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mc_training.py
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mc_training.py
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# Copyright 2022 The nn_inconsistency Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
from enum import Enum
import numpy as np
import time
from TrainingSetup import TrainingSetup
import utils
import multiprocessing
class TrainingStatus(Enum):
UNFINISHED = 0 # neural network has not been stopped yet
X_DEGENERATE = 1 # all x points have the same sign
A_DEGENERATE = 2 # all a_i values have the same sign
CROSSED = 3 # a kink crossed a datapoint
LOCALLY_CONVERGED = 4 # a kink will never cross a datapoint
EARLY_STOPPED = 5 # an early stopping criterion was satisfied
def expand(x, dims):
for d in dims:
x = np.expand_dims(x, d)
return x
def get_standard_dataset():
return np.array([-3., -2., -1., 1., 2., 3.]), np.array([-1.0, 2.0, -1.0, 1.0, -2.0, 1.0])
# contains temporary variables for training that should not be saved
class TrainingVariables(object):
def __init__(self, num_parallel, num_hidden, x, y, x_weights, lrs, use_adam=False):
self.num_parallel = num_parallel
self.batch_size = len(x)
self.num_hidden = num_hidden
# temporary variables for intermediate results during forward- and backpropagation
self.relu_result = np.zeros(shape=(self.num_parallel, self.batch_size, self.num_hidden))
self.inactive = np.zeros(shape=(self.num_parallel, self.batch_size, self.num_hidden), dtype=np.bool)
self.wr = np.copy(self.relu_result)
self.f_minus_y_times_lr = np.zeros(shape=(self.num_parallel, self.batch_size, 1))
self.step_c = np.zeros(shape=(self.num_parallel, 1, 1))
self.step = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.fmy_lr_w = np.copy(self.wr)
# for early stopping
self.wait_times = np.zeros(num_parallel, dtype=np.int)
self.best_validation_losses = np.inf * np.ones(num_parallel)
self.X = expand(x, [0, 2])
self.Y = expand(y, [0, 2])
self.X_weights = np.expand_dims(x_weights, axis=2)
self.neg_lrs = -expand(lrs, [1, 2])
self.use_adam = use_adam
if use_adam:
self.beta_1 = 0.9
self.beta_2 = 0.999
self.eps = 1e-8
self.beta_1_power = 1.0
self.beta_2_power = 1.0
self.grad_acc_a = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.grad_acc_b = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.grad_acc_c = np.zeros(shape=(self.num_parallel, 1, 1))
self.grad_acc_w = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.sq_grad_acc_a = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.sq_grad_acc_b = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
self.sq_grad_acc_c = np.zeros(shape=(self.num_parallel, 1, 1))
self.sq_grad_acc_w = np.zeros(shape=(self.num_parallel, 1, self.num_hidden))
# stops all neural nets where a kink has potentially crossed a datapoint, i.e. |x_{kink}| >= min_j |x_j|
# where x_j are the datapoints
class CrossingStoppingCriterion(object):
def check(self, net, vars):
crossed_point_indices = net.max_kink_movement[net.orig_indices] >= net.min_abs_x
net.terminate_instances(vars, [crossed_point_indices], [TrainingStatus.CROSSED])
# stops all neural nets if during the last $patience$ checks, the validation loss did not improve by at least $min_delta$
class EarlyStoppingCriterion(object):
def __init__(self, min_delta, patience):
self.min_delta = min_delta
self.patience = patience
def check(self, net, vars):
vars.wait_times += 1
val_losses = net.compute_validation_losses()
improved_indices = val_losses < vars.best_validation_losses - self.min_delta
vars.best_validation_losses[improved_indices] = val_losses[improved_indices]
vars.wait_times[improved_indices] = 0
early_stopping_indices = vars.wait_times >= self.patience
net.terminate_instances(vars, [early_stopping_indices],
[TrainingStatus.EARLY_STOPPED])
# stops all neural nets where theory ensures that no kink will ever cross a datapoint (using gradient descent)
class SufficientStoppingCriterion(object):
def check(self, net, vars):
locally_converged_indices = np.array([
net.train_setups[net.orig_indices[i]].check_convergence(net.a[i, 0, :], net.b[i, 0, :],
net.c[i, 0, 0], net.w[i, 0, :],
net.lrs[net.orig_indices[i]])
for i in range(net.a.shape[0])])
# indices where all neurons point to the same side (i. e. the same sign)
a_degenerate_indices = np.logical_or(np.all(net.a[:, 0, :] > 0, axis=1), np.all(net.a[:, 0, :] < 0, axis=1))
x_degenerate_indices = np.logical_or(
np.count_nonzero(net.x_weights[net.orig_indices, :][:, net.x > 0], axis=1) <= 1,
np.count_nonzero(net.x_weights[net.orig_indices, :][:, net.x < 0], axis=1) <= 1)
net.terminate_instances(vars, [locally_converged_indices, a_degenerate_indices,
x_degenerate_indices],
[TrainingStatus.LOCALLY_CONVERGED, TrainingStatus.A_DEGENERATE,
TrainingStatus.X_DEGENERATE])
