def main():
lr = 0.001
input_size = 50
output_size = 10
n_iterations = 100
# Both input and "ground truth" are random vectors
x = np.random.random(input_size)
y = np.random.random(output_size)
# Randomly initialize neural network weights
#weights = to_value(np.random.random((input_size, output_size)))
nn = MLP(input_size, output_size, [5, 10, 20])
print(nn.layers[0])
losses = []
for i in tqdm(range(100)):
y_pred = nn(x)
loss = np.sum((y - y_pred) * (y - y_pred))
losses.append(loss.data)
loss.backward()
for p in nn.parameters():
p.data -= lr * p.grad
nn.zero_grad()
plt.plot(losses)
plt.ylabel('Loss')
plt.xlabel('Iteration')
plt.title('Multilayer perceptron fitting random noise')
plt.show()
def __init__(self, generator=MLP(), discriminator=MLP()):
super().__init__()
if generator != None and discriminator != None:
self.generator = generator
self.discriminator = discriminator
self.layers = self.generator.layers + self.discriminator.layers
self.generator.loss = CrossEntropy()
self.discriminator.loss = CrossEntropy()
def __init__(self, input_dim, n_actions, gamma=0.9):
self.input_dim = input_dim
self.n_actions = n_actions
self.gamma = gamma
self.model = MLP(input_dim, [32, 32], n_actions)
self.optim = optim.Adam(self.model.parameters(), lr=1e-2)
self.action_reward = []
def __init__(self, encoder=MLP(), decoder=MLP(), noise=None):
"""
An Autoencoder consists of an Encoder network and a a Decoder network.
In the constructor merged these two networks.
"""
super().__init__()
self.layers += encoder.layers + decoder.layers
self.encoder = encoder
self.decoder = decoder
self.noise = noise
def __init__(self,
in_channels,
num_classes,
num_seg_classes,
stem_channels=(64, 128, 128),
local_channels=(512, 2048),
cls_channels=(256, 256),
seg_channels=(256, 256, 128),
dropout_prob_cls=0.3,
dropout_prob_seg=0.2,
with_transform=True):
"""
Args:
in_channels (int): the number of input channels
out_channels (int): the number of output channels
stem_channels (tuple of int): the numbers of channels in stem feature extractor
local_channels (tuple of int): the numbers of channels in local mlp
cls_channels (tuple of int): the numbers of channels in classification mlp
seg_channels (tuple of int): the numbers of channels in segmentation mlp
dropout_prob_cls (float): the probability to dropout in classification mlp
dropout_prob_seg (float): the probability to dropout in segmentation mlp
with_transform (bool): whether to use TNet to transform features.
"""
super(PointNetPartSeg, self).__init__()
self.in_channels = in_channels
self.num_classes = num_classes
self.num_seg_classes = num_seg_classes
# stem
self.stem = Stem(in_channels, stem_channels, with_transform=with_transform)
self.mlp_local = SharedMLP(stem_channels[-1], local_channels)
# classification
# Notice that we apply dropout to each classification mlp.
self.mlp_cls = MLP(local_channels[-1], cls_channels, dropout=dropout_prob_cls)
self.cls_logit = nn.Linear(cls_channels[-1], num_classes, bias=True)
