class GPU(Backend):
"""
Sets up a NervanaGPU based backend for matrix operations.
Note that some functions defined in the generic Backend class such as are
cross-map pooling and normalization and adaDelta are not implemented for
this backend.
"""
default_dtype = np.float32
def __init__(self, rng_seed, stochastic_round=False, device_id=0):
self.ng = NervanaGPU(stochastic_round=stochastic_round)
logger.info("Initialized NervanaGPU with stochastic_round=%s",
stochastic_round)
self.rng_seed = rng_seed
self.rng_init()
self.device_id = device_id if device_id is not None else 0
def __getstate__(self):
"""
Defines what and how we go about serializing an instance of this class.
Returns:
self.__dict__: The full contents of the backend class instance,
except for the mem_pool which is on device and
cannot be serialized.
"""
if hasattr(self, 'mem_pool') and self.mem_pool is not None:
self.mem_pool_pickle = {'shape': self.mem_pool.shape,
'dtype': np.float32}
self.mem_pool = None
return self.__dict__
def __setstate__(self, state):
"""
Defines how we go about deserializing into an instance of this class.
Arguments:
self.__dict__: The full contents of the backend class instance,
except for the mem_pool which is on device and
cannot be serialized.
"""
self.__dict__.update(state)
self.mem_pool = self.ng.empty(self.mem_pool_pickle['shape'],
dtype=self.mem_pool_pickle['dtype'])
def init_mempool(self, shape, dtype=default_dtype):
"""
Allocates a memory pool for temporary storage
"""
self.mem_pool = self.ng.empty(shape, dtype=dtype)
def alloc_host_mem(self, shape, dtype):
return drv.pagelocked_empty(shape, dtype, order="C", mem_flags=0)
def create_stream(self):
return drv.Stream()
def async_copy(self, dest, src, stream=None):
drv.memcpy_htod_async(dest.gpudata, src, stream)
def rng_init(self):
"""
Initialize and seed the pseudo random number genrator. Random numbers
are generated on the host using numpy, then transfered to device.
"""
seed = None
if 'rng_seed' in self.__dict__:
seed = self.rng_seed
logger.info("Seeding random number generator with: %s", str(seed))
np.random.seed(seed)
def flop_timing_init(self, decorate_fc, decorate_conv, decorate_ew):
"""
Initialize FLOP timing. Wraps the specified MOP calls via a decorator
to record elapsed time and number of operations.
Arguments:
decorate_fc (list): string giving the function names of fully
connected layer forward/backward/update calls
to time.
decorate_conv (list): string giving the function names of
convolutional layer forward/backward/update
calls to time.
decorate_ew (list): string giving the function names of element-wise
calls to time.
Notes:
Must be called prior to first flop_timing_start call
"""
self.start = drv.Event()
self.end = drv.Event()
self.flop_timer = FlopsDecorator(self)
self.flop_timer.decorate(decorate_fc=decorate_fc,
decorate_conv=decorate_conv,
decorate_ew=decorate_ew)
def flop_timinig_start(self):
"""
Start a new FLOP timer.
Returns:
None: dummy value (not used)
"""
return self.start.record()
def flop_timing_finish(self, start_time):
"""
Complete current FLOP timing.
Arguments:
start_time (unused): ignored.
Returns:
float: elapsed time in seconds since prior flop_timing_start call.
"""
self.end.record()
self.end.synchronize()
return self.end.time_since(self.start)
def uniform(self, low=0.0, high=1.0, shape=1, dtype=default_dtype,
persist_values=True, name=None, allocator=drv.mem_alloc):
"""
generate numpy random number and convert to a GPUTensor.
If called with dype=None it will probably explode
"""
ary = np.random.uniform(low, high, shape)
return GPUTensor(ary.shape, dtype, allocator=allocator, name=name,
rounding=self.ng.round_mode).set(ary)
def normal(self, loc=0.0, scale=1.0, size=1, dtype=default_dtype,
persist_values=True, name=None, allocator=drv.mem_alloc):
"""
Gaussian/Normal random number sample generation
"""
ary = np.random.normal(loc, scale, size)
return GPUTensor(ary.shape, dtype, allocator=allocator, name=name,
rounding=self.ng.round_mode).set(ary)
def fprop_fc(self, out, inputs, weights, layer=None):
"""
Forward propagate the inputs of a fully connected network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
layer (Layer): The layer object.
"""
self.ng.dot(weights, inputs, out)
def bprop_fc(self, out, weights, deltas, layer=None):
"""
Backward propagate the error through a fully connected network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
layer (Layer): The layer object.
"""
self.ng.dot(weights.T, deltas, out)
def update_fc(self, out, inputs, deltas, layer=None):
"""
Compute the updated gradient for a fully connected network layer.
Arguments:
out (GPUTensor): Where to store the updated gradient value.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
deltas (GPUTensor): The error values for this layer
layer (Layer): The layer object.
"""
self.ng.dot(deltas, inputs.T, out)
def fprop_conv(self, out, inputs, weights, ofmshape, ofmsize, ofmlocs,
ifmshape, links, nifm, padding, stride, ngroups, fpropbuf,
local=False):
"""
Forward propagate the inputs of a convolutional network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
ofmshape (tuple): Dimensions of each output feature map (typically
number of height and width neurons).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element
in each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
number of height and width neurons). For this
backend we expect these values to be square.
