwishFeatureMap(nn.Module):
def __init__(
self,
) -> SwishFeatureMap:
super().__init__()
def forward(self, x: torch.Tensor):
return swish(x)
class SigmoidFeatureMap(nn.Module):
def __init__(
self,
) -> SigmoidFeatureMap:
super().__init__()
def forward(self, x: torch.Tensor):
return sigmoid(x)
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