def __init__(self, n_actions):
Serializable.__init__(self, n_actions)
cgt.set_precision('double')
n_in = 128
o_no = cgt.matrix("o_no",fixed_shape=(None,n_in))
a_n = cgt.vector("a_n",dtype='i8')
q_n = cgt.vector("q_n")
oldpdist_np = cgt.matrix("oldpdists")
h0 = (o_no - 128.0)/128.0
nhid = 64
h1 = cgt.tanh(nn.Affine(128,nhid,weight_init=nn.IIDGaussian(std=.1))(h0))
probs_na = nn.softmax(nn.Affine(nhid,n_actions,weight_init=nn.IIDGaussian(std=0.01))(h1))
logprobs_na = cgt.log(probs_na)
b = cgt.size(o_no, 0)
logps_n = logprobs_na[cgt.arange(b), a_n]
surr = (logps_n*q_n).mean()
kl = (oldpdist_np * cgt.log(oldpdist_np/probs_na)).sum(axis=1).mean()
params = nn.get_parameters(surr)
gradsurr = cgt.grad(surr, params)
flatgrad = cgt.concatenate([p.flatten() for p in gradsurr])
lam = cgt.scalar()
penobj = surr - lam * kl
self._f_grad_lagrangian = cgt.function([lam, oldpdist_np, o_no, a_n, q_n],
cgt.concatenate([p.flatten() for p in cgt.grad(penobj,params)]))
self.f_pdist = cgt.function([o_no], probs_na)
self.f_probs = cgt.function([o_no], probs_na)
self.f_surr_kl = cgt.function([oldpdist_np, o_no, a_n, q_n], [surr, kl])
self.f_gradlogp = cgt.function([oldpdist_np, o_no, a_n, q_n], flatgrad)
self.pc = ParamCollection(params)
def test_devices():
N = 10
K = 3
compile_info = cgt.compilation.get_compile_info()
cuda_enabled = compile_info["CGT_ENABLE_CUDA"]
if not cuda_enabled:
raise SkipTest("cuda disabled")
Xval = np.random.randn(N, K).astype(cgt.floatX)
wval = np.random.randn(K).astype(cgt.floatX)
bval = np.asarray(np.random.randn()).astype(cgt.floatX)
yval = np.random.randn(N).astype(cgt.floatX)
with cgt.scoped_update_config(default_device=cgt.Device(devtype="gpu")):
X_nk = cgt.shared(Xval, "X", device=cgt.Device(devtype='gpu'))
y_n = cgt.shared(yval, "y")
w_k = cgt.shared(wval, "w")
b = cgt.shared(bval, name="b")
print "bval", bval
ypred = cgt.dot(cgt.square(X_nk), w_k) + b
err = cgt.sum(cgt.sin(ypred - y_n))
g = cgt.grad(err, [w_k, b])
outputs = [err] + g
f = cgt.function([], [err] + g)
results = f()
print results
assert np.allclose(
results[0],
np.sin(np.square(Xval).dot(wval) + bval - yval).sum())
def momentum(cost, params, learning_rate, mu=0.9):
"""Stochastic Gradient Descent (SGD) updates with momentum
Math:
* ``velocity := mu * velocity - learning_rate * grad``
* ``param := param + velocity``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
momentum: float
Tunes the weight given to the velocity term.
Returns
-------
list of tuples of the form (param, new_param) and (velocity, new_velocity)
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
velocity = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
new_velocity = mu * velocity - learning_rate * grad
new_param = param + new_velocity
updates.append((velocity, new_velocity))
updates.append((param, new_param))
return updates
def nesterov_momentum(cost, params, learning_rate, momentum=0.9):
"""Stochastic Gradient Descent (SGD) updates with Nesterov momentum
Math:
* ``velocity := momentum * velocity - learning_rate * grad``
* ``param := momentum*velocity + param - learning_rate * grad``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
momentum: float
Tunes the weight given to the velocity term.
Returns
-------
list of tuples of the form [(param, updates) (velocity, velocity_update)]
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
value = param.op.get_value()
velocity = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
x = momentum * velocity - learning_rate * grad
updates.append((velocity, x))
updates.append((param, momentum * x + param - learning_rate * grad))
return updates
def test_devices():
N = 10
K = 3
compile_info = cgt.compilation.get_compile_info()
cuda_enabled = compile_info["CGT_ENABLE_CUDA"]
if not cuda_enabled:
raise SkipTest("cuda disabled")
Xval = np.random.randn(N,K).astype(cgt.floatX)
wval = np.random.randn(K).astype(cgt.floatX)
bval = np.asarray(np.random.randn()).astype(cgt.floatX)
yval = np.random.randn(N).astype(cgt.floatX)
with cgt.scoped_update_config(default_device=cgt.Device(devtype="gpu")):
X_nk = cgt.shared(Xval, "X", device=cgt.Device(devtype='gpu'))
y_n = cgt.shared(yval, "y")
w_k = cgt.shared(wval, "w")
b = cgt.shared(bval, name="b")
print "bval",bval
ypred = cgt.dot(cgt.square(X_nk), w_k) + b
err = cgt.sum(cgt.sin(ypred - y_n))
g = cgt.grad(err, [w_k, b])
outputs = [err]+g
f = cgt.function([], [err]+g)
results = f()
print results
assert np.allclose(results[0] , np.sin(np.square(Xval).dot(wval)+bval-yval).sum())
def test_cudnn():
with cgt.scoped_update_config(precision="double",backend="native"):
if not get_compile_info()["CGT_ENABLE_CUDNN"]:
raise SkipTest("CUDNN not enabled. Skipping this test")
Xval = nr.randn(2,3,19,18)
Wval = nr.randn(5,3,3,3)
bval = nr.randn(1,5,1,1)
X = cgt.tensor4("X", fixed_shape=Xval.shape)
W = cgt.tensor4("W", fixed_shape=Wval.shape)
b = cgt.tensor4("b", fixed_shape=bval.shape)
Y = cgt.core.Result(cudnn_ops.CudnnConvForward(1,1,1,1),[X, W, b])
Y2 = nr.randn(*cgt.core.infer_shape(Y))
fY = cgt.function([X,W,b],Y)
Yval = fY(Xval,Wval,bval)
cost = (Y*Y2).sum()
fcost = cgt.function([X,W,b],cost)
fgrad = cgt.function([X,W,b],cgt.grad(cost, [X,W,b]))
angrads = fgrad(Xval,Wval,bval)
nugrads = numeric_grad_multi(fcost, [Xval, Wval, bval],eps=1e-3)
for (nugrad,angrad) in zip(nugrads,angrads):
assert np.allclose(nugrad, angrad)
def nesterov_momentum(cost, params, learning_rate, momentum=0.9):
"""Stochastic Gradient Descent (SGD) updates with Nesterov momentum
Math:
* ``velocity := momentum * velocity - learning_rate * grad``
* ``param := momentum*velocity + param - learning_rate * grad``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
momentum: float
Tunes the weight given to the velocity term.
