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ixaxaar 2017-11-24 16:41:19 +05:30
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#!/usr/bin/env python3
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 SparseMemory(nn.Module):
def __init__(
self,
input_size,
mem_size=512,
cell_size=32,
read_heads=4,
gpu_id=-1,
independent_linears=True,
sparse_reads=4
):
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
self.K = sparse_reads
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_(δ), 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_(δ), gpu_id=self.gpu_id),
'write_weights': cuda(T.zeros(b, 1, m).fill_(δ), 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_(δ)
hidden['link_matrix'].data.zero_()
hidden['precedence'].data.zero_()
hidden['read_weights'].data.fill_(δ)
hidden['write_weights'].data.fill_(δ)
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, TODO: unstable territory, revisit this shit
# essential for correct scaling of allocation_weights to prevent memory pollution
# during write operations
# https://discuss.pytorch.org/t/cumprod-exclusive-true-equivalences/2614/8
v = var(T.ones(batch_size, 1))
if self.gpu_id != -1:
v = v.cuda(self.gpu_id)
cat_sorted_usage = T.cat((v, sorted_usage), 1)[:, :-1]
prod_sorted_usage = fake_cumprod(cat_sorted_usage, self.gpu_id)
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.long())
# update usage after allocating
# usage += ((1 - usage) * write_gate * allocation_weights)
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
# elaborate 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)
strengths = F.softplus(strengths).unsqueeze(2)
return σ(d * strengths, 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 = self.read_keys_transform(ξ).view(b, r, w)
# r read strengths (b * r)
read_strengths = self.read_strengths_transform(ξ).view(b, r)
# write key (b * 1 * w)
write_key = self.write_key_transform(ξ).view(b, 1, w)
# write strength (b * 1)
write_strength = 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 = 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 = ξ[:, :r * w].contiguous().view(b, r, w)
# r read strengths (b * r)
read_strengths = 1 + F.relu(ξ[:, r * w:r * w + r].contiguous().view(b, r))
# write key (b * w * 1)
write_key = ξ[:, r * w + r:r * w + r + w].contiguous().view(b, 1, w)
# write strength (b * 1)
write_strength = 1 + F.relu(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 = 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)