def test_exponential_update():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.ExponentialLayer(num_visible_units)
hid_layer = layers.ExponentialLayer(num_hidden_units)
rbm = hidden.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
# for the exponential layers, we need a > 0, b > 0, and W < 0
a = be.rand((num_visible_units, ))
b = be.rand((num_hidden_units, ))
W = -be.rand((num_visible_units, num_hidden_units))
rbm.layers[0].int_params['loc'] = a
rbm.layers[1].int_params['loc'] = b
rbm.weights[0].int_params['matrix'] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute extrinsic parameters
hidden_rate = -be.dot(vdata, W) # (batch_size, num_hidden_units)
hidden_rate += be.broadcast(b, hidden_rate)
visible_rate = -be.dot(hdata,
be.transpose(W)) # (batch_size, num_visible_units)
visible_rate += be.broadcast(a, visible_rate)
# update the extrinsic parameter using the layer functions
rbm.layers[1].update(vdata, rbm.weights[0].W())
rbm.layers[0].update(hdata, be.transpose(rbm.weights[0].W()))
assert be.allclose(hidden_rate, rbm.layers[1].ext_params['rate']), \
"hidden rate wrong in exponential-exponential rbm"
assert be.allclose(visible_rate, rbm.layers[0].ext_params['rate']), \
"visible rate wrong in exponential-exponential rbm"
def test_bernoulli_update():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.BernoulliLayer(num_visible_units)
hid_layer = layers.BernoulliLayer(num_hidden_units)
rbm = hidden.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units, ))
b = be.randn((num_hidden_units, ))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].int_params['loc'] = a
rbm.layers[1].int_params['loc'] = b
rbm.weights[0].int_params['matrix'] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute extrinsic parameters
hidden_field = be.dot(vdata, W) # (batch_size, num_hidden_units)
hidden_field += be.broadcast(b, hidden_field)
visible_field = be.dot(hdata,
be.transpose(W)) # (batch_size, num_visible_units)
visible_field += be.broadcast(a, visible_field)
# update the extrinsic parameter using the layer functions
rbm.layers[0].update(hdata, be.transpose(rbm.weights[0].W()))
rbm.layers[1].update(vdata, rbm.weights[0].W())
assert be.allclose(hidden_field, rbm.layers[1].ext_params['field']), \
"hidden field wrong in bernoulli-bernoulli rbm"
assert be.allclose(visible_field, rbm.layers[0].ext_params['field']), \
"visible field wrong in bernoulli-bernoulli rbm"
def test_exponential_derivatives():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.ExponentialLayer(num_visible_units)
hid_layer = layers.ExponentialLayer(num_hidden_units)
rbm = hidden.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
# for the exponential layers, we need a > 0, b > 0, and W < 0
a = be.rand((num_visible_units, ))
b = be.rand((num_hidden_units, ))
W = -be.rand((num_visible_units, num_hidden_units))
rbm.layers[0].int_params['loc'] = a
rbm.layers[1].int_params['loc'] = b
rbm.weights[0].int_params['matrix'] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
vdata_scaled = rbm.layers[0].rescale(vdata)
# compute the mean of the hidden layer
rbm.layers[1].update(vdata, rbm.weights[0].W())
hid_mean = rbm.layers[1].mean()
hid_mean_scaled = rbm.layers[1].rescale(hid_mean)
# compute the derivatives
d_visible_loc = be.mean(vdata, axis=0)
d_hidden_loc = be.mean(hid_mean_scaled, axis=0)
d_W = -be.batch_outer(vdata, hid_mean_scaled) / len(vdata)
# compute the derivatives using the layer functions
vis_derivs = rbm.layers[0].derivatives(vdata, hid_mean_scaled,
rbm.weights[0].W())
hid_derivs = rbm.layers[1].derivatives(hid_mean, vdata_scaled,
