Source code for elektronn3.modules.axial_attention

# Based on https://github.com/lucidrains/axial-attention/blob/890a6d6/axial_attention/
# (C) 2020 Phil Wang, MIT License

from operator import itemgetter

import torch
from torch import nn
from torch.autograd.function import Function
from torch.utils.checkpoint import get_device_states, set_device_states


# helper functions



def exists(val):
    return val is not None





def map_el_ind(arr, ind):
    return list(map(itemgetter(ind), arr))





def sort_and_return_indices(arr):
    indices = [ind for ind in range(len(arr))]
    arr = zip(arr, indices)
    arr = sorted(arr)
    return map_el_ind(arr, 0), map_el_ind(arr, 1)



# calculates the permutation to bring the input tensor to something attend-able
# also calculates the inverse permutation to bring the tensor back to its original shape



def calculate_permutations(num_dimensions, emb_dim):
    total_dimensions = num_dimensions + 2
    emb_dim = emb_dim if emb_dim > 0 else (emb_dim + total_dimensions)
    axial_dims = [ind for ind in range(1, total_dimensions) if ind != emb_dim]

    permutations = []

    for axial_dim in axial_dims:
        last_two_dims = [axial_dim, emb_dim]
        dims_rest = set(range(0, total_dimensions)) - set(last_two_dims)
        permutation = [*dims_rest, *last_two_dims]
        permutations.append(permutation)

    return permutations



# helper classes



class Rezero(nn.Module):
    def __init__(self, fn):
        super().__init__()
        self.fn = fn
        self.g = nn.Parameter(torch.tensor(0.))



    def forward(self, x):
        return self.fn(x) * self.g






class Sequential(nn.Module):
    def __init__(self, blocks):
        super().__init__()
        self.blocks = blocks



    def forward(self, x):
        for f, g in self.blocks:
            x = x + f(x) + g(x)
        return x






class PermuteToFrom(nn.Module):
    def __init__(self, permutation, fn):
        super().__init__()
        self.fn = fn
        _, inv_permutation = sort_and_return_indices(permutation)
        self.permutation = permutation
        self.inv_permutation = inv_permutation



    def forward(self, x, **kwargs):
        axial = x.permute(*self.permutation).contiguous()

        shape = axial.shape
        *_, t, d = shape

        # merge all but axial dimension
        axial = axial.reshape(-1, t, d)

        # attention
        axial = self.fn(axial, **kwargs)

        # restore to original shape and permutation
        axial = axial.reshape(*shape)
        axial = axial.permute(*self.inv_permutation).contiguous()
        return axial




# axial pos emb



class AxialPositionalEmbedding(nn.Module):
    def __init__(self, dim, shape, emb_dim_index=1):
        super().__init__()
        parameters = []
        total_dimensions = len(shape) + 2
        ax_dim_indexes = [i for i in range(1, total_dimensions) if i != emb_dim_index]

        for axial_dim, axial_dim_index in zip(shape, ax_dim_indexes):
            shape = [1] * total_dimensions
            shape[emb_dim_index] = dim
            shape[axial_dim_index] = axial_dim
            parameter = nn.Parameter(torch.randn(*shape))
            parameters.append(parameter)

        self.params = nn.ParameterList(parameters)



    def forward(self, x):
        for param in self.params:
            x = x + param
        return x