# Neural net class which uses numpy to evaluate multiple
# two-layer relu networks with one input and one output neuron in parallel.
# It can also check whether certain networks satisfy a stopping criterion and remove them from the training process.
class CheckingNN(object):
def __init__(self, initial_weights, train_setups, lrs, val_x_weights=None):
(initial_a, initial_b, initial_c, initial_w) = initial_weights
# dimensions: num_parallel_networks x batch_size x (num_hidden or 1)
# Important: Stopped networks are removed from some of the arrays in the terminate_instances() method
# while they are kept in others (to have some statistics about training afterwards)
# Of course, these arrays have to be indexed differently. The link is the array orig_indices, which initially
# contains [0, 1, ..., num_parallel_networks - 1] and from which the stopped networks then are removed.
# Hence, if stopped networks are not removed from array A,
# then A[orig_indices] is the array A with the stopped indices removed.
# network parameters
self.a = np.copy(initial_a)
self.b = np.copy(initial_b)
self.c = np.copy(initial_c)
self.w = np.copy(initial_w)
self.num_hidden = self.a.shape[2]
self.num_parallel = self.a.shape[0]
# a copy such that the initial values can be retrieved later on
self.a_initial = np.copy(self.a)
self.b_initial = np.copy(self.b)
self.c_initial = np.copy(self.c)
self.c_initial = np.copy(self.w)
# will be filled whenever a network stops
self.a_terminal = np.zeros(self.a.shape)
self.b_terminal = np.zeros(self.b.shape)
self.c_terminal = np.zeros(self.c.shape)
self.w_terminal = np.zeros(self.w.shape)
self.iteration_count = 0
self.check_count = 0
# whenever a network is stopped for a reason, the reason is stored in this array
self.training_status = np.array([TrainingStatus.UNFINISHED] * self.num_parallel)
self.stop_iteration = np.array([-1] * self.num_parallel) # the iteration count in which a network was stopped
# see above
self.orig_indices = np.arange(self.num_parallel)
# stores the maximum absolute kink value of each network,
# where the maximum is taken over all training iterations and hidden neurons
self.max_kink_movement = np.zeros(self.num_parallel)
self.train_setups = train_setups
self.lrs = lrs
# assumes that all the train_setups have the same x and y values, although they might have different weights
self.x = np.copy(self.train_setups[0].x)
self.y = np.copy(self.train_setups[0].y)
self.x_weights = np.copy(np.array([train_setups[i].x_weights for i in range(self.num_parallel)]))
self.min_abs_x = np.min(np.abs(self.x))
self.val_x_weights = val_x_weights # validation weights (for the x and y values above)
def create_training_vars(self, use_adam=False):
# creates an intermediate object which contains temporary variables
# these are in a different class so that they are not saved when an object of CheckingNN is serialized
return TrainingVariables(self.get_num_unfinished(), self.num_hidden, self.x, self.y,
self.x_weights[self.orig_indices], self.lrs[self.orig_indices], use_adam=use_adam)
# trains for one epoch using gradient descent (no minibatching)
def train_one_epoch(self, vars : TrainingVariables):
np.multiply(self.a, vars.X, out=vars.relu_result)
vars.relu_result += self.b
np.less(vars.relu_result, 0, out=vars.inactive)
vars.relu_result[vars.inactive] = 0
np.multiply(self.w, vars.relu_result, out=vars.wr)
np.sum(vars.wr, axis=2, keepdims=True, out=vars.f_minus_y_times_lr)
vars.f_minus_y_times_lr += self.c