be.transpose(rbm.weights[0].W()))
weight_derivs = rbm.weights[0].derivatives(vdata, hid_mean_scaled)
assert be.allclose(d_visible_loc, vis_derivs['loc']), \
"derivative of visible loc wrong in exponential-exponential rbm"
assert be.allclose(d_hidden_loc, hid_derivs['loc']), \
"derivative of hidden loc wrong in exponential-exponential rbm"
assert be.allclose(d_W, weight_derivs['matrix']), \
"derivative of weights wrong in exponential-exponential rbm"
def test_exponential_conditional_params():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.ExponentialLayer(num_visible_units)
hid_layer = layers.ExponentialLayer(num_hidden_units)
rbm = model.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
# for the exponential layers, we need a > 0, b > 0, and W < 0
a = be.rand((num_visible_units, ))
b = be.rand((num_hidden_units, ))
W = -be.rand((num_visible_units, num_hidden_units))
rbm.layers[0].params.loc[:] = a
rbm.layers[1].params.loc[:] = b
rbm.weights[0].params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute conditional parameters
hidden_rate = -be.dot(vdata, W) # (batch_size, num_hidden_units)
hidden_rate += be.broadcast(b, hidden_rate)
visible_rate = -be.dot(hdata,
be.transpose(W)) # (batch_size, num_visible_units)
visible_rate += be.broadcast(a, visible_rate)
# compute the conditional parameters using the layer functions
hidden_rate_func = rbm.layers[1]._conditional_params([vdata],
[rbm.weights[0].W()])
visible_rate_func = rbm.layers[0]._conditional_params(
[hdata], [rbm.weights[0].W_T()])
assert be.allclose(hidden_rate, hidden_rate_func), \
"hidden rate wrong in exponential-exponential rbm"
assert be.allclose(visible_rate, visible_rate_func), \
"visible rate wrong in exponential-exponential rbm"
def test_bernoulli_conditional_params():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.BernoulliLayer(num_visible_units)
hid_layer = layers.BernoulliLayer(num_hidden_units)
rbm = model.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units, ))
b = be.randn((num_hidden_units, ))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].params.loc[:] = a
rbm.layers[1].params.loc[:] = b
rbm.weights[0].params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute conditional parameters
hidden_field = be.dot(vdata, W) # (batch_size, num_hidden_units)
hidden_field += b
visible_field = be.dot(hdata,
be.transpose(W)) # (batch_size, num_visible_units)
visible_field += a
# compute conditional parameters with layer funcitons
hidden_field_layer = rbm.layers[1]._conditional_params(
[vdata], [rbm.weights[0].W()])
visible_field_layer = rbm.layers[0]._conditional_params(
[hdata], [rbm.weights[0].W_T()])
assert be.allclose(hidden_field, hidden_field_layer), \
"hidden field wrong in bernoulli-bernoulli rbm"
assert be.allclose(visible_field, visible_field_layer), \
"visible field wrong in bernoulli-bernoulli rbm"
def pdist(x: be.Tensor, y: be.Tensor) -> be.Tensor:
"""
Compute the pairwise distance matrix between the rows of x and y.
Args:
x (tensor (num_samples_1, num_units))
y (tensor (num_samples_2, num_units))
Returns:
tensor (num_samples_1, num_samples_2)
"""
inner = be.dot(x, be.transpose(y))
x_mag = be.norm(x, axis=1)**2
y_mag = be.norm(y, axis=1)**2
squared = be.add(be.unsqueeze(y_mag, axis=0),
be.add(be.unsqueeze(x_mag, axis=1), -2 * inner))
return be.sqrt(be.clip(squared, a_min=0))
def test_pdist():
n = 500
a_shape = (1000, n)
b_shape = (1000, n)
# distance distributions
a_mean, a_scale = 1, 1
b_mean, b_scale = -1, 1
be.set_seed()
a = a_mean + a_scale * be.randn(a_shape)
b = b_mean + b_scale * be.randn(b_shape)
dists = math_utils.pdist(a, b)