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
fpropbuf (GPUTensor): Temporary storage buffer used to hold the
convolved outputs for a single receptive
field. Not used for this backend.
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
"""
'''
N: Number of images in mini-batch
C: Number of input feature maps
K: Number of output feature maps
D: Depth of input image
H: Height of input image
W: Width of input image
T: Depth of filter kernel
R: Height of filter kernel
S: Width of filter kernel
'''
self.ng.fprop_conv(layer=fpropbuf, I=inputs, F=weights, O=out,
alpha=1.0, repeat=1)
def bprop_conv(self, out, weights, deltas, ofmshape, ofmsize, ofmlocs,
ifmshape, links, padding, stride, nifm, ngroups, bpropbuf,
local=False):
"""
Backward propagate the error through a convolutional network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
bpropbuf (GPUTensor): Temporary storage buffer used to hold the
backpropagated error for a single receptive
field
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
"""
self.ng.bprop_conv(layer=bpropbuf, F=weights, E=deltas, grad_I=out,
alpha=1.0, repeat=1)
def update_conv(self, out, inputs, weights, deltas, ofmshape, ofmsize,
ofmlocs, ifmshape, links, nifm, padding, stride, ngroups,
fwidth, updatebuf, local=False, layer=None):
"""
Compute the updated gradient for a convolutional network layer.
Arguments:
out (GPUTensor): Where to store the updated gradient value.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
fwidth (int): Filter width.
updatebuf (GPUTensor): Temporary storage buffer used to hold the
updated gradient for a single receptive
field
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
layer (Layer): The layer object.
"""
self.ng.update_conv(layer=updatebuf, I=inputs, E=deltas, grad_F=out,
alpha=1.0, repeat=1)
def fprop_pool(self, out, inputs, op, ofmshape, ofmsize, ofmlocs, fshape,
ifmshape, links, nifm, padding, stride, fpropbuf):
"""
Forward propagate the inputs of a Pooling network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
op (string): The type of pooling operation to apply. We support
"max", "avg", "l2" currently.
ofmshape (tuple): Dimensions of each output feature map (typically
number of height and width neurons).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
fshape (tuple): Dimensions of each filter (typically height and
width).
ifmshape (tuple): Dimensions of each input feature map (typically
number of height and width neurons).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
pooling operation.
stride (int): Number of neurons to shift the filter at each step.
fpropbuf (GPUTensor): Temporary storage buffer used to hold the
pooled outputs for a single receptive field.
"""
op = op.lower()
if op == "max":
self.ng.fprop_pool(layer=fpropbuf, I=inputs, O=out, repeat=1)
else:
raise AttributeError("unexpected pooling op type: %s", op)
def bprop_pool(self, out, fouts, inputs, deltas, op, ofmshape, ofmsize,
ofmlocs, fshape, fpsize, ifmshape, links, nifm, padding,
stride, bpropbuf):
"""
Backward propagate the error through a pooling network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
fouts (GPUTensor): Forward propagated outputs from the previous
layer.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
deltas (GPUTensor): The error values for this layer
op (string): The type of pooling operation to apply. We support
"max", "avg", "l2" currently.
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
fshape (tuple): Dimensions of each filter (typically height and
width).
fpsize (int): The size of each filter.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
pooling operation.
stride (int): Number of neurons to shift the filter at each step.
bpropbuf (GPUTensor): Temporary storage buffer used to hold the
backpropagated error for a single receptive
field
"""
op = op.lower()
if op == "max":
self.ng.bprop_pool(layer=bpropbuf, I=inputs, E=deltas, grad_I=out,
repeat=1)
else:
raise AttributeError("unexpected pooling op type: %s", op)
def logistic(self, x, out):
"""
Logistic sigmoid nonlinearity, 1/(1+exp(-x))
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
"""
self.ng.sig(x, out=out)
return out
def rectlin(self, x, out):
"""
Rectified Linear nonlinearity
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
"""
self.ng.maximum(x, 0., out=out)
return out
def rectleaky(self, x, slope, out):
out[:] = self.ng.maximum(x, x*slope)
def rectleaky_derivative(self, x, slope, out):
out[:] = self.ng.greater(x, 0) * (1.0 - slope) + slope
def sum(self, tsr, axes, out):
"""
Sum
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.sum(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.sum(tsr, axis=axes, out=out)
return out
def mean(self, tsr, axes, out):
"""
Calculates the arithmetic mean of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.mean(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.mean(tsr, axis=axes, out=out)
return out
def min(self, tsr, axes, out):
"""
Calculates the minimum of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.min(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.min(tsr, axis=axes, out=out)
return out
def max(self, tsr, axes, out):
"""
Calculates the maximum of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.max(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.max(tsr, axis=axes, out=out)
return out
def variance(self, tsr, axes, out, mean=None):
"""
Calculates the variance of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): the tensor on which to compute the variance
axes (int, list, optional): the dimension(s) along which to
variance. If set to None, we will
variance over all dimensions.
out (GPUTensor): where the result will be stored.
mean (GPUTensor): the tensor containing mean of tsr
Returns:
GPUTensor: reference to out
"""
if mean is None:
logger.error("GPUTensor requires mean to be specified.")
raise ValueError("mean not specified")
self.ng.mean(self.ng.square(tsr-mean), axis=axes, out=out)
return out
def fabs(self, x, out):
"""
Calculates absolute value of the elements in a tensor
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
Returns:
GPUTensor: reference to out
"""
self.ng.fabs(x, out=out)
return out
def sqrt(self, x, out):
"""
Calculates square root of the elements in a tensor
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
Returns:
GPUTensor: reference to out
"""
self.ng.sqrt(x, out=out)
return out
def zeros(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor and fill it with zeros.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.zeros(shape, dtype=dtype)
def ones(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor and fill it with ones.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.ones(shape, dtype=dtype)
def empty(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.empty(shape, dtype=dtype)
def array(self, ary, dtype=default_dtype, persist_values=True, name=None,
allocator=drv.mem_alloc):
"""
Allocate a new GPUTensor and fill it with supplied numpy array.
