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eca.py
491 lines (398 loc) · 16.4 KB
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eca.py
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from time import time
import numpy as np
import theano
import theano.tensor as T
from theano.sandbox.linalg.ops import diag as theano_diag
from utils import rect
from theano.ifelse import ifelse
DEBUG_INFO = False
PRINT_CONVERGENCE = False
FLOATX = theano.config.floatX
def lerp(old, new, min_tau=0.0, en=None):
"""
Return new interpolated value and a relative difference
"""
diff = T.mean(T.sqr(new) - T.sqr(old), axis=1, keepdims=True)
rel_diff = diff / (T.mean(T.sqr(old), axis=1, keepdims=True) + 1e-5)
t = rel_diff * 20.
t = T.where(t < 5, 5, t)
t = T.where(t > 100, 100, t)
t = t + min_tau
if en is not None:
lmbd = T.diagonal(en).dimshuffle(0, 'x') * (1. / t)
else:
lmbd = 1. / t
return ((1 - lmbd) * old + lmbd * new,
t, rel_diff)
class Signal(object):
""" Object that represents any kind of state U, X, X_y, z, ...
"""
def __init__(self, n, k, name, next, layer):
rng = np.random.RandomState(0)
self.var = theano.shared(np.float32(rng.uniform(size=(n, k))), name=name)
self.n = n
self.k = k
self.name = name
self.modulation = None
self.next = next
self.layer = layer
def val(self):
return self.var.get_value()
def set_modulation(self, mod):
assert self.modulation is None
self.modulation = mod
def variance(self):
return np.average(np.log(np.var(self.var.get_value(), axis=1)))
def energy(self):
return np.average(np.square(self.var.get_value()), axis=1)
class LayerBase(object):
def __init__(self, name, n, prev):
self.n = n
self.m = n if prev is [] else [p.n for p in prev]
self.name = name
self.signal_key = name
# Nonlinearity applied to the estimate coming from next layer
self.nonlin_est = lambda x: x
self.nonlin = None
self.merge_op = None
self.enabled = theano.shared(1, name='enable')
self.enable = lambda: self.enabled.set_value(1)
self.disable = lambda: self.enabled.set_value(0)
self.persistent = False
self.E_XU = []
self.phi = []
self.prev = prev
self.next = []
for p in self.prev:
assert self not in p.next
p.next += [self]
def signal(self, signals):
key = self.signal_key
if key not in signals.signal:
# TODO: Might want to support several next signals
next_sig = self.next[0].signal(signals) if len(self.next) > 0 else None
s = Signal(self.n, signals.k, self.name, next_sig, self)
signals.signal[key] = s
return signals.signal[key]
def compile_prop_f(self, signals, has_input, min_tau=0.0):
tau_in = T.scalar('min_tau', dtype=FLOATX)
inputs = [tau_in]
x = self.signal(signals)
# Get estimate of the state from layer above
estimate = self.estimate(signals)
# Feedforward originates from previous layer's state or given input
if not has_input:
feedforward = self.feedforward(signals)
has_nans = T.as_tensor_variable(0)
nans = 0.0
else:
input_t = T.matrix('input', dtype=FLOATX)
inputs += [input_t]
nans = T.isnan(input_t)
has_nans = T.any(nans)
feedforward = T.where(nans, 0.0, input_t)
self.info('Compiling propagation: [%6s] -> %4s <- [%6s]' %
(",".join([p.name for p in self.prev] if self.prev else 'u/y'),
self.name,
",".join([p.name for p in self.next] if self.next else '')))
# Apply nonlinearity to feedforward path only
if self.nonlin:
feedforward = self.nonlin(feedforward)
if self.merge_op:
assert not self.persistent, 'cannot combine with merge_op'
new_value = self.merge_op(feedforward, estimate)
elif self.persistent:
new_value = feedforward
else:
new_value = feedforward - estimate
# If predicting missing values, force them to zero in residual so
# that they don't influence learning
new_value = ifelse(has_nans, T.where(nans, 0.0, new_value), new_value)
(new_X, t, d) = lerp(x.var, new_value, tau_in)
d = T.max(d)
updates = [(x.var, ifelse(self.enabled, new_X, x.var))]
return theano.function(inputs=inputs,
outputs=d,
updates=updates)
def estimate(self, signals):
""" Ask the next for feedback and apply nonlinearity """
if self.next == []:
return 0.0
fb = [n.feedback(signals, self) for n in self.next]
return self.nonlin_est(T.sum(fb, axis=0))
def feedback(self, signals, to):
phi = self.phi[self.prev.index(to)]
x = T.dot(phi, self.signal(signals).var)
return ifelse(self.enabled, x, T.zeros_like(x))
def feedforward(self, signals):
xs = []
for i, p in enumerate(self.prev):
sig = p.signal(signals).var
xs += [T.dot(self.phi[i].T, sig)]
x = T.sum(xs, axis=0)
return ifelse(self.enabled, x, T.zeros_like(x))
def info(self, str):
if DEBUG_INFO:
print '%5s:' % self.name, str
class Layer(LayerBase):
def __init__(self, name, n, prev, nonlin, min_tau=0.0, stiffx=1.0):
assert prev is not None
if type(prev) is not list:
prev = [prev]
super(Layer, self).__init__(name, n, prev)
n = self.n
rng = np.random.RandomState(0)
self.nonlin = nonlin
self.stiffx = stiffx
self.min_tau = theano.shared(np.float32(min_tau))
for p in prev:
m = p.n
rand_init = np.float32(rng.uniform(size=(n, m)) - 0.5)
self.E_XU += [theano.shared(rand_init, name='E_' + name + p.name)]
self.phi += [theano.shared(rand_init.T, name='phi' + name)]
self.Q = theano.shared(np.identity(n, dtype=FLOATX), name='Q' + name)
self.E_XX = theano.shared(np.identity(n, dtype=FLOATX), name='E_' + name * 2)
def compile_adapt_f(self, signals):
x = self.signal(signals)
x_prev = [p.signal(signals) for p in self.prev]
assert np.all([x.k == xp.k for xp in x_prev])
assert self.m == [xp.n for xp in x_prev]
assert x.n == self.n
k = np.float32(x.k)
# Modulate x
if x.modulation is not None:
x_ = x.var * T.as_tensor_variable(x.modulation)
else:
x_ = x.var
updates = []
upd = lambda en, old, new: [(old, ifelse(en, new, old))]
E_XX_new, _, d = lerp(self.E_XX, T.dot(x_, x_.T) / k, self.min_tau)
updates += upd(self.enabled, self.E_XX, E_XX_new)
b = 1.
d = T.diagonal(E_XX_new)
stiff = T.scalar('stiffnes', dtype=FLOATX)
Q_new = theano_diag(b / T.where(d < stiff * self.stiffx,
stiff * self.stiffx, d))
updates += upd(self.enabled, self.Q, Q_new)
for i, x_p in enumerate(x_prev):
E_XU_new, _, d_ = lerp(self.E_XU[i], T.dot(x_, x_p.var.T) / k,
self.min_tau)
updates += upd(self.enabled, self.E_XU[i], E_XU_new)
d = T.maximum(d, d_)
updates += upd(self.enabled, self.phi[i], T.dot(Q_new, E_XU_new).T)
self.info('Compile layer update between: ' + self.name + ' and '
+ ', '.join([p.name for p in self.prev]))
return theano.function(
inputs=[stiff],
outputs=d,
updates=updates)
def __str__(self):
return "Layer %3s (%d) %.2f, %.2f, %s" % (self.name, self.n,
self.stiffx,
self.min_tau.get_value(),
self.nonlin)
class Input(LayerBase):
def __init__(self, name, n, persistent=False):
super(Input, self).__init__(name, n, [])
self.persistent = persistent
def compile_adapt_f(self, signals):
return lambda stiff: 0.0
def __str__(self):
return "Input %3s (%d)" % (self.name, self.n)
class RegressionLayer(LayerBase):
def __init__(self, name, n, prev, nonlin,
min_tau=0.0, stiffx=1.0, merge_op=None):
super(RegressionLayer, self).__init__(name, n, [])
assert len(prev) == 2
self.u_side = Layer(name + 'u', n, prev[0], lambda x: x, 0.0)
self.y_side = Layer(name + 'y', n, prev[1], lambda x: x, 0.0)
self.u_side.signal_key = name
self.y_side.signal_key = name
# TODO: figure out how to expose bot u_side and y_side phi
self.phi = self.u_side.phi
# To make u and y update the same shared state, it must happen
# simultaneously, so route u to ask y for its feedback as an estimate.
self.u_side.estimate = lambda i: self.y_side.feedforward(i)
#self.u_side.merge_op = lambda fromu, fromy: nonlin(fromy + fromu)
#self.u_side.merge_op = lambda fromu, fromy: nonlin(fromu)
self.u_side.merge_op = lambda fromu, fromy: nonlin(-fromy + fromu)
#self.u_side.merge_op = lambda fromu, fromy: T.sqrt(fromu * fromy + 0.1)
if merge_op:
self.u_side.merge_op = merge_op
# Disable state updates on the y side so that X is updated only once
self.y_side.compile_prop_f = lambda s, is_input: lambda min_tau: 0.0
def compile_adapt_f(self, signals):
assert False, "should not be called"
def __str__(self):
return super(RegressionLayer, self).__str__() + str(self.merge_op)
class CCALayer(Layer):
def __init__(self, name, (m, n)):
self.E_ZZ = []
super(CCALayer, self).__init__(name, (m, n), nonlin=None)
# Phi of this layer is not in use, mark it as nan
self.phi = np.zeros((1, 1))
# TODO: Update
def update_state(self, id, input, min_tau):
z = self.X[id]
E_ZZ = self.E_ZZ[id]
assert input is None, "CCA state cannot use input"
assert self.next is None, 'CCA cannot have next items'
assert len(self.prev) == 2, 'CCA should have exactly 2 prevs'
assert z.n == self.n, "Output dim mismatch"
# Update state-specific E_ZZ and calculate q for z update
(E_ZZ.value, di) = lerp(E_ZZ.value,
np.dot(z.value, z.value.T) / z.k)
assert E_ZZ.value.shape == (1, 1), 'E_ZZ is not a scalar!?'
b = 1.
q = b / np.max([0.05, E_ZZ.value[0, 0]])
# Update z
[x1, x2] = [self.prev[j].X[id].value for j in (0, 1)]
new_value = q * np.sum(x1 * x2, axis=0)
(z.value, dz) = lerp(z.value, new_value)
self.E_XU = None
return np.max((np.abs(di), np.average(np.abs(dz))))
# TODO: Update
def feedback(self, id, prev=None):
assert prev is not None, 'CCA needs prev'
assert len(self.prev) == 2, 'CCA should have exactly 2 prevs'
# XXX: Uncomment the following to avoid signal propagation
# back from CCA layer
#return np.zeros(())
z = self.X[id]
# Find the other branch connecting to this z
x_other = list(set(self.prev) - set([prev]))[0]
# This is roughly: x_u_delta = self.Q * x_y * z
phi = self.Q * x_other.X[id].value
return phi * z.value
class ECA(object):
"""
Constructs chains of layers connected together. Each layer contains phi
matrix and corresponding signal vector X.
Typical loop u -- U -- X would represented by two of these layers; one for
U and another one for X.
U branch would look something like this, where --- indicates signal
and /\\/ mapping:
------------ u
//|\//\\/\|/ phi_0 = identity
-------------- layer x0 = U = phi_1^T x-1 - phi_1 X1 = u - phi_1 X1
//|\//\\/\|/ phi_1 (learned mapping)
-------------- layer x1 = phi_1^T x0 - phi_2 x2
//|\//\\/\|/ phi_2 (learned mapping)
-------------- layer x2 = phi_2^T x1 - phi_3 x3
.
.
.
