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models.py
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models.py
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# -*- coding: utf-8 -*-
import theano, cPickle
import theano.tensor as T
import numpy as np
import pdb
from fftconv import cufft, cuifft
def initialize_matrix(n_in, n_out, name, rng):
bin = np.sqrt(6. / (n_in + n_out))
# STEPH: again with the built-in names, sadface
values = np.asarray(rng.uniform(low=-bin,
high=bin,
size=(n_in, n_out)),
dtype=theano.config.floatX)
return theano.shared(value=values, name=name)
def do_fft(input, n_hidden):
fft_input = T.reshape(input, (input.shape[0], 2, n_hidden))
fft_input = fft_input.dimshuffle(0,2,1)
fft_output = cufft(fft_input) / T.sqrt(n_hidden)
# STEPH: see fftconv for cufft
fft_output = fft_output.dimshuffle(0,2,1)
output = T.reshape(fft_output, (input.shape[0], 2*n_hidden))
return output
def do_ifft(input, n_hidden):
ifft_input = T.reshape(input, (input.shape[0], 2, n_hidden))
ifft_input = ifft_input.dimshuffle(0,2,1)
ifft_output = cuifft(ifft_input) / T.sqrt(n_hidden)
ifft_output = ifft_output.dimshuffle(0,2,1)
output = T.reshape(ifft_output, (input.shape[0], 2*n_hidden))
return output
def times_diag(input, n_hidden, diag, swap_re_im):
# STEPH: built-in names, sadface
d = T.concatenate([diag, -diag])
# STEPH: theano concatenation, minus for reasons yet unknown... something
# possibly to do with phase?
# TODO: resolve this uncertainty
# suspicion: to do with a + ib -> a - ib somehow, since sin(-x) = -sin(x)
Re = T.cos(d).dimshuffle('x',0)
Im = T.sin(d).dimshuffle('x',0)
# STEPH: d is the phase of the complex number, splitting it into real
# and imaginary parts here
input_times_Re = input * Re
input_times_Im = input * Im
# STEPH: np does row-wise multiplication between matrix and vectors
output = input_times_Re + input_times_Im[:, swap_re_im]
return output
def vec_permutation(input, index_permute):
return input[:, index_permute]
def times_reflection(input, n_hidden, reflection):