# attention



class SelfAttention(nn.Module):
    def __init__(self, dim, heads, dim_heads=None):
        super().__init__()
        self.dim_heads = (dim // heads) if dim_heads is None else dim_heads
        dim_hidden = self.dim_heads * heads

        self.heads = heads
        self.to_q = nn.Linear(dim, dim_hidden, bias=False)
        self.to_kv = nn.Linear(dim, 2 * dim_hidden, bias=False)
        self.to_out = nn.Linear(dim_hidden, dim)



    def forward(self, x, kv=None):
        kv = x if kv is None else kv
        q, k, v = (self.to_q(x), *self.to_kv(kv).chunk(2, dim=-1))

        b, t, d, h, e = *q.shape, self.heads, self.dim_heads

        merge_heads = lambda x: x.reshape(b, -1, h, e).transpose(1, 2).reshape(b * h, -1, e)
        q, k, v = map(merge_heads, (q, k, v))

        dots = torch.einsum('bie,bje->bij', q, k) * (e ** -0.5)
        dots = dots.softmax(dim=-1)
        out = torch.einsum('bij,bje->bie', dots, v)

        out = out.reshape(b, h, -1, e).transpose(1, 2).reshape(b, -1, d)
        out = self.to_out(out)
        return out




# axial attention class



class AxialAttention(nn.Module):
    def __init__(self, dim, num_dimensions=2, heads=8, dim_heads=None, dim_index=-1, sum_axial_out=True):
        assert (dim % heads) == 0, 'hidden dimension must be divisible by number of heads'
        super().__init__()
        self.dim = dim
        self.total_dimensions = num_dimensions + 2
        self.dim_index = dim_index if dim_index > 0 else (dim_index + self.total_dimensions)

        attentions = []
        for permutation in calculate_permutations(num_dimensions, dim_index):
            attentions.append(PermuteToFrom(permutation, SelfAttention(dim, heads, dim_heads)))

        self.axial_attentions = nn.ModuleList(attentions)
        self.sum_axial_out = sum_axial_out



    def forward(self, x):
        assert len(x.shape) == self.total_dimensions, 'input tensor does not have the correct number of dimensions'
        assert x.shape[self.dim_index] == self.dim, 'input tensor does not have the correct input dimension'

        if self.sum_axial_out:
            return sum(map(lambda axial_attn: axial_attn(x), self.axial_attentions))

        out = x
        for axial_attn in self.axial_attentions:
            out = axial_attn(out)
        return out




# axial image transformer



class AxialImageTransformer(nn.Module):
    def __init__(self, dim, depth, heads=8, dim_heads=None, dim_index=1, reversible=True, axial_pos_emb_shape=None):
        super().__init__()
        permutations = calculate_permutations(2, dim_index)

        get_ff = lambda: nn.Sequential(
            nn.Conv2d(dim, dim, 3, padding=1),
            nn.LeakyReLU(inplace=True),
            nn.Conv2d(dim, dim, 3, padding=1)
        )

        self.pos_emb = AxialPositionalEmbedding(dim, axial_pos_emb_shape, dim_index) if exists(
            axial_pos_emb_shape) else nn.Identity()

        layers = nn.ModuleList([])
        for _ in range(depth):
            attn_functions = nn.ModuleList(
                [PermuteToFrom(permutation, Rezero(SelfAttention(dim, heads, dim_heads))) for permutation in
                 permutations])
            conv_functions = nn.ModuleList([Rezero(get_ff()), Rezero(get_ff())])
            layers.append(attn_functions)
            layers.append(conv_functions)

        execute_type = ReversibleSequence if reversible else Sequential
        self.layers = execute_type(layers)



    def forward(self, x):
        x = self.pos_emb(x)
        x = torch.cat((x, x), dim=-1)
        x = self.layers(x)
        return torch.stack(x.chunk(2, dim=-1)).mean(dim=0)




#
# Contents below are from https://github.com/lucidrains/axial-attention/blob/master/axial_attention/reversible.py
#

# following example for saving and setting rng here https://pytorch.org/docs/stable/_modules/torch/utils/checkpoint.html


class Deterministic(nn.Module):
    def __init__(self, net):
        super().__init__()
        self.net = net
        self.cpu_state = None
        self.cuda_in_fwd = None
        self.gpu_devices = None
        self.gpu_states = None



    def record_rng(self, *args):
        self.cpu_state = torch.get_rng_state()
        if torch.cuda._initialized:
            self.cuda_in_fwd = True
            self.gpu_devices, self.gpu_states = get_device_states(*args)