# part segmentation
# Notice that the original repo concatenates global feature, one hot class embedding,
# stem features and local features. However, the paper does not use last local feature.
# Here, we follow the released repo.
in_channels_seg = local_channels[-1] + num_classes + sum(stem_channels) + sum(local_channels)
self.mlp_seg = SharedMLP(in_channels_seg, seg_channels[:-1], dropout=dropout_prob_seg)
self.conv_seg = Conv1d(seg_channels[-2], seg_channels[-1], 1)
self.seg_logit = nn.Conv1d(seg_channels[-1], num_seg_classes, 1, bias=True)
self.init_weights()
def load(self, name):
modelDir = f"./models/{name}"
self.encoder = MLP()
self.decoder = MLP()
self.decoder.loss = MSE()
# load encoder and decoder
for name, model in [("encoder", self.encoder),
("decoder", self.decoder)]:
layerDir = [
dir for dir in os.listdir(modelDir)
if os.path.isdir(os.path.join(modelDir, dir)) and name in dir
]
layerDir.sort(key=lambda x: int(x.strip(f"{name}_layer")))
for dir in layerDir:
layerFolder = os.path.join(modelDir, dir)
if "dense.json" in os.listdir(layerFolder):
# this is a dense layer
newLayer = Dense()
newLayer.load(layerFolder)
model.layers.append(newLayer)
# load aditional information about sampler
with open(f"{modelDir}/sampler.json", "r") as file:
data = json.load(file)
inputDim = data["inputDim"]
outputDim = data["outputDim"]
self.sampler = Sampler(inputDim, outputDim)
# load mean and logvar layer
self.sampler.mean = Dense()
self.sampler.mean.load(os.path.join(modelDir, f"sampler_mean"))
self.sampler.logVar = Dense()
self.sampler.logVar.load(os.path.join(modelDir, f"sampler_logvar"))
self.layers = self.encoder.layers + [
self.sampler.mean, self.sampler.logVar
] + self.decoder.layers
def init_model():
# Select the model
if FLAGS.model == 'mlp':
model = MLP()
elif FLAGS.model == 'shallow':
model = Shallow_CNN()
elif FLAGS.model == 'deep':
model = Deep_CNN()
else:
raise ValueError('--model should be "mlp", "shallow", or "deep"')
return model
def _init_model(self, model_name):
# Select the model
if model_name == 'mlp':
model = MLP()
elif model_name == 'shallow':
model = Shallow_CNN()
elif model_name == 'deep':
model = Deep_CNN()
else:
raise ValueError('--model should be "shallow" or "deep"')
return model
def get_evals(approx):
if approx == True:
model = MLP(params.neural_net_hiddens)
model.load_state_dict(torch.load('./model.pth'))
model.eval()
# Make data.
X = np.arange(params.x_0[0] - params.delta_0,
params.x_0[0] + params.delta_0, 0.05)
Y = np.arange(params.x_0[1] - params.delta_0,
params.x_0[0] + params.delta_0, 0.05)
X, Y = np.meshgrid(X, Y)
Z = []
for j in range(len(X)):
for i in range(len(X[0])):
# your loop order was backwards
point = np.array([[X[j][i], Y[j][i]]], dtype=np.float32)
inp = torch.from_numpy(point)
if approx == False:
val = f(point)
else:
val = model(inp).data.numpy()
Z.append(val)
Z = np.array(Z).reshape(X.shape)
return X, Y, Z
def __init__(self, embedding, encoder, encoder_type, mlp_input,
mlp_arc_hidden, mlp_lab_hidden, mlp_dropout, num_labels,
criterion):
super(BiAffineParser, self).__init__()
self.embedding = embedding
self.encoder = encoder
self.encoder_type = encoder_type
# Arc MLPs
self.arc_mlp_h = MLP(mlp_input, mlp_arc_hidden, 2, 'ReLU', mlp_dropout)
self.arc_mlp_d = MLP(mlp_input, mlp_arc_hidden, 2, 'ReLU', mlp_dropout)
# Label MLPs
self.lab_mlp_h = MLP(mlp_input, mlp_lab_hidden, 2, 'ReLU', mlp_dropout)
self.lab_mlp_d = MLP(mlp_input, mlp_lab_hidden, 2, 'ReLU', mlp_dropout)
# BiAffine layers
self.arc_biaffine = BiAffine(mlp_arc_hidden, 1)
self.lab_biaffine = BiAffine(mlp_lab_hidden, num_labels)
# Loss criterion
self.criterion = criterion()
def __init__(self, layer_num=2, hidden_dim=200):
super().__init__()
self.action_size = 3
self.state_size = 768 * 2
self.memory = deque(maxlen=2000)
self.gamma = 0.95
self.epsilon = 0.900
self.epsilon_min = 0.03
self.epsilon_decay = 0.995
self.temperature = 768
self.selection_epsilon = 0.900
self.selection_epsilon_min = 0.03
self.selection_epsilon_decay = 0.995
self.encoder = LocalGlobalEncoder()
self.mlp = MLP(in_dim=self.state_size,
hid_dim=hidden_dim,
out_dim=self.action_size,
layer_num=layer_num)
self.to(DEVICE)
class Policy(object):
def __init__(self, input_dim, n_actions, gamma=0.9):
self.input_dim = input_dim
self.n_actions = n_actions
self.gamma = gamma
self.model = MLP(input_dim, [32, 32], n_actions)
self.optim = optim.Adam(self.model.parameters(), lr=1e-2)
self.action_reward = []
def get_action(self, observation, stochastic=True):
pred = self.model(observation)
if stochastic:
return pred.multinomial()
return pred[0].argmax()
def update(self):
R = 0
rewards = []
for action, reward in self.action_reward:
R = reward + self.gamma * R
rewards.insert(0, R)
rewards = T.Tensor(rewards)
rewards = (rewards - rewards.mean()) / (rewards.std() +
np.finfo(np.float32).eps)
actions = []
for (action, _), reward in zip(self.action_reward, rewards):
action.reinforce(reward)
actions.append(action)
self.optim.zero_grad()
T.autograd.backward(actions, [None for _ in actions])
self.optim.step()
self.action_reward = []
def record(self, action, reward):
self.action_reward.append((action, reward))
def main():
# Learning the XOR
# (obs.: sensitive to standard dev. we use to init. weights)
# X = np.array([[.1, .1], [.1, .9], [.9, .1], [.9, .9]], dtype=float)
# Y = np.array([[.1], [.9], [.9], [.1]], dtype=float)
# xor = MLP(learning_rate=1.0, layers=[2, 2, 1], loss=MeanSquaredError, sigma=0.05)
# perf_xor = xor.fit(X, Y)
# plot_perf(perf_xor, 'perf_xor')
parser = argparse.ArgumentParser()
parser.add_argument(
"--bench_name",
type=str,
help="To choose the task. Available: monks-1, monks-2, monks-3."
)
parser.add_argument(
"--do_grid_search",
action="store_true",
help="Wheter to do hyper-params search via grid-search."
)
parser.add_argument(
"--lr",
default=1e-1,
type=float,
help="The learning rate. Default: 1e-1.",
)
parser.add_argument(
"--momentum",
default=0.0,
type=float,
help="The momentum. Default: 0.0.",
)
parser.add_argument(
"--reg",
default=0.0,
type=float,
help="The regularization term. Default: 0.0.",
)
parser.add_argument(
"--max_epochs",
default=100,
type=int,
help="The maximum number of epochs.",
)
parser.add_argument(
"--sigma",
default=1.0,
type=float,
help="To init weights with normal distribution N(mu, sigma), and scale sigma.",
)
parser.add_argument(
"--mu",
default=0.0,
type=float,
help="To init weights with normal distribution N(mu, sigma), and center mu.",
)
parser.add_argument(
'--layers',
nargs='+',
help='The layers\' inputs. E.g. n_input n_hid_i n_hid_k n_class, where n_input is the size of the input to the MLP,\
n_hid_j is the size of hidden layers, and n_class is the size of last layer for regression/classification tasks.'
)
parser.add_argument(
"--activation",
default='Linear',
type=str,
help="The activation function. Available: Linear, Sigmoid."
)
parser.add_argument(
"--activation_last_layer",
default='Sigmoid',
type=str,
help="The activation function to be applied after the classification or regression layer. Available: Linear, Sigmoid."
)
parser.add_argument(
"--task",
type=str,
help="The type of task to be solved. Available: classification, regression."
)
parser.add_argument(
"--verbose",
default='no',
type=str,
help="If output in verbose mode."
)
parser.add_argument(
"--debug_interval",
default=100,
type=int,
help="To output training info every debug_interval epochs."
)
parser.add_argument(
"--do_early_stopping",
action="store_true",
help="Wheter to do early stopping."
)
args = parser.parse_args()
X_train, Y_train = retrieveSamplesFromMonk(
f"monks-data/{args.bench_name}.train")
X_test, Y_test = retrieveSamplesFromMonk(
f"monks-data/{args.bench_name}.test")
logger.info(f"Training set len = {len(X_train)}")
logger.info(f"Test set len = {len(X_test)}")
logger.warning(
"do_grid_search: %s",
bool(args.do_grid_search)
)
if args.do_grid_search:
n_input, n_output = 17, 1
hyperspace = {
'learning_rate': [i/10 for i in range(1, 10)],
'momentum': [i/10 for i in range(1, 10)],
'lambda': [0.0], # [10**(-i) for i in range(1,6)],
'topology': [[n_input, 2**j, n_output] for j in range(1, 6)]
}
logger.info('Starting hyper-parameter grid-search.')
start = timer()
monk = HyperOptimizer(
hyperspace,
X_train,
Y_train,
loss=MeanSquaredError,
p=.70,
k=5,
scoring=['valid_err', 'test_err', 'accuracy'],
task=args.task,
X_ts=X_test,
Y_ts=Y_test
)
monk.hoptimize()
end = timer()
logger.info(
f'Grid-search for task {args.bench_name} has taken = {np.ceil((end-start)*1000)} ms')
monk = MLP(
learning_rate=args.lr,
momentum=args.momentum,
lamda=args.reg,
max_epochs=args.max_epochs,
layers=[int(l) for l in args.layers],
task=args.task,
verbose=args.verbose,
activation=Linear if args.activation == 'Linear' else Sigmoid,
activation_out=Linear if args.activation_last_layer == 'Linear' else Sigmoid,
do_early_stopping=args.do_early_stopping,
debug_interval=args.debug_interval
)
logger.info(f'Starting training for task {args.bench_name}.')
start = timer()
perf_monk = monk.fit(X_train, Y_train)
end = timer()
logger.info(
f'Training for task {args.bench_name} has taken = {np.ceil((end-start)*1000)} ms')
test_err = monk.score(X_test, Y_test)
logger.info(f'Test error = {test_err}')
plot_perf(perf_monk, f'perf_{args.bench_name}')
plot_accuracy(perf_monk, f'acc_{args.bench_name}')
def accuracy(predictions, label):
total_corr = 0
index = 0
for c in predictions.flatten():
if (c.item() > 0.5):
r = 1.0
else:
r = 0.0
if (r == label[index].item()):
total_corr += 1
index += 1
return (total_corr / len(label))
# Takes as input states (9 inputs), and outputs Q_value(a|s) for all possible a
Qnet = MLP()
# Target net is same as Qnet except is only updated every n runs
Tnet = MLP()
# MDP Hyperparams
numep = 10
# Agent can make at MOST 5 actions before forced termination
numt = 5
epsilon = 0.90
# Episode Loop
for ep in range(numep):
print('new game')
# Initialize tictactoe game
x = tictactoe()
terminate = False
newLayer.load(layerFolder)
model.layers.append(newLayer)
self.layers = self.generator.layers + self.discriminator.layers
if __name__ == "__main__":
dataset = Dataset(name="mnist",
train_size=60000,
test_size=10000,
batch_size=128)
LATENT_SIZE = 28 * 28
# set the learning rate and optimizer for training
optimizer = Adam(0.0002, 0.5)
generator = MLP()
generator.addLayer(
Dense(inputDim=LATENT_SIZE,
outputDim=256,
activation=LeakyReLU(0.2),
optimizer=optimizer))
generator.addLayer(
Dense(inputDim=256,
outputDim=512,
activation=LeakyReLU(0.2),
optimizer=optimizer))
generator.addLayer(
Dense(inputDim=512,
outputDim=1024,
activation=LeakyReLU(0.2),
optimizer=optimizer))
from nn import MLP
from datasets import BreastCancer
import matplotlib.pyplot as plt
x_train, y_train, x_test, y_test, _ = BreastCancer.load_data(pp='mms')
# Training
in_shape = (519, 30
) # input format -> (number_of_samples, number_of_attributes)
layers = (30, 30, 1) # Three Layers with 30-30-1 neurons
functions = ('relu', 'relu', 'sigmoid') # Activation function of each layer
epochs = 300
model = MLP(input_shape=in_shape,
layers=layers,
activations=functions,
initializer='he')
history = model.run(x_train, y_train, epochs=epochs, batch_size=32)
# Testing
prediction = model.predict(x_test)
# Plotting the Loss
plt.plot(range(epochs), history)
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.show()
def crossValidate(data, meta, folds, topology, iterations, weights, graph=None):
"k-fold cross validation"
if folds <= 1:
raise Exception("Cross validation folds must be > 1")
averageError = 0.0
for counter, (training, validation) in enumerate(
crossValidateIndices(items=range(data.shape[0]), k=folds, randomize=True)
):
# setup training and validation matricies
train = data.ix[training].reset_index(drop=True)
validate = data.ix[validation].reset_index(drop=True)
trainingFeatures = train.drop(meta.categoricalLabelColumns, axis=1) # remove output columns
validationFeatures = validate.drop(meta.categoricalLabelColumns, axis=1) # remove output columns
trainingLabels = train[meta.categoricalLabelColumns] # use only output columns
validationLabels = validate[meta.categoricalLabelColumns] # use only output columns
# setup MLP and start training
li(
"Fold {2}/{3} - Training with {1}/{4} rows ({0} epochs)".format(
iterations, trainingFeatures.shape[0], counter + 1, folds, data.shape[0]
)
)
mlp = MLP()
mlp.trainingIterations = iterations
mlp.initalWeightsMultiplier = weights
mlp.features = (
trainingFeatures.values
) # convert from pandas dataframe to numpy arrays. they are faster for the computationally intensive training phase.
mlp.labels = trainingLabels.values
mlp.validationFeatures = validationFeatures # for validation, send in pandas dataframes.
mlp.validationLabels = validationLabels
mlp.meta = meta
mlp.topology = topology
if graph:
mlp.trackLearning = True
mlp.setupHiddenLayers()
mlp.train()
if graph:
li("Plotting Learning to file '{0}'".format(graph))
mlp.plotLearning(graph)
# validate model
li(
"Fold {0}/{1} - Testing with {2}/{3} rows".format(
counter + 1, folds, validationFeatures.shape[0], data.shape[0]
)
)
error = mlp.validateModel(printToScreen=True)
averageError += error
averageError = averageError / folds
li("Average error across all folds: {0}".format(averageError))
return averageError
class PointNetPartSeg(nn.Module):
"""PointNet for part segmentation
References:
https://github.com/charlesq34/pointnet/blob/master/part_seg/pointnet_part_seg.py
"""
def __init__(self,
in_channels,
num_classes,
num_seg_classes,
stem_channels=(64, 128, 128),
local_channels=(512, 2048),
cls_channels=(256, 256),
seg_channels=(256, 256, 128),
dropout_prob_cls=0.3,
dropout_prob_seg=0.2,
with_transform=True):
"""
Args:
in_channels (int): the number of input channels
out_channels (int): the number of output channels
stem_channels (tuple of int): the numbers of channels in stem feature extractor
local_channels (tuple of int): the numbers of channels in local mlp
cls_channels (tuple of int): the numbers of channels in classification mlp
seg_channels (tuple of int): the numbers of channels in segmentation mlp
dropout_prob_cls (float): the probability to dropout in classification mlp
dropout_prob_seg (float): the probability to dropout in segmentation mlp
with_transform (bool): whether to use TNet to transform features.
"""
super(PointNetPartSeg, self).__init__()
self.in_channels = in_channels
self.num_classes = num_classes
self.num_seg_classes = num_seg_classes
# stem
self.stem = Stem(in_channels, stem_channels, with_transform=with_transform)
self.mlp_local = SharedMLP(stem_channels[-1], local_channels)
# classification
# Notice that we apply dropout to each classification mlp.
self.mlp_cls = MLP(local_channels[-1], cls_channels, dropout=dropout_prob_cls)
self.cls_logit = nn.Linear(cls_channels[-1], num_classes, bias=True)
# part segmentation
# Notice that the original repo concatenates global feature, one hot class embedding,
# stem features and local features. However, the paper does not use last local feature.
# Here, we follow the released repo.
in_channels_seg = local_channels[-1] + num_classes + sum(stem_channels) + sum(local_channels)
self.mlp_seg = SharedMLP(in_channels_seg, seg_channels[:-1], dropout=dropout_prob_seg)
self.conv_seg = Conv1d(seg_channels[-2], seg_channels[-1], 1)
self.seg_logit = nn.Conv1d(seg_channels[-1], num_seg_classes, 1, bias=True)
self.init_weights()
def forward(self, data_batch):
x = data_batch["points"]
cls_label = data_batch["cls_label"]
num_points = x.shape[2]
end_points = {}
# stem
stem_feature, end_points_stem = self.stem(x)
end_points["trans_input"] = end_points_stem["trans_input"]
end_points["trans_feature"] = end_points_stem["trans_feature"]
stem_features = end_points_stem["stem_features"]
# mlp for local features
local_features = []
x = stem_feature
for ind, mlp in enumerate(self.mlp_local):
x = mlp(x)
local_features.append(x)
# max pool over points
global_feature, max_indices = torch.max(x, 2) # (batch_size, local_channels[-1])
end_points['key_point_inds'] = max_indices
# classification
x = global_feature
x = self.mlp_cls(x)
cls_logit = self.cls_logit(x)
# segmentation
global_feature_expand = global_feature.unsqueeze(2).expand(-1, -1, num_points)
with torch.no_grad():
I = torch.eye(self.num_classes, dtype=global_feature.dtype, device=global_feature.device)
one_hot = I[cls_label] # (batch_size, num_classes)
one_hot_expand = one_hot.unsqueeze(2).expand(-1, -1, num_points)
x = torch.cat(stem_features + local_features + [global_feature_expand, one_hot_expand], dim=1)
x = self.mlp_seg(x)
x = self.conv_seg(x)
seg_logit = self.seg_logit(x)
preds = {
"cls_logit": cls_logit,
"seg_logit": seg_logit
}
preds.update(end_points)
return preds
def init_weights(self):
self.mlp_local.init_weights(xavier_uniform)
self.mlp_cls.init_weights(xavier_uniform)
self.mlp_seg.init_weights(xavier_uniform)
self.conv_seg.init_weights(xavier_uniform)
nn.init.xavier_uniform_(self.cls_logit.weight)
nn.init.zeros_(self.cls_logit.bias)
nn.init.xavier_uniform_(self.seg_logit.weight)
nn.init.zeros_(self.seg_logit.bias)
# Set batch normalization to 0.01 as default
set_bn(self, momentum=0.01)
def crossValidate(data, meta, folds, topology, iterations, weights, graph=None):
"k-fold cross validation"
if folds <= 1:
raise Exception("Cross validation folds must be > 1")
averageError = 0.0
for counter, (training, validation) in enumerate(crossValidateIndices(items=range(data.shape[0]), k=folds, randomize=True)):
# setup training and validation matricies
train = data.ix[training].reset_index(drop=True)
validate = data.ix[validation].reset_index(drop=True)
trainingFeatures = train.drop(meta.categoricalLabelColumns, axis=1) # remove output columns
validationFeatures = validate.drop(meta.categoricalLabelColumns, axis=1) # remove output columns
trainingLabels = train[meta.categoricalLabelColumns] # use only output columns
validationLabels = validate[meta.categoricalLabelColumns] # use only output columns
#setup MLP and start training
li("Fold {2}/{3} - Training with {1}/{4} rows ({0} epochs)".format(iterations, trainingFeatures.shape[0], counter + 1, folds, data.shape[0]))
mlp = MLP()
mlp.trainingIterations = iterations
mlp.initalWeightsMultiplier = weights
mlp.features = trainingFeatures.values # convert from pandas dataframe to numpy arrays. they are faster for the computationally intensive training phase.
mlp.labels = trainingLabels.values
mlp.validationFeatures = validationFeatures # for validation, send in pandas dataframes.
mlp.validationLabels = validationLabels
mlp.meta = meta
mlp.topology = topology
if graph:
mlp.trackLearning = True
mlp.setupHiddenLayers()
mlp.train()
if graph:
li("Plotting Learning to file '{0}'".format(graph))
mlp.plotLearning(graph)
#validate model
li("Fold {0}/{1} - Testing with {2}/{3} rows".format(counter + 1, folds, validationFeatures.shape[0], data.shape[0]))
error = mlp.validateModel(printToScreen=True)
averageError += error
averageError = averageError / folds
li("Average error across all folds: {0}".format(averageError))
return averageError
num_layers = 2
network = "RBF"
if network == "RBF":
net = RBF(input_size, output_size, hidden_size)
# training of the centres and variances
X = torch.randn(train_size/2,input_size)
Y = 2*X
loss_hist = fit_model(net,X,Y,5)
# training of the weights
X = torch.randn(train_size/2,input_size)
Y = 2*X
loss_hist = fit_model(net,X,Y,5)
else
net = MLP(input_size, output_size, num_layers, hidden_size)
X = torch.randn(train_size,input_size)
Y = 2*X
loss_hist = fit_model(net,X,Y,5)
# In[3]:
# You should see loss get to effectively zero
loss_hist = fit_model(net,X,Y,5)
plt.plot(loss_hist)
# In[4]:
# test error should be close to zero, MLP got to ~.0002 after 5 epochs of training on 4000 examples
X_test = torch.randn(train_size,input_size)