# comments here are Steph working through the maths
# OK so the equation they give is:
# (I - 2 outer(v, v*)/|v|**2) h
# (v is the reflection, h is the input)
# this gets us to: (using Einstein notation)
# h_i - (2/|v|**2) v_i v*_j h_j
# Looking at the final few lines of this function, what we would like to
# show is: (since :n_hidden is the imaginary part of the output tensor)
# re(v_i v*_j h_j) = d - c
# im(v_i v*_j h_j) = a + b
#
# v = mu + i nu
# h = alpha + i beta
# v_i v*_j h_j = (mu_i + i nu_i) (mu_j - i nu_j) (alpha_j + i beta_j)
# = (mu_i mu_j - i mu_i nu_j + i nu_i mu_j + nu_i nu_j) (alpha_j + i beta_j)
# = (mu_i mu_j alpha_j + i mu_i mu_j beta_j +
# -i mu_i nu_j alpha_j + mu_i nu_j beta_j +
# i nu_i mu_j alpha_j - nu_i mu_j beta_j +
# nu_i nu_j alpha_j + i nu_i nu_j beta_j) = K
#
# What an expression!
# Let's split it up:
# re(K) = (mu_i mu_j alpha_j + mu_i nu_j beta_j +
# -nu_i mu_j beta_j + nu_i nu_j alpha_j)
# im(K) = (mu_i mu_j beta_j - mu_i nu_j alpha_j +
# + nu_i mu_j alpha_j + nu_i nu_j beta_j)
#
# Now let's replace the scalar parts (the repeated js...)
# αμ = alpha_j mu_j
# αν = alpha_j nu_j
# βμ = beta_j mu_j
# βν = beta_j nu_j
#
# re(K) = (mu_i αμ + mu_i βν - nu_i βμ + nu_i αν )
# im(K) = (mu_i βμ - mu_i αν + nu_i αμ + nu_i βν )
#
# Simplifying further...
#
# re(K) = mu_i ( αμ + βν ) - nu_i ( βμ - αν ) = nope - nope
# im(K) = mu_i ( βμ - αν ) + nu_i ( αμ + βν ) = nope + nope
#
# Jumping ahead (see below) to the definitions of a, b, c, d...
#
# a = mu_i ( αμ - βν )
# b = nu_i ( αν + βμ )
# c = nu_i ( αμ - βν )
# d = mu_i ( αν + βμ )
#
# And so:
# d - c = mu_i ( αν + βμ ) - nu_i ( αμ - βν )
# a + b = mu_i ( αμ - βν ) + nu_i ( αν + βμ )
#
# ... huh, what is going on?
# ... double-checking my maths!
# ... double-checking their maths!
# ... looks OK?
# ... will need to TRIPLE-check my maths when it's not 1am.
#
# Possibility: when they used a * in the paper, they meant *transpose*
# and not *conjugate transpose*...
#
# This would result in...
#
# v_i v_j h_j = (mu_i + i nu_i) (mu_j + i nu_j) (alpha_j + i beta_j)
# = (mu_i mu_j + i mu_i nu_j + i nu_i mu_j - nu_i nu_j) (alpha_j + i beta_j)
# = (mu_i mu_j alpha_j + i mu_i mu_j beta_j +
# + i mu_i nu_j alpha_j - mu_i nu_j beta_j +
# i nu_i mu_j alpha_j - nu_i mu_j beta_j +
# - nu_i nu_j alpha_j - i nu_i nu_j beta_j) = J
#
# re(J) = (mu_i mu_j alpha_j - mu_i nu_j beta_j +
# - nu_i mu_j beta_j - nu_i nu_j alpha_j)
# im(J) = (mu_i mu_j beta_j + mu_i nu_j alpha_j +
# nu_i mu_j alpha_j - nu_i nu_j beta_j)
#
# Replacing scalar parts...
# re(J) = mu_i αμ - mu_i βν - nu_i βμ - nu_i αν
# im(J) = mu_i βμ + mu_i αν + nu_i αμ - nu_i βν
#
# Further simplifying...
#
# re(J) = mu_i ( αμ - βν ) - nu_i ( βμ + αν ) = a - b
# im(J) = mu_i ( βμ + αν ) + nu_i ( αμ - βν ) = d + c
#
# ... closer but NOT THE SAME
# WHAT IS GOING ON HERE?
input_re = input[:, :n_hidden]
# alpha
input_im = input[:, n_hidden:]
# beta
reflect_re = reflection[:n_hidden]
# mu
reflect_im = reflection[n_hidden:]
# nu
vstarv = (reflection**2).sum()
# (the following things are roughly scalars)
# (they actually are as long as the batch size, e.g. input[0])
input_re_reflect_re = T.dot(input_re, reflect_re)
# αμ
input_re_reflect_im = T.dot(input_re, reflect_im)
# αν
input_im_reflect_re = T.dot(input_im, reflect_re)
# βμ
input_im_reflect_im = T.dot(input_im, reflect_im)
# βν
#
a = T.outer(input_re_reflect_re - input_im_reflect_im, reflect_re)
# outer(αμ - βν, mu)
b = T.outer(input_re_reflect_im + input_im_reflect_re, reflect_im)
# outer(αν + βμ, nu)
c = T.outer(input_re_reflect_re - input_im_reflect_im, reflect_im)
# outer(αμ - βν, nu)
d = T.outer(input_re_reflect_im + input_im_reflect_re, reflect_re)
# outer(αν + βμ, mu)
output = input
output = T.inc_subtensor(output[:, :n_hidden], - 2. / vstarv * (a + b))
output = T.inc_subtensor(output[:, n_hidden:], - 2. / vstarv * (d - c))
return output
#
def compute_cost_t(lin_output, loss_function, y_t):
if loss_function == 'CE':
RNN_output = T.nnet.softmax(lin_output)
cost_t = T.nnet.categorical_crossentropy(RNN_output, y_t).mean()
# TODO: (STEPH) review maths on this
acc_t =(T.eq(T.argmax(RNN_output, axis=-1), y_t)).mean(dtype=theano.config.floatX)
elif loss_function == 'MSE':
cost_t = ((lin_output - y_t)**2).mean()
acc_t = theano.shared(np.float32(0.0))
return cost_t, acc_t
def initialize_data_nodes(loss_function, input_type, out_every_t):
# initialises the theano objects for data and labels
x = T.tensor3() if input_type == 'real' else T.matrix(dtype='int32')
