class SET_MLP:
def __init__(self, dimensions, activations, epsilon=20):
"""
:param dimensions: (tpl/ list) Dimensions of the neural net. (input, hidden layer, output)
:param activations: (tpl/ list) Activations functions.
Example of three hidden layer with
- 3312 input features
- 3000 hidden neurons
- 3000 hidden neurons
- 3000 hidden neurons
- 5 output classes
layers --> [1, 2, 3, 4, 5]
----------------------------------------
dimensions = (3312, 3000, 3000, 3000, 5)
activations = ( Relu, Relu, Relu, Sigmoid)
"""
self.n_layers = len(dimensions)
self.loss = None
self.dropout_rate = 0. # dropout rate
self.learning_rate = None
self.momentum = None
self.weight_decay = None
self.epsilon = epsilon # control the sparsity level as discussed in the paper
self.zeta = None # the fraction of the weights removed
self.dimensions = dimensions
self.save_filename = ""
self.input_layer_connections = []
self.monitor = None
# Weights and biases are initiated by index. For a one hidden layer net you will have a w[1] and w[2]
self.w = {}
self.b = {}
self.pdw = {}
self.pdd = {}
# Activations are also initiated by index. For the example we will have activations[2] and activations[3]
self.activations = {}
for i in range(len(dimensions) - 1):
self.w[i + 1] = create_sparse_weights(
self.epsilon, dimensions[i],
dimensions[i + 1]) # create sparse weight matrices
self.b[i + 1] = np.zeros(dimensions[i + 1], dtype='float32')
self.activations[i + 2] = activations[i]
def _feed_forward(self, x, drop=False):
"""
Execute a forward feed through the network.
:param x: (array) Batch of input data vectors.
:return: (tpl) Node outputs and activations per layer. The numbering of the output is equivalent to the layer numbers.
"""
# w(x) + b
z = {}
# activations: f(z)
a = {
1: x
} # First layer has no activations as input. The input x is the input.
masks = {}
for i in range(1, self.n_layers):
z[i + 1] = a[i] @ self.w[i] + self.b[i]
a[i + 1] = self.activations[i + 1].activation(z[i + 1])
if drop:
if i < self.n_layers - 1:
# apply dropout
a[i + 1], keep_mask = dropout(a[i + 1], self.dropout_rate)
masks[i + 1] = keep_mask
return z, a, masks
def _back_prop(self, z, a, masks, y_true):
"""
The input dicts keys represent the layers of the net.
a = { 1: x,
2: f(w1(x) + b1)
3: f(w2(a2) + b2)
4: f(w3(a3) + b3)
5: f(w4(a4) + b4)
}
:param z: (dict) w(x) + b
:param a: (dict) f(z)
:param y_true: (array) One hot encoded truth vector.
:return:
"""
keep_prob = 1.
if self.dropout_rate > 0:
keep_prob = np.float32(1. - self.dropout_rate)
# Determine partial derivative and delta for the output layer.
# delta output layer
delta = self.loss.delta(y_true, a[self.n_layers])
dw = coo_matrix(self.w[self.n_layers - 1], dtype='float32')
# compute backpropagation updates
backpropagation_updates_numpy(a[self.n_layers - 1], delta, dw.row,
dw.col, dw.data)
update_params = {
self.n_layers - 1: (dw.tocsr(), np.mean(delta, axis=0))
}
# In case of three layer net will iterate over i = 2 and i = 1
# Determine partial derivative and delta for the rest of the layers.
# Each iteration requires the delta from the previous layer, propagating backwards.
for i in reversed(range(2, self.n_layers)):
# dropout for the backpropagation step
if keep_prob != 1:
delta = (delta @ self.w[i].transpose()
) * self.activations[i].prime(z[i])
delta = delta * masks[i]
delta /= keep_prob
else:
delta = (delta @ self.w[i].transpose()
) * self.activations[i].prime(z[i])
dw = coo_matrix(self.w[i - 1], dtype='float32')
# compute backpropagation updates
backpropagation_updates_numpy(a[i - 1], delta, dw.row, dw.col,
dw.data)
update_params[i - 1] = (dw.tocsr(), np.mean(delta, axis=0))
for k, v in update_params.items():
self._update_w_b(k, v[0], v[1])
def _update_w_b(self, index, dw, delta):
"""
Update weights and biases.
