def create_vae(batch_size, Ds, seed, leakiness=0.1, lr=0.0002, scaler=1):
x = T.Placeholder([batch_size, Ds[-1]], 'float32')
# ENCODER
enc = encoder(x, Ds[0])
mu = enc[-1][:, :Ds[0]]
logvar = enc[-1][:, Ds[0]:]
var = T.exp(logvar)
z = mu + T.exp(0.5 * logvar) * T.random.randn((batch_size, Ds[0]))
z_ph = T.Placeholder((batch_size, Ds[0]), 'float32')
# DECODER
Ws, bs = init_weights(Ds, seed, scaler)
Ws = [T.Variable(w) for w in Ws]
bs = [T.Variable(b) for b in bs]
logvar_x = T.Variable(T.zeros(1), name='logvar_x')
var_x = T.exp(logvar_x)
h, h_ph = [z], [z_ph]
for w, b in zip(Ws[:-1], bs[:-1]):
h.append(T.matmul(h[-1], w.transpose()) + b)
h.append(h[-1] * relu_mask(h[-1], leakiness))
h_ph.append(T.matmul(h_ph[-1], w.transpose()) + b)
h_ph.append(h_ph[-1] * relu_mask(h_ph[-1], leakiness))
h.append(T.matmul(h[-1], Ws[-1].transpose()) + bs[-1])
h_ph.append(T.matmul(h_ph[-1], Ws[-1].transpose()) + bs[-1])
prior = sum([T.mean(w**2) for w in Ws], 0.) / cov_W\
+ sum([T.mean(v**2) for v in bs[:-1]], 0.) / cov_b
kl = 0.5 * (1 + logvar - var - mu ** 2).sum(1)
px = - 0.5 * (logvar_x + ((x - h[-1])**2 / var_x)).sum(1)
loss = - (px + kl).mean() + prior
variables = Ws + bs + sj.layers.get_variables(enc) + [logvar_x]
opti = sj.optimizers.Adam(loss, lr, params=variables)
train = sj.function(x, outputs=loss, updates=opti.updates)
g = sj.function(z_ph, outputs=h_ph[-1])
params = sj.function(outputs = Ws + bs + [T.exp(logvar_x) * T.ones(Ds[-1])])
get_varx = sj.function(outputs = var_x)
output = {'train': train, 'g':g, 'params':params}
output['model'] = 'VAE'
output['varx'] = get_varx
output['kwargs'] = {'batch_size': batch_size, 'Ds':Ds, 'seed':seed,
'leakiness':leakiness, 'lr':lr, 'scaler':scaler,
'prior': sj.function(outputs=prior)}
def sample(n):
samples = []
for i in range(n // batch_size):
samples.append(g(np.random.randn(batch_size, Ds[0])))
return np.concatenate(samples)
output['sample'] = sample
return output
def create_glo(batch_size, Ds, seed, leakiness=0.1, lr=0.0002, scaler=1,
GLO=False):
x = T.Placeholder([batch_size, Ds[-1]], 'float32')
z = T.Variable(T.random.randn((batch_size, Ds[0])))
logvar_x = T.Variable(T.ones(1))
# DECODER
Ws, bs = init_weights(Ds, seed, scaler)
Ws = [T.Variable(w) for w in Ws]
bs = [T.Variable(b) for b in bs]
h = [z]
for w, b in zip(Ws[:-1], bs[:-1]):
h.append(T.matmul(h[-1], w.transpose()) + b)
h.append(h[-1] * relu_mask(h[-1], leakiness))
h.append(T.matmul(h[-1], Ws[-1].transpose()) + bs[-1])
# LOSS
prior = sum([T.sum(w**2) for w in Ws], 0.) / cov_W + sum([T.sum(v**2) for v in bs[:-1]], 0.) / cov_b
if GLO:
loss = T.sum((x - h[-1])**2) / batch_size + prior
variables = Ws + bs
else:
loss = Ds[-1] * logvar_x.sum() + T.sum((x - h[-1])**2 / T.exp(logvar_x)) / batch_size + (z**2).sum() / batch_size + prior
variables = Ws + bs
prior = sum([(b**2).sum() for b in bs], 0.) / cov_b\
+ sum([(w**2).sum() for w in Ws], 0.) / cov_W
opti = sj.optimizers.Adam(loss + prior, lr, params=variables)