Arguments:
ary (ndarray): Numpy array with source data
dtype (dtype, optional): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
name (string): Name for the GPUTensor
allocator (pycuda): Pycuda memory allocator
Returns:
GPUTensor: output
"""
return GPUTensor(ary.shape, dtype, allocator=allocator, name=name,
rounding=self.ng.round_mode).set(ary)
def add(self, left, right, out):
"""
Elementwise addition
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.add(left, right, out=out)
return out
def subtract(self, left, right, out):
"""
Elementwise subtraction
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.subtract(left, right, out=out)
return out
def multiply(self, left, right, out):
"""
Elementwise multiplication
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.multiply(left, right, out=out)
return out
def divide(self, left, right, out):
"""
Elementwise division
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.divide(left, right, out=out)
return out
def greater(self, left, right, out):
"""
Elementwise greater than testing
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.greater(left, right, out=out)
return out
def equal(self, left, right, out):
"""
Performs element-wise equality testing on each element of left and
right, storing the result in out. Each operand is assumed to be the
same shape (or broadcastable as such).
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.equal(left, right, out=out)
return out
def not_equal(self, left, right, out):
"""
Elementwise not equal testing
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.not_equal(left, right, out=out)
return out
def clip(self, a, a_min, a_max, out):
"""
Elementwise clipping between a range of specified values
Arguments:
a (GPUTensor): input tensor.
a_min (float): floor value.
a_max (float): ceiling value.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.clip(a, a_min, a_max, out=out)
return out
def log(self, a, out):
"""
Elementwise base-e logarithm
Arguments:
a (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.log(a, out=out)
return out
def tanh(self, a, out):
"""
Elementwise tanh
Arguments:
a (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.tanh(a, out=out)
return out
def argmax(self, a, out, axis=0):
"""
Calculates the indices of the maximal element value along the specified
axis. If multiple elements contain the maximum, only the elements of
the first are returned.
Arguments:
tsr (GPUTensor): The GPUTensor on which to find the maximum indices
axis (int): The dimension along which to find the maximum. If set
to None, find the overall maximum index of a flattened
representation of tsr.
out (GPUTensor): Where to store the result. Should be of the
appropriate type and expected shape
Returns:
GPUTensor: reference to out
"""
self.ng.argmax(a, out=out, axis=axis)
return out
def softmax(self, x, out):
"""
Softmax nonlinearity. Computes exp(x-max(x)) / sum_i exp(x_i-max(x_i))
Arguments:
x (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
out[:] = (self.ng.reciprocal(self.ng.sum(
self.ng.exp(x - self.ng.max(x, axis=0)), axis=0)) *
self.ng.exp(x - self.ng.max(x, axis=0)))
return out
def softmax_gradient(self, y, err, out):
"""
Gradient of the softmax nonlinearity.
Arguments:
y (GPUTensor): input tensor.
err (GPUTensor): backpropagated error.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
raise NotImplementedError("Softmax gradient should use shortcut")
return out
def make_binary_mask(self, tsr, keepthresh=0.5, dtype=default_dtype):
"""
Create a binary mask for dropout layers.
Arguments:
tsr (GPUTensor): Output tensor
keepthresh (float): fraction of ones
"""
self.ng.dropout(keep=keepthresh, out=tsr)
def gdm_compound(self, ps_item, us_item, vs_item, momentum_coef,
learning_rate, epoch):
"""
Perform gradient descent update with momentum.
Arguments:
ps_item (GPUTensor): parameter tensor (e.g. a weight matrix)
us_item (GPUTensor): update tensor, contains gradient wrt. weights
vs_item (GPUTensor): velocity tensor.
momentum_coef (float): momentum coefficient.
learning_rate (float): learning rate.
epoch (int): epoch (used in conjunction with diagnostics).
Outputs are written to vs_item (updated velocity)
and ps_item (updated weights)
"""
vs_item[:] = vs_item * momentum_coef - us_item * learning_rate
ps_item[:] = ps_item + vs_item
def gdmwd_compound(self, ps_item, us_item, vs_item, momentum_coef,
learning_rate, wd, epoch):
"""
Perform gradient descent update with momentum and weight decay.
Arguments:
ps_item (GPUTensor): parameter tensor (e.g. a weight matrix)
us_item (GPUTensor): update tensor, contains gradient wrt. weights
vs_item (GPUTensor): velocity tensor.
momentum_coef (float): momentum coefficient.
learning_rate (float): learning rate.
wd (float): weight decay parameter.
epoch (int): epoch (used in conjunction with diagnostics).
Outputs:
ps_item, the updated weights.
vs_item, the updated velocity.
us_item, used as a temp buffer.