:param index: (int) Number of the layer
:param dw: (array) Partial derivatives
:param delta: (array) Delta error.
"""
# perform the update with momentum
if index not in self.pdw:
self.pdw[index] = -self.learning_rate * dw
self.pdd[index] = -self.learning_rate * delta
else:
self.pdw[index] = self.momentum * self.pdw[
index] - self.learning_rate * dw
self.pdd[index] = self.momentum * self.pdd[
index] - self.learning_rate * delta
self.w[index] += self.pdw[index] - self.weight_decay * self.w[index]
self.b[index] += self.pdd[index] - self.weight_decay * self.b[index]
def fit(self,
x,
y_true,
x_test,
y_test,
loss,
epochs,
batch_size,
learning_rate=1e-3,
momentum=0.9,
weight_decay=0.0002,
zeta=0.3,
dropoutrate=0.,
testing=True,
save_filename="",
monitor=False):
"""
:param x: (array) Containing parameters
:param y_true: (array) Containing one hot encoded labels.
:return (array) A 2D array of metrics (epochs, 3).
"""
if not x.shape[0] == y_true.shape[0]:
raise ValueError("Length of x and y arrays don't match")
self.monitor = Monitor(
save_filename=save_filename) if monitor else None
# Initiate the loss object with the final activation function
self.loss = loss()
self.learning_rate = learning_rate
self.momentum = momentum
self.weight_decay = weight_decay
self.zeta = zeta
self.dropout_rate = dropoutrate
self.save_filename = save_filename
self.input_layer_connections.append(self.get_core_input_connections())
np.savez_compressed(self.save_filename + "_input_connections.npz",
inputLayerConnections=self.input_layer_connections)
maximum_accuracy = 0
metrics = np.zeros((epochs, 4))
for i in range(epochs):
# Shuffle the data
seed = np.arange(x.shape[0])
np.random.shuffle(seed)
x_ = x[seed]
y_ = y_true[seed]
if self.monitor:
self.monitor.start_monitor()
# training
t1 = datetime.datetime.now()
for j in range(x.shape[0] // batch_size):
k = j * batch_size
l = (j + 1) * batch_size
z, a, masks = self._feed_forward(x_[k:l], True)
self._back_prop(z, a, masks, y_[k:l])
t2 = datetime.datetime.now()
if self.monitor:
self.monitor.stop_monitor()
print("\nSET-MLP Epoch ", i)
print("Training time: ", t2 - t1)
# test model performance on the test data at each epoch
# this part is useful to understand model performance and can be commented for production settings
if testing:
t3 = datetime.datetime.now()
accuracy_test, activations_test = self.predict(x_test, y_test)
accuracy_train, activations_train = self.predict(x, y_true)
t4 = datetime.datetime.now()
maximum_accuracy = max(maximum_accuracy, accuracy_test)
loss_test = self.loss.loss(y_test, activations_test)
loss_train = self.loss.loss(y_true, activations_train)
metrics[i, 0] = loss_train
metrics[i, 1] = loss_test
metrics[i, 2] = accuracy_train
metrics[i, 3] = accuracy_test
print(f"Testing time: {t4 - t3}\n; Loss test: {loss_test}; \n"
f"Accuracy test: {accuracy_test}; \n"
f"Maximum accuracy val: {maximum_accuracy}")
t5 = datetime.datetime.now()
if i < epochs - 1: # do not change connectivity pattern after the last epoch
# self.weights_evolution_I() # this implementation is more didactic, but slow.
self.weights_evolution_II(
) # this implementation has the same behaviour as the one above, but it is much faster.