# STEPH: x is either real or ... integers?
if loss_function == 'CE':
y = T.matrix(dtype='int32') if out_every_t else T.vector(dtype='int32')
else:
# STEPH: if not CE, then RSE, btw...
y = T.tensor3() if out_every_t else T.matrix()
return x, y
def IRNN(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE'):
# STEPH: this differs from tanhRNN in two places, see below
np.random.seed(1234)
rng = np.random.RandomState(1234)
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
inputs = [x, y]
h_0 = theano.shared(np.zeros((1, n_hidden), dtype=theano.config.floatX))
V = initialize_matrix(n_input, n_hidden, 'V', rng)
W = theano.shared(np.identity(n_hidden, dtype=theano.config.floatX))
# STEPH: W differs from that of tanhRNN: this is just identity!
out_mat = initialize_matrix(n_hidden, n_output, 'out_mat', rng)
hidden_bias = theano.shared(np.zeros((n_hidden,), dtype=theano.config.floatX))
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX))
parameters = [h_0, V, W, out_mat, hidden_bias, out_bias]
def recurrence(x_t, y_t, h_prev, cost_prev, acc_prev, V, W, hidden_bias, out_mat, out_bias):
if loss_function == 'CE':
data_lin_output = V[x_t]
else:
data_lin_output = T.dot(x_t, V)
h_t = T.nnet.relu(T.dot(h_prev, W) + data_lin_output + hidden_bias.dimshuffle('x', 0))
# STEPH: differs from tanhRNN: here we have relu, there they had tanh
if out_every_t:
lin_output = T.dot(h_t, out_mat) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t
non_sequences = [V, W, hidden_bias, out_mat, out_bias]
h_0_batch = T.tile(h_0, [x.shape[1], 1])
if out_every_t:
sequences = [x, y]
else:
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
outputs_info = [h_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
[hidden_states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info = outputs_info)
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], out_mat) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return inputs, parameters, costs
def tanhRNN(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE'):
np.random.seed(1234)
rng = np.random.RandomState(1234)
# STEPH: initialising np's generic RNG and a specific rng identically
# uncertain why but maybe we'll find out soon
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
inputs = [x, y]
h_0 = theano.shared(np.zeros((1, n_hidden), dtype=theano.config.floatX))
V = initialize_matrix(n_input, n_hidden, 'V', rng)
W = initialize_matrix(n_hidden, n_hidden, 'W', rng)
# STEPH: W is the weights of the recurrence (can tell cause of its shape!)
out_mat = initialize_matrix(n_hidden, n_output, 'out_mat', rng)
hidden_bias = theano.shared(np.zeros((n_hidden,), dtype=theano.config.floatX))
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX))
parameters = [h_0, V, W, out_mat, hidden_bias, out_bias]
def recurrence(x_t, y_t, h_prev, cost_prev, acc_prev, V, W, hidden_bias, out_mat, out_bias):
# all of this is to get the hidden state, and possibly cost/accuracy
if loss_function == 'CE':
data_lin_output = V[x_t]
# STEPH: uncertain why this is named thusly
# STEPH: in CE case, the data is just an index, I guess...
# basically, an indicator vector
# I think this may be confounded with the experimental setup
# CE appears in ?
else:
data_lin_output = T.dot(x_t, V)
# STEPH: 'as normal', folding the data from the sequence in
h_t = T.tanh(T.dot(h_prev, W) + data_lin_output + hidden_bias.dimshuffle('x', 0))
# STEPH: dimshuffle (theano) here, makes row out of 1d vector, N -> 1xN
if out_every_t:
lin_output = T.dot(h_t, out_mat) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
# STEPH: no cost/accuracy until the end!
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t
non_sequences = [V, W, hidden_bias, out_mat, out_bias]
# STEPH: naming due to scan (theano); these are 'fixed' values in scan
h_0_batch = T.tile(h_0, [x.shape[1], 1])
# STEPH: tile (theano) repeats input x according to pattern
# pattern is number of times to tile in each direction
if out_every_t:
sequences = [x, y]
else:
# STEPH: the 'y' here is just... a bunch of weirdly-shaped zeros?
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
# STEPH: sequences here are the input we loop over...
outputs_info = [h_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
# STEPH: naming due to scan, these are initialisation values... see return
# value of recurrence: h_t, cost_t, acc_t...
[hidden_states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
# STEPH: remembering how to do scan!
# outputs_info: contains initialisation, naming is bizarre, whatever
# non_sequences: unchanging variables
# sequences: tensors to be looped over
# so fn receives (sequences, previous output, non_sequences):
# this seems to square with the order of arguments in 'recurrence'
# TODO: read scan more carefully to confirm this
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], out_mat) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
# STEPH: cost is computed off the final hidden state
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return inputs, parameters, costs
def LSTM(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE'):
np.random.seed(1234)
rng = np.random.RandomState(1234)
# STEPH: i for input, f for forget, c for candidate, o for output
W_i = initialize_matrix(n_input, n_hidden, 'W_i', rng)
W_f = initialize_matrix(n_input, n_hidden, 'W_f', rng)
W_c = initialize_matrix(n_input, n_hidden, 'W_c', rng)
W_o = initialize_matrix(n_input, n_hidden, 'W_o', rng)
U_i = initialize_matrix(n_hidden, n_hidden, 'U_i', rng)
U_f = initialize_matrix(n_hidden, n_hidden, 'U_f', rng)
U_c = initialize_matrix(n_hidden, n_hidden, 'U_c', rng)
U_o = initialize_matrix(n_hidden, n_hidden, 'U_o', rng)
# STEPH: note that U is not out_mat as it was in complex_RNN
V_o = initialize_matrix(n_hidden, n_hidden, 'V_o', rng)
b_i = theano.shared(np.zeros((n_hidden,), dtype=theano.config.floatX))
b_f = theano.shared(np.ones((n_hidden,), dtype=theano.config.floatX))
b_c = theano.shared(np.zeros((n_hidden,), dtype=theano.config.floatX))
b_o = theano.shared(np.zeros((n_hidden,), dtype=theano.config.floatX))
h_0 = theano.shared(np.zeros((1, n_hidden), dtype=theano.config.floatX))
state_0 = theano.shared(np.zeros((1, n_hidden), dtype=theano.config.floatX))
out_mat = initialize_matrix(n_hidden, n_output, 'out_mat', rng)
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX))
parameters = [W_i, W_f, W_c, W_o, U_i, U_f, U_c, U_o, V_o, b_i, b_f, b_c, b_o, h_0, state_0, out_mat, out_bias]
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
def recurrence(x_t, y_t, h_prev, state_prev, cost_prev, acc_prev,
W_i, W_f, W_c, W_o, U_i, U_f, U_c, U_o, V_o, b_i, b_f, b_c, b_o, out_mat, out_bias):
if loss_function == 'CE':
x_t_W_i = W_i[x_t]
x_t_W_c = W_c[x_t]
x_t_W_f = W_f[x_t]
x_t_W_o = W_o[x_t]
else:
x_t_W_i = T.dot(x_t, W_i)
x_t_W_c = T.dot(x_t, W_c)
x_t_W_f = T.dot(x_t, W_f)
x_t_W_o = T.dot(x_t, W_o)
input_t = T.nnet.sigmoid(x_t_W_i + T.dot(h_prev, U_i) + b_i.dimshuffle('x', 0))
# STEPH: save candidate?
candidate_t = T.tanh(x_t_W_c + T.dot(h_prev, U_c) + b_c.dimshuffle('x', 0))
forget_t = T.nnet.sigmoid(x_t_W_f + T.dot(h_prev, U_f) + b_f.dimshuffle('x', 0))
# STEPH: forget previosu state?
state_t = input_t * candidate_t + forget_t * state_prev
# STEPH: so we can both save the input and not forget the previous, OK
output_t = T.nnet.sigmoid(x_t_W_o + T.dot(h_prev, U_o) + T.dot(state_t, V_o) + b_o.dimshuffle('x', 0))
# TODO: (STEPH) double-check maths, here!
h_t = output_t * T.tanh(state_t)
# STEPH: same as other models...
if out_every_t:
lin_output = T.dot(h_t, out_mat) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, state_t, cost_t, acc_t
non_sequences = [W_i, W_f, W_c, W_o, U_i, U_f, U_c, U_o, V_o, b_i, b_f, b_c, b_o, out_mat, out_bias]