"""
def __init__(self):
self.U = None
self.Y = None
self.structure()
assert self.U is not None
# TODO: Add more checks for layer structure, e.g. avoid loops
for l in self.iter_layers():
print l
def structure(self):
raise NotImplemented
def iter_layers(self, skip_inputs=False):
def recurse(l):
if not l:
return
yield l
for n in l.next:
for x in recurse(n):
yield x
s = set(list(recurse(self.U)) + list(recurse(self.Y)))
if skip_inputs:
s -= set([self.U, self.Y])
return s
def new_signals(self, k):
return Signals(k, self)
def first_phi(self):
# index is omitted for now, and the lowest layer is plotted
return self.U.next[0].phi[0].get_value()
def phi_norms(self):
f = lambda l: (l.name, (np.linalg.norm(l.phi[0].get_value(), axis=0)))
return map(f, self.iter_layers(skip_inputs=True))
class SimpleECA(ECA):
""" Simplest possible one loop system """
def __init__(self, n_input, n_layer):
self.n_input = n_input
self.n_layer = n_layer
super(SimpleECA, self).__init__()
def structure(self):
self.U = Input('U', self.n_input)
self.X = Layer('X', self.n_layer, self.U, rect, 1.0)
class Signals(object):
def __init__(self, k, eca):
self.mdl = eca
self.k = k
self.adaptf = {}
self.propf = {}
self.signal = {}
self.name = None
print 'Creating signals with k =', k
for l in eca.iter_layers():
is_input = l is eca.U or l is eca.Y
self.propf[l.name] = l.compile_prop_f(self, is_input)
self.U = self.signal[eca.U.name]
self.Y = self.signal[eca.Y.name] if eca.Y else None
def adapt_layers(self, stiffness):
# Compile adaptation functions lazily
if self.adaptf == {}:
for l in self.mdl.iter_layers():
self.adaptf[l.name] = l.compile_adapt_f(self)
for l in self.mdl.iter_layers():
self.adaptf[l.name](stiffness)
def propagate(self, u, y, min_tau=0.0):
assert u is None or self.k == u.shape[1], "Sample size mismatch"
assert y is None or self.k == y.shape[1], "Sample size mismatch"
d = 0.0
for l in self.mdl.iter_layers():
args = [min_tau]
args += [u] if l is self.mdl.U else []
args += [y] if l is self.mdl.Y else []
d = max(d, self.propf[l.name](*args))
return d
def converge(self, u, y, min_tau=0.0, d_limit=1e-3):
t = 20
t_limit, i_limit = time() + t, 200
d, i, = np.inf, 0
while d > d_limit and time() < t_limit and i < i_limit:
d = self.propagate(u, y, min_tau)
i += 1
if PRINT_CONVERGENCE:
print 'Converged in', "%.1f" % (time() - t_limit + t), 's,',
print i, 'iters, delta %.4f' % d,
print 'Limits: i:', i_limit, 't:', t, 'd:', d_limit
return self
def x_est(self, no_eval=False):
# TODO: Might not be reliable, fix.
l = self.mdl.U
while l.next and not isinstance(l.next, CCALayer):
l = l.next
# Should this be Xbar or the feedforward ?
v = l.signal(self).var
return v if no_eval else v.eval()
def u_est(self, no_eval=False):
v = self.mdl.U.estimate(self)
return v if no_eval else v.eval()
def y_est(self, no_eval=False):
v = self.mdl.Y.estimate(self)
return v if no_eval else v.eval()
def u_err(self, u):
return T.mean(T.sqr(self.u_est(no_eval=True) - u)).eval()
def first_phi(self):
# index is omitted for now, and the lowest layer is plotted
return self.mdl.U.next.phi[0].get_value()
def variance(self, states=None):
f = lambda s: (s.name, s.variance())
return map(f, self.signal.values())
def energy(self):
f = lambda s: (s.name, np.average(s.energy()))
return map(f, self.signal.values())
def avg_levels(self):
f = lambda s: (s.name, np.linalg.norm(np.average(s.var.get_value(), axis=1)))
return map(f, self.signal.values())
def phi_norms(self):
f = lambda l: (l.name, (np.linalg.norm(l.phi[0].get_value(), axis=0)))
return map(f, self.iter_layers(skip_inputs=True))