t6 = datetime.datetime.now()
print("Weights evolution time ", t6 - t5)
# save performance metrics values in a file
if self.save_filename != "":
np.savetxt(self.save_filename + ".txt", metrics)
if self.save_filename != "" and self.monitor:
with open(self.save_filename + "_monitor.json", 'w') as file:
file.write(
json.dumps(self.monitor.get_stats(),
indent=4,
sort_keys=True,
default=str))
return metrics
def get_core_input_connections(self):
values = np.sort(self.w[1].data)
first_zero_pos = find_first_pos(values, 0)
last_zero_pos = find_last_pos(values, 0)
largest_negative = values[int((1 - self.zeta) * first_zero_pos)]
smallest_positive = values[int(
min(values.shape[0] - 1, last_zero_pos + self.zeta *
(values.shape[0] - last_zero_pos)))]
wlil = self.w[1].tolil()
wdok = dok_matrix((self.dimensions[0], self.dimensions[1]),
dtype="float32")
# remove the weights closest to zero
keep_connections = 0
for ik, (row, data) in enumerate(zip(wlil.rows, wlil.data)):
for jk, val in zip(row, data):
if (val < largest_negative) or (val > smallest_positive):
wdok[ik, jk] = val
keep_connections += 1
return wdok.tocsr().getnnz(axis=1)
def weights_evolution_I(self):
# this represents the core of the SET procedure. It removes the weights closest to zero in each layer and add new random weights
for i in range(1, self.n_layers - 1):
values = np.sort(self.w[i].data)
first_zero_pos = find_first_pos(values, 0)
last_zero_pos = find_last_pos(values, 0)
largest_negative = values[int((1 - self.zeta) * first_zero_pos)]
smallest_positive = values[int(
min(
values.shape[0] - 1, last_zero_pos + self.zeta *
(values.shape[0] - last_zero_pos)))]
wlil = self.w[i].tolil()
pdwlil = self.pdw[i].tolil()
wdok = dok_matrix((self.dimensions[i - 1], self.dimensions[i]),
dtype="float32")
pdwdok = dok_matrix((self.dimensions[i - 1], self.dimensions[i]),
dtype="float32")
# remove the weights closest to zero
keep_connections = 0
for ik, (row, data) in enumerate(zip(wlil.rows, wlil.data)):
for jk, val in zip(row, data):
if (val < largest_negative) or (val > smallest_positive):
wdok[ik, jk] = val
pdwdok[ik, jk] = pdwlil[ik, jk]
keep_connections += 1
limit = np.sqrt(6. / float(self.dimensions[i]))
# add new random connections
for kk in range(self.w[i].data.shape[0] - keep_connections):
ik = np.random.randint(0, self.dimensions[i - 1])
jk = np.random.randint(0, self.dimensions[i])
while (wdok[ik, jk] != 0):
ik = np.random.randint(0, self.dimensions[i - 1])
jk = np.random.randint(0, self.dimensions[i])
wdok[ik, jk] = np.random.uniform(-limit, limit)
pdwdok[ik, jk] = 0
self.pdw[i] = pdwdok.tocsr()
self.w[i] = wdok.tocsr()
def weights_evolution_II(self):
# this represents the core of the SET procedure. It removes the weights closest to zero in each layer and add new random weights
# improved running time using numpy routines - Amarsagar Reddy Ramapuram Matavalam ([email protected])
for i in range(1, self.n_layers - 1):
# uncomment line below to stop evolution of dense weights more than 80% non-zeros
# if self.w[i].count_nonzero() / (self.w[i].get_shape()[0]*self.w[i].get_shape()[1]) < 0.8:
t_ev_1 = datetime.datetime.now()
# converting to COO form - Added by Amar
wcoo = self.w[i].tocoo()
vals_w = wcoo.data
rows_w = wcoo.row
cols_w = wcoo.col
pdcoo = self.pdw[i].tocoo()
vals_pd = pdcoo.data
rows_pd = pdcoo.row
cols_pd = pdcoo.col
# print("Number of non zeros in W and PD matrix before evolution in layer",i,[np.size(valsW), np.size(valsPD)])
values = np.sort(self.w[i].data)