    def forward(self, *args, record_rng = False, set_rng = False, **kwargs):
        if record_rng:
            self.record_rng(*args)

        if not set_rng:
            return self.net(*args, **kwargs)

        rng_devices = []
        if self.cuda_in_fwd:
            rng_devices = self.gpu_devices

        with torch.random.fork_rng(devices=rng_devices, enabled=True):
            torch.set_rng_state(self.cpu_state)
            if self.cuda_in_fwd:
                set_device_states(self.gpu_devices, self.gpu_states)
            return self.net(*args, **kwargs)




# heavily inspired by https://github.com/RobinBruegger/RevTorch/blob/master/revtorch/revtorch.py
# once multi-GPU is confirmed working, refactor and send PR back to source


class ReversibleBlock(nn.Module):
    def __init__(self, f, g):
        super().__init__()
        self.f = Deterministic(f)
        self.g = Deterministic(g)



    def forward(self, x, f_args = {}, g_args = {}):
        x1, x2 = torch.chunk(x, 2, dim=2)
        y1, y2 = None, None

        with torch.no_grad():
            y1 = x1 + self.f(x2, record_rng=self.training, **f_args)
            y2 = x2 + self.g(y1, record_rng=self.training, **g_args)

        return torch.cat([y1, y2], dim=2)




    def backward_pass(self, y, dy, f_args = {}, g_args = {}):
        y1, y2 = torch.chunk(y, 2, dim=2)
        del y

        dy1, dy2 = torch.chunk(dy, 2, dim=2)
        del dy

        with torch.enable_grad():
            y1.requires_grad = True
            gy1 = self.g(y1, set_rng=True, **g_args)
            torch.autograd.backward(gy1, dy2)

        with torch.no_grad():
            x2 = y2 - gy1
            del y2, gy1

            dx1 = dy1 + y1.grad
            del dy1
            y1.grad = None

        with torch.enable_grad():
            x2.requires_grad = True
            fx2 = self.f(x2, set_rng=True, **f_args)
            torch.autograd.backward(fx2, dx1, retain_graph=True)

        with torch.no_grad():
            x1 = y1 - fx2
            del y1, fx2

            dx2 = dy2 + x2.grad
            del dy2
            x2.grad = None

            x = torch.cat([x1, x2.detach()], dim=2)
            dx = torch.cat([dx1, dx2], dim=2)

        return x, dx






class IrreversibleBlock(nn.Module):
    def __init__(self, f, g):
        super().__init__()
        self.f = f
        self.g = g



    def forward(self, x, f_args, g_args):
        x1, x2 = torch.chunk(x, 2, dim=2)
        y1 = x1 + self.f(x2, **f_args)
        y2 = x2 + self.g(y1, **g_args)
        return torch.cat([y1, y2], dim=2)




class _ReversibleFunction(Function):
    @staticmethod
    def forward(ctx, x, blocks, kwargs):
        ctx.kwargs = kwargs
        for block in blocks:
            x = block(x, **kwargs)
        ctx.y = x.detach()
        ctx.blocks = blocks
        return x

    @staticmethod
    def backward(ctx, dy):
        y = ctx.y
        kwargs = ctx.kwargs
        for block in ctx.blocks[::-1]:
            y, dy = block.backward_pass(y, dy, **kwargs)
        return dy, None, None




class ReversibleSequence(nn.Module):
    def __init__(self, blocks, ):
        super().__init__()
        self.blocks = nn.ModuleList([ReversibleBlock(f, g) for (f, g) in blocks])



    def forward(self, x, arg_route = (True, True), **kwargs):
        f_args, g_args = map(lambda route: kwargs if route else {}, arg_route)
        block_kwargs = {'f_args': f_args, 'g_args': g_args}
        return _ReversibleFunction.apply(x, self.blocks, block_kwargs)