"""
vs_item[:] = vs_item * momentum_coef - us_item * \
learning_rate - learning_rate * wd * ps_item
ps_item[:] = ps_item + vs_item
def ada_update(self, ps_item, us_item, gs_item, ds_item, ls_item, ss_item,
rho, epsilon):
"""
Update rule for AdaDelta (Zeiler, http://arxiv.org/abs/1212.5701)
Arguments:
ps_item: weight / parameter (will be updated)
us_item: update
gs_item: expected value of Gradient Squared (will be updated)
ds_item: expected value of Delta Squared (will be updated)
ls_item: learning rate (will be updated)
ss_item: Scratch Space
rho: decay constant (determines window size)
epsilon: small positive constant for numerical stability
"""
# Accumulate E[Grad^2]
gs_item[:] = gs_item * rho + (1.0 - rho) * us_item * us_item
# Calculate Updates
ls_item[:] = self.ng.sqrt((ds_item + epsilon) /
(gs_item + epsilon)) * (-1.0) * us_item
# Accumulate E[Delt^2]
ds_item[:] = ds_item * rho + (1.0 - rho) * ls_item * ls_item
# Final update to the params
ps_item[:] = ps_item + ls_item
def rms_update(self, params, updates, run_squares, velocity, scratch_space,
gamma, epsilon, learning_rate, momentum_coef):
# Update running squares
run_squares[:] = gamma * run_squares + (1. - gamma) * updates * updates
# Now scale the gradient by lr / rms(grad) (with a epsilon term for
# stability) and use it to update the params
if momentum_coef == 0:
params[:] = params - learning_rate * updates * self.ng.reciprocal(
self.ng.sqrt(run_squares) + epsilon)
else:
velocity[:] = velocity * momentum_coef - \
learning_rate * updates * \
self.ng.reciprocal(self.ng.sqrt(run_squares) + epsilon)
params[:] = params + velocity
def fprop_bn_compound(self, inputs, beta, gamma, eps, xvar, xhat, out):
"""
Batch normalization forward pass, compounded to run in 3 kernel calls.
Arguments:
inputs: input data to be normalized
beta: location parameter
gamma: scale parameter
eps: small constant for numerical stability
xvar: variance (updated)
xhat: normalized input (updated)
out: normalized and rescaled input (updated)
"""
xvar[:] = self.ng.reciprocal(self.ng.sqrt(self.ng.var(inputs, axis=1) +
eps))
xhat[:] = xvar * (inputs - self.ng.mean(inputs, axis=1))
out[:] = xhat * gamma + beta
return out
def bprop_bn_compound(self, xhat, error, xvar, gamma,
beta_updates, gamma_updates):
"""
Batch normalization backward pass, compounded to run with 4 kernel
calls.
Arguments:
xhat: normalized input data (updated)
error: backpropagated deltas (updated)
xvar: precomputed variance
gamma: scale parameter
beta_updates: gradient update for beta (updated)
gamma_updates: gradient update for gamma (updated)
"""
gamma_updates[:] = self.ng.sum(xhat * error, axis=1)
beta_updates[:] = self.ng.sum(error, axis=1)
xhat[:] = (xhat * gamma_updates + beta_updates) / float(xhat.shape[1])
error[:] = xvar * gamma * (error - xhat)
cpuI[-1,:] = np.finfo(cpuI.dtype).min
else:
cpuI[-1,:] = 0
# cpu output arrays
cpuO = np.empty(dimO, dtype=np.float32)
cpuB = np.zeros(slicable(dimI,1), dtype=np.float32)
# give gpu the input array without zero padding (not needed)
devI = ng.array(cpuI[:-1,:].reshape(dimI), dtype=dtype)
devO = ng.zeros(dimO, dtype=dtype)
devB = ng.empty(dimI, dtype=dtype)
ng.fprop_pool(pool, devI, devO, repeat=repeat)
ng.bprop_pool(pool, devI, devO, devB, repeat=repeat)
def pixel_indices(kj, mt, pr, qs):
C = pool.C
J,T,R,S = pool.JTRS
D,H,W = pool.DHW
HW = H*W
DHW = D*H*W
imax = C*D*H*W
idx = []
for j in range(J):
c = kj + j
ci = c*DHW
cb = c >= 0 and c < C
cpuI[-1, :] = np.finfo(cpuI.dtype).min
else:
cpuI[-1, :] = 0
# cpu output arrays
cpuO = np.empty(dimO, dtype=np.float32)
cpuB = np.zeros(slicable(dimI, 1), dtype=np.float32)
# give gpu the input array without zero padding (not needed)
devI = ng.array(cpuI[:-1, :].reshape(dimI), dtype=dtype)
devO = ng.zeros(dimO, dtype=dtype)
devB = ng.empty(dimI, dtype=dtype)
ng.fprop_pool(pool, devI, devO, repeat=repeat)
ng.bprop_pool(pool, devI, devO, devB, repeat=repeat)
def pixel_indices(kj, mt, pr, qs):
C = pool.C
J, T, R, S = pool.JTRS
D, H, W = pool.DHW
HW = H * W
DHW = D * H * W
imax = C * D * H * W
idx = []
for j in range(J):
c = kj + j
ci = c * DHW
class GPU(Backend):
"""
Sets up a NervanaGPU based backend for matrix operations.