first_zero_pos = find_first_pos(values, 0)
last_zero_pos = find_last_pos(values, 0)
largest_negative = values[int((1 - self.zeta) * first_zero_pos)]
smallest_positive = values[int(
min(
values.shape[0] - 1, last_zero_pos + self.zeta *
(values.shape[0] - last_zero_pos)))]
#remove the weights (W) closest to zero and modify PD as well
vals_w_new = vals_w[(vals_w > smallest_positive) |
(vals_w < largest_negative)]
rows_w_new = rows_w[(vals_w > smallest_positive) |
(vals_w < largest_negative)]
cols_w_new = cols_w[(vals_w > smallest_positive) |
(vals_w < largest_negative)]
new_w_row_col_index = np.stack((rows_w_new, cols_w_new), axis=-1)
old_pd_row_col_index = np.stack((rows_pd, cols_pd), axis=-1)
new_pd_row_col_index_flag = array_intersect(
old_pd_row_col_index,
new_w_row_col_index) # careful about order
vals_pd_new = vals_pd[new_pd_row_col_index_flag]
rows_pd_new = rows_pd[new_pd_row_col_index_flag]
cols_pd_new = cols_pd[new_pd_row_col_index_flag]
self.pdw[i] = coo_matrix(
(vals_pd_new, (rows_pd_new, cols_pd_new)),
(self.dimensions[i - 1], self.dimensions[i])).tocsr()
if i == 1:
self.input_layer_connections.append(
coo_matrix(
(vals_w_new, (rows_w_new, cols_w_new)),
(self.dimensions[i - 1], self.dimensions[i])).getnnz(
axis=1))
np.savez_compressed(
self.save_filename + "_input_connections.npz",
inputLayerConnections=self.input_layer_connections)
# add new random connections
keep_connections = np.size(rows_w_new)
length_random = vals_w.shape[0] - keep_connections
limit = np.sqrt(6. / float(self.dimensions[i - 1]))
random_vals = np.random.uniform(-limit, limit, length_random)
zero_vals = 0 * random_vals # explicit zeros
# adding (wdok[ik,jk]!=0): condition
while length_random > 0:
ik = np.random.randint(0,
self.dimensions[i - 1],
size=length_random,
dtype='int32')
jk = np.random.randint(0,
self.dimensions[i],
size=length_random,
dtype='int32')
random_w_row_col_index = np.stack((ik, jk), axis=-1)
random_w_row_col_index = np.unique(
random_w_row_col_index,
axis=0) # removing duplicates in new rows&cols
oldW_row_col_index = np.stack((rows_w_new, cols_w_new),
axis=-1)
unique_flag = ~array_intersect(
random_w_row_col_index,
oldW_row_col_index) # careful about order & tilda
ik_new = random_w_row_col_index[unique_flag][:, 0]
jk_new = random_w_row_col_index[unique_flag][:, 1]
# be careful - row size and col size needs to be verified
rows_w_new = np.append(rows_w_new, ik_new)
cols_w_new = np.append(cols_w_new, jk_new)
length_random = vals_w.shape[0] - np.size(
rows_w_new) # this will constantly reduce lengthRandom
# adding all the values along with corresponding row and column indices - Added by Amar
vals_w_new = np.append(
vals_w_new,
random_vals) # be careful - we can add to an existing link ?
# vals_pd_new = np.append(vals_pd_new, zero_vals) # be careful - adding explicit zeros - any reason??
if vals_w_new.shape[0] != rows_w_new.shape[0]:
print("not good")
self.w[i] = coo_matrix(
(vals_w_new, (rows_w_new, cols_w_new)),
(self.dimensions[i - 1], self.dimensions[i])).tocsr()
# print("Number of non zeros in W and PD matrix after evolution in layer",i,[(self.w[i].data.shape[0]), (self.pdw[i].data.shape[0])])
t_ev_2 = datetime.datetime.now()
print("Weights evolution time for layer", i, "is", t_ev_2 - t_ev_1)
def predict(self, x_test, y_test, batch_size=100):
"""
:param x_test: (array) Test input
:param y_test: (array) Correct test output
:param batch_size:
:return: (flt) Classification accuracy
:return: (array) A 2D array of shape (n_cases, n_classes).