vars.f_minus_y_times_lr -= vars.Y
vars.f_minus_y_times_lr *= vars.X_weights # allows different weighting for the different dataset samples
vars.f_minus_y_times_lr *= vars.neg_lrs # lr should be a vector of learning rates for each parallel instance
np.sum(vars.f_minus_y_times_lr, axis=1, keepdims=True, out=vars.step_c)
self.c += vars.step_c
np.multiply(vars.f_minus_y_times_lr, self.w, out=vars.fmy_lr_w)
vars.fmy_lr_w[vars.inactive] = 0
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
self.b += vars.step
np.multiply(vars.fmy_lr_w, vars.X, out=vars.fmy_lr_w)
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
self.a += vars.step
np.multiply(vars.f_minus_y_times_lr, vars.relu_result, out=vars.fmy_lr_w)
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
self.w += vars.step
self.max_kink_movement[self.orig_indices] = np.maximum(self.max_kink_movement[self.orig_indices],
np.max(np.abs(self.b / self.a), axis=2).flatten())
self.iteration_count += 1
def adam_step(self, vars : TrainingVariables):
vars.beta_1_power *= vars.beta_1
vars.beta_2_power *= vars.beta_2
np.multiply(self.a, vars.X, out=vars.relu_result)
vars.relu_result += self.b
np.less(vars.relu_result, 0, out=vars.inactive)
vars.relu_result[vars.inactive] = 0
np.multiply(self.w, vars.relu_result, out=vars.wr)
np.sum(vars.wr, axis=2, keepdims=True, out=vars.f_minus_y_times_lr)
vars.f_minus_y_times_lr += self.c
vars.f_minus_y_times_lr -= vars.Y
vars.f_minus_y_times_lr *= vars.X_weights # allows different weighting for the different dataset samples
#vars.f_minus_y_times_lr *= vars.neg_lrs # lr should be a vector of learning rates for each parallel instance
np.sum(vars.f_minus_y_times_lr, axis=1, keepdims=True, out=vars.step_c)
vars.sq_grad_acc_c *= vars.beta_2
vars.sq_grad_acc_c += (1-vars.beta_2) * vars.step_c**2
vars.grad_acc_c *= vars.beta_1
vars.grad_acc_c += (1 - vars.beta_1) * vars.step_c
self.c += vars.neg_lrs * (vars.grad_acc_c / (1.0 - vars.beta_1_power)) \
/ (np.sqrt(vars.sq_grad_acc_c / (1.0 - vars.beta_2_power)) + vars.eps)
np.multiply(vars.f_minus_y_times_lr, self.w, out=vars.fmy_lr_w)
vars.fmy_lr_w[vars.inactive] = 0
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
vars.sq_grad_acc_b *= vars.beta_2
vars.sq_grad_acc_b += (1 - vars.beta_2) * vars.step ** 2
vars.grad_acc_b *= vars.beta_1
vars.grad_acc_b += (1 - vars.beta_1) * vars.step
self.b += vars.neg_lrs * (vars.grad_acc_b / (1.0 - vars.beta_1_power)) \
/ (np.sqrt(vars.sq_grad_acc_b / (1.0 - vars.beta_2_power)) + vars.eps)
np.multiply(vars.fmy_lr_w, vars.X, out=vars.fmy_lr_w)
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
vars.sq_grad_acc_a *= vars.beta_2
vars.sq_grad_acc_a += (1 - vars.beta_2) * vars.step ** 2
vars.grad_acc_a *= vars.beta_1
vars.grad_acc_a += (1 - vars.beta_1) * vars.step
self.a += vars.neg_lrs * (vars.grad_acc_a / (1.0 - vars.beta_1_power)) \
/ (np.sqrt(vars.sq_grad_acc_a / (1.0 - vars.beta_2_power)) + vars.eps)
np.multiply(vars.f_minus_y_times_lr, vars.relu_result, out=vars.fmy_lr_w)
np.sum(vars.fmy_lr_w, axis=1, keepdims=True, out=vars.step)
vars.sq_grad_acc_w *= vars.beta_2
vars.sq_grad_acc_w += (1 - vars.beta_2) * vars.step ** 2
vars.grad_acc_w *= vars.beta_1
vars.grad_acc_w += (1 - vars.beta_1) * vars.step
self.w += vars.neg_lrs * (vars.grad_acc_w / (1.0 - vars.beta_1_power)) \
/ (np.sqrt(vars.sq_grad_acc_w / (1.0 - vars.beta_2_power)) + vars.eps)
self.max_kink_movement[self.orig_indices] = np.maximum(self.max_kink_movement[self.orig_indices],
np.max(np.abs(self.b / self.a), axis=2).flatten())