Note that some functions defined in the generic Backend class such as are
cross-map pooling and normalization and adaDelta are not implemented for
this backend.
"""
default_dtype = np.float32
def __init__(self, rng_seed, stochastic_round=False, device_id=0):
self.ng = NervanaGPU(stochastic_round=stochastic_round)
logger.info("Initialized NervanaGPU with stochastic_round=%s",
stochastic_round)
self.rng_seed = rng_seed
self.rng_init()
self.device_id = device_id if device_id is not None else 0
def __getstate__(self):
"""
Defines what and how we go about serializing an instance of this class.
Returns:
self.__dict__: The full contents of the backend class instance,
except for the mem_pool which is on device and
cannot be serialized.
"""
if hasattr(self, 'mem_pool') and self.mem_pool is not None:
self.mem_pool_pickle = {'shape': self.mem_pool.shape,
'dtype': np.float32}
self.mem_pool = None
return self.__dict__
def __setstate__(self, state):
"""
Defines how we go about deserializing into an instance of this class.
Arguments:
self.__dict__: The full contents of the backend class instance,
except for the mem_pool which is on device and
cannot be serialized.
"""
self.__dict__.update(state)
self.mem_pool = self.ng.empty(self.mem_pool_pickle['shape'],
dtype=self.mem_pool_pickle['dtype'])
def init_mempool(self, shape, dtype=default_dtype):
"""
Allocates a memory pool for temporary storage
"""
self.mem_pool = self.ng.empty(shape, dtype=dtype)
def alloc_host_mem(self, shape, dtype):
return drv.pagelocked_empty(shape, dtype, order="C", mem_flags=0)
def create_stream(self):
return drv.Stream()
def async_copy(self, dest, src, stream=None):
drv.memcpy_htod_async(dest.gpudata, src, stream)
def rng_init(self):
"""
Initialize and seed the pseudo random number genrator. Random numbers
are generated on the host using numpy, then transfered to device.
"""
seed = None
if 'rng_seed' in self.__dict__:
seed = self.rng_seed
logger.info("Seeding random number generator with: %s", str(seed))
np.random.seed(seed)
def flop_timing_init(self, decorate_fc, decorate_conv, decorate_ew):
"""
Initialize FLOP timing. Wraps the specified MOP calls via a decorator
to record elapsed time and number of operations.
Arguments:
decorate_fc (list): string giving the function names of fully
connected layer forward/backward/update calls
to time.
decorate_conv (list): string giving the function names of
convolutional layer forward/backward/update
calls to time.
decorate_ew (list): string giving the function names of element-wise
calls to time.
Notes:
Must be called prior to first flop_timing_start call
"""
self.start = drv.Event()
self.end = drv.Event()
self.flop_timer = FlopsDecorator(self)
self.flop_timer.decorate(decorate_fc=decorate_fc,
decorate_conv=decorate_conv,
decorate_ew=decorate_ew)
def flop_timinig_start(self):
"""
Start a new FLOP timer.
Returns:
None: dummy value (not used)
"""
return self.start.record()
def flop_timing_finish(self, start_time):
"""
Complete current FLOP timing.
Arguments:
start_time (unused): ignored.
Returns:
float: elapsed time in seconds since prior flop_timing_start call.
"""
self.end.record()
self.end.synchronize()
return self.end.time_since(self.start)
def uniform(self, low=0.0, high=1.0, shape=1, dtype=default_dtype,
persist_values=True, name=None, allocator=drv.mem_alloc):
"""
generate numpy random number and convert to a GPUTensor.
If called with dype=None it will probably explode
"""
ary = np.random.uniform(low, high, shape)
return self.ng.array(ary, dtype=dtype, name=name)
def normal(self, loc=0.0, scale=1.0, size=1, dtype=default_dtype,
persist_values=True, name=None, allocator=drv.mem_alloc):
"""
Gaussian/Normal random number sample generation
"""
ary = np.random.normal(loc, scale, size)
return self.ng.array(ary, dtype=dtype, name=name)
def fprop_fc(self, out, inputs, weights, layer=None):
"""
Forward propagate the inputs of a fully connected network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
layer (Layer): The layer object.
"""
self.ng.dot(weights, inputs, out)
def bprop_fc(self, out, weights, deltas, layer=None):
"""
Backward propagate the error through a fully connected network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
layer (Layer): The layer object.
"""
self.ng.dot(weights.T, deltas, out)
def update_fc(self, out, inputs, deltas, layer=None):
"""
Compute the updated gradient for a fully connected network layer.
Arguments:
out (GPUTensor): Where to store the updated gradient value.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
deltas (GPUTensor): The error values for this layer
layer (Layer): The layer object.
"""
self.ng.dot(deltas, inputs.T, out)
def fprop_conv(self, out, inputs, weights, ofmshape, ofmsize, ofmlocs,
ifmshape, links, nifm, padding, stride, ngroups, fpropbuf,
local=False):
"""
Forward propagate the inputs of a convolutional network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
ofmshape (tuple): Dimensions of each output feature map (typically
number of height and width neurons).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element
in each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
number of height and width neurons). For this
backend we expect these values to be square.
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
fpropbuf (GPUTensor): Temporary storage buffer used to hold the
convolved outputs for a single receptive
field. Not used for this backend.