Returns
-------
list of tuples of the form [(param, updates) (velocity, velocity_update)]
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
value = param.op.get_value()
velocity = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
x = momentum * velocity - learning_rate * grad
updates.append((velocity, x))
updates.append((param, momentum*x + param - learning_rate * grad))
return updates
def test_flatvec():
cgt.reset_config
cgt.set_precision('double')
cgt.core.update_config(backend="python") # XXX
N = 10
K = 3
Xval = np.random.randn(N, K)
wval = np.random.randn(K)
bval = np.random.randn()
yval = np.random.randn(N)
X_nk = cgt.shared(Xval, "X")
y_n = cgt.shared(yval, "y")
w_k = cgt.shared(wval, "w")
b = cgt.shared(bval, name="b")
ypred = cgt.dot(X_nk, w_k) + b
err = cgt.sum(cgt.square(ypred - y_n))
g = cgt.grad(err, [w_k, b])
g = core.simplify(g)
pars = [w_k, b]
flatx = nn.setup_contiguous_storage(pars)
f = cgt.function([], [err, cgt.flatcat(g)])
def test_cudnn():
if not get_compile_info()["CGT_ENABLE_CUDNN"]:
raise SkipTest("CUDNN not enabled. Skipping this test")
Xval = nr.randn(2, 3, 19, 18)
Wval = nr.randn(5, 3, 3, 3)
bval = nr.randn(1, 5, 1, 1)
X = cgt.tensor4("X", fixed_shape=Xval.shape)
W = cgt.tensor4("W", fixed_shape=Wval.shape)
b = cgt.tensor4("b", fixed_shape=bval.shape)
Y = cgt.core.Result(cudnn_ops.CudnnConvForward(1, 1, 1, 1), [X, W, b])
Y2 = nr.randn(*cgt.core.infer_shape(Y))
fY = cgt.function([X, W, b], Y)
Yval = fY(Xval, Wval, bval)
cost = (Y * Y2).sum()
fcost = cgt.function([X, W, b], cost)
fgrad = cgt.function([X, W, b], cgt.grad(cost, [X, W, b]))
angrads = fgrad(Xval, Wval, bval)
nugrads = numeric_grad_multi(fcost, [Xval, Wval, bval], eps=1e-3)
for (nugrad, angrad) in zip(nugrads, angrads):
assert np.allclose(nugrad, angrad)
def test_flatvec():
cgt.reset_config
cgt.set_precision('double')
cgt.core.update_config(backend="python") # XXX
N = 10
K = 3
Xval = np.random.randn(N,K)
wval = np.random.randn(K)
bval = np.random.randn()
yval = np.random.randn(N)
X_nk = cgt.shared(Xval, "X")
y_n = cgt.shared(yval, "y")
w_k = cgt.shared(wval, "w")
b = cgt.shared(bval, name="b")
ypred = cgt.dot(X_nk, w_k) + b
err = cgt.sum(cgt.square(ypred - y_n))
g = cgt.grad(err, [w_k, b])
g = core.simplify(g)
pars = [w_k, b]
flatx = nn.setup_contiguous_storage(pars)
f = cgt.function([], [err,cgt.flatcat(g)])
def momentum(cost, params, learning_rate, mu=0.9):
"""Stochastic Gradient Descent (SGD) updates with momentum
Math:
* ``velocity := mu * velocity - learning_rate * grad``
* ``param := param + velocity``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
momentum: float
Tunes the weight given to the velocity term.
Returns
-------
list of tuples of the form (param, new_param) and (velocity, new_velocity)
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
velocity = cgt.shared(np.zeros(param.op.get_shape(),
dtype=param.dtype))
new_velocity = mu * velocity - learning_rate * grad
new_param = param + new_velocity
updates.append((velocity, new_velocity))
updates.append((param, new_param))
return updates
def gradcheck_model(cost,
params,
extravars=(),
extravals=(),
atol=1e-8,
eps=1e-9):
precision = cgt.get_precision()
if precision == "single":
cgt.utils.warn(
"You're doing a gradient check with %s precision. Use double or better yet quad for best results"
% (precision))
assert all(param.is_input() for param in params)
assert len(extravars) == len(extravals)
# Convert to Argument nodes
param_args = [
cgt.core.Argument(typ=s.typ, name=s.name) if s.is_data() else s
for s in params
]
# Get new cost in terms o farguments
cost = cgt.core.clone(cost, replace=dict(zip(params, param_args)))
grads = cgt.grad(cost, param_args)
paramvals = [param.op.get_value() for param in params]
fcost = cgt.function(param_args, cost, givens=zip(extravars, extravals))
fgrad = cgt.function(param_args, grads, givens=zip(extravars, extravals))
angrads = fgrad(*paramvals)
nugrads = numeric_grad_multi(fcost, paramvals, eps=eps)
for (angrad, nugrad) in zip(angrads, nugrads):
assert np.allclose(angrad, nugrad, atol=atol)
def test_cudnn():
compile_info = get_compile_info()
if not (compile_info["CGT_ENABLE_CUDNN"] and compile_info["CGT_ENABLE_CUDA"]):
raise SkipTest("CUDNN not enabled. Skipping this test")
Xval = nr.randn(2,3,19,18)
Wval = nr.randn(5,3,3,3)
bval = nr.randn(1,5,1,1)
X = cgt.tensor4("X", fixed_shape=Xval.shape)
W = cgt.tensor4("W", fixed_shape=Wval.shape)
b = cgt.tensor4("b", fixed_shape=bval.shape)
Y = cgt.core.Result(cudnn_ops.CudnnConvForward(1,1,1,1),[X, W, b])
Y2 = nr.randn(*cgt.core.infer_shape(Y))
fY = cgt.function([X,W,b],Y)
Yval = fY(Xval,Wval,bval)
cost = (Y*Y2).sum()
fcost = cgt.function([X,W,b],cost)
fgrad = cgt.function([X,W,b],cgt.grad(cost, [X,W,b]))
angrads = fgrad(Xval,Wval,bval)
nugrads = numeric_grad_multi(fcost, [Xval, Wval, bval],eps=1e-3)
for (nugrad,angrad) in zip(nugrads,angrads):
assert np.allclose(nugrad, angrad, rtol=9e-3, atol=1e-7)
def make_updater_fc():
X = cgt.matrix("X", fixed_shape=(None, 28 * 28))
y = cgt.vector("y", dtype="i8")
stepsize = cgt.scalar("stepsize")
loss = build_fc_return_loss(X, y)
params = nn.get_parameters(loss)
gparams = cgt.grad(loss, params)
updates = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], loss, updates=updates)
def check_scalar_grads(precision, backend):
cgt.reset_config()
np.random.seed(0)
cgt.set_precision(precision)
cgt.core.update_config(backend=backend)
x = cgt.scalar('x')
y = cgt.scalar('y')
z = cgt.scalar('z')
vars = [x,y,z] #pylint: disable=W0622
vals = nr.rand(len(vars))+1
PROB2RESULT = {}
for ((key,_), cls) in it.chain(
it.izip(core.UNARY_INFO.items(),it.repeat(core.ElwiseUnary)),
it.izip(core.BINARY_INFO.items(),it.repeat(core.ElwiseBinary))
):
if key == "conj":
print "skipping conj"
continue
utils.colorprint(utils.Color.YELLOW, "Testing %s\n"%key)
if cls == core.ElwiseUnary:
n_in = 1
op = cls(key)
else:
n_in = 2
op = cls(key, (True,True))
inputvars = vars[0:n_in]
inputvals = vals[0:n_in]
out = core.Result(op, inputvars)
f = cgt.function(inputvars, out)
try:
grads = cgt.grad(out, inputvars)
except core.NonDifferentiable:
print "nondiff"
continue
if DISPLAY:
print "Function:"
cgt.print_tree(out)
print "Gradient original:"
cgt.print_tree(grads)
print "Gradient simplified:"
grads_simple = core.simplify(grads)
if DISPLAY: cgt.print_tree(grads_simple)
gradf = cgt.function(inputvars, grads)
eps = {"single":1e-4,"double":1e-9}[precision]
nugrad = numeric_grad(lambda li: f(*li), inputvals,eps=eps) #pylint: disable=W0640