self.iteration_count += 1
def terminate_instances(self, vars, bool_arrays, statuses, testing=False):
# takes a list of boolean arrays that indicate for different reasons
# which instances should be terminated for that reason
# statuses contains the reasons represented by TrainingStatus enumeration items
# order matters for setting the statuses in case that an instance should be terminated for more than one reason
# (later reasons are dominant)
# if testing is true, locally_converged entries will be kept running to check that they are not crossing later
if testing:
reduced_bool_arrays = [bool_arrays[i] for i in range(len(bool_arrays)) if statuses[i] != TrainingStatus.LOCALLY_CONVERGED]
finished_indices = np.any(reduced_bool_arrays, axis=0)
else:
finished_indices = np.any(bool_arrays, axis=0)
unfinished_indices = ~finished_indices
self.a_terminal[self.orig_indices[finished_indices], :, :] = self.a[finished_indices, :, :]
self.b_terminal[self.orig_indices[finished_indices], :, :] = self.b[finished_indices, :, :]
self.c_terminal[self.orig_indices[finished_indices], :, :] = self.c[finished_indices, :, :]
self.w_terminal[self.orig_indices[finished_indices], :, :] = self.w[finished_indices, :, :]
for arr, status in zip(bool_arrays, statuses):
# this can be used with the above code to test that no locally_converged net will also cross later
if testing:
if status == TrainingStatus.CROSSED and np.any(self.training_status[self.orig_indices[arr]] == TrainingStatus.LOCALLY_CONVERGED):
print('Error: Locally converged and crossed')
exit()
self.training_status[self.orig_indices[arr]] = status
self.stop_iteration[self.orig_indices[finished_indices]] = self.iteration_count
# remove values for finished networks
self.a = self.a[unfinished_indices, :, :]
self.b = self.b[unfinished_indices, :, :]
self.c = self.c[unfinished_indices, :, :]
self.w = self.w[unfinished_indices, :, :]
vars.neg_lrs = vars.neg_lrs[unfinished_indices, :, :]
vars.X_weights = vars.X_weights[unfinished_indices, :, :]
vars.relu_result = vars.relu_result[unfinished_indices, :, :]
vars.inactive = vars.inactive[unfinished_indices, :, :]
vars.wr = vars.wr[unfinished_indices, :, :]
vars.f_minus_y_times_lr = vars.f_minus_y_times_lr[unfinished_indices, :, :]
vars.step_c = vars.step_c[unfinished_indices, :, :]
vars.step = vars.step[unfinished_indices, :, :]
vars.fmy_lr_w = vars.fmy_lr_w[unfinished_indices, :, :]
vars.wait_times = vars.wait_times[unfinished_indices]
vars.best_validation_losses = vars.best_validation_losses[unfinished_indices]
if vars.use_adam:
vars.sq_grad_acc_a = vars.sq_grad_acc_a[unfinished_indices, :, :]
vars.sq_grad_acc_b = vars.sq_grad_acc_b[unfinished_indices, :, :]
vars.sq_grad_acc_c = vars.sq_grad_acc_c[unfinished_indices, :, :]
vars.sq_grad_acc_w = vars.sq_grad_acc_w[unfinished_indices, :, :]
vars.grad_acc_a = vars.grad_acc_a[unfinished_indices, :, :]
vars.grad_acc_b = vars.grad_acc_b[unfinished_indices, :, :]
vars.grad_acc_c = vars.grad_acc_c[unfinished_indices, :, :]
vars.grad_acc_w = vars.grad_acc_w[unfinished_indices, :, :]
self.orig_indices = self.orig_indices[unfinished_indices]
# computes validation losses for each network
def compute_validation_losses(self):
pred = self.predict(self.x)
errors = expand(self.y, [0]) - pred
return np.sum(errors * errors * self.val_x_weights[self.orig_indices], axis=1)
def train(self, stopping_criteria, max_num_checks, num_minibatches_per_check, minibatch_size=None, verbose=True, use_adam=False):