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
"""
'''
N: Number of images in mini-batch
C: Number of input feature maps
K: Number of output feature maps
D: Depth of input image
H: Height of input image
W: Width of input image
T: Depth of filter kernel
R: Height of filter kernel
S: Width of filter kernel
'''
self.ng.fprop_conv(layer=fpropbuf, I=inputs, F=weights, O=out,
alpha=1.0, repeat=1)
def bprop_conv(self, out, weights, deltas, ofmshape, ofmsize, ofmlocs,
ifmshape, links, padding, stride, nifm, ngroups, bpropbuf,
local=False):
"""
Backward propagate the error through a convolutional network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
bpropbuf (GPUTensor): Temporary storage buffer used to hold the
backpropagated error for a single receptive
field
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
"""
self.ng.bprop_conv(layer=bpropbuf, F=weights, E=deltas, grad_I=out,
alpha=1.0, repeat=1)
def update_conv(self, out, inputs, weights, deltas, ofmshape, ofmsize,
ofmlocs, ifmshape, links, nifm, padding, stride, ngroups,
fwidth, updatebuf, local=False, layer=None):
"""
Compute the updated gradient for a convolutional network layer.
Arguments:
out (GPUTensor): Where to store the updated gradient value.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
weights (GPUTensor): The weight coefficient values for this layer.
deltas (GPUTensor): The error values for this layer
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
convolution operation.
stride (int): Number of neurons to shift the filter at each step.
ngroups (int): Number of groups.
fwidth (int): Filter width.
updatebuf (GPUTensor): Temporary storage buffer used to hold the
updated gradient for a single receptive
field
local (bool, optional): Whether to do local filtering (True) or
convolution (False, the default)
layer (Layer): The layer object.
"""
self.ng.update_conv(layer=updatebuf, I=inputs, E=deltas, grad_F=out,
alpha=1.0, repeat=1)
def fprop_pool(self, out, inputs, op, ofmshape, ofmsize, ofmlocs, fshape,
ifmshape, links, nifm, padding, stride, fpropbuf):
"""
Forward propagate the inputs of a Pooling network layer to
produce output pre-activations (ready for transformation by an
activation function).
Arguments:
out (GPUTensor): Where to store the forward propagated results.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
op (string): The type of pooling operation to apply. We support
"max", "avg", "l2" currently.
ofmshape (tuple): Dimensions of each output feature map (typically
number of height and width neurons).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
fshape (tuple): Dimensions of each filter (typically height and
width).
ifmshape (tuple): Dimensions of each input feature map (typically
number of height and width neurons).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
pooling operation.
stride (int): Number of neurons to shift the filter at each step.
fpropbuf (GPUTensor): Temporary storage buffer used to hold the
pooled outputs for a single receptive field.
"""
op = op.lower()
if op == "max":
self.ng.fprop_pool(layer=fpropbuf, I=inputs, O=out, repeat=1)
else:
raise AttributeError("unexpected pooling op type: %s", op)
def bprop_pool(self, out, fouts, inputs, deltas, op, ofmshape, ofmsize,
ofmlocs, fshape, fpsize, ifmshape, links, nifm, padding,
stride, bpropbuf):
"""
Backward propagate the error through a pooling network layer.
Arguments:
out (GPUTensor): Where to store the backward propagated errors.
fouts (GPUTensor): Forward propagated outputs from the previous
layer.
inputs (GPUTensor): Will be either the dataset input values (first
layer), or the outputs from the previous layer.
deltas (GPUTensor): The error values for this layer
op (string): The type of pooling operation to apply. We support
"max", "avg", "l2" currently.
ofmshape (tuple): Dimensions of each output feature map (typically
height and width).
ofmsize (int): Total size of each output feature map.
ofmlocs (GPUTensor): Indices giving the location of each element in
each output feature map stored in out.
fshape (tuple): Dimensions of each filter (typically height and
width).
fpsize (int): The size of each filter.
ifmshape (tuple): Dimensions of each input feature map (typically
height and width).
links (GPUTensor): Input receptive field indices.
nifm (int): Total number of input feature maps.
padding (int): Number of additional elements to include along each
dimension of each local receptive field during the
pooling operation.
stride (int): Number of neurons to shift the filter at each step.
bpropbuf (GPUTensor): Temporary storage buffer used to hold the
backpropagated error for a single receptive
field
"""
op = op.lower()
if op == "max":
self.ng.bprop_pool(layer=bpropbuf, I=inputs, E=deltas, grad_I=out,
repeat=1)
else:
raise AttributeError("unexpected pooling op type: %s", op)
def logistic(self, x, out):
"""
Logistic sigmoid nonlinearity, 1/(1+exp(-x))
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
"""
self.ng.sig(x, out=out)
return out
def rectlin(self, x, out):
"""
Rectified Linear nonlinearity
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
"""
self.ng.maximum(x, 0., out=out)
return out
def rectleaky(self, x, slope, out):
out[:] = self.ng.maximum(x, x*slope)
def rectleaky_derivative(self, x, slope, out):
out[:] = self.ng.greater(x, 0) * (1.0 - slope) + slope
def sum(self, tsr, axes, out):
"""
Sum
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.sum(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.sum(tsr, axis=axes, out=out)
return out
def mean(self, tsr, axes, out):
"""
Calculates the arithmetic mean of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.mean(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.mean(tsr, axis=axes, out=out)
return out
def min(self, tsr, axes, out):
"""
Calculates the minimum of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.min(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.min(tsr, axis=axes, out=out)
return out
def max(self, tsr, axes, out):
"""
Calculates the maximum of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): Input tensor
axes (int): Axis along which the reduction is performed. If axes
is None, the tensor is flattened and reduced over
both dimensions.
out (GPUTensor): Output tensor
"""
if axes is None:
sze = tsr.shape[0]*tsr.shape[1]
self.ng.max(tsr.reshape(sze, 1), axis=0, out=out)
else:
self.ng.max(tsr, axis=axes, out=out)
return out
def variance(self, tsr, axes, out, mean=None):
"""
Calculates the variance of the elements along the specified
axes.
