def test_graph_diamond():
npr.seed(2)
N = 10
D = 5
H1 = 6
H2 = 7
X = kayak.Inputs(npr.randn(N,D))
W1 = kayak.Parameter(npr.randn(D,H1))
W2a = kayak.Parameter(npr.randn(H1,H2))
W2b = kayak.Parameter(npr.randn(H1,H2))
W3 = kayak.Parameter(npr.randn(H2,1))
U1 = kayak.SoftReLU(kayak.MatMult(X, W1))
U2a = kayak.SoftReLU(kayak.MatMult(U1, W2a))
U2b = kayak.SoftReLU(kayak.MatMult(U1, W2b))
U3a = kayak.SoftReLU(kayak.MatMult(U2a, W3))
U3b = kayak.SoftReLU(kayak.MatMult(U2b, W3))
out = kayak.MatSum(kayak.MatAdd(U3a, U3b))
out.value
print kayak.util.checkgrad(W1, out)
print kayak.util.checkgrad(W2a, out)
print kayak.util.checkgrad(W2b, out)
print kayak.util.checkgrad(W3, out)
assert kayak.util.checkgrad(W1, out) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(W2a, out) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(W2b, out) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(W3, out) < MAX_GRAD_DIFF
def test_matadd_values_5():
npr.seed(5)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(1, 6)
np_B = npr.randn(5, 1)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
C = kayak.MatAdd(A, B)
assert C.shape == (5, 6)
assert np.all(close_float(C.value, np_A + np_B))
def test_matadd_values_7():
npr.seed(7)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 6)
np_B = npr.randn(5, 6)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
D = kayak.MatAdd(A, B, A)
assert D.shape == (5, 6)
assert np.all(close_float(D.value, 2 * np_A + np_B))
def test_matadd_grad_8():
npr.seed(15)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 6)
np_B = npr.randn(5, 6)
A = kayak.Parameter(np_A)
D = kayak.MatAdd(A, A)
E = kayak.MatSum(D)
E.value
assert E.grad(A).shape == np_A.shape
assert kayak.util.checkgrad(A, E) < MAX_GRAD_DIFF
def test_graph_dag():
npr.seed(3)
num_layers = 7
num_dims = 5
for ii in xrange(NUM_TRIALS):
probs = npr.rand()
X = kayak.Inputs(npr.randn(25,num_dims))
wts = []
layers = []
for jj in xrange(num_layers):
U = kayak.Constant(np.zeros((25,num_dims)))
if npr.rand() < probs:
W = kayak.Parameter(0.1*npr.randn(num_dims, num_dims))
wts.append(W)
U = kayak.MatAdd( U, kayak.SoftReLU(kayak.MatMult(X, W)) )
for kk in xrange(jj):
if npr.rand() < probs:
W = kayak.Parameter(0.1*npr.randn(num_dims, num_dims))
wts.append(W)
U = kayak.MatAdd( U, kayak.SoftReLU(kayak.MatMult(layers[kk], W)) )
layers.append(U)
out = kayak.MatSum(layers[-1])
out.value
for jj, wt in enumerate(wts):
diff = kayak.util.checkgrad(wt, out, 1e-4)
print diff
assert diff < 1e-4
def test_matadd_values_2():
npr.seed(2)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 6)
np_B = npr.randn(5, 6)
np_C = npr.randn(5, 6)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
C = kayak.Parameter(np_C)
D = kayak.MatAdd(A, B, C)
assert D.shape == np_A.shape
assert np.all(close_float(D.value, np_A + np_B + np_C))
def test_matadd_grad_1():
npr.seed(8)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 6)
np_B = npr.randn(5, 6)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
C = kayak.MatAdd(A, B)
D = kayak.MatSum(C)
D.value
assert kayak.util.checkgrad(A, D) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(B, D) < MAX_GRAD_DIFF
def test_matadd_grad_5():
npr.seed(12)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 1)
np_B = npr.randn(1, 6)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
C = kayak.MatAdd(A, B)
D = kayak.MatSum(C)
D.value
assert D.grad(A).shape == np_A.shape
assert D.grad(B).shape == np_B.shape
assert kayak.util.checkgrad(A, D) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(B, D) < MAX_GRAD_DIFF
def test_cache_utility():
npr.seed(3)
num_layers = 17
num_dims = 3
X = kayak.Inputs(npr.randn(10, num_dims))
W1 = kayak.Parameter(npr.randn(num_dims, num_dims))
W2 = kayak.Parameter(npr.randn(num_dims, num_dims))
Z = kayak.MatMult(X, W1)
for jj in xrange(num_layers):
Z = kayak.SoftReLU(kayak.MatAdd(kayak.MatMult(Z, W2),
kayak.MatMult(Z, W2)))
out = kayak.MatSum(Z)
assert kayak.util.checkgrad(W1, out) < 1e-4
def test_matadd_grad_2():
npr.seed(9)
for ii in xrange(NUM_TRIALS):
np_A = npr.randn(5, 6)
np_B = npr.randn(5, 6)
np_C = npr.randn(5, 6)
A = kayak.Parameter(np_A)
B = kayak.Parameter(np_B)
C = kayak.Parameter(np_C)
D = kayak.MatAdd(A, B, C)
E = kayak.MatSum(D)
E.value
assert kayak.util.checkgrad(A, E) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(B, E) < MAX_GRAD_DIFF
assert kayak.util.checkgrad(C, E) < MAX_GRAD_DIFF
def train(inputs, targets, batch_size, learn_rate, momentum, l1_weight,
l2_weight, dropout, improvement_thresh):
# Create a batcher object.
batcher = kayak.Batcher(batch_size, inputs.shape[0])
# Inputs and targets need access to the batcher.
X = kayak.Inputs(inputs, batcher)
T = kayak.Targets(targets, batcher)
# Put some dropout regularization on the inputs
H = kayak.Dropout(X, dropout)
# Weights and biases, with random initializations.
W = kayak.Parameter(0.1 * npr.randn(inputs.shape[1], 10))
B = kayak.Parameter(0.1 * npr.randn(1, 10))
# Nothing fancy here: inputs times weights, plus bias, then softmax.
Y = kayak.LogSoftMax(kayak.ElemAdd(kayak.MatMult(H, W), B))
# The training loss is negative multinomial log likelihood.
loss = kayak.MatAdd(kayak.MatSum(kayak.LogMultinomialLoss(Y, T)),
kayak.L2Norm(W, l2_weight), kayak.L1Norm(W, l1_weight))
# Use momentum for the gradient-based optimization.
mom_grad_W = np.zeros(W.shape)
best_loss = np.inf
best_epoch = -1
# Loop over epochs.
for epoch in range(100):
# Track the total loss.
total_loss = 0.0
# Loop over batches -- using batcher as iterator.
for batch in batcher:
# Draw new random dropouts
H.draw_new_mask()
# Compute the loss of this minibatch by asking the Kayak
# object for its value and giving it reset=True.
total_loss += loss.value
# Now ask the loss for its gradient in terms of the
# weights and the biases -- the two things we're trying to
# learn here.
grad_W = loss.grad(W)
grad_B = loss.grad(B)
# Use momentum on the weight gradient.
mom_grad_W *= momentum
mom_grad_W += (1.0 - momentum) * grad_W
# Now make the actual parameter updates.
W.value -= learn_rate * mom_grad_W
B.value -= learn_rate * grad_B
print("Epoch: %d, total loss: %f" % (epoch, total_loss))
if not np.isfinite(total_loss):
print("Training diverged. Returning constraint violation.")
break
if total_loss < best_loss:
best_epoch = epoch
else:
if (epoch - best_epoch) > improvement_thresh:
print("Has been %d epochs without improvement. Aborting." %
(epoch - best_epoch))
break
# After we've trained, we return a sugary little function handle
# that makes things easy. Basically, what we're doing here is
# simply replacing the inputs in the above defined graph and then
# running through it to produce the outputs.
# The point here is that we wind up with a function
# handle the can be called with a numpy object and it produces the
# target values for novel data, using the parameters we just learned.
def predict(x):
X.value = x
H.reinstate_units()
return Y.value
return predict
def initial_latent_trace(body, inpt, voltage, t):
I_true = np.diff(voltage) * body.C
T = I_true.shape[0]
gs = np.diag([c.g for c in body.children])
D = int(sum([c.D for c in body.children]))
driving_voltage = np.dot(np.ones((len(body.children), 1)),
np.array([voltage]))[:, :T]
child_i = 0
for i in range(D):
driving_voltage[i, :] = voltage[:T] - body.children[child_i].E
K = np.array([[max(i - j, 0) for i in range(T)] for j in range(T)])
K = K.T + K
K = -1 * (K**2)
K = np.exp(K / 2)
L = np.linalg.cholesky(K + (1e-7) * np.eye(K.shape[0]))
Linv = scipy.linalg.solve_triangular(L.transpose(),
np.identity(K.shape[0]))
N = 1
batch_size = 5000
learn = .0000001
runs = 10000
batcher = kayak.Batcher(batch_size, N)
inputs = kayak.Parameter(driving_voltage)
targets = kayak.Targets(np.array([I_true]), batcher)
g_params = kayak.Parameter(gs)
I_input = kayak.Parameter(inpt.T[:, :T])
Kinv = kayak.Parameter(np.dot(Linv.transpose(), Linv))
initial_latent = np.random.randn(D, T)
latent_trace = kayak.Parameter(initial_latent)
sigmoid = kayak.Logistic(latent_trace)
quadratic = kayak.ElemMult(
sigmoid,
kayak.MatMult(
kayak.Parameter(np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])),
sigmoid))
three_quadratic = kayak.MatMult(
kayak.Parameter(np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]])),
quadratic)
linear = kayak.MatMult(
kayak.Parameter(np.array([[0, 0, 0], [0, 0, 0], [0, 0, 1]])), sigmoid)
leak_open = kayak.Parameter(np.vstack((np.ones((1, T)), np.ones((2, T)))))
open_fractions = kayak.ElemAdd(leak_open,
kayak.ElemAdd(three_quadratic, linear))
I_channels = kayak.ElemMult(kayak.MatMult(g_params, inputs),
open_fractions)
I_ionic = kayak.MatMult(kayak.Parameter(np.array([[1, 1, 1]])), I_channels)
predicted = kayak.MatAdd(I_ionic, I_input)
nll = kayak.ElemPower(predicted - targets, 2)
hack_vec = kayak.Parameter(np.array([1, 0, 0, 0, 1, 0, 0, 0, 1]))
kyk_loss = kayak.MatSum(nll) + kayak.MatMult(
kayak.Reshape(
kayak.MatMult(kayak.MatMult(latent_trace, Kinv),
kayak.Transpose(latent_trace)),
(9, )), hack_vec) + kayak.MatSum(kayak.ElemPower(I_channels, 2))
grad = kyk_loss.grad(latent_trace)
for ii in xrange(runs):
for batch in batcher:
loss = kyk_loss.value
if ii % 100 == 0:
print ii, loss, np.sum(np.power(predicted.value - I_true,
2)) / T
grad = kyk_loss.grad(latent_trace) + .5 * grad
latent_trace.value -= learn * grad
return sigmoid.value
def kayak_mlp(X, y):
"""
Kayak implementation of a mlp with relu hidden layers and dropout
"""
# Create a batcher object.
batcher = kayak.Batcher(batch_size, X.shape[0])
# count number of rows and columns
num_examples, num_features = np.shape(X)
X = kayak.Inputs(X, batcher)
T = kayak.Targets(y, batcher)
# ----------------------------- first hidden layer -------------------------------
# set up weights for our input layer
# use the same scheme as our numpy mlp
input_range = 1.0 / num_features**(1 / 2)
weights_1 = kayak.Parameter(0.1 * np.random.randn(X.shape[1], layer1_size))
bias_1 = kayak.Parameter(0.1 * np.random.randn(1, layer1_size))
# linear combination of weights and inputs
hidden_1_input = kayak.ElemAdd(kayak.MatMult(X, weights_1), bias_1)
# apply activation function to hidden layer
hidden_1_activation = kayak.HardReLU(hidden_1_input)
# apply a dropout for regularization
hidden_1_out = kayak.Dropout(hidden_1_activation,
layer1_dropout,
batcher=batcher)
# ----------------------------- output layer -----------------------------------
weights_out = kayak.Parameter(0.1 * np.random.randn(layer1_size, 9))
bias_out = kayak.Parameter(0.1 * np.random.randn(1, 9))
# linear combination of layer2 output and output weights
out = kayak.ElemAdd(kayak.MatMult(hidden_1_out, weights_out), bias_out)
# apply activation function to output
yhat = kayak.SoftMax(out)
# ----------------------------- loss function -----------------------------------
loss = kayak.MatAdd(kayak.MatSum(kayak.L2Loss(yhat, T)),
kayak.L2Norm(weights_1, layer1_l2))
# Use momentum for the gradient-based optimization.
mom_grad_W1 = np.zeros(weights_1.shape)
mom_grad_W2 = np.zeros(weights_out.shape)
# Loop over epochs.
plot_loss = np.ones((iterations, 2))
for epoch in xrange(iterations):
# Track the total loss.
total_loss = 0.0
for batch in batcher:
# Compute the loss of this minibatch by asking the Kayak
# object for its value and giving it reset=True.
total_loss += loss.value
# Now ask the loss for its gradient in terms of the
# weights and the biases -- the two things we're trying to
# learn here.
grad_W1 = loss.grad(weights_1)
grad_B1 = loss.grad(bias_1)
grad_W2 = loss.grad(weights_out)
grad_B2 = loss.grad(bias_out)
# Use momentum on the weight gradients.
mom_grad_W1 = momentum * mom_grad_W1 + (1.0 - momentum) * grad_W1
mom_grad_W2 = momentum * mom_grad_W2 + (1.0 - momentum) * grad_W2
# Now make the actual parameter updates.
weights_1.value -= learn_rate * mom_grad_W1
bias_1.value -= learn_rate * grad_B1
weights_out.value -= learn_rate * mom_grad_W2
bias_out.value -= learn_rate * grad_B2
# save values into table to print learning curve at the end of trianing
plot_loss[epoch, 0] = epoch
plot_loss[epoch, 1] = total_loss
print epoch, total_loss
#pyplot.plot(plot_loss[:,0], plot_loss[:,1], linewidth=2.0)
#pyplot.show()
def compute_predictions(x):
X.data = x
batcher.test_mode()
return yhat.value
return compute_predictions
def train(inputs, targets, batch_size, learn_rate, momentum, l1_weight, l2_weight, dropout):
# Create a batcher object.
batcher = kayak.Batcher(batch_size, inputs.shape[0])
# Inputs and targets need access to the batcher.
X = kayak.Inputs(inputs, batcher)
T = kayak.Targets(targets, batcher)
# Weights and biases, with random initializations.
W = kayak.Parameter( 0.1*npr.randn( inputs.shape[1], 10 ))
B = kayak.Parameter( 0.1*npr.randn(1,10) )
# Nothing fancy here: inputs times weights, plus bias, then softmax.
dropout_layer = kayak.Dropout(X, dropout, batcher=batcher)
Y = kayak.LogSoftMax( kayak.ElemAdd( kayak.MatMult(dropout_layer, W), B ) )
# The training loss is negative multinomial log likelihood.
loss = kayak.MatAdd(kayak.MatSum(kayak.LogMultinomialLoss(Y, T)),
kayak.L2Norm(W, l2_weight),
kayak.L1Norm(W, l1_weight))
# Use momentum for the gradient-based optimization.
mom_grad_W = np.zeros(W.shape)
# Loop over epochs.
for epoch in xrange(10):
# Track the total loss and the overall gradient.
total_loss = 0.0
total_grad_W = np.zeros(W.shape)
# Loop over batches -- using batcher as iterator.
for batch in batcher:
# Compute the loss of this minibatch by asking the Kayak
# object for its value and giving it reset=True.
total_loss += loss.value
# Now ask the loss for its gradient in terms of the
# weights and the biases -- the two things we're trying to
# learn here.
grad_W = loss.grad(W)
grad_B = loss.grad(B)
# Use momentum on the weight gradient.
mom_grad_W = momentum*mom_grad_W + (1.0-momentum)*grad_W
# Now make the actual parameter updates.
W.value -= learn_rate * mom_grad_W
B.value -= learn_rate * grad_B
# Keep track of the gradient to see if we're converging.
total_grad_W += grad_W
#print epoch, total_loss, np.sum(total_grad_W**2)
# After we've trained, we return a sugary little function handle
# that makes things easy. Basically, what we're doing here is
# handing the output object (not the loss!) a dictionary where the
# key is the Kayak input object 'X' (that is the features being
# used here for logistic regression) and the value in that
# dictionary is being determined by the argument to the lambda
# expression. The point here is that we wind up with a function
# handle the can be called with a numpy object and it produces the
# target values for novel data, using the parameters we just learned.
def compute_predictions(x):
X.data = x
batcher.test_mode()
return Y.value
return compute_predictions