# If minibatch_size is None, non-stochastic gradient descent is used.
# For stochastic gradient descent,
# minibatches are subsampled independently from the data and not cycled through the data.
vars = self.create_training_vars(use_adam=use_adam)
for check_count in range(max_num_checks):
if minibatch_size is None:
for i in range(num_minibatches_per_check):
if verbose and ((num_minibatches_per_check < 10) or (i % (num_minibatches_per_check // 10) == 0)):
print('.', end='', flush=True)
if use_adam:
self.adam_step(vars)
else:
self.train_one_epoch(vars)
else:
relevant_x_weights = self.x_weights[self.orig_indices, :]
stochastic_X_weights = np.asarray([np.random.multinomial(minibatch_size, relevant_x_weights[i, :], num_minibatches_per_check) / minibatch_size
for i in range(relevant_x_weights.shape[0])])
for i in range(num_minibatches_per_check):
vars.X_weights = np.expand_dims(stochastic_X_weights[:, i, :], axis=2)
if verbose and ((num_minibatches_per_check < 10) or (i % (num_minibatches_per_check // 10) == 0)):
print('.', end='', flush=True)
if use_adam:
self.adam_step(vars)
else:
self.train_one_epoch(vars)
for stopping_criterion in stopping_criteria:
stopping_criterion.check(self, vars)
if self.get_num_unfinished() == 0:
break
self.check_count += 1
print('Check {} [{} unfinished, {} crossed, {} early stopped, {} locally converged, {} a-degenerate, {} x-degenerate] for n_hidden={}'.format(
self.check_count, self.get_num_unfinished(), self.get_num_crossed(), self.get_num_early_stopped(),
self.get_num_locally_converged(), self.get_num_a_degenerate(), self.get_num_x_degenerate(),
self.num_hidden))
if self.get_num_unfinished() == 0:
break
print(
'Terminated [{} unfinished, {} crossed, {} early stopped, {} locally converged, {} a-degenerate, {} x-degenerate] for n_hidden={}'.format(
self.get_num_unfinished(), self.get_num_crossed(),
self.get_num_early_stopped(), self.get_num_locally_converged(), self.get_num_a_degenerate(),
self.get_num_x_degenerate(), self.num_hidden))
print('')
def get_num_crossed(self):
return np.count_nonzero(self.training_status == TrainingStatus.CROSSED)
def get_num_a_degenerate(self):
return np.count_nonzero(self.training_status == TrainingStatus.A_DEGENERATE)
def get_num_x_degenerate(self):
return np.count_nonzero(self.training_status == TrainingStatus.X_DEGENERATE)
def get_num_locally_converged(self):
return np.count_nonzero(self.training_status == TrainingStatus.LOCALLY_CONVERGED)
def get_num_unfinished(self):
return np.count_nonzero(self.training_status == TrainingStatus.UNFINISHED)
def get_num_early_stopped(self):
return np.count_nonzero(self.training_status == TrainingStatus.EARLY_STOPPED)
def predict(self, x, instance=None):
# evaluates all nets (if instance is None) or a single net on a list x of input points
if instance is None:
X = expand(x, [0, 2])
relu_result = self.a * X + self.b
relu_result[relu_result < 0] = 0
pred = np.sum(self.w * relu_result, axis=2, keepdims=True) + self.c
return pred[:, :, 0]
else:
X = expand(x, [1])
a = self.a[instance, :, :]
b = self.b[instance, :, :]
c = self.c[instance, :, :]
w = self.w[instance, :, :]
relu_result = a * X + b
inactive = relu_result < 0
relu_result[inactive] = 0
pred = np.sum(w * relu_result, axis=1, keepdims=True) + c
return pred[:, 0]
def reset_locally_converged(self):
# resets locally converged to unfinished. Does not reset a vars instance,
# hence must not be called during a training run
self.a_terminal[self.orig_indices, :, :] = self.a
self.b_terminal[self.orig_indices, :, :] = self.b