Arguments:
tsr (GPUTensor): the tensor on which to compute the variance
axes (int, list, optional): the dimension(s) along which to
variance. If set to None, we will
variance over all dimensions.
out (GPUTensor): where the result will be stored.
mean (GPUTensor): the tensor containing mean of tsr
Returns:
GPUTensor: reference to out
"""
if mean is None:
logger.error("GPUTensor requires mean to be specified.")
raise ValueError("mean not specified")
self.ng.mean(self.ng.square(tsr-mean), axis=axes, out=out)
return out
def fabs(self, x, out):
"""
Calculates absolute value of the elements in a tensor
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
Returns:
GPUTensor: reference to out
"""
self.ng.fabs(x, out=out)
return out
def sqrt(self, x, out):
"""
Calculates square root of the elements in a tensor
Arguments:
x (GPUTensor): Input tensor
out (GPUTensor): Output tensor
Returns:
GPUTensor: reference to out
"""
self.ng.sqrt(x, out=out)
return out
def zeros(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor and fill it with zeros.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.zeros(shape, dtype=dtype)
def ones(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor and fill it with ones.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.ones(shape, dtype=dtype)
def empty(self, shape, dtype=default_dtype, persist_values=True):
"""
Allocate a new GPUTensor.
Arguments:
shape (tupel): Shape of the desired GPUTensor
dtype (dtype): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
Returns:
GPUTensor: output
"""
return self.ng.empty(shape, dtype=dtype)
def array(self, ary, dtype=default_dtype, persist_values=True, name=None,
allocator=drv.mem_alloc):
"""
Allocate a new GPUTensor and fill it with supplied numpy array.
Arguments:
ary (ndarray): Numpy array with source data
dtype (dtype, optional): Optional datatype
persist_values (bool, optional): If set to True (the default), the
values assigned to this Tensor
will persist across multiple begin
and end calls. Setting to False
may provide a performance increase
if values do not need to be
maintained across such calls
name (string): Name for the GPUTensor
allocator (pycuda): Pycuda memory allocator
Returns:
GPUTensor: output
"""
return self.ng.array(ary, dtype=dtype, name=name)
def add(self, left, right, out):
"""
Elementwise addition
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.add(left, right, out=out)
return out
def subtract(self, left, right, out):
"""
Elementwise subtraction
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.subtract(left, right, out=out)
return out
def multiply(self, left, right, out):
"""
Elementwise multiplication
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.multiply(left, right, out=out)
return out
def divide(self, left, right, out):
"""
Elementwise division
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.divide(left, right, out=out)
return out
def greater(self, left, right, out):
"""
Elementwise greater than testing
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.greater(left, right, out=out)
return out
def equal(self, left, right, out):
"""
Performs element-wise equality testing on each element of left and
right, storing the result in out. Each operand is assumed to be the
same shape (or broadcastable as such).
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.equal(left, right, out=out)
return out
def not_equal(self, left, right, out):
"""
Elementwise not equal testing
Arguments:
left (GPUTensor, numeric): left-hand side operand.
right (GPUTensor, numeric): right-hand side operand.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.not_equal(left, right, out=out)
return out
def clip(self, a, a_min, a_max, out):
"""
Elementwise clipping between a range of specified values
Arguments:
a (GPUTensor): input tensor.
a_min (float): floor value.
a_max (float): ceiling value.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.clip(a, a_min, a_max, out=out)
return out
def log(self, a, out):
"""
Elementwise base-e logarithm
Arguments:
a (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.log(a, out=out)
return out
def tanh(self, a, out):
"""
Elementwise tanh
Arguments:
a (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
self.ng.tanh(a, out=out)
return out
def argmax(self, a, out, axis=0):
"""
Calculates the indices of the maximal element value along the specified
axis. If multiple elements contain the maximum, only the elements of
the first are returned.
Arguments:
tsr (GPUTensor): The GPUTensor on which to find the maximum indices
axis (int): The dimension along which to find the maximum. If set
to None, find the overall maximum index of a flattened
representation of tsr.
out (GPUTensor): Where to store the result. Should be of the
appropriate type and expected shape
Returns:
GPUTensor: reference to out
"""
self.ng.argmax(a, out=out, axis=axis)
return out
def softmax(self, x, out):
"""
Softmax nonlinearity. Computes exp(x-max(x)) / sum_i exp(x_i-max(x_i))
Arguments:
x (GPUTensor): input tensor.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
out[:] = (self.ng.reciprocal(self.ng.sum(
self.ng.exp(x - self.ng.max(x, axis=0)), axis=0)) *
self.ng.exp(x - self.ng.max(x, axis=0)))
return out
def softmax_gradient(self, y, err, out):
"""
Gradient of the softmax nonlinearity.