dists_t = math_utils.pdist(b, a)
assert be.shape(dists) == (1000, 1000)
assert be.allclose(be.transpose(dists_t), dists)
assert be.mean(dists) > 2 * math.sqrt(n) and be.mean(
dists) < 3 * math.sqrt(n)
def test_gaussian_derivatives():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.GaussianLayer(num_visible_units)
hid_layer = layers.GaussianLayer(num_hidden_units)
rbm = hidden.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units, ))
b = be.randn((num_hidden_units, ))
log_var_a = 0.1 * be.randn((num_visible_units, ))
log_var_b = 0.1 * be.randn((num_hidden_units, ))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].int_params.loc[:] = a
rbm.layers[1].int_params.loc[:] = b
rbm.layers[0].int_params.log_var[:] = log_var_a
rbm.layers[1].int_params.log_var[:] = log_var_b
rbm.weights[0].int_params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
visible_var = be.exp(log_var_a)
vdata_scaled = vdata / be.broadcast(visible_var, vdata)
# compute the mean of the hidden layer
rbm.layers[1].update([vdata_scaled], [rbm.weights[0].W()])
hidden_var = be.exp(log_var_b)
hid_mean = rbm.layers[1].mean()
hid_mean_scaled = rbm.layers[1].rescale(hid_mean)
# compute the derivatives
d_vis_loc = -be.mean(vdata_scaled, axis=0)
d_vis_logvar = -0.5 * be.mean(be.square(be.subtract(a, vdata)), axis=0)
d_vis_logvar += be.batch_dot(
hid_mean_scaled, be.transpose(W), vdata, axis=0) / len(vdata)
d_vis_logvar /= visible_var
d_hid_loc = -be.mean(hid_mean_scaled, axis=0)
d_hid_logvar = -0.5 * be.mean(
be.square(hid_mean - be.broadcast(b, hid_mean)), axis=0)
d_hid_logvar += be.batch_dot(vdata_scaled, W, hid_mean,
axis=0) / len(hid_mean)
d_hid_logvar /= hidden_var
d_W = -be.batch_outer(vdata_scaled, hid_mean_scaled) / len(vdata_scaled)
# compute the derivatives using the layer functions
rbm.layers[1].update([vdata_scaled], [rbm.weights[0].W()])
rbm.layers[0].update([hid_mean_scaled], [rbm.weights[0].W_T()])
vis_derivs = rbm.layers[0].derivatives(vdata, [hid_mean_scaled],
[rbm.weights[0].W()])
hid_derivs = rbm.layers[1].derivatives(hid_mean, [vdata_scaled],
[rbm.weights[0].W_T()])
weight_derivs = rbm.weights[0].derivatives(vdata_scaled, hid_mean_scaled)
assert be.allclose(d_vis_loc, vis_derivs.loc), \
"derivative of visible loc wrong in gaussian-gaussian rbm"
assert be.allclose(d_hid_loc, hid_derivs.loc), \
"derivative of hidden loc wrong in gaussian-gaussian rbm"
assert be.allclose(d_vis_logvar, vis_derivs.log_var, rtol=1e-05, atol=1e-01), \
"derivative of visible log_var wrong in gaussian-gaussian rbm"
assert be.allclose(d_hid_logvar, hid_derivs.log_var, rtol=1e-05, atol=1e-01), \
"derivative of hidden log_var wrong in gaussian-gaussian rbm"
assert be.allclose(d_W, weight_derivs.matrix), \
"derivative of weights wrong in gaussian-gaussian rbm"
def test_gaussian_update():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.GaussianLayer(num_visible_units)
hid_layer = layers.GaussianLayer(num_hidden_units)
rbm = hidden.Model([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units, ))
b = be.randn((num_hidden_units, ))
log_var_a = 0.1 * be.randn((num_visible_units, ))
log_var_b = 0.1 * be.randn((num_hidden_units, ))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].int_params.loc[:] = a
rbm.layers[1].int_params.loc[:] = b
rbm.layers[0].int_params.log_var[:] = log_var_a
rbm.layers[1].int_params.log_var[:] = log_var_b
rbm.weights[0].int_params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute the variance
visible_var = be.exp(log_var_a)
hidden_var = be.exp(log_var_b)
# rescale the data
vdata_scaled = vdata / be.broadcast(visible_var, vdata)
hdata_scaled = hdata / be.broadcast(hidden_var, hdata)
# test rescale
assert be.allclose(vdata_scaled, rbm.layers[0].rescale(vdata)),\
"visible rescale wrong in gaussian-gaussian rbm"
assert be.allclose(hdata_scaled, rbm.layers[1].rescale(hdata)),\
"hidden rescale wrong in gaussian-gaussian rbm"
# compute the mean
hidden_mean = be.dot(vdata_scaled, W) # (batch_size, num_hidden_units)
hidden_mean += be.broadcast(b, hidden_mean)
visible_mean = be.dot(hdata_scaled,
be.transpose(W)) # (batch_size, num_hidden_units)
visible_mean += be.broadcast(a, visible_mean)
# update the extrinsic parameters using the layer functions
rbm.layers[0].update([hdata_scaled], [rbm.weights[0].W_T()])
rbm.layers[1].update([vdata_scaled], [rbm.weights[0].W()])
assert be.allclose(visible_var, rbm.layers[0].ext_params.variance),\
"visible variance wrong in gaussian-gaussian rbm"
assert be.allclose(hidden_var, rbm.layers[1].ext_params.variance),\
"hidden variance wrong in gaussian-gaussian rbm"
assert be.allclose(visible_mean, rbm.layers[0].ext_params.mean),\
"visible mean wrong in gaussian-gaussian rbm"
assert be.allclose(hidden_mean, rbm.layers[1].ext_params.mean),\
"hidden mean wrong in gaussian-gaussian rbm"
def test_gaussian_derivatives():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.GaussianLayer(num_visible_units)
hid_layer = layers.GaussianLayer(num_hidden_units)
rbm = BoltzmannMachine([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units,))
b = be.randn((num_hidden_units,))
log_var_a = 0.1 * be.randn((num_visible_units,))
log_var_b = 0.1 * be.randn((num_hidden_units,))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].params.loc[:] = a
rbm.layers[1].params.loc[:] = b
rbm.layers[0].params.log_var[:] = log_var_a
rbm.layers[1].params.log_var[:] = log_var_b
rbm.connections[0].weights.params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
visible_var = be.exp(log_var_a)
vdata_scaled = vdata / visible_var
# compute the mean of the hidden layer
hid_mean = rbm.layers[1].conditional_mean(
[vdata_scaled], [rbm.connections[0].W()])
hidden_var = be.exp(log_var_b)
hid_mean_scaled = rbm.layers[1].rescale(hid_mean)
# compute the derivatives
d_vis_loc = be.mean((a-vdata)/visible_var, axis=0)
d_vis_logvar = -0.5 * be.mean(be.square(be.subtract(a, vdata)), axis=0)
d_vis_logvar += be.batch_quadratic(hid_mean_scaled, be.transpose(W), vdata,
axis=0) / len(vdata)
d_vis_logvar /= visible_var
d_hid_loc = be.mean((b-hid_mean)/hidden_var, axis=0)
d_hid_logvar = -0.5 * be.mean(be.square(hid_mean - b), axis=0)
d_hid_logvar += be.batch_quadratic(vdata_scaled, W, hid_mean,
axis=0) / len(hid_mean)
d_hid_logvar /= hidden_var
d_W = -be.batch_outer(vdata_scaled, hid_mean_scaled) / len(vdata_scaled)
# compute the derivatives using the layer functions
vis_derivs = rbm.layers[0].derivatives(vdata, [hid_mean_scaled],
[rbm.connections[0].W(trans=True)])
hid_derivs = rbm.layers[1].derivatives(hid_mean, [vdata_scaled],
[rbm.connections[0].W()])
weight_derivs = rbm.connections[0].weights.derivatives(vdata_scaled, hid_mean_scaled)
# compute simple weighted derivatives using the layer functions
scale = 2
scale_func = partial(be.multiply, be.float_scalar(scale))
vis_derivs_scaled = rbm.layers[0].derivatives(vdata, [hid_mean_scaled],
[rbm.connections[0].W(trans=True)], weighting_function=scale_func)
hid_derivs_scaled = rbm.layers[1].derivatives(hid_mean, [vdata_scaled],
[rbm.connections[0].W()], weighting_function=scale_func)
weight_derivs_scaled = rbm.connections[0].weights.derivatives(vdata_scaled, hid_mean_scaled,
weighting_function=scale_func)
assert be.allclose(d_vis_loc, vis_derivs[0].loc), \