cgtgrad = gradf(*inputvals)
np.testing.assert_almost_equal(nugrad,cgtgrad,decimal={"single":3,"double":6}[precision])
grad_count = core.count_nodes(grads_simple)
PROB2RESULT[key] = {}
PROB2RESULT[key]["grad"] = grad_count
if DISPLAY:
from thirdparty.tabulate import tabulate
print tabulate([[key,val["grad"]] for (key,val) in PROB2RESULT.iteritems()],headers=["funcname","gradcount"])
def make_updater_fc():
X = cgt.matrix("X", fixed_shape=(None, 28 * 28))
y = cgt.vector("y", dtype='i8')
stepsize = cgt.scalar("stepsize")
loss = build_fc_return_loss(X, y)
params = nn.get_parameters(loss)
gparams = cgt.grad(loss, params)
updates = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], loss, updates=updates)
def initialize(self, loss, scale):
self._iter = 0
self.pc = Params(self.params)
cur_val = self.pc.get_value_flat()
idx = cur_val.nonzero()
new_val = np.random.uniform(-scale, scale, size=(self.pc.get_total_size(),))
new_val[idx] = cur_val[idx]
self.sync(new_val)
grad = cgt.concatenate([g.flatten() for g in cgt.grad(loss, self.params)])
return grad
def make_updater_convnet():
X = cgt.tensor4("X", fixed_shape=(None, 1, 28, 28)) # so shapes can be inferred
y = cgt.vector("y", dtype="i8")
stepsize = cgt.scalar("stepsize")
loss = build_convnet_return_loss(X, y)
params = nn.get_parameters(loss)
gparams = cgt.grad(loss, params)
updates = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], loss, updates=updates)
def __init__(self, obs_dim, ctrl_dim):
cgt.set_precision('double')
Serializable.__init__(self, obs_dim, ctrl_dim)
self.obs_dim = obs_dim
self.ctrl_dim = ctrl_dim
o_no = cgt.matrix("o_no",fixed_shape=(None,obs_dim))
a_na = cgt.matrix("a_na",fixed_shape = (None, ctrl_dim))
adv_n = cgt.vector("adv_n")
oldpdist_np = cgt.matrix("oldpdist", fixed_shape=(None, 2*ctrl_dim))
self.logstd = logstd_1a = nn.parameter(np.zeros((1, self.ctrl_dim)), name="std_1a")
std_1a = cgt.exp(logstd_1a)
# Here's where we apply the network
h0 = o_no
nhid = 32
h1 = cgt.tanh(nn.Affine(obs_dim,nhid,weight_init=nn.IIDGaussian(std=0.1))(h0))
h2 = cgt.tanh(nn.Affine(nhid,nhid,weight_init=nn.IIDGaussian(std=0.1))(h1))
mean_na = nn.Affine(nhid,ctrl_dim,weight_init=nn.IIDGaussian(std=0.01))(h2)
b = cgt.size(o_no, 0)
std_na = cgt.repeat(std_1a, b, axis=0)
oldmean_na = oldpdist_np[:, 0:self.ctrl_dim]
oldstd_na = oldpdist_np[:, self.ctrl_dim:2*self.ctrl_dim]
logp_n = ((-.5) * cgt.square( (a_na - mean_na) / std_na ).sum(axis=1)) - logstd_1a.sum()
oldlogp_n = ((-.5) * cgt.square( (a_na - oldmean_na) / oldstd_na ).sum(axis=1)) - cgt.log(oldstd_na).sum(axis=1)
ratio_n = cgt.exp(logp_n - oldlogp_n)
surr = (ratio_n*adv_n).mean()
pdists_np = cgt.concatenate([mean_na, std_na], axis=1)
# kl = cgt.log(sigafter/)
params = nn.get_parameters(surr)
oldvar_na = cgt.square(oldstd_na)
var_na = cgt.square(std_na)
kl = (cgt.log(std_na / oldstd_na) + (oldvar_na + cgt.square(oldmean_na - mean_na)) / (2 * var_na) - .5).sum(axis=1).mean()
lam = cgt.scalar()
penobj = surr - lam * kl
self._compute_surr_kl = cgt.function([oldpdist_np, o_no, a_na, adv_n], [surr, kl])
self._compute_grad_lagrangian = cgt.function([lam, oldpdist_np, o_no, a_na, adv_n],
cgt.concatenate([p.flatten() for p in cgt.grad(penobj,params)]))
self.f_pdist = cgt.function([o_no], pdists_np)
self.f_objs = cgt.function([oldpdist_np, o_no, a_na, adv_n], [surr, kl])
self.pc = ParamCollection(params)
def rmsprop_updates(cost, params, stepsize=0.001, rho=0.9, epsilon=1e-6):
grads = cgt.grad(cost, params)
updates = []
for p, g in zip(params, grads):
acc = cgt.shared(p.op.get_value() * 0.)
acc_new = rho * acc + (1 - rho) * cgt.square(g)
gradient_scaling = cgt.sqrt(acc_new + epsilon)
g = g / gradient_scaling
updates.append((acc, acc_new))
updates.append((p, p - stepsize * g))
return updates
def test_scalars():
np.random.seed(0)
x = cgt.scalar('x')
y = cgt.scalar('y')
z = cgt.scalar('z')
vars = [x,y,z] #pylint: disable=W0622
vals = nr.rand(len(vars))+1
PROB2RESULT = {}
for ((key,_), cls) in it.chain(
it.izip(core.UNARY_INFO.items(),it.repeat(core.ElwiseUnary)),
it.izip(core.BINARY_INFO.items(),it.repeat(core.ElwiseBinary))
):
if key == "conj":
print "skipping conj"
continue
utils.colorprint(utils.Color.YELLOW, "Testing %s\n"%key)
if cls == core.ElwiseUnary:
n_in = 1
op = cls(key)
else:
n_in = 2
op = cls(key, (True,True))
inputvars = vars[0:n_in]
inputvals = vals[0:n_in]
out = core.Result(op, inputvars)
f = cgt.function(inputvars, out)
try:
grads = cgt.grad(out, inputvars)
except core.NonDifferentiable:
print "nondiff"
continue
if DISPLAY:
print "Function:"
cgt.print_tree(out)
print "Gradient original:"
cgt.print_tree(grads)
print "Gradient simplified:"
grads_simple = core.simplify(grads)
if DISPLAY: cgt.print_tree(grads_simple)
gradf = cgt.function(inputvars, grads)
eps = {"single":1e-4,"double":1e-9}[cgt.get_precision()]
nugrad = numeric_grad(lambda li: f(*li), inputvals,eps=eps) #pylint: disable=W0640
cgtgrad = gradf(*inputvals)
np.testing.assert_almost_equal(nugrad,cgtgrad,decimal={"single":3,"double":6}[cgt.get_precision()])
grad_count = core.count_nodes(grads_simple)
PROB2RESULT[key] = {}
PROB2RESULT[key]["grad"] = grad_count
if DISPLAY:
from thirdparty.tabulate import tabulate
print tabulate([[key,val["grad"]] for (key,val) in PROB2RESULT.iteritems()],headers=["funcname","gradcount"])
def rmsprop_updates(cost, params, stepsize=0.001, rho=0.9, epsilon=1e-6):
grads = cgt.grad(cost, params)
updates = []
for p, g in zip(params, grads):
acc = cgt.shared(p.op.get_value() * 0.)
acc_new = rho * acc + (1 - rho) * cgt.square(g)
gradient_scaling = cgt.sqrt(acc_new + epsilon)
g = g / gradient_scaling
updates.append((acc, acc_new))
updates.append((p, p - stepsize * g))
return updates
def make_updater_convnet():
X = cgt.tensor4("X", fixed_shape=(None, 1, 28,
28)) # so shapes can be inferred
y = cgt.vector("y", dtype='i8')
stepsize = cgt.scalar("stepsize")
loss = build_convnet_return_loss(X, y)
params = nn.get_parameters(loss)
gparams = cgt.grad(loss, params)
updates = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], loss, updates=updates)
def CGT_dvLJ(x):
N = len(x)
xt = cgt.vector('xt')
vLJt = 0
for j in range(1,N):
for i in range(j):
rho = ((xt[i*D:i*D+D] - xt[j*D:j*D+D])**2).sum()
vLJt += rho**(-6.0)-(rho**(-3.0))
dvLJc = cgt.grad(4*vLJt, xt)
df = cgt.function([xt],dvLJc)
return df(np.ravel(x))
def adadelta(cost, params, learning_rate=1.0, rho=0.95, epsilon=1e-6):
""" Adadelta updates
The learning rate is scaled by the ratio of accumulated gradients to the ratio of accumulated step sizes.