"""
activations = np.zeros((y_test.shape[0], y_test.shape[1]))
for j in range(x_test.shape[0] // batch_size):
k = j * batch_size
l = (j + 1) * batch_size
_, a_test, _ = self._feed_forward(x_test[k:l], drop=False)
activations[k:l] = a_test[self.n_layers]
accuracy = compute_accuracy(activations, y_test)
return accuracy, activations
class Dense_MLP:
def __init__(self, dimensions, activations):
"""
:param dimensions: (tpl/ list) Dimensions of the neural net. (input, hidden layer, output)
:param activations: (tpl/ list) Activations functions.
Example of three hidden layer with
- 3312 input features
- 3000 hidden neurons
- 3000 hidden neurons
- 3000 hidden neurons
- 5 output classes
layers --> [1, 2, 3, 4, 5]
----------------------------------------
dimensions = (3312, 3000, 3000, 3000, 5)
activations = ( Relu, Relu, Relu, Sigmoid)
"""
self.n_layers = len(dimensions)
self.loss = None
self.learning_rate = None
self.momentum = None
self.weight_decay = None
self.dropout_rate = 0. # dropout rate
self.dimensions = dimensions
self.save_filename = ""
self.monitor = None
# Weights and biases are initiated by index. For a one hidden layer net you will have a w[1] and w[2]
self.w = {}
self.b = {}
self.pdw = {}
self.pdd = {}
# Activations are also initiated by index. For the example we will have activations[2] and activations[3]
self.activations = {}
for i in range(len(dimensions) - 1):
# He uniform initialization
limit = np.sqrt(6. / float(dimensions[i]))
self.w[i + 1] = np.random.uniform(
-limit, limit, (dimensions[i], dimensions[i + 1]))
self.b[i + 1] = np.zeros(dimensions[i + 1])
self.activations[i + 2] = activations[i]
def _feed_forward(self, x, drop=False):
"""
Execute a forward feed through the network.
:param x: (array) Batch of input data vectors.
:return: (tpl) Node outputs and activations per layer. The numbering of the output is equivalent to the layer numbers.
"""
# w(x) + b
z = {}
# activations: f(z)
a = {
1: x
} # First layer has no activations as input. The input x is the input.
masks = {}
for i in range(1, self.n_layers):
z[i + 1] = a[i] @ self.w[i] + self.b[i]
a[i + 1] = self.activations[i + 1].activation(z[i + 1])
if drop:
if i < self.n_layers - 1:
# apply dropout
a[i + 1], keep_mask = dropout(a[i + 1], self.dropout_rate)
masks[i + 1] = keep_mask
return z, a, masks
def _back_prop(self, z, a, masks, y_true):
"""
The input dicts keys represent the layers of the net.
a = { 1: x,
2: f(w1(x) + b1)
3: f(w2(a2) + b2)
4: f(w3(a3) + b3)
5: f(w4(a4) + b4)
}
:param z: (dict) w(x) + b
:param a: (dict) f(z)
:param y_true: (array) One hot encoded truth vector.
:return:
"""
keep_prob = 1.
if self.dropout_rate > 0:
keep_prob = np.float32(1. - self.dropout_rate)
# Determine partial derivative and delta for the output layer.
# delta output layer
delta = self.loss.delta(y_true, a[self.n_layers])
dw = np.dot(a[self.n_layers - 1].T, delta)
update_params = {self.n_layers - 1: (dw, np.mean(delta, axis=0))}
# In case of three layer net will iterate over i = 2 and i = 1
# Determine partial derivative and delta for the rest of the layers.
# Each iteration requires the delta from the previous layer, propagating backwards.
for i in reversed(range(2, self.n_layers)):
# dropout for the backpropagation step
if keep_prob != 1:
delta = (delta @ self.w[i].transpose()
) * self.activations[i].prime(z[i])
delta = delta * masks[i]
delta /= keep_prob
else:
delta = (delta @ self.w[i].transpose()
) * self.activations[i].prime(z[i])
dw = np.dot(a[i - 1].T, delta)
update_params[i - 1] = (dw, np.mean(delta, axis=0))
for k, v in update_params.items():
self._update_w_b(k, v[0], v[1])
def _update_w_b(self, index, dw, delta):
"""
Update weights and biases.
