262 lines
10 KiB
Python
262 lines
10 KiB
Python
#!/usr/bin/env python3
|
||
# -*- coding: utf-8 -*-
|
||
|
||
import torch.nn as nn
|
||
import torch as T
|
||
from torch.autograd import Variable as var
|
||
import torch.nn.functional as F
|
||
import numpy as np
|
||
|
||
from .util import *
|
||
|
||
|
||
class Memory(nn.Module):
|
||
|
||
def __init__(self, input_size, mem_size=512, cell_size=32, read_heads=4, gpu_id=-1, independent_linears=True):
|
||
super(Memory, self).__init__()
|
||
|
||
self.mem_size = mem_size
|
||
self.cell_size = cell_size
|
||
self.read_heads = read_heads
|
||
self.gpu_id = gpu_id
|
||
self.input_size = input_size
|
||
self.independent_linears = independent_linears
|
||
|
||
m = self.mem_size
|
||
w = self.cell_size
|
||
r = self.read_heads
|
||
|
||
if self.independent_linears:
|
||
self.read_keys_transform = nn.Linear(self.input_size, w * r)
|
||
self.read_strengths_transform = nn.Linear(self.input_size, r)
|
||
self.write_key_transform = nn.Linear(self.input_size, w)
|
||
self.write_strength_transform = nn.Linear(self.input_size, 1)
|
||
self.erase_vector_transform = nn.Linear(self.input_size, w)
|
||
self.write_vector_transform = nn.Linear(self.input_size, w)
|
||
self.free_gates_transform = nn.Linear(self.input_size, r)
|
||
self.allocation_gate_transform = nn.Linear(self.input_size, 1)
|
||
self.write_gate_transform = nn.Linear(self.input_size, 1)
|
||
self.read_modes_transform = nn.Linear(self.input_size, 3 * r)
|
||
else:
|
||
self.interface_size = (w * r) + (3 * w) + (5 * r) + 3
|
||
self.interface_weights = nn.Linear(self.input_size, self.interface_size)
|
||
|
||
self.I = cuda(1 - T.eye(m).unsqueeze(0), gpu_id=self.gpu_id) # (1 * n * n)
|
||
|
||
def reset(self, batch_size=1, hidden=None, erase=True):
|
||
m = self.mem_size
|
||
w = self.cell_size
|
||
r = self.read_heads
|
||
b = batch_size
|
||
|
||
if hidden is None:
|
||
return {
|
||
'memory': cuda(T.zeros(b, m, w).fill_(0), gpu_id=self.gpu_id),
|
||
'link_matrix': cuda(T.zeros(b, 1, m, m), gpu_id=self.gpu_id),
|
||
'precedence': cuda(T.zeros(b, 1, m), gpu_id=self.gpu_id),
|
||
'read_weights': cuda(T.zeros(b, r, m).fill_(0), gpu_id=self.gpu_id),
|
||
'write_weights': cuda(T.zeros(b, 1, m).fill_(0), gpu_id=self.gpu_id),
|
||
'usage_vector': cuda(T.zeros(b, m), gpu_id=self.gpu_id)
|
||
}
|
||
else:
|
||
hidden['memory'] = hidden['memory'].clone()
|
||
hidden['link_matrix'] = hidden['link_matrix'].clone()
|
||
hidden['precedence'] = hidden['precedence'].clone()
|
||
hidden['read_weights'] = hidden['read_weights'].clone()
|
||
hidden['write_weights'] = hidden['write_weights'].clone()
|
||
hidden['usage_vector'] = hidden['usage_vector'].clone()
|
||
|
||
if erase:
|
||
hidden['memory'].data.fill_(0)
|
||
hidden['link_matrix'].data.zero_()
|
||
hidden['precedence'].data.zero_()
|
||
hidden['read_weights'].data.fill_(0)
|
||
hidden['write_weights'].data.fill_(0)
|
||
hidden['usage_vector'].data.zero_()
|
||
return hidden
|
||
|
||
def get_usage_vector(self, usage, free_gates, read_weights, write_weights):
|
||
# write_weights = write_weights.detach() # detach from the computation graph
|
||
usage = usage + (1 - usage) * (1 - T.prod(1 - write_weights, 1))
|
||
ψ = T.prod(1 - free_gates.unsqueeze(2) * read_weights, 1)
|
||
return usage * ψ
|
||
|
||
def allocate(self, usage, write_gate):
|
||
# ensure values are not too small prior to cumprod.
|
||
usage = δ + (1 - δ) * usage
|
||
batch_size = usage.size(0)
|
||
# free list
|
||
sorted_usage, φ = T.topk(usage, self.mem_size, dim=1, largest=False)
|
||
|
||
# cumprod with exclusive=True
|
||
# https://discuss.pytorch.org/t/cumprod-exclusive-true-equivalences/2614/8
|
||
v = var(sorted_usage.data.new(batch_size, 1).fill_(1))
|
||
cat_sorted_usage = T.cat((v, sorted_usage), 1)
|
||
prod_sorted_usage = T.cumprod(cat_sorted_usage, 1)[:, :-1]
|
||
|
||
sorted_allocation_weights = (1 - sorted_usage) * prod_sorted_usage.squeeze()
|
||
|
||
# construct the reverse sorting index https://stackoverflow.com/questions/2483696/undo-or-reverse-argsort-python
|
||
_, φ_rev = T.topk(φ, k=self.mem_size, dim=1, largest=False)
|
||
allocation_weights = sorted_allocation_weights.gather(1, φ_rev.long())
|
||
|
||
return allocation_weights.unsqueeze(1), usage
|
||
|
||
def write_weighting(self, memory, write_content_weights, allocation_weights, write_gate, allocation_gate):
|
||
ag = allocation_gate.unsqueeze(-1)
|
||
wg = write_gate.unsqueeze(-1)
|
||
|
||
return wg * (ag * allocation_weights + (1 - ag) * write_content_weights)
|
||
|
||
def get_link_matrix(self, link_matrix, write_weights, precedence):
|
||
precedence = precedence.unsqueeze(2)
|
||
write_weights_i = write_weights.unsqueeze(3)
|
||
write_weights_j = write_weights.unsqueeze(2)
|
||
|
||
prev_scale = 1 - write_weights_i - write_weights_j
|
||
new_link_matrix = write_weights_i * precedence
|
||
|
||
link_matrix = prev_scale * link_matrix + new_link_matrix
|
||
# trick to delete diag elems
|
||
return self.I.expand_as(link_matrix) * link_matrix
|
||
|
||
def update_precedence(self, precedence, write_weights):
|
||
return (1 - T.sum(write_weights, 2, keepdim=True)) * precedence + write_weights
|
||
|
||
def write(self, write_key, write_vector, erase_vector, free_gates, read_strengths, write_strength, write_gate, allocation_gate, hidden):
|
||
# get current usage
|
||
hidden['usage_vector'] = self.get_usage_vector(
|
||
hidden['usage_vector'],
|
||
free_gates,
|
||
hidden['read_weights'],
|
||
hidden['write_weights']
|
||
)
|
||
|
||
# lookup memory with write_key and write_strength
|
||
write_content_weights = self.content_weightings(hidden['memory'], write_key, write_strength)
|
||
|
||
# get memory allocation
|
||
alloc, _ = self.allocate(
|
||
hidden['usage_vector'],
|
||
allocation_gate * write_gate
|
||
)
|
||
|
||
# get write weightings
|
||
hidden['write_weights'] = self.write_weighting(
|
||
hidden['memory'],
|
||
write_content_weights,
|
||
alloc,
|
||
write_gate,
|
||
allocation_gate
|
||
)
|
||
|
||
weighted_resets = hidden['write_weights'].unsqueeze(3) * erase_vector.unsqueeze(2)
|
||
reset_gate = T.prod(1 - weighted_resets, 1)
|
||
# Update memory
|
||
hidden['memory'] = hidden['memory'] * reset_gate
|
||
|
||
hidden['memory'] = hidden['memory'] + \
|
||
T.bmm(hidden['write_weights'].transpose(1, 2), write_vector)
|
||
|
||
# update link_matrix
|
||
hidden['link_matrix'] = self.get_link_matrix(
|
||
hidden['link_matrix'],
|
||
hidden['write_weights'],
|
||
hidden['precedence']
|
||
)
|
||
hidden['precedence'] = self.update_precedence(hidden['precedence'], hidden['write_weights'])
|
||
|
||
return hidden
|
||
|
||
def content_weightings(self, memory, keys, strengths):
|
||
d = θ(memory, keys)
|
||
return σ(d * strengths.unsqueeze(2), 2)
|
||
|
||
def directional_weightings(self, link_matrix, read_weights):
|
||
rw = read_weights.unsqueeze(1)
|
||
|
||
f = T.matmul(link_matrix, rw.transpose(2, 3)).transpose(2, 3)
|
||
b = T.matmul(rw, link_matrix)
|
||
return f.transpose(1, 2), b.transpose(1, 2)
|
||
|
||
def read_weightings(self, memory, content_weights, link_matrix, read_modes, read_weights):