infer = sj.optimizers.Adam(loss, lr, params=[z])
estimate = sj.function(x, outputs=z, updates=infer.updates)
train = sj.function(x, outputs=loss, updates=opti.updates)
lossf = sj.function(x, outputs=loss)
params = sj.function(outputs = Ws + bs + [T.ones(Ds[-1]) * T.exp(logvar_x)])
output = {'train': train, 'estimate':estimate, 'params':params}
output['reset'] = lambda v: z.assign(v)
if GLO:
output['model'] = 'GLO'
else:
output['model'] = 'HARD'
output['loss'] = lossf
output['kwargs'] = {'batch_size': batch_size, 'Ds':Ds, 'seed':seed,
'leakiness':leakiness, 'lr':lr, 'scaler':scaler}
return output
def create_fns(input, in_signs, Ds):
cumulative_units = np.concatenate([[0], np.cumsum(Ds[:-1])])
Ws = [sj.initializers.he((j, i)) for j, i in zip(Ds[1:], Ds[:-1])]
bs = [sj.initializers.he((j,)) for j in Ds[1:]]
A_w = [T.eye(Ds[0])]
B_w = [T.zeros(Ds[0])]
A_q = [T.eye(Ds[0])]
B_q = [T.zeros(Ds[0])]
maps = [input]
signs = []
masks = [T.ones(Ds[0])]
in_masks = T.where(T.concatenate([T.ones(Ds[0]), in_signs]) > 0, 1.,
0.1)
for w, b in zip(Ws[:-1], bs[:-1]):
pre_activation = T.matmul(w, maps[-1]) + b
signs.append(T.sign(pre_activation))
masks.append(T.where(pre_activation > 0, 1., 0.1))
maps.append(pre_activation * masks[-1])
maps.append(T.matmul(Ws[-1], maps[-1]) + bs[-1])
# compute per region A and B
for start, end, w, b, m in zip(cumulative_units[:-1],
cumulative_units[1:], Ws, bs, masks):
A_w.append(T.matmul(w * m, A_w[-1]))
B_w.append(T.matmul(w * m, B_w[-1]) + b)
A_q.append(T.matmul(w * in_masks[start:end], A_q[-1]))
B_q.append(T.matmul(w * in_masks[start:end], B_q[-1]) + b)
signs = T.concatenate(signs)
ineq_b = T.concatenate(B_w[1:-1])
ineq_A = T.vstack(A_w[1:-1])
inequalities = T.hstack([ineq_b[:, None], ineq_A])
inequalities = inequalities * signs[:, None] / T.linalg.norm(ineq_A, 2,
1, keepdims=True)
inequalities_code = T.hstack([T.concatenate(B_q[1:-1])[:, None],
T.vstack(A_q[1:-1])])
inequalities_code = inequalities_code * in_signs[:, None]
f = sj.function(input, outputs=[maps[-1], A_w[-1], B_w[-1],
inequalities, signs])
g = sj.function(in_signs, outputs=[A_q[-1], B_q[-1]])
all_g = sj.function(in_signs, outputs=inequalities_code)
h = sj.function(input, outputs=maps[-1])
return f, g, h, all_g
def generate_gaussian_filterbank(N, M, J, f0, f1, modes=1):
# gaussian parameters
freqs = get_scaled_freqs(f0, f1, J)
freqs *= (J - 1) * 10
if modes > 1:
other_modes = np.random.randint(0, J, J * (modes - 1))
freqs = np.concatenate([freqs, freqs[other_modes]])
# crate the average vectors
mu_init = np.stack([freqs, 0.1 * np.random.randn(J * modes)], 1)
mu = T.Variable(mu_init.astype('float32'), name='mu')
# create the covariance matrix
cor = T.Variable(0.01 * np.random.randn(J * modes).astype('float32'),
name='cor')
sigma_init = np.stack([freqs / 6, 1. + 0.01 * np.random.randn(J * modes)],
1)
sigma = T.Variable(sigma_init.astype('float32'), name='sigma')