self.c_terminal[self.orig_indices, :, :] = self.c
self.w_terminal[self.orig_indices, :, :] = self.w
self.training_status[self.training_status == TrainingStatus.LOCALLY_CONVERGED] = TrainingStatus.UNFINISHED
self.orig_indices = np.arange(self.num_parallel)[self.training_status == TrainingStatus.UNFINISHED]
self.a = self.a_terminal[self.orig_indices, :, :]
self.b = self.b_terminal[self.orig_indices, :, :]
self.c = self.c_terminal[self.orig_indices, :, :]
self.w = self.w_terminal[self.orig_indices, :, :]
@staticmethod
def createRandomWeights(n_parallel, n_hidden, swap_variances=False):
# creates random weights according to He et al. (for swap_variances = False)
# or with swapped variances for a and w (for swap_variances = True)
a_variance = 2/1
w_variance = 2/n_hidden
if swap_variances:
tmp = a_variance
a_variance = w_variance
w_variance = tmp
a = np.sqrt(a_variance) * np.random.randn(n_parallel, 1, n_hidden)
b = np.zeros(shape=(n_parallel, 1, n_hidden))
c = np.zeros(shape=(n_parallel, 1, 1))
w = np.sqrt(w_variance) * np.random.randn(n_parallel, 1, n_hidden)
return a, b, c, w
class MCConfiguration(object):
# Configuration for a monte carlo run
def __init__(self, n_parallel, n_hidden, n_samples, seed, index, description=None):
self.n_parallel = n_parallel
self.n_hidden = n_hidden
self.n_samples = n_samples
self.index = index
self.seed = seed # each thread should have a different seed, otherwise they all use the same random samples
self.description = description
def get_param_combinations():
# computes a list of MCConfiguration objects such that computations are done for various network sizes
param_combinations = []
np.random.seed(1234567890)
np.random.randn(1000) # generate some random samples for warming up
min_log = 4 # 16
max_log = 11 # 2048
num_mc_runs = 10000 # use 10000 runs per network size
index = 0
for k in range(min_log, max_log + 1):
n_hidden = 2 ** k
n_samples = n_hidden ** 2
n_parallel = min(2 ** (max(16 - k, 3)), num_mc_runs) # the larger each individual net, the less nets per worker
num_remaining_parallel = num_mc_runs
while num_remaining_parallel > 0:
num_parallel_here = min(n_parallel, num_remaining_parallel)
seed = np.random.randint(2**30)
param_combinations.append(MCConfiguration(num_parallel_here, n_hidden, n_samples, seed, index))
num_remaining_parallel -= num_parallel_here
index += 1
return param_combinations
def mc_runner(config, offset_str, base_dir, use_sgd, use_early_stopping, use_sufficient_stopping, use_small_lr, initialize_custom, use_adam):
# method that can be run for a MCConfiguration object to do the computations and save them to a folder
start_time = time.time()
np.random.seed(config.seed)
x = np.array([-1.0, -2.0, -3.0, 1.0, 2.0, 3.0])
y = np.array([-1.0, 2.0, -1.0, 1.0, -2.0, 1.0]) + float(offset_str)
x_weights = np.random.multinomial(config.n_samples, [1. / 6.] * 6, size=config.n_parallel) / config.n_samples
val_x_weights = np.random.multinomial(config.n_samples, [1. / 6.] * 6, size=config.n_parallel) / config.n_samples
# x_weights = 1./6. * np.ones(shape=(n_parallel, 6))
(a, b, c, w) = CheckingNN.createRandomWeights(config.n_parallel, config.n_hidden, swap_variances=initialize_custom)
train_setups = [TrainingSetup(x, x_weights[i, :], y) for i in range(config.n_parallel)]
if use_small_lr:
lrs = np.array([1e-2 / config.n_hidden] * config.n_parallel)
else:
lrs = np.array([train_setups[i].compute_lr(a[i, 0, :], b[i, 0, :], w[i, 0, :]) for i in range(config.n_parallel)])
net = CheckingNN((a, b, c, w), train_setups, lrs, val_x_weights=val_x_weights)
max_num_checks = 10000 if initialize_custom else 1000
num_minibatches_per_check = 100 if initialize_custom else 1000
minibatch_size = 16 if (use_sgd or use_adam) else None # non-stochastic gradient descent
stopping_criteria = [CrossingStoppingCriterion()]
if use_early_stopping:
stopping_criteria.append(EarlyStoppingCriterion(min_delta=1e-8, patience=10))
if use_sufficient_stopping:
stopping_criteria.append(SufficientStoppingCriterion())
net.train(stopping_criteria=stopping_criteria, max_num_checks=max_num_checks,
num_minibatches_per_check=num_minibatches_per_check, minibatch_size=minibatch_size, verbose=False,
use_adam=use_adam)
target_folder = base_dir + 'mc-data-{}/hidden-{}_parallel-{}_id-{}_time-{}/'.format(offset_str, config.n_hidden, config.n_parallel, config.index, int(start_time*1000))
utils.serialize(target_folder+'net.p', net)
utils.serialize(target_folder+'config.p', config)
class OffsetMCRunner(object):
# Class that saves some more parameters for mc_runner
def __init__(self, offset_str, base_dir, use_sgd, use_early_stopping, use_sufficient_stopping, use_small_lr, initialize_custom, use_adam):
self.offset_str = offset_str
self.use_sgd = use_sgd
self.base_dir = base_dir
self.use_early_stopping = use_early_stopping
self.use_sufficient_stopping = use_sufficient_stopping
self.use_small_lr = use_small_lr
self.initialize_custom = initialize_custom
self.use_adam = use_adam
def __call__(self, config):
mc_runner(config, self.offset_str, self.base_dir, self.use_sgd, self.use_early_stopping, self.use_sufficient_stopping, self.use_small_lr, self.initialize_custom, self.use_adam)
def execute_mc(offset_str, base_dir='./mc-data/', use_sgd=False, use_early_stopping=False, use_sufficient_stopping=True,
use_small_lr=False, initialize_custom=False, use_adam=False):
# creates a thread pool and runs all computation tasks
param_combinations = get_param_combinations()
num_processes = max(1, multiprocessing.cpu_count()//2)
pool = multiprocessing.Pool(processes=num_processes)
utils.ensureDir(base_dir + 'mc-data-{}/'.format(offset_str))
pool.map(OffsetMCRunner(offset_str, base_dir, use_sgd, use_early_stopping, use_sufficient_stopping, use_small_lr, initialize_custom, use_adam), param_combinations, chunksize=1)
pool.terminate()
pool.join()
if __name__ == '__main__':
# always add a / at the end of all directories
# (code is intended for linux use, otherwise you need to convert / to \\)
base_dir = './mc-data/'
use_sgd = False # whether sgd or gd should be used
use_early_stopping = False # should be used for sgd since sufficient stopping is not constructed for sgd
# the sufficient stopping criterion only works provably for (non-stochastic) gradient descent
use_sufficient_stopping = True
use_small_lr = False # if true, use 0.01*n^{-1} instead of \lambda_{max}(A^{ref} M)^{-1}
initialize_custom = False # if true, swap the variances of a and w initialization
use_adam = False
for offset_str in ['0', '0.01', '0.1']:
execute_mc(offset_str, base_dir=base_dir, use_sgd=use_sgd, use_early_stopping=use_early_stopping,
use_sufficient_stopping=use_sufficient_stopping, use_small_lr=use_small_lr, initialize_custom=initialize_custom, use_adam=use_adam)
# this can be used to run a single task for quick experiments
#OffsetMCRunner('0', './mc-data-sgd/', use_sgd=False, use_early_stopping=False,
# use_sufficient_stopping=True, use_small_lr=False, initialize_custom=True)(MCConfiguration(n_parallel=100, n_hidden=2048, n_samples=2048**2, seed=0, index=0))