# STEPH: same as tanhRNN, etc... the scan part is generally duplicated!
h_0_batch = T.tile(h_0, [x.shape[1], 1])
state_0_batch = T.tile(state_0, [x.shape[1], 1])
if out_every_t:
sequences = [x, y]
else:
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
outputs_info = [h_0_batch, state_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
[hidden_states, states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], out_mat) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return [x, y], parameters, costs
def complex_RNN(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE'):
np.random.seed(1234)
rng = np.random.RandomState(1234)
# Initialize parameters: theta, V_re, V_im, hidden_bias, U, out_bias, h_0
V = initialize_matrix(n_input, 2*n_hidden, 'V', rng)
U = initialize_matrix(2 * n_hidden, n_output, 'U', rng)
# STEPH: U was previously known as out_mat
hidden_bias = theano.shared(np.asarray(rng.uniform(low=-0.01,
high=0.01,
size=(n_hidden,)),
dtype=theano.config.floatX),
name='hidden_bias')
# STEPH: hidden bias is simply initialised differently in this case
reflection = initialize_matrix(2, 2*n_hidden, 'reflection', rng)
# STEPH: part of recurrence (~W)
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX), name='out_bias')
theta = theano.shared(np.asarray(rng.uniform(low=-np.pi,
high=np.pi,
size=(3, n_hidden)),
dtype=theano.config.floatX),
name='theta')
# STEPH: theta is used in recurrence several times (~W)
bucket = np.sqrt(3. / 2 / n_hidden)
h_0 = theano.shared(np.asarray(rng.uniform(low=-bucket,
high=bucket,
size=(1, 2 * n_hidden)),
dtype=theano.config.floatX),
name='h_0')
# STEPH: special way of initialising hidden state
parameters = [V, U, hidden_bias, reflection, out_bias, theta, h_0]
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
index_permute = np.random.permutation(n_hidden)
# STEPH: permutation used in recurrence (~W)
index_permute_long = np.concatenate((index_permute, index_permute + n_hidden))
# STEPH: do the same permutation to both real and imaginary parts
swap_re_im = np.concatenate((np.arange(n_hidden, 2*n_hidden), np.arange(n_hidden)))
# STEPH: this is a permutation which swaps imaginary and real indices
# define the recurrence used by theano.scan
def recurrence(x_t, y_t, h_prev, cost_prev, acc_prev, theta, V, hidden_bias, out_bias, U):
# Compute hidden linear transform
# STEPH: specific set of transformations, sliiightly not that important
step1 = times_diag(h_prev, n_hidden, theta[0,:], swap_re_im)
step2 = do_fft(step1, n_hidden)
step3 = times_reflection(step2, n_hidden, reflection[0,:])
step4 = vec_permutation(step3, index_permute_long)
step5 = times_diag(step4, n_hidden, theta[1,:], swap_re_im)
step6 = do_ifft(step5, n_hidden)
step7 = times_reflection(step6, n_hidden, reflection[1,:])
step8 = times_diag(step7, n_hidden, theta[2,:], swap_re_im)
hidden_lin_output = step8
# STEPH: hidden_lin_output isn't complex enough to have its own name
# in the other models
# Compute data linear transform
if loss_function == 'CE':
data_lin_output = V[T.cast(x_t, 'int32')]
else:
data_lin_output = T.dot(x_t, V)
# Total linear output
lin_output = hidden_lin_output + data_lin_output
# Apply non-linearity ----------------------------
# scale RELU nonlinearity
modulus = T.sqrt(lin_output**2 + lin_output[:, swap_re_im]**2)
# STEPH: I think this comes to twice the modulus...
# TODO: check that
rescale = T.maximum(modulus + T.tile(hidden_bias, [2]).dimshuffle('x', 0), 0.) / (modulus + 1e-5)
h_t = lin_output * rescale
if out_every_t:
lin_output = T.dot(h_t, U) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t
# compute hidden states
# STEPH: the same as in tanhRNN, here (except U ~ out_mat)
h_0_batch = T.tile(h_0, [x.shape[1], 1])
non_sequences = [theta, V, hidden_bias, out_bias, U]
if out_every_t:
sequences = [x, y]
else:
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
outputs_info=[h_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
[hidden_states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], U) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return [x, y], parameters, costs