# create the mixing coefficients
mixing = T.Variable(np.ones((modes, 1, 1)).astype('float32'))
# now apply our parametrization
coeff = T.stop_gradient(T.sqrt((T.abs(sigma) + 0.1).prod(1))) * 0.95
Id = T.eye(2)
cov = Id * T.expand_dims((T.abs(sigma)+0.1),1) +\
T.flip(Id, 0) * (T.tanh(cor) * coeff).reshape((-1, 1, 1))
cov_inv = T.linalg.inv(cov)
# get the gaussian filters
time = T.linspace(-5, 5, M)
freq = T.linspace(0, J * 10, N)
x, y = T.meshgrid(time, freq)
grid = T.stack([y.flatten(), x.flatten()], 1)
centered = grid - T.expand_dims(mu, 1)
# asdf
gaussian = T.exp(-(T.matmul(centered, cov_inv)**2).sum(-1))
norm = T.linalg.norm(gaussian, 2, 1, keepdims=True)
gaussian_2d = T.abs(mixing) * T.reshape(gaussian / norm, (J, modes, N, M))
return gaussian_2d.sum(1, keepdims=True), mu, cor, sigma, mixing
def create_fns(input,
in_signs,
Ds,
x,
m0,
m1,
m2,
batch_in_signs,
alpha=0.1,
sigma=1,
sigma_x=1,
lr=0.0002):
cumulative_units = np.concatenate([[0], np.cumsum(Ds[:-1])])
BS = batch_in_signs.shape[0]
Ws = [
T.Variable(sj.initializers.glorot((j, i)) * sigma)
for j, i in zip(Ds[1:], Ds[:-1])
]
bs = [T.Variable(sj.initializers.he((j,)) * sigma) for j in Ds[1:-1]]\
+ [T.Variable(T.zeros((Ds[-1],)))]
A_w = [T.eye(Ds[0])]
B_w = [T.zeros(Ds[0])]
A_q = [T.eye(Ds[0])]
B_q = [T.zeros(Ds[0])]
batch_A_q = [T.eye(Ds[0]) * T.ones((BS, 1, 1))]
batch_B_q = [T.zeros((BS, Ds[0]))]
maps = [input]
signs = []
masks = [T.ones(Ds[0])]
in_masks = T.where(T.concatenate([T.ones(Ds[0]), in_signs]) > 0, 1., alpha)
batch_in_masks = T.where(
T.concatenate([T.ones((BS, Ds[0])), batch_in_signs], 1) > 0, 1., alpha)
for w, b in zip(Ws[:-1], bs[:-1]):
pre_activation = T.matmul(w, maps[-1]) + b
signs.append(T.sign(pre_activation))
masks.append(T.where(pre_activation > 0, 1., alpha))
maps.append(pre_activation * masks[-1])
maps.append(T.matmul(Ws[-1], maps[-1]) + bs[-1])
# compute per region A and B
for start, end, w, b, m in zip(cumulative_units[:-1], cumulative_units[1:],
Ws, bs, masks):
A_w.append(T.matmul(w * m, A_w[-1]))
B_w.append(T.matmul(w * m, B_w[-1]) + b)
A_q.append(T.matmul(w * in_masks[start:end], A_q[-1]))
B_q.append(T.matmul(w * in_masks[start:end], B_q[-1]) + b)
batch_A_q.append(
T.matmul(w * batch_in_masks[:, None, start:end], batch_A_q[-1]))
batch_B_q.append((w * batch_in_masks[:, None, start:end]\
* batch_B_q[-1][:, None, :]).sum(2) + b)
batch_B_q = batch_B_q[-1]
batch_A_q = batch_A_q[-1]
signs = T.concatenate(signs)
inequalities = T.hstack(
[T.concatenate(B_w[1:-1])[:, None],
T.vstack(A_w[1:-1])]) * signs[:, None]
inequalities_code = T.hstack(
[T.concatenate(B_q[1:-1])[:, None],
T.vstack(A_q[1:-1])]) * in_signs[:, None]
#### loss
log_sigma2 = T.Variable(sigma_x)
sigma2 = T.exp(log_sigma2)
Am1 = T.einsum('qds,nqs->nqd', batch_A_q, m1)
Bm0 = T.einsum('qd,nq->nd', batch_B_q, m0)
B2m0 = T.einsum('nq,qd->n', m0, batch_B_q**2)
AAm2 = T.einsum('qds,qdu,nqup->nsp', batch_A_q, batch_A_q, m2)
inner = -(x * (Am1.sum(1) + Bm0)).sum(1) + (Am1 * batch_B_q).sum((1, 2))
loss_2 = (x**2).sum(1) + B2m0 + T.trace(AAm2, axis1=1, axis2=2).squeeze()
loss_z = T.trace(m2.sum(1), axis1=1, axis2=2).squeeze()
cst = 0.5 * (Ds[0] + Ds[-1]) * T.log(2 * np.pi)
loss = cst + 0.5 * Ds[-1] * log_sigma2 + inner / sigma2\
+ 0.5 * loss_2 / sigma2 + 0.5 * loss_z
mean_loss = loss.mean()
adam = sj.optimizers.NesterovMomentum(mean_loss, Ws + bs, lr, 0.9)
train_f = sj.function(batch_in_signs,
x,
m0,
m1,
m2,
outputs=mean_loss,
updates=adam.updates)
f = sj.function(input,
outputs=[maps[-1], A_w[-1], B_w[-1], inequalities, signs])
g = sj.function(in_signs, outputs=[A_q[-1], B_q[-1]])
all_g = sj.function(in_signs, outputs=inequalities_code)
h = sj.function(input, outputs=maps[-1])
return f, g, h, all_g, train_f, sigma2
def create_fns(batch_size, R, Ds, seed, leakiness=0.1, lr=0.0002, scaler=1,
var_x=1):
alpha = T.Placeholder((1,), 'float32')
x = T.Placeholder((Ds[0],), 'float32')
X = T.Placeholder((batch_size, Ds[-1]), 'float32')
signs = T.Placeholder((np.sum(Ds[1:-1]),), 'float32')
SIGNS = T.Placeholder((R, np.sum(Ds[1:-1])), 'float32')
m0 = T.Placeholder((batch_size, R), 'float32')
m1 = T.Placeholder((batch_size, R, Ds[0]), 'float32')
m2 = T.Placeholder((batch_size, R, Ds[0], Ds[0]), 'float32')
Ws, vs = init_weights(Ds, seed, scaler)
Ws = [T.Variable(w, name='W' + str(l)) for l, w in enumerate(Ws)]
vs = [T.Variable(v, name='v' + str(l)) for l, v in enumerate(vs)]
var_x = T.Variable(T.ones(Ds[-1]) * var_x)
var_z = T.Variable(T.ones(Ds[0]))
# create the placeholders
Ws_ph = [T.Placeholder(w.shape, w.dtype) for w in Ws]
vs_ph = [T.Placeholder(v.shape, v.dtype) for v in vs]
var_x_ph = T.Placeholder(var_x.shape, var_x.dtype)
############################################################################
# Compute the output of g(x)
############################################################################
maps = [x]
xsigns = []
masks = []
for w, v in zip(Ws[:-1], vs[:-1]):
pre_activation = T.matmul(w, maps[-1]) + v
xsigns.append(T.sign(pre_activation))
masks.append(relu_mask(pre_activation, leakiness))
maps.append(pre_activation * masks[-1])
xsigns = T.concatenate(xsigns)
maps.append(T.matmul(Ws[-1], maps[-1]) + vs[-1])
############################################################################
# compute the masks and then the per layer affine mappings
############################################################################
cumulative_units = np.cumsum([0] + Ds[1:])
xqs = relu_mask([xsigns[None, cumulative_units[i]:cumulative_units[i + 1]]
for i in range(len(Ds) - 2)], leakiness)
qs = relu_mask([signs[None, cumulative_units[i]:cumulative_units[i + 1]]
for i in range(len(Ds) - 2)], leakiness)
Qs = relu_mask([SIGNS[:, cumulative_units[i]:cumulative_units[i + 1]]
for i in range(len(Ds) - 2)], leakiness)
Axs, bxs = get_Abs(Ws, vs, xqs)
Aqs, bqs = get_Abs(Ws, vs, qs)
AQs, bQs = get_Abs(Ws, vs, Qs)
all_bxs = T.hstack(bxs[:-1]).transpose()
all_Axs = T.hstack(Axs[:-1])[0]
all_bqs = T.hstack(bqs[:-1]).transpose()
all_Aqs = T.hstack(Aqs[:-1])[0]
x_inequalities = T.hstack([all_Axs, all_bxs]) * xsigns[:, None]
q_inequalities = T.hstack([all_Aqs, all_bqs]) * signs[:, None]
############################################################################
# loss (E-step NLL)
############################################################################
Bm0 = T.einsum('nd,Nn->Nd', bQs[-1], m0)
B2m0 = T.einsum('nd,Nn->Nd', bQs[-1] ** 2, m0)
Am1 = T.einsum('nds,Nns->Nd', AQs[-1], m1)
ABm1 = T.einsum('nds,nd,Nns->Nd', AQs[-1], bQs[-1], m1)
Am2ATdiag = T.diagonal(T.einsum('nds,Nnsc,npc->Ndp', AQs[-1], m2, AQs[-1]),
axis1=1, axis2=2)
xAm1Bm0 = X * (Am1 + Bm0)
M2diag = T.diagonal(m2.sum(1), axis1=1, axis2=2)
prior = sum([T.mean(w**2) for w in Ws], 0.) / cov_W\
+ sum([T.mean(v**2) for v in vs[:-1]], 0.) / cov_b
loss = - 0.5 * (T.log(var_x).sum() + T.log(var_z).sum()\
+ (M2diag / var_z).sum(1).mean() + ((X ** 2 - 2 * xAm1Bm0 + B2m0\
+ Am2ATdiag + 2 * ABm1) / var_x).sum(1).mean())
mean_loss = - (loss + 0.5 * prior)
adam = sj.optimizers.SGD(mean_loss, 0.001, params=Ws + vs)
############################################################################
# update of var_x
############################################################################
update_varx = (X ** 2 - 2 * xAm1Bm0 + B2m0 + Am2ATdiag + 2 * ABm1).mean()\
* T.ones(Ds[-1])
update_varz = M2diag.mean() * T.ones(Ds[0])
############################################################################
# update for biases IT IS DONE FOR ISOTROPIC COVARIANCE MATRIX
############################################################################
FQ = get_forward(Ws, Qs)
update_vs = {}
for i in range(len(vs)):
if i < len(vs) - 1:
# now we forward each bias to the x-space except the ith
separated_bs = bQs[-1] - T.einsum('nds,s->nd', FQ[i], vs[i])
# compute the residual and apply sigma
residual = (X[:, None, :] - separated_bs) * m0[:, :, None]\
- T.einsum('nds,Nns->Nnd', AQs[-1], m1)
back_error = T.einsum('nds,nd->s', FQ[i], residual.mean(0))
whiten = T.einsum('ndc,nds,n->cs', FQ[i] , FQ[i], m0.mean(0))\
+ T.eye(back_error.shape[0]) / (Ds[i] * cov_b)
update_vs[vs[i]] = T.linalg.solve(whiten, back_error)
else:
back_error = (X - (Am1 + Bm0) + vs[-1])
update_vs[vs[i]] = back_error.mean(0)
############################################################################
# update for slopes IT IS DONE FOR ISOTROPIC COVARIANCE MATRIX
############################################################################
update_Ws = {}
for i in range(len(Ws)):
U = T.einsum('nds,ndc->nsc', FQ[i], FQ[i])
if i == 0:
V = m2.mean(0)
else:
V1 = T.einsum('nd,nq,Nn->ndq', bQs[i-1], bQs[i-1], m0)
V2 = T.einsum('nds,nqc,Nnsc->ndq', AQs[i-1], AQs[i-1], m2)
V3 = T.einsum('nds,nq,Nns->ndq', AQs[i-1], bQs[i-1], m1)
Q = T.einsum('nd,nq->ndq', Qs[i - 1], Qs[i - 1])
V = Q * (V1 + V2 + V3 + V3.transpose((0, 2, 1))) / batch_size
whiten = T.stack([T.kron(U[n], V[n]) for n in range(V.shape[0])]).sum(0)
whiten = whiten + T.eye(whiten.shape[-1]) / (Ds[i]*Ds[i+1]*cov_W)
# compute the residual (bottom up)
if i == len(Ws) - 1:
bottom_up = (X[:, None, :] - vs[-1])
else:
if i == 0:
residual = (X[:, None, :] - bQs[-1])
else:
residual = (X[:, None, :] - bQs[-1]\
+ T.einsum('nds,ns->nd', FQ[i - 1], bQs[i-1]))
bottom_up = T.einsum('ndc,Nnd->Nnc', FQ[i], residual)
# compute the top down vector
if i == 0:
top_down = m1
else:
top_down = Qs[i - 1] * (T.einsum('nds,Nns->Nnd', AQs[i - 1], m1) +\
T.einsum('nd,Nn->Nnd', bQs[i - 1], m0))
vector = T.einsum('Nnc,Nns->cs', bottom_up, top_down) / batch_size
condition = T.diagonal(whiten)
update_W = T.linalg.solve(whiten, vector.reshape(-1)).reshape(Ws[i].shape)
update_Ws[Ws[i]] = update_W
############################################################################
# create the io functions
############################################################################
params = sj.function(outputs = Ws + vs + [var_x])
ll = T.Placeholder((), 'int32')
selector = T.one_hot(ll, len(vs))
for i in range(len(vs)):
update_vs[vs[i]] = ((1 - alpha) * vs[i] + alpha * update_vs[vs[i]])\
* selector[i] + vs[i] * (1 - selector[i])
for i in range(len(Ws)):
update_Ws[Ws[i]] = ((1 - alpha) * Ws[i] + alpha * update_Ws[Ws[i]])\
* selector[i] + Ws[i] * (1 - selector[i])
output = {'train':sj.function(SIGNS, X, m0, m1, m2, outputs=mean_loss,
updates=adam.updates),
'update_var':sj.function(SIGNS, X, m0, m1, m2, outputs=mean_loss,
updates = {var_x: update_varx}),
'update_vs':sj.function(alpha, ll, SIGNS, X, m0, m1, m2, outputs=mean_loss,
updates = update_vs),
'loss':sj.function(SIGNS, X, m0, m1, m2, outputs=mean_loss),
'update_Ws':sj.function(alpha, ll, SIGNS, X, m0, m1, m2, outputs=mean_loss,
updates = update_Ws),
'signs2Ab': sj.function(signs, outputs=[Aqs[-1][0], bqs[-1][0]]),
'signs2ineq': sj.function(signs, outputs=q_inequalities),
'g': sj.function(x, outputs=maps[-1]),
'input2all': sj.function(x, outputs=[maps[-1], Axs[-1][0],
bxs[-1][0], x_inequalities, xsigns]),
'get_nll': sj.function(SIGNS, X, m0, m1, m2, outputs=mean_loss),
'assign': sj.function(*Ws_ph, *vs_ph, var_x_ph,
updates=dict(zip(Ws + vs + [var_x],
Ws_ph + vs_ph + [var_x_ph]))),
'varx': sj.function(outputs=var_x),
'prior': sj.function(outputs=prior),
'varz': sj.function(outputs=var_z),
'params': params,
# 'probed' : sj.function(SIGNS, X, m0, m1, m2, outputs=probed),
'input2signs': sj.function(x, outputs=xsigns),
'S' : Ds[0], 'D': Ds[-1], 'R': R, 'model': 'EM', 'L':len(Ds)-1,
'kwargs': {'batch_size': batch_size, 'Ds':Ds, 'seed':seed,
'leakiness':leakiness, 'lr':lr, 'scaler':scaler}}
def sample(n):
samples = []
for i in range(n):
samples.append(output['g'](np.random.randn(Ds[0])))
return np.array(samples)
output['sample'] = sample
return output
def rnn_cell(carry, x, w):
output = T.sigmoid(T.matmul(w, x) + T.matmul(carry, h) + b)
return output, output