|
||
forward_weight, backward_weight = self.directional_weightings(link_matrix, read_weights)
|
||
|
||
content_mode = read_modes[:, :, 2].contiguous().unsqueeze(2) * content_weights
|
||
backward_mode = T.sum(read_modes[:, :, 0:1].contiguous().unsqueeze(3) * backward_weight, 2)
|
||
forward_mode = T.sum(read_modes[:, :, 1:2].contiguous().unsqueeze(3) * forward_weight, 2)
|
||
|
||
return backward_mode + content_mode + forward_mode
|
||
|
||
def read_vectors(self, memory, read_weights):
|
||
return T.bmm(read_weights, memory)
|
||
|
||
def read(self, read_keys, read_strengths, read_modes, hidden):
|
||
content_weights = self.content_weightings(hidden['memory'], read_keys, read_strengths)
|
||
|
||
hidden['read_weights'] = self.read_weightings(
|
||
hidden['memory'],
|
||
content_weights,
|
||
hidden['link_matrix'],
|
||
read_modes,
|
||
hidden['read_weights']
|
||
)
|
||
read_vectors = self.read_vectors(hidden['memory'], hidden['read_weights'])
|
||
return read_vectors, hidden
|
||
|
||
def forward(self, ξ, hidden):
|
||
|
||
# ξ = ξ.detach()
|
||
m = self.mem_size
|
||
w = self.cell_size
|
||
r = self.read_heads
|
||
b = ξ.size()[0]
|
||
|
||
if self.independent_linears:
|
||
# r read keys (b * r * w)
|
||
read_keys = F.tanh(self.read_keys_transform(ξ).view(b, r, w))
|
||
# r read strengths (b * r)
|
||
read_strengths = F.softplus(self.read_strengths_transform(ξ).view(b, r))
|
||
# write key (b * 1 * w)
|
||
write_key = F.tanh(self.write_key_transform(ξ).view(b, 1, w))
|
||
# write strength (b * 1)
|
||
write_strength = F.softplus(self.write_strength_transform(ξ).view(b, 1))
|
||
# erase vector (b * 1 * w)
|
||
erase_vector = F.sigmoid(self.erase_vector_transform(ξ).view(b, 1, w))
|
||
# write vector (b * 1 * w)
|
||
write_vector = F.tanh(self.write_vector_transform(ξ).view(b, 1, w))
|
||
# r free gates (b * r)
|
||
free_gates = F.sigmoid(self.free_gates_transform(ξ).view(b, r))
|
||
# allocation gate (b * 1)
|
||
allocation_gate = F.sigmoid(self.allocation_gate_transform(ξ).view(b, 1))
|
||
# write gate (b * 1)
|
||
write_gate = F.sigmoid(self.write_gate_transform(ξ).view(b, 1))
|
||
# read modes (b * r * 3)
|
||
read_modes = σ(self.read_modes_transform(ξ).view(b, r, 3), 1)
|
||
else:
|
||
ξ = self.interface_weights(ξ)
|
||
# r read keys (b * w * r)
|
||
read_keys = F.tanh(ξ[:, :r * w].contiguous().view(b, r, w))
|
||
# r read strengths (b * r)
|
||
read_strengths = F.softplus(ξ[:, r * w:r * w + r].contiguous().view(b, r))
|
||
# write key (b * w * 1)
|
||
write_key = F.tanh(ξ[:, r * w + r:r * w + r + w].contiguous().view(b, 1, w))
|
||
# write strength (b * 1)
|
||
write_strength = F.softplus(ξ[:, r * w + r + w].contiguous().view(b, 1))
|
||
# erase vector (b * w)
|
||
erase_vector = F.sigmoid(ξ[:, r * w + r + w + 1: r * w + r + 2 * w + 1].contiguous().view(b, 1, w))
|
||
# write vector (b * w)
|
||
write_vector = F.tanh(ξ[:, r * w + r + 2 * w + 1: r * w + r + 3 * w + 1].contiguous().view(b, 1, w))
|
||
# r free gates (b * r)
|
||
free_gates = F.sigmoid(ξ[:, r * w + r + 3 * w + 1: r * w + 2 * r + 3 * w + 1].contiguous().view(b, r))
|
||
# allocation gate (b * 1)
|
||
allocation_gate = F.sigmoid(ξ[:, r * w + 2 * r + 3 * w + 1].contiguous().unsqueeze(1).view(b, 1))
|
||
# write gate (b * 1)
|
||
write_gate = F.sigmoid(ξ[:, r * w + 2 * r + 3 * w + 2].contiguous()).unsqueeze(1).view(b, 1)
|
||
# read modes (b * 3*r)
|
||
read_modes = σ(ξ[:, r * w + 2 * r + 3 * w + 2: r * w + 5 * r + 3 * w + 2].contiguous().view(b, r, 3), 1)
|
||
|
||
hidden = self.write(write_key, write_vector, erase_vector, free_gates,
|
||
read_strengths, write_strength, write_gate, allocation_gate, hidden)
|
||
return self.read(read_keys, read_strengths, read_modes, hidden)
|