# STEPH: note that tanhRNN and IRNN return 'inputs' (= [x, y]), whereas
# complex_RNN and LSTM return [x, y]... I think this should not matter
# as x and y are (in theory) unchanged, but I'm still making a note of it.
#
def orthogonal_RNN(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE', basis=None):
np.random.seed(1234)
rng = np.random.RandomState(1234)
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
inputs = [x, y]
# ---- encoder ---- #
V = initialize_matrix(n_input, n_hidden, 'V', rng)
# ---- decoder ---- #
U = initialize_matrix(n_hidden, n_output, 'U', rng)
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX), name='out_bias')
# ---- hidden part ---- #
dim_of_lie_algebra = n_hidden*(n_hidden-1)/2
lambdas = theano.shared(np.asarray(rng.uniform(low=-1,
high=1,
size=(dim_of_lie_algebra,)),
dtype=theano.config.floatX),
name='lambdas')
# warning: symbolic_basis is expensive, memory-wise!
if basis is None:
symbolic_basis = theano.shared(np.asarray(rng.normal(size=(dim_of_lie_algebra,
n_hidden,
n_hidden)),
dtype=theano.config.floatX),
name='symbolic_basis')
else:
symbolic_basis = theano.shared(basis, name='symbolic_basis')
# here it is!
#O = T.expm(T.dot(lambdas, symbolic_basis))
# YOLO
#O = T.tensordot(lambdas, symbolic_basis, axes=[0, 0])
#O = lambdas[0]*symbolic_basis[0] + lambdas[10]*symbolic_basis[10]
O = lambdas[dim_of_lie_algebra-1]*symbolic_basis[0]
#lambdas[n_hidden*(n_hidden-1)/2 -1]*symbolic_basis[n_hidden*(n_hidden-1)/2 -1]
# RIDICULOUS HACK THEANO IS WEIRD
#for k in xrange(1, n_hidden*(n_hidden-1)/2):
# O += lambdas[k]*symbolic_basis[k]
# pdb.set_trace()
#O = T.eye(n_hidden, n_hidden)
# END YOLO
# TODO: check maths on bucket
bucket = np.sqrt(3. / 2 / n_hidden)
h_0 = theano.shared(np.asarray(rng.uniform(low=-bucket,
high=bucket,
size=(1, n_hidden)),
dtype=theano.config.floatX),
name='h_0')
hidden_bias = theano.shared(np.asarray(rng.uniform(low=-0.01,
high=0.01,
size=(n_hidden,)),
dtype=theano.config.floatX),
name='hidden_bias')
# ---- all the parameters! ---- #
parameters = [V, U, out_bias, lambdas, h_0, hidden_bias]
def recurrence(x_t, y_t, h_prev, cost_prev, acc_prev, V, O, hidden_bias, out_bias, U):
if loss_function == 'CE':
# STEPH: why is this cast here???
data_lin_output = V[T.cast(x_t, 'int32')]
else:
data_lin_output = T.dot(x_t, V)
h_t = T.nnet.relu(T.dot(h_prev, O) + data_lin_output + hidden_bias.dimshuffle('x', 0))
if out_every_t:
lin_output = T.dot(h_t, U) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t
# compute hidden states
h_0_batch = T.tile(h_0, [x.shape[1], 1])
non_sequences = [V, O, hidden_bias, out_bias, U]
if out_every_t:
sequences = [x, y]
else:
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
outputs_info=[h_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
[hidden_states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], U) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return inputs, parameters, costs
def general_unitary_RNN(n_input, n_hidden, n_output, input_type='real', out_every_t=False, loss_function='CE'):