Math:
* ``accu_new = rho * accu + (1 - rho) * grad ** 2``
* ``update = (grad * cgt.sqrt(delta_accu + epsilon) / cgt.sqrt(accu_new + epsilon))``
* ``param = param - learning_rate * update``
* ``delta_accu_new = rho * delta_accu + (1 - rho) * update ** 2``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
rho : float
Controls decay of gradient moving average.
epsilon : float
Avoid division by 0 while scaling. Small constant.
Returns
-------
list of tuples of the form
(param, updates), (accumulated_grads, accumulated_grads_new), (step_accum, step_accum_new)
References
----------
.. [1] Zeiler, M. D. (2012):
ADADELTA: An Adaptive Learning Rate Method.
arXiv Preprint arXiv:1212.5701.
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
accu = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
delta_accu = cgt.shared(
np.zeros(param.op.get_shape(), dtype=param.dtype))
accu_new = rho * accu + (1 - rho) * grad**2
updates.append((accu, accu_new))
update = (grad * cgt.sqrt(delta_accu + epsilon) /
cgt.sqrt(accu_new + epsilon))
updates.append((param, param - learning_rate * update))
delta_accu_new = rho * delta_accu + (1 - rho) * update**2
updates.append((delta_accu, delta_accu_new))
return updates
def check_affine(f, *nu_inputs):
types = ",".join(["{%s,%s}" % (x.dtype, x.ndim) for x in nu_inputs])
cgt.utils.colorprint(cgt.utils.Color.YELLOW,
"Testing %s(%s)\n" % (f.__name__, types))
sy_inputs = map(tensor_like, nu_inputs)
for (i, sy) in enumerate(sy_inputs):
sy.name = "x%i" % i
sy_result = f(*sy_inputs)
def maybeprint(msg):
if DISPLAY: print msg
maybeprint("Function:")
if DISPLAY: cgt.print_tree([sy_result])
f_cgt = cgt.function(sy_inputs, sy_result)
sy_grads = cgt.grad(sy_result, sy_inputs)
gradf_cgt = cgt.function(sy_inputs, sy_grads)
sy_result_simple = core.simplify([sy_result])
sy_grads_simple = core.simplify(sy_grads)
maybeprint("Gradient:")
if DISPLAY: cgt.print_tree(sy_grads)
maybeprint("Gradient after simplification:")
if DISPLAY: cgt.print_tree(sy_grads_simple)
out_true = f(*nu_inputs)
out_cgt = f_cgt(*nu_inputs)
grads_true = gradients_affine(f_cgt,
nu_inputs,
h=1e-4 if "max" in f.__name__ else 1e-1)
grads_cgt = gradf_cgt(*nu_inputs)
rtol = {"single": 1e-3, "double": 1e-5}[cgt.get_precision()]
np.testing.assert_allclose(out_cgt, out_true, rtol=rtol)
for (g_cgt, g_true) in zip(grads_cgt, grads_true):
np.testing.assert_allclose(g_cgt, g_true, rtol=rtol)
result_count = cgt.count_nodes(sy_result_simple)
grad_count = cgt.count_nodes(sy_grads_simple)
maybeprint("Result before: %i. after: %i" %
(cgt.count_nodes([sy_result]), result_count))
maybeprint("Grad before: %i. after: %i" %
(cgt.count_nodes(sy_grads), grad_count))
PROB2RESULT[f.__name__] = {}
PROB2RESULT[f.__name__]["fn"] = result_count
PROB2RESULT[f.__name__]["grad"] = grad_count
def check_affine(f, *nu_inputs):
types = ",".join(["{%s,%s}" % (x.dtype, x.ndim) for x in nu_inputs])
cgt.utils.colorprint(cgt.utils.Color.YELLOW, "Testing %s(%s)\n" % (f.__name__, types))
sy_inputs = map(tensor_like, nu_inputs)
for (i, sy) in enumerate(sy_inputs):
sy.name = "x%i" % i
sy_result = f(*sy_inputs)
def maybeprint(msg):
if DISPLAY:
print msg
maybeprint("Function:")
if DISPLAY:
cgt.print_tree([sy_result])
f_cgt = cgt.function(sy_inputs, sy_result)
sy_grads = cgt.grad(sy_result, sy_inputs)
gradf_cgt = cgt.function(sy_inputs, sy_grads)
sy_result_simple = core.simplify([sy_result])
sy_grads_simple = core.simplify(sy_grads)
maybeprint("Gradient:")
if DISPLAY:
cgt.print_tree(sy_grads)
maybeprint("Gradient after simplification:")
if DISPLAY:
cgt.print_tree(sy_grads_simple)
out_true = f(*nu_inputs)
out_cgt = f_cgt(*nu_inputs)
grads_true = gradients_affine(f_cgt, nu_inputs, h=1e-4 if "max" in f.__name__ else 1e-1)
grads_cgt = gradf_cgt(*nu_inputs)
rtol = {"single": 1e-3, "double": 1e-5}[cgt.get_precision()]
np.testing.assert_allclose(out_cgt, out_true, rtol=rtol)
for (g_cgt, g_true) in zip(grads_cgt, grads_true):
np.testing.assert_allclose(g_cgt, g_true, rtol=rtol)
result_count = cgt.count_nodes(sy_result_simple)
grad_count = cgt.count_nodes(sy_grads_simple)
maybeprint("Result before: %i. after: %i" % (cgt.count_nodes([sy_result]), result_count))
maybeprint("Grad before: %i. after: %i" % (cgt.count_nodes(sy_grads), grad_count))
PROB2RESULT[f.__name__] = {}
PROB2RESULT[f.__name__]["fn"] = result_count
PROB2RESULT[f.__name__]["grad"] = grad_count
def __init__(self, n_actions):
Serializable.__init__(self, n_actions)
cgt.set_precision('double')
n_in = 128
o_no = cgt.matrix("o_no", fixed_shape=(None, n_in))
a_n = cgt.vector("a_n", dtype='i8')
q_n = cgt.vector("q_n")
oldpdist_np = cgt.matrix("oldpdists")
h0 = (o_no - 128.0) / 128.0
nhid = 64
h1 = cgt.tanh(
nn.Affine(128, nhid, weight_init=nn.IIDGaussian(std=.1))(h0))
probs_na = nn.softmax(
nn.Affine(nhid, n_actions,
weight_init=nn.IIDGaussian(std=0.01))(h1))
logprobs_na = cgt.log(probs_na)
b = cgt.size(o_no, 0)
logps_n = logprobs_na[cgt.arange(b), a_n]
surr = (logps_n * q_n).mean()
kl = (oldpdist_np * cgt.log(oldpdist_np / probs_na)).sum(axis=1).mean()
params = nn.get_parameters(surr)
gradsurr = cgt.grad(surr, params)
flatgrad = cgt.concatenate([p.flatten() for p in gradsurr])
lam = cgt.scalar()
penobj = surr - lam * kl
self._f_grad_lagrangian = cgt.function(
[lam, oldpdist_np, o_no, a_n, q_n],
cgt.concatenate([p.flatten() for p in cgt.grad(penobj, params)]))
self.f_pdist = cgt.function([o_no], probs_na)
self.f_probs = cgt.function([o_no], probs_na)
self.f_surr_kl = cgt.function([oldpdist_np, o_no, a_n, q_n],
[surr, kl])
self.f_gradlogp = cgt.function([oldpdist_np, o_no, a_n, q_n], flatgrad)
self.pc = ParamCollection(params)
def make_loss_and_grad(net):
X_b = inps[0] #cgt.matrix(dtype=cgt.floatX)
y_onehot = cgt.matrix(dtype='i4')
outputs = [logprobs]
loss = nn.crossent(outputs[0], y_onehot) / b_size
#gradloss = cgt.grad(loss, params)
gradloss = cgt.grad(loss, param_list)
# XXX use flatcat function
grad = cgt.concatenate([x.flatten() for x in gradloss])
#grad = gradloss
return cgt.make_function([X_b, y_onehot], [loss, grad, logprobs])
def adadelta(cost, params, learning_rate=1.0, rho=0.95, epsilon=1e-6):
""" Adadelta updates
The learning rate is scaled by the ratio of accumulated gradients to the ratio of accumulated step sizes.