:param index: (int) Number of the layer
:param dw: (array) Partial derivatives
:param delta: (array) Delta error.
"""
# perform the update with momentum
if index not in self.pdw:
self.pdw[index] = -self.learning_rate * dw
self.pdd[index] = -self.learning_rate * delta
else:
self.pdw[index] = self.momentum * self.pdw[
index] - self.learning_rate * dw
self.pdd[index] = self.momentum * self.pdd[
index] - self.learning_rate * delta
self.w[index] += self.pdw[index] - self.weight_decay * self.w[index]
self.b[index] += self.pdd[index] - self.weight_decay * self.b[index]
def fit(self,
x,
y_true,
x_test,
y_test,
loss,
epochs,
batch_size,
learning_rate=1e-3,
momentum=0.9,
weight_decay=0.0002,
dropoutrate=0.,
testing=True,
save_filename="",
monitor=False):
"""
:param x: (array) Containing parameters
:param y_true: (array) Containing one hot encoded labels.
:return (array) A 2D array of metrics (epochs, 3).
"""
if not x.shape[0] == y_true.shape[0]:
raise ValueError("Length of x and y arrays don't match")
self.monitor = Monitor(
save_filename=save_filename) if monitor else None
# Initiate the loss object with the final activation function
self.loss = loss()
self.learning_rate = learning_rate
self.momentum = momentum
self.weight_decay = weight_decay
self.dropout_rate = dropoutrate
self.save_filename = save_filename
maximum_accuracy = 0
metrics = np.zeros((epochs, 4))
for i in range(epochs):
# Shuffle the data
seed = np.arange(x.shape[0])
np.random.shuffle(seed)
x_ = x[seed]
y_ = y_true[seed]
if self.monitor:
self.monitor.start_monitor()
# training
t1 = datetime.datetime.now()
for j in range(x.shape[0] // batch_size):
k = j * batch_size
l = (j + 1) * batch_size
z, a, masks = self._feed_forward(x_[k:l], True)
self._back_prop(z, a, masks, y_[k:l])
t2 = datetime.datetime.now()
if self.monitor:
self.monitor.stop_monitor()
print("\nDense-MLP Epoch ", i)
print("Training time: ", t2 - t1)
# test model performance on the test data at each epoch
# this part is useful to understand model performance and can be commented for production settings
if (testing):
t3 = datetime.datetime.now()
accuracy_test, activations_test = self.predict(
x_test, y_test, batch_size)
accuracy_train, activations_train = self.predict(
x, y_true, batch_size)
t4 = datetime.datetime.now()
maximum_accuracy = max(maximum_accuracy, accuracy_test)
loss_test = self.loss.loss(y_test, activations_test)
loss_train = self.loss.loss(y_true, activations_train)
metrics[i, 0] = loss_train
metrics[i, 1] = loss_test
metrics[i, 2] = accuracy_train
metrics[i, 3] = accuracy_test
print(f"Testing time: {t4 - t3}\n; Loss test: {loss_test}; \n"
f"Accuracy test: {accuracy_test}; \n"
f"Maximum accuracy val: {maximum_accuracy}")
# save performance metrics values in a file
if save_filename != "":
np.savetxt(save_filename + ".txt", metrics)
if self.save_filename != "" and self.monitor:
with open(self.save_filename + "_monitor.json", 'w') as file:
file.write(
json.dumps(self.monitor.get_stats(),
indent=4,
sort_keys=True,
default=str))
return metrics
def predict(self, x_test, y_test, batch_size=100):
"""
:param x_test: (array) Test input
:param y_test: (array) Correct test output
:param batch_size:
:return: (flt) Classification accuracy
:return: (array) A 2D array of shape (n_cases, n_classes).
"""
activations = np.zeros((y_test.shape[0], y_test.shape[1]))
for j in range(x_test.shape[0] // batch_size):
k = j * batch_size
l = (j + 1) * batch_size
_, a_test, _ = self._feed_forward(x_test[k:l], drop=False)
activations[k:l] = a_test[self.n_layers]
accuracy = compute_accuracy(activations, y_test)
return accuracy, activations