# STEPH: hey, it's mine! copying proclivity towards boilerplate from rest
# of code: this is derived from complex_RNN!
np.random.seed(1234)
rng = np.random.RandomState(1234)
# TODO: all from here (requires some engineering thoughts)
# TODO TODO TODO
# Initialize parameters: theta, V_re, V_im, hidden_bias, U, out_bias, h_0
V = initialize_matrix(n_input, 2*n_hidden, 'V', rng)
U = initialize_matrix(2 * n_hidden, n_output, 'U', rng)
# STEPH: U was previously known as out_mat
hidden_bias = theano.shared(np.asarray(rng.uniform(low=-0.01,
high=0.01,
size=(n_hidden,)),
dtype=theano.config.floatX),
name='hidden_bias')
# STEPH: hidden bias is simply initialised differently in this case
reflection = initialize_matrix(2, 2*n_hidden, 'reflection', rng)
# STEPH: part of recurrence (~W)
out_bias = theano.shared(np.zeros((n_output,), dtype=theano.config.floatX), name='out_bias')
theta = theano.shared(np.asarray(rng.uniform(low=-np.pi,
high=np.pi,
size=(3, n_hidden)),
dtype=theano.config.floatX),
name='theta')
# STEPH: theta is used in recurrence several times (~W)
bucket = np.sqrt(3. / 2 / n_hidden)
h_0 = theano.shared(np.asarray(rng.uniform(low=-bucket,
high=bucket,
size=(1, 2 * n_hidden)),
dtype=theano.config.floatX),
name='h_0')
# STEPH: special way of initialising hidden state
parameters = [V, U, hidden_bias, reflection, out_bias, theta, h_0]
x, y = initialize_data_nodes(loss_function, input_type, out_every_t)
index_permute = np.random.permutation(n_hidden)
# STEPH: permutation used in recurrence (~W)
index_permute_long = np.concatenate((index_permute, index_permute + n_hidden))
# STEPH: do the same permutation to both real and imaginary parts
swap_re_im = np.concatenate((np.arange(n_hidden, 2*n_hidden), np.arange(n_hidden)))
# STEPH: this is a permutation which swaps imaginary and real indices
# define the recurrence used by theano.scan
def recurrence(x_t, y_t, h_prev, cost_prev, acc_prev, theta, V, hidden_bias, out_bias, U):
# Compute hidden linear transform
# STEPH: specific set of transformations, sliiightly not that important
step1 = times_diag(h_prev, n_hidden, theta[0,:], swap_re_im)
step2 = do_fft(step1, n_hidden)
step3 = times_reflection(step2, n_hidden, reflection[0,:])
step4 = vec_permutation(step3, index_permute_long)
step5 = times_diag(step4, n_hidden, theta[1,:], swap_re_im)
step6 = do_ifft(step5, n_hidden)
step7 = times_reflection(step6, n_hidden, reflection[1,:])
step8 = times_diag(step7, n_hidden, theta[2,:], swap_re_im)
hidden_lin_output = step8
# STEPH: hidden_lin_output isn't complex enough to have its own name
# in the other models
# Compute data linear transform
if loss_function == 'CE':
data_lin_output = V[T.cast(x_t, 'int32')]
else:
data_lin_output = T.dot(x_t, V)
# Total linear output
lin_output = hidden_lin_output + data_lin_output
# Apply non-linearity ----------------------------
# scale RELU nonlinearity
modulus = T.sqrt(lin_output**2 + lin_output[:, swap_re_im]**2)
# STEPH: I think this comes to twice the modulus...
# TODO: check that
rescale = T.maximum(modulus + T.tile(hidden_bias, [2]).dimshuffle('x', 0), 0.) / (modulus + 1e-5)
h_t = lin_output * rescale
if out_every_t:
lin_output = T.dot(h_t, U) + out_bias.dimshuffle('x', 0)
cost_t, acc_t = compute_cost_t(lin_output, loss_function, y_t)
else:
cost_t = theano.shared(np.float32(0.0))
acc_t = theano.shared(np.float32(0.0))
return h_t, cost_t, acc_t
# compute hidden states
# STEPH: the same as in tanhRNN, here (except U ~ out_mat)
h_0_batch = T.tile(h_0, [x.shape[1], 1])
non_sequences = [theta, V, hidden_bias, out_bias, U]
if out_every_t:
sequences = [x, y]
else:
sequences = [x, T.tile(theano.shared(np.zeros((1,1), dtype=theano.config.floatX)), [x.shape[0], 1, 1])]
outputs_info=[h_0_batch, theano.shared(np.float32(0.0)), theano.shared(np.float32(0.0))]
[hidden_states, cost_steps, acc_steps], updates = theano.scan(fn=recurrence,
sequences=sequences,
non_sequences=non_sequences,
outputs_info=outputs_info)
if not out_every_t:
lin_output = T.dot(hidden_states[-1,:,:], U) + out_bias.dimshuffle('x', 0)
costs = compute_cost_t(lin_output, loss_function, y)
else:
cost = cost_steps.mean()
accuracy = acc_steps.mean()
costs = [cost, accuracy]
return [x, y], parameters, costs
# STEPH: note that tanhRNN and IRNN return 'inputs' (= [x, y]), whereas
# complex_RNN and LSTM return [x, y]... I think this should not matter
# as x and y are (in theory) unchanged, but I'm still making a note of it.