"derivative of visible loc wrong in gaussian-gaussian rbm"
assert be.allclose(d_hid_loc, hid_derivs[0].loc), \
"derivative of hidden loc wrong in gaussian-gaussian rbm"
assert be.allclose(d_vis_logvar, vis_derivs[0].log_var, rtol=1e-05, atol=1e-01), \
"derivative of visible log_var wrong in gaussian-gaussian rbm"
assert be.allclose(d_hid_logvar, hid_derivs[0].log_var, rtol=1e-05, atol=1e-01), \
"derivative of hidden log_var wrong in gaussian-gaussian rbm"
assert be.allclose(d_W, weight_derivs[0].matrix), \
"derivative of weights wrong in gaussian-gaussian rbm"
assert be.allclose(scale * d_vis_loc, vis_derivs_scaled[0].loc), \
"weighted derivative of visible loc wrong in gaussian-gaussian rbm"
assert be.allclose(scale * d_hid_loc, hid_derivs_scaled[0].loc), \
"weighted derivative of hidden loc wrong in gaussian-gaussian rbm"
assert be.allclose(scale * d_vis_logvar, vis_derivs_scaled[0].log_var, rtol=1e-05, atol=1e-01), \
"weighted derivative of visible log_var wrong in gaussian-gaussian rbm"
assert be.allclose(scale * d_hid_logvar, hid_derivs_scaled[0].log_var, rtol=1e-05, atol=1e-01), \
"weighted derivative of hidden log_var wrong in gaussian-gaussian rbm"
assert be.allclose(scale * d_W, weight_derivs_scaled[0].matrix), \
"weighted derivative of weights wrong in gaussian-gaussian rbm"
def test_gaussian_conditional_params():
num_visible_units = 100
num_hidden_units = 50
batch_size = 25
# set a seed for the random number generator
be.set_seed()
# set up some layer and model objects
vis_layer = layers.GaussianLayer(num_visible_units)
hid_layer = layers.GaussianLayer(num_hidden_units)
rbm = BoltzmannMachine([vis_layer, hid_layer])
# randomly set the intrinsic model parameters
a = be.randn((num_visible_units,))
b = be.randn((num_hidden_units,))
log_var_a = 0.1 * be.randn((num_visible_units,))
log_var_b = 0.1 * be.randn((num_hidden_units,))
W = be.randn((num_visible_units, num_hidden_units))
rbm.layers[0].params.loc[:] = a
rbm.layers[1].params.loc[:] = b
rbm.layers[0].params.log_var[:] = log_var_a
rbm.layers[1].params.log_var[:] = log_var_b
rbm.connections[0].weights.params.matrix[:] = W
# generate a random batch of data
vdata = rbm.layers[0].random((batch_size, num_visible_units))
hdata = rbm.layers[1].random((batch_size, num_hidden_units))
# compute the variance
visible_var = be.exp(log_var_a)
hidden_var = be.exp(log_var_b)
# rescale the data
vdata_scaled = vdata / visible_var
hdata_scaled = hdata / hidden_var
# test rescale
assert be.allclose(vdata_scaled, rbm.layers[0].rescale(vdata)),\
"visible rescale wrong in gaussian-gaussian rbm"
assert be.allclose(hdata_scaled, rbm.layers[1].rescale(hdata)),\
"hidden rescale wrong in gaussian-gaussian rbm"
# compute the mean
hidden_mean = be.dot(vdata_scaled, W) # (batch_size, num_hidden_units)
hidden_mean += b
visible_mean = be.dot(hdata_scaled, be.transpose(W)) # (batch_size, num_hidden_units)
visible_mean += a
# update the conditional parameters using the layer functions
vis_mean_func, vis_var_func = rbm.layers[0].conditional_params(
[hdata_scaled], [rbm.connections[0].W(trans=True)])
hid_mean_func, hid_var_func = rbm.layers[1].conditional_params(
[vdata_scaled], [rbm.connections[0].W()])
assert be.allclose(visible_var, vis_var_func),\
"visible variance wrong in gaussian-gaussian rbm"
assert be.allclose(hidden_var, hid_var_func),\
"hidden variance wrong in gaussian-gaussian rbm"
assert be.allclose(visible_mean, vis_mean_func),\
"visible mean wrong in gaussian-gaussian rbm"
assert be.allclose(hidden_mean, hid_mean_func),\
"hidden mean wrong in gaussian-gaussian rbm"