Math:
* ``accu_new = rho * accu + (1 - rho) * grad ** 2``
* ``update = (grad * cgt.sqrt(delta_accu + epsilon) / cgt.sqrt(accu_new + epsilon))``
* ``param = param - learning_rate * update``
* ``delta_accu_new = rho * delta_accu + (1 - rho) * update ** 2``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
rho : float
Controls decay of gradient moving average.
epsilon : float
Avoid division by 0 while scaling. Small constant.
Returns
-------
list of tuples of the form
(param, updates), (accumulated_grads, accumulated_grads_new), (step_accum, step_accum_new)
References
----------
.. [1] Zeiler, M. D. (2012):
ADADELTA: An Adaptive Learning Rate Method.
arXiv Preprint arXiv:1212.5701.
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
accu = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
delta_accu = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
accu_new = rho * accu + (1 - rho) * grad ** 2
updates.append((accu, accu_new))
update = (grad * cgt.sqrt(delta_accu + epsilon) / cgt.sqrt(accu_new + epsilon))
updates.append((param, param - learning_rate * update))
delta_accu_new = rho * delta_accu + (1 - rho) * update ** 2
updates.append((delta_accu, delta_accu_new))
return updates
def __init__(self, xdim, args, dec="bernoulli"):
self.xdim = xdim
self.hdim = args.hdim
self.zdim = args.zdim
self.lmbda = args.lmbda # weight decay coefficient * 2
self.x = cgt.matrix("x", dtype=cgt.floatX)
self.eps = cgt.matrix("eps", dtype=cgt.floatX)
self.enc_mlp = GaussianMLP(self.x, self.xdim, self.hdim, self.zdim, nlayers=args.nlayers, eps=self.eps)
if dec == "bernoulli":
# log p(x | z) defined as -CE(x, y) = dec_mlp.cost(y)
self.dec_mlp = BernoulliMLP(self.enc_mlp.out, self.zdim, self.hdim, self.xdim, nlayers=args.nlayers, y=self.x)
elif dec == "gaussian":
self.dec_mlp = GaussianMLP(self.enc_mlp.out, self.zdim, self.hdim, self.xdim, nlayers=args.nlayers, y=self.x)
else:
raise RuntimeError("unrecognized decoder %" % dec)
self.cost = (-cgt.sum(kld_unit_mvn(self.enc_mlp.mu, self.enc_mlp.var)) + self.dec_mlp.cost) / args.batch_size
self.params = self.enc_mlp.params + self.dec_mlp.params
# L2 regularization
self.gparams = [cgt.grad(self.cost, [p])[0] + self.lmbda * p for p in self.params]
self.gaccums = [cgt.shared(np.zeros(p.op.get_value().shape, dtype=cgt.floatX)) for p in self.params]
# XXX replace w/ adagrad update from nn
ADAGRAD_EPS = 1e-10 # for stability
self.updates = [
(param, param - args.lr * gparam / cgt.sqrt(gaccum + cgt.square(gparam) + ADAGRAD_EPS))
for param, gparam, gaccum in zip(self.params, self.gparams, self.gaccums)
]
self.updates += [
(gaccum, gaccum + cgt.square(gparam))
for gaccum, gparam in zip(self.gaccums, self.gparams)
]
self.train = cgt.function(
[self.x, self.eps],
self.cost,
updates=self.updates
)
self.test = cgt.function(
[self.x, self.eps],
self.cost,
updates=None
)
# can be used for semi-supervised learning for example
self.encode = cgt.function(
[self.x, self.eps],
self.enc_mlp.out
)
def test_im2col():
for settings in [ ((4,4),(0,0),(1,1)), ((3,3),(1,1),(2,2)), ((3,3),(1,1),(3,3)) ]:
xval = np.arange(2*1*28*28).reshape(2,1,28,28).astype(cgt.floatX)
x = cgt.tensor4("x", fixed_shape=xval.shape)
y = im2col(x, *settings)
h = cgt.constant(np.random.randn(*cgt.infer_shape(y)))
cost = (y*h).sum()
fcost = cgt.function([x],cost)
fgrad = cgt.function([x], cgt.grad(cost, [x])[0])
from cgt.numeric_diff import numeric_grad
gnum = numeric_grad(fcost, xval,eps=1e-5)
gana = fgrad(xval)
assert np.allclose(gnum, gana)
def make_updater_fc_parallel():
X = cgt.matrix("X", fixed_shape=(None,28*28))
y = cgt.vector("y",dtype='i8')
stepsize = cgt.scalar("stepsize")
loss = build_fc_return_loss(X,y)
params = nn.get_parameters(loss)
m = nn.Module([X,y], [loss])
split_loss = 0
for start in xrange(0, batch_size, batch_size//4):
sli = slice(start, start+batch_size//4)
split_loss += m([X[sli], y[sli]])[0]
split_loss /= 4
gparams = cgt.grad(split_loss, params)
updates2 = [(p, p-stepsize*gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X,y, stepsize], split_loss, updates=updates2)
def make_updater_fc_parallel():
X = cgt.matrix("X", fixed_shape=(None, 28 * 28))
y = cgt.vector("y", dtype='i8')
stepsize = cgt.scalar("stepsize")
loss = build_fc_return_loss(X, y)
params = nn.get_parameters(loss)
m = nn.Module([X, y], [loss])
split_loss = 0
for start in xrange(0, batch_size, batch_size // 4):
sli = slice(start, start + batch_size // 4)
split_loss += m([X[sli], y[sli]])[0]
split_loss /= 4
gparams = cgt.grad(split_loss, params)
updates2 = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], split_loss, updates=updates2)
def make_updater_convnet_parallel():
X = cgt.tensor4("X", fixed_shape=(None, 1, 28, 28)) # so shapes can be inferred
y = cgt.vector("y", dtype="i8")
stepsize = cgt.scalar("stepsize")
loss = build_convnet_return_loss(X, y)
m = nn.Module([X, y], [loss])
split_loss = 0
for start in xrange(0, batch_size, batch_size // 4):
sli = slice(start, start + batch_size // 4)
split_loss += m([X[sli], y[sli]])[0]
split_loss /= 4
params = nn.get_parameters(loss)
gparams = cgt.grad(split_loss, params)
updates2 = [(p, p - stepsize * gp) for (p, gp) in zip(params, gparams)]
return cgt.function([X, y, stepsize], split_loss, updates=updates2)
def make_loss_and_grad_and_step(arch, size_input, size_output, size_mem,
size_batch, n_layers, n_unroll, k_in, k_h):
# symbolic variables
x_tnk = cgt.tensor3()
targ_tnk = cgt.tensor3()
#make_network = make_deep_lstm if arch=="lstm" else make_deep_gru
make_network = make_deep_rrnn_rot_relu
network = make_network(size_input, size_mem, n_layers, size_output,
size_batch, k_in, k_h)
init_hiddens = [
cgt.matrix() for _ in xrange(get_num_hiddens(arch, n_layers))
]
# TODO fixed sizes
cur_hiddens = init_hiddens
loss = 0
for t in xrange(n_unroll):
outputs = network([x_tnk[t]] + cur_hiddens)
cur_hiddens, prediction_logprobs = outputs[:-1], outputs[-1]
# loss = loss + nn.categorical_negloglik(prediction_probs, targ_tnk[t]).sum()
loss = loss - (prediction_logprobs * targ_tnk[t]).sum()
cur_hiddens = outputs[:-1]
final_hiddens = cur_hiddens
loss = loss / (n_unroll * size_batch)
params = network.get_parameters()
gradloss = cgt.grad(loss, params)
flatgrad = flatcat(gradloss)
with utils.Message("compiling loss+grad"):
f_loss_and_grad = cgt.function([x_tnk, targ_tnk] + init_hiddens,
[loss, flatgrad] + final_hiddens)
f_loss = cgt.function([x_tnk, targ_tnk] + init_hiddens, loss)
assert len(init_hiddens) == len(final_hiddens)
x_nk = cgt.matrix('x')
outputs = network([x_nk] + init_hiddens)
f_step = cgt.function([x_nk] + init_hiddens, outputs)
# print "node count", cgt.count_nodes(flatgrad)
return network, f_loss, f_loss_and_grad, f_step
def test_im2col():
for settings in [((4, 4), (0, 0), (1, 1)), ((3, 3), (1, 1), (2, 2)),
((3, 3), (1, 1), (3, 3))]:
xval = np.arange(2 * 1 * 28 * 28).reshape(2, 1, 28,
28).astype(cgt.floatX)
x = cgt.tensor4("x", fixed_shape=xval.shape)
y = im2col(x, *settings)
h = cgt.constant(np.random.randn(*cgt.infer_shape(y)))
cost = (y * h).sum()
fcost = cgt.function([x], cost)
fgrad = cgt.function([x], cgt.grad(cost, [x])[0])
from cgt.numeric_diff import numeric_grad
gnum = numeric_grad(fcost, xval, eps=1e-5)
gana = fgrad(xval)
assert np.allclose(gnum, gana)
def test_pool(**kwargs):
np.random.seed(0)
x = cgt.tensor4("x", fixed_shape=(2,3,5,7))
y = max_pool_2d(x, (4,4),(0,0),(1,1))
xval = np.random.randn(2,3,5,7)
hval = np.random.randn(*cgt.infer_shape(y))
h = cgt.constant(hval)
cost = (y*h).sum()
fcost = cgt.function([x], cost)
fgrad = cgt.function([x], cgt.grad(cost, [x])[0])
from cgt.numeric_diff import numeric_grad
gnum = numeric_grad(fcost, xval)
gana = fgrad(xval)
assert np.allclose(gnum,gana)
def test_cpu_pool(**kwargs):
np.random.seed(0)
x = cgt.tensor4("x", fixed_shape=(2, 3, 5, 7))
y = max_pool_2d(x, (4, 4), (0, 0), (1, 1))
xval = np.random.randn(2, 3, 5, 7)
hval = np.random.randn(*cgt.infer_shape(y))
h = cgt.constant(hval)
cost = (y * h).sum()
fcost = cgt.function([x], cost)
fgrad = cgt.function([x], cgt.grad(cost, [x])[0])
from cgt.numeric_diff import numeric_grad
gnum = numeric_grad(fcost, xval)
gana = fgrad(xval)
assert np.allclose(gnum, gana)
def adagrad_updates(cost, params, stepsize=0.001, rho=0.9, epsilon=1e-6):
grads = cgt.grad(cost, params)
updates = []
for param, grad in zip(params, grads):
value = param.op.get_value()
accu = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
delta_accu = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
accu_new = rho * accu + (1 - rho) * grad**2
updates.append((accu, accu_new))
update = (grad * cgt.sqrt(delta_accu + epsilon) /
cgt.sqrt(accu_new + epsilon))
updates.append((param, param - stepsize * update))
delta_accu_new = rho * delta_accu + (1 - rho) * update**2
updates.append((delta_accu, delta_accu_new))
return updates
def rmsprop(cost, params, learning_rate=1.0, rho=0.9, epsilon=1e-6):
"""RMSProp updates
Divide learning rate by moving average of RMS gradients. See [1]
Math:
* ``accu_new = rho * accu + (1 - rho) * grad ** 2``
* ``param = param - (learning_rate * grad / cgt.sqrt(accu_new + epsilon))``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
rho : float
Controls decay of gradient moving average.
epsilon : float
Avoid division by 0 while scaling. Small constant.
Returns
-------
list of tuples of the form [(param, updates), (accumulated_RMS_grads, accumulated_RMS_grads_new)]
References
----------
.. [1] Yann N. Dauphin, Harm de Vries, Junyoung Chung, Yoshua Bengio (2015):
RMSProp and equilibrated adaptive learning rates for non-convex optimization
arXiv:1502.04390 http://arxiv.org/abs/1502.04390
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
value = param.op.get_value()
accu = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
accu_new = rho * accu + (1 - rho) * grad**2
updates.append((accu, accu_new))
updates.append(
(param,
param - (learning_rate * grad / cgt.sqrt(accu_new + epsilon))))
return updates
def make_funcs(config, dbg_out=None):
params, Xs, Ys, C_0, H_0, C_T, H_T, C_1, H_1 = lstm_network(
config['rnn_steps'], config['num_inputs'], config['num_outputs'],
config['num_units'], config['num_mems'])
# basic
size_batch = Xs[0].shape[0]
dY = Ys[0].shape[-1]
Ys_gt = [
cgt.matrix(fixed_shape=(size_batch, dY), name='Y%d' % t)
for t in range(len(Ys))
]
Ys_var = [cgt.tensor3(fixed_shape=(size_batch, dY, dY)) for _ in Ys]
net_inputs, net_outputs = Xs + C_0 + H_0 + Ys_var, Ys + C_T + H_T
# calculate loss
loss_vec = []
for i in range(len(Ys)):
# if i == 0: continue
_l = dist.gaussian.logprob(Ys_gt[i], Ys[i], Ys_var[i])
loss_vec.append(_l)
loss_vec = cgt.add_multi(loss_vec)
if config['weight_decay'] > 0.:
params_flat = cgt.concatenate([p.flatten() for p in params])
loss_param = config['weight_decay'] * cgt.sum(params_flat**2)
loss_vec -= loss_param # / size_batch
loss = cgt.sum(loss_vec) / config['rnn_steps'] / size_batch
grad = cgt.grad(loss, params)
# functions
def f_init(size_batch):
c_0, h_0 = [], []
for _n_m in config['num_mems']:
if _n_m > 0:
c_0.append(np.zeros((size_batch, _n_m)))
h_0.append(np.zeros((size_batch, _n_m)))
return c_0, h_0
f_step = cgt.function([Xs[0]] + C_0 + H_0, [Ys[0]] + C_1 + H_1)
f_loss = cgt.function(net_inputs + Ys_gt, loss)
f_grad = cgt.function(net_inputs + Ys_gt, grad)
f_surr = cgt.function(net_inputs + Ys_gt, [loss] + net_outputs + grad)
return params, f_step, f_loss, f_grad, f_init, f_surr
def test_linreg():
cgt.reset_config()
cgt.set_precision('double')
N = 10
K = 3
Xval = np.random.randn(N, K)
wval = np.random.randn(K)
bval = np.random.randn()
yval = np.random.randn(N)
X_nk = cgt.matrix("X")
y_n = cgt.vector("y")
w_k = cgt.vector("w")
b = cgt.scalar(name="b")
ypred = cgt.dot(X_nk, w_k) + b
err = cgt.sum(cgt.square(ypred - y_n))
g = cgt.grad(err, [w_k, b])
g_simple, an, _ = cgt.core.simplify_and_analyze(g)
print "Loss function:"
cgt.print_tree([err])
print "Gradient:"
cgt.print_tree(g)
print "Gradient simplified"
cgt.print_tree(
g_simple,
nodefn=lambda node, o: o.write(" " + an["node2hash"][node][:5]))
print "-------"
d = {X_nk: Xval, w_k: wval, b: bval, y_n: yval}
np.testing.assert_allclose(cgt.numeric_eval(err, d),
np.linalg.norm(Xval.dot(wval) + bval - yval)**2)
np.testing.assert_allclose(cgt.numeric_eval(g[0], d),
2 * Xval.T.dot(Xval.dot(wval) + bval - yval))
np.testing.assert_allclose(cgt.numeric_eval(g[1], d),
2 * np.sum(Xval.dot(wval) + bval - yval, 0))
def __init__(self, num_features=None, num_hidden=100):
stepsize = 0.01
# with shape (batchsize, ncols)
X = cgt.matrix("X", fixed_shape=(1, num_features))
# y: a symbolic variable representing the rewards, which are integers
y = cgt.scalar("y", dtype='float64')
hid1 = nn.rectify(
nn.Affine(num_features, num_hidden, weight_init=nn.IIDGaussian(std=.1), bias_init=nn.Constant(1))(X)
)
# One final fully-connected layer, and then a linear activation output for reward
output = nn.Affine(num_hidden, 1, weight_init=nn.IIDGaussian(std=.1), bias_init=nn.Constant(1))(hid1)
abs_deviation = cgt.abs(output - y).mean()
params = nn.get_parameters(abs_deviation)
gparams = cgt.grad(abs_deviation, params)
updates = [(p, p-stepsize*gp) for (p, gp) in zip(params, gparams)]
self.predictor = cgt.function([X], output)
self.updater = cgt.function([X, y], abs_deviation, updates=updates)
def CGT_vLJ_Optimize(x):
N = len(x)
#cgt.set_precision('double')
xt = cgt.vector('xt')
vLJt = 0
for j in range(1,N):
for i in range(j):
rho = ((xt[i*D:i*D+D] - xt[j*D:j*D+D])**2).sum()
vLJt += rho**(-6.0)-(rho**(-3.0))
f = cgt.function([xt],4*vLJt)
dvLJc = cgt.grad(4*vLJt, xt)
df = cgt.function([xt],dvLJc)
CGT_BFGSres = optimize.minimize(f, np.ravel(x), \
method='L-BFGS-B', \
jac = df, \
options={'disp': False})
return np.reshape(CGT_BFGSres.x, (N,D))
def make_loss_and_grad_and_step(arch, size_input, size_output, size_mem, size_batch, n_layers, n_unroll, k_in, k_h):
# symbolic variables
x_tnk = cgt.tensor3()
targ_tnk = cgt.tensor3()
#make_network = make_deep_lstm if arch=="lstm" else make_deep_gru
make_network = make_deep_rrnn_rot_relu
network = make_network(size_input, size_mem, n_layers, size_output, size_batch, k_in, k_h)
init_hiddens = [cgt.matrix() for _ in xrange(get_num_hiddens(arch, n_layers))]
# TODO fixed sizes
cur_hiddens = init_hiddens
loss = 0
for t in xrange(n_unroll):
outputs = network([x_tnk[t]] + cur_hiddens)
cur_hiddens, prediction_logprobs = outputs[:-1], outputs[-1]
# loss = loss + nn.categorical_negloglik(prediction_probs, targ_tnk[t]).sum()
loss = loss - (prediction_logprobs*targ_tnk[t]).sum()
cur_hiddens = outputs[:-1]
final_hiddens = cur_hiddens
loss = loss / (n_unroll * size_batch)
params = network.get_parameters()
gradloss = cgt.grad(loss, params)
flatgrad = flatcat(gradloss)
with utils.Message("compiling loss+grad"):
f_loss_and_grad = cgt.function([x_tnk, targ_tnk] + init_hiddens, [loss, flatgrad] + final_hiddens)
f_loss = cgt.function([x_tnk, targ_tnk] + init_hiddens, loss)
assert len(init_hiddens) == len(final_hiddens)
x_nk = cgt.matrix('x')
outputs = network([x_nk] + init_hiddens)
f_step = cgt.function([x_nk]+init_hiddens, outputs)
# print "node count", cgt.count_nodes(flatgrad)
return network, f_loss, f_loss_and_grad, f_step
def rmsprop(cost, params, learning_rate=1.0, rho=0.9, epsilon=1e-6):
"""RMSProp updates
Divide learning rate by moving average of RMS gradients. See [1]
Math:
* ``accu_new = rho * accu + (1 - rho) * grad ** 2``
* ``param = param - (learning_rate * grad / cgt.sqrt(accu_new + epsilon))``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
rho : float
Controls decay of gradient moving average.
epsilon : float
Avoid division by 0 while scaling. Small constant.
Returns
-------
list of tuples of the form (param, updates), (accumulated_RMS_grads, accumulated_RMS_grads_new)
References
----------
.. [1] Yann N. Dauphin, Harm de Vries, Junyoung Chung, Yoshua Bengio (2015):
RMSProp and equilibrated adaptive learning rates for non-convex optimization
arXiv:1502.04390 http://arxiv.org/abs/1502.04390
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
accu = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
accu_new = rho * accu + (1 - rho) * grad ** 2
updates.append((accu, accu_new))
updates.append((param, param - (learning_rate * grad / cgt.sqrt(accu_new + epsilon))))
return updates
def make_funcs(config, dbg_out=None):
params, Xs, Ys, C_0, H_0, C_T, H_T, C_1, H_1 = lstm_network(
config['rnn_steps'], config['num_inputs'], config['num_outputs'],
config['num_units'], config['num_mems']
)
# basic
size_batch = Xs[0].shape[0]
dY = Ys[0].shape[-1]
Ys_gt = [cgt.matrix(fixed_shape=(size_batch, dY), name='Y%d'%t)
for t in range(len(Ys))]
Ys_var = [cgt.tensor3(fixed_shape=(size_batch, dY, dY)) for _ in Ys]
net_inputs, net_outputs = Xs + C_0 + H_0 + Ys_var, Ys + C_T + H_T
# calculate loss
loss_vec = []
for i in range(len(Ys)):
# if i == 0: continue
_l = dist.gaussian.logprob(Ys_gt[i], Ys[i], Ys_var[i])
loss_vec.append(_l)
loss_vec = cgt.add_multi(loss_vec)
if config['weight_decay'] > 0.:
params_flat = cgt.concatenate([p.flatten() for p in params])
loss_param = config['weight_decay'] * cgt.sum(params_flat ** 2)
loss_vec -= loss_param # / size_batch
loss = cgt.sum(loss_vec) / config['rnn_steps'] / size_batch
grad = cgt.grad(loss, params)
# functions
def f_init(size_batch):
c_0, h_0 = [], []
for _n_m in config['num_mems']:
if _n_m > 0:
c_0.append(np.zeros((size_batch, _n_m)))
h_0.append(np.zeros((size_batch, _n_m)))
return c_0, h_0
f_step = cgt.function([Xs[0]] + C_0 + H_0, [Ys[0]] + C_1 + H_1)
f_loss = cgt.function(net_inputs + Ys_gt, loss)
f_grad = cgt.function(net_inputs + Ys_gt, grad)
f_surr = cgt.function(net_inputs + Ys_gt, [loss] + net_outputs + grad)
return params, f_step, f_loss, f_grad, f_init, f_surr
def adagrad(cost, params, learning_rate=1.0, epsilon=1e-6):
"""Adagrad updates
The learning rate will be scaled by dividing it by the sqaure root of the sum of accumulated squared gradients.