Arguments:
y (GPUTensor): input tensor.
err (GPUTensor): backpropagated error.
out (GPUTensor): where the result will be stored.
Returns:
GPUTensor: reference to out
"""
raise NotImplementedError("Softmax gradient should use shortcut")
return out
def make_binary_mask(self, tsr, keepthresh=0.5, dtype=default_dtype):
"""
Create a binary mask for dropout layers.
Arguments:
tsr (GPUTensor): Output tensor
keepthresh (float): fraction of ones
"""
self.ng.dropout(keep=keepthresh, out=tsr)
def gdm_compound(self, ps_item, us_item, vs_item, momentum_coef,
learning_rate, epoch):
"""
Perform gradient descent update with momentum.
Arguments:
ps_item (GPUTensor): parameter tensor (e.g. a weight matrix)
us_item (GPUTensor): update tensor, contains gradient wrt. weights
vs_item (GPUTensor): velocity tensor.
momentum_coef (float): momentum coefficient.
learning_rate (float): learning rate.
epoch (int): epoch (used in conjunction with diagnostics).
Outputs are written to vs_item (updated velocity)
and ps_item (updated weights)
"""
vs_item[:] = vs_item * momentum_coef - us_item * learning_rate
ps_item[:] = ps_item + vs_item
def gdmwd_compound(self, ps_item, us_item, vs_item, momentum_coef,
learning_rate, wd, epoch):
"""
Perform gradient descent update with momentum and weight decay.
Arguments:
ps_item (GPUTensor): parameter tensor (e.g. a weight matrix)
us_item (GPUTensor): update tensor, contains gradient wrt. weights
vs_item (GPUTensor): velocity tensor.
momentum_coef (float): momentum coefficient.
learning_rate (float): learning rate.
wd (float): weight decay parameter.
epoch (int): epoch (used in conjunction with diagnostics).
Outputs:
ps_item, the updated weights.
vs_item, the updated velocity.
us_item, used as a temp buffer.
"""
vs_item[:] = vs_item * momentum_coef - us_item * \
learning_rate - learning_rate * wd * ps_item
ps_item[:] = ps_item + vs_item
def exp_mavg(self, mavg, newval, rho):
"""
Calculate the exponential moving average
Arguments:
mavg: The running value of the moving average
newval: New sample to be added to the moving average
rho: Interpolation value
"""
mavg[:] = rho * mavg + (1.0 - rho) * newval
def ada_update(self, ps_item, us_item, gs_item, ds_item, ls_item, ss_item,
rho, epsilon):
"""
Update rule for AdaDelta (Zeiler, http://arxiv.org/abs/1212.5701)
Arguments:
ps_item: weight / parameter (will be updated)
us_item: update
gs_item: expected value of Gradient Squared (will be updated)
ds_item: expected value of Delta Squared (will be updated)
ls_item: learning rate (will be updated)
ss_item: Scratch Space
rho: decay constant (determines window size)
epsilon: small positive constant for numerical stability
"""
# Accumulate E[Grad^2]
gs_item[:] = gs_item * rho + (1.0 - rho) * us_item * us_item
# Calculate Updates
ls_item[:] = self.ng.sqrt((ds_item + epsilon) /
(gs_item + epsilon)) * (-1.0) * us_item
# Accumulate E[Delt^2]
ds_item[:] = ds_item * rho + (1.0 - rho) * ls_item * ls_item
# Final update to the params
ps_item[:] = ps_item + ls_item
def rms_update(self, params, updates, run_squares, velocity, scratch_space,
gamma, epsilon, learning_rate, momentum_coef):
# Update running squares
run_squares[:] = gamma * run_squares + (1. - gamma) * updates * updates
# Now scale the gradient by lr / rms(grad) (with a epsilon term for
# stability) and use it to update the params
if momentum_coef == 0:
params[:] = params - learning_rate * updates * self.ng.reciprocal(
self.ng.sqrt(run_squares) + epsilon)
else:
velocity[:] = velocity * momentum_coef - \
learning_rate * updates * \
self.ng.reciprocal(self.ng.sqrt(run_squares) + epsilon)
params[:] = params + velocity
def fprop_bn_compound(self, inputs, beta, gamma, eps, xhat,
xmean, xvar, gmean, gvar, rho, out):
"""
Batch normalization forward pass, compounded to run in 3 kernel calls.
Arguments:
inputs: input data to be normalized
beta: location parameter
gamma: scale parameter
eps: small constant for numerical stability
xvar: variance (updated)
xhat: normalized input (updated)
out: normalized and rescaled input (updated)
"""
xvar[:] = self.ng.var(inputs, axis=1)
xmean[:] = self.ng.mean(inputs, axis=1)
gmean[:] = gmean * rho + (1.0 - rho) * xmean
gvar[:] = gvar * rho + (1.0 - rho) * xvar
xvar[:] = self.ng.reciprocal(self.ng.sqrt(xvar + eps))
xhat[:] = xvar * (inputs - xmean)
out[:] = xhat * gamma + beta
return out
def bprop_bn_compound(self, xhat, error, xvar, gamma,
beta_updates, gamma_updates):
"""
Batch normalization backward pass, compounded to run with 4 kernel
calls.
Arguments:
xhat: normalized input data (updated)
error: backpropagated deltas (updated)
xvar: precomputed variance
gamