def test_theano_vs_by_hand_outputs(self):
"""
compare theano and by hand network evaluations
"""
EPSILON = 1E-7
np.random.seed(9124)
x = np.zeros((self.l, np.max([self.model.max_n, self.model.max_m])))
x[:, :self.ns[0]] = np.random.rand(self.l, self.ns[0])
test_val = x[:, :self.ns[0]]
model_val = self.model.network(x)
for i in range(self.n_layers):
lstm = T_lstm(self.ns[i], self.ms[i], np.zeros(self.ms[i]),
np.zeros(self.ms[i]), logistic(self.ms[i]),
hyptan(self.ms[i]), identity(self.ms[i]))
lstm.W = self.model.Ws.get_value()[i, :4 * self.ms[i], :self.ns[i]]
lstm.U = self.model.Us.get_value()[i, :4 * self.ms[i], :self.ms[i]]
lstm.b = self.model.bs.get_value()[i, :4 * self.ms[i]]
test_val = lstm(test_val)
self.assertLess(
np.max(np.fabs(test_val - model_val[i, :, :self.ms[i]])),
EPSILON)
def test_uni_vs_multi_t_lstm(self):
"""
compare evaluation and differentiate of univatiate and
multivarate traditional neurons
"""
EPSILON = 1E-17
k = 100
lstm = T_lstm(1,
1,
np.zeros(1),
np.zeros(1),
logistic(1),
hyptan(1),
identity(1),
seed=0)
U_lstm = Univariat_T_lstm(0.,
0.,
logistic(1),
hyptan(1),
identity(1),
seed=0)
lstm.W[:, 0] = U_lstm.W
lstm.U[:, 0] = U_lstm.U
lstm.b = U_lstm.b.copy()
xs = np.random.rand(k)
ys = np.random.rand(k)
v = lstm(xs.reshape(k, 1)).flatten() - U_lstm(xs)
self.assertLess(np.sqrt(v.dot(v)), EPSILON)
U_grad = U_lstm.ss_grad(xs, ys)
grad = lstm.ss_grad(xs.reshape(k, 1), ys.reshape(k, 1))
v = U_grad - grad
self.assertLess(np.sqrt(v.dot(v)), EPSILON)
def test_grad_loss(self):
"""
compare the gradient computations of the by hand and theano models
"""
TOL = 1E-5
start = time.clock()
self.one_layer_model.compile_grad_loss()
test_lstm.one_layer_grad_loss_compile_time = time.clock() - start
lstm_bh = T_lstm(self.nn, self.mm, np.zeros(self.mm),
np.zeros(self.mm), logistic(self.mm), hyptan(self.mm),
identity(self.mm))
lstm_bh.W = self.one_layer_model.Ws.get_value()[0, :4 *
self.mm, :self.nn]
lstm_bh.U = self.one_layer_model.Us.get_value()[0, :4 *
self.mm, :self.mm]
lstm_bh.b = self.one_layer_model.bs.get_value()[0, :4 * self.mm]
x = np.random.rand(self.l, max([self.nn, self.mm]))
y = np.random.rand(self.l, self.mm)
# scale on the by hand model doesn't match that on the theano model
grad = lstm_bh.ss_grad(x[:, :self.nn], y) * 2. / float(self.l)
dW, dU, db = self.one_layer_model.grad_loss(np.array([x]),
np.array([y]))
j = 0
mm = self.mm
nn = self.nn
for i in range(4):
i_mm = i * mm
val = np.max(
np.fabs(grad[j:j + mm * nn] -
dW[0, i_mm:i_mm + mm, :nn].flatten()))
self.assertLess(val, TOL)
j += mm * nn
val = np.max(
np.fabs(grad[j:j + mm * mm] -
dU[0, i_mm:i_mm + mm, :mm].flatten()))
self.assertLess(val, TOL)
j += mm * mm
val = np.max(
np.fabs(grad[j:j + mm] - db[0, i_mm:i_mm + mm, ].flatten()))
self.assertLess(val, TOL)
j += mm
def test_multivariate_t_lstm_num_vs_analytic(self):
"""
compare numerical and analytic derivatives of the multivariate
traditional lstm neuron
"""
EPSILON = 1E-3
np.random.seed(0)
k = 50
n = 20
m = 10
xs = np.random.rand(k, n)
ys = np.random.rand(k, m)
lstm = T_lstm(n,
m,
np.zeros(m),
np.zeros(m),
logistic(m),
hyptan(m),
identity(m),
seed=0)
grad = lstm.ss_grad(xs, ys)
grad_i = 0
for i in range(3):
for flag, sz in [['W', n * m], ['U', m * m], ['b', m]]:
for j in range(sz):
WW = None
if flag == 'W':
WW = lstm.W
coord = (i * m + int(j / n), j % n)
elif flag == 'U':
WW = lstm.U
coord = (i * m + int(j / m), j % m)
else:
WW = lstm.b
coord = i * m + j
num_der = lstm.ss_numerical_derivative(
WW[coord], 1E-7, xs, ys, flag, coord)
self.assertLess(np.fabs(num_der - grad[grad_i]), EPSILON)
grad_i += 1
def test_univariate_t_lstm(self):
"""
compare numerical and analytic derivatives of the univariate
traditional lstm neuron
"""
EPSILON = 1E-3
np.random.seed(0)
k = 100
xs = np.random.rand(k)
ys = np.random.rand(k)
lstm = Univariat_T_lstm(0.,
0.,
logistic(1),
hyptan(1),
identity(1),
seed=0)
grad = lstm.ss_grad(xs, ys)
grad_i = 0
for i in range(3):
for flag in ['W', 'U', 'b']:
WW = None
if flag == 'W':
WW = lstm.W
elif flag == 'U':
WW = lstm.U
else:
WW = lstm.b
num_der = lstm.ss_numerical_derivative(WW[i], 1E-7, xs, ys,
flag, i)
self.assertLess(np.fabs(num_der - grad[grad_i]), EPSILON)
grad_i += 1
def test_multivariate_t_lstm_full_derivative(self):
"""
compare analytic_derivative result to full derivative result
"""
EPSILON = 1E-12
np.random.seed(0)
k = 100
n = 20
m = 18
xs = np.random.rand(k, n)
ys = np.random.rand(k, m)
lstm = T_lstm(n,
m,
np.zeros(m),
np.zeros(m),
logistic(m),
hyptan(m),
identity(m),
seed=0)
# gradient of sum of squares loss
grad = lstm.ss_grad(xs, ys)
# full derivative tensor
D = lstm.full_derivative(xs)
# gradient by multiplication by full derivative tensor
fd_grad = np.einsum('ij,ij...', (lstm(xs) - ys), D)
# check the results
v = grad - fd_grad
self.assertLess(np.sqrt(v.dot(v)), EPSILON)