Math:
* ``accu_new = accu + grad ** 2``
* ``param = param - (learning_rate * grad) / cgt.sqrt(accu_new + epsilon)``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
epsilon: avoids division close to zero. Small float.
Returns
-------
list of tuples of the form [(param, updates), (accumulated_grads, accumulated_grads_new)]
References
----------
.. [1] Duchi, J., Hazan, E., & Singer, Y. (2011):
Adaptive subgradient methods for online learning and stochastic
optimization. JMLR, 12:2121-2159.
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
value = param.op.get_value()
accu = cgt.shared(np.zeros(value.shape, dtype=value.dtype))
accu_new = accu + grad**2
updates.append((accu, accu_new))
updates.append(
(param,
param - (learning_rate * grad) / cgt.sqrt(accu_new + epsilon)))
return updates
def sgd(cost, params, learning_rate):
"""Stochastic Gradient Descent (SGD) updates
Math:
* ``param := param - learning_rate * gradient``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Returns
-------
list of tuples of the form (param, new_param)
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
updates.append((param, param - learning_rate * grad))
return updates
def sgd(cost, params, learning_rate):
"""Stochastic Gradient Descent (SGD) updates
Math:
* ``param := param - learning_rate * gradient``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
Returns
-------
list of tuples of the form (param, updates)
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
updates.append((param, param - learning_rate * grad))
return updates
def make_funcs(opt, ntm, total_time, loss_timesteps):
x_tbk = cgt.tensor3("x", fixed_shape=(total_time, opt.b, opt.k))
y_tbp = cgt.tensor3("y", fixed_shape=(total_time, opt.b, opt.p))
loss_timesteps = set(loss_timesteps)
initial_states = make_ntm_initial_states(opt)
params = ntm.get_parameters() + get_parameters(initial_states)
# params = ntm.get_parameters()
lossCE = 0
loss01 = 0
state_arrs = initial_states
for t in xrange(total_time):
tmp = ntm([x_tbk[t]] + state_arrs)
raw_pred = tmp[0]
state_arrs = tmp[1:4]
if t in loss_timesteps:
p_pred = cgt.sigmoid(raw_pred)
ce = bernoulli_crossentropy(
y_tbp[t],
p_pred).sum() # cross-entropy of bernoulli distribution
lossCE = lossCE + ce
loss01 = loss01 + cgt.cast(cgt.equal(y_tbp[t], round01(p_pred)),
cgt.floatX).sum()
lossCE = lossCE / (len(loss_timesteps) * opt.p * opt.b) / np.log(2)
loss01 = loss01 / (len(loss_timesteps) * opt.p * opt.b)
gradloss = cgt.grad(lossCE, params)
flatgrad = flatcat(gradloss)
f_loss = cgt.function([x_tbk, y_tbp], lossCE)
f_loss_and_grad = cgt.function([x_tbk, y_tbp], [lossCE, loss01, flatgrad])
print "number of nodes in computation graph:", core.count_nodes(
[lossCE, loss01, flatgrad])
return f_loss, f_loss_and_grad, params
def test_linreg():
N = 10
K = 3
Xval = np.random.randn(N,K)
wval = np.random.randn(K)
bval = np.random.randn()
yval = np.random.randn(N)
X_nk = cgt.matrix("X")
y_n = cgt.vector("y")
w_k = cgt.vector("w")
b = cgt.scalar(name="b")
ypred = cgt.dot(X_nk, w_k) + b
err = cgt.sum(cgt.square(ypred - y_n))
g = cgt.grad(err, [w_k, b])
g_simple,an,_ = cgt.core.simplify_and_analyze(g)
print "Loss function:"
cgt.print_tree([err])
print "Gradient:"
cgt.print_tree(g)
print "Gradient simplified"
cgt.print_tree(g_simple, nodefn=lambda node,o: o.write(" " + an["node2hash"][node][:5]))
print "-------"
d = {X_nk : Xval, w_k : wval, b : bval, y_n : yval}
np.testing.assert_allclose(cgt.numeric_eval(err,d), np.linalg.norm(Xval.dot(wval) + bval - yval)**2,
atol={"single":1e-3,"double":1e-6}[cgt.get_precision()])
np.testing.assert_allclose(cgt.numeric_eval(g[0],d), 2 * Xval.T.dot(Xval.dot(wval) + bval - yval),
atol={"single":1e-3,"double":1e-6}[cgt.get_precision()])
np.testing.assert_allclose(cgt.numeric_eval(g[1],d), 2 * np.sum(Xval.dot(wval) + bval - yval, 0),
atol={"single":1e-3,"double":1e-6}[cgt.get_precision()])
def adagrad(cost, params, learning_rate=1.0, epsilon=1e-6):
"""Adagrad updates
The learning rate will be scaled by dividing it by the sqaure root of the sum of accumulated squared gradients.
Math:
* ``accu_new = accu + grad ** 2``
* ``param = param - (learning_rate * grad) / cgt.sqrt(accu_new + epsilon)``
Parameters
----------
cost : a scalar loss.
params : a list of cgt shared variables. We generate update
expressions w.r.t. these variables.
learning_rate : float
Tunes the size of the update step.
epsilon: avoids division close to zero. Small float.
Returns
-------
list of tuples of the form [(param, updates), (accumulated_grads, accumulated_grads_new)]
References
----------
.. [1] Duchi, J., Hazan, E., & Singer, Y. (2011):
Adaptive subgradient methods for online learning and stochastic
optimization. JMLR, 12:2121-2159.
"""
updates = []
grads = cgt.grad(cost, params)
for param, grad in zip(params, grads):
assert isinstance(param.op, core.GetData)
accu = cgt.shared(np.zeros(param.op.get_shape(), dtype=param.dtype))
accu_new = accu + grad ** 2
updates.append((accu, accu_new))
updates.append((param, param - (learning_rate * grad) / cgt.sqrt(accu_new + epsilon)))
return updates
def test_cpu_pool():
with cgt.scoped_update_config(precision="quad", backend="native"):
print cgt.get_precision()
ci = get_compile_info()
np.random.seed(0)
x = cgt.tensor4("x", fixed_shape=(2, 3, 5, 7))
y = max_pool_2d(x, (4, 4), (0, 0), (1, 1))
xval = np.random.randn(2, 3, 5, 7)
hval = np.random.randn(*cgt.infer_shape(y))
h = cgt.constant(hval)
cost = (y * h).sum()
fcost = cgt.function([x], cost)
fgrad = cgt.function([x], cgt.grad(cost, [x])[0])
from cgt.numeric_diff import numeric_grad
gnum = numeric_grad(fcost, xval)
gana = fgrad(xval)
assert np.allclose(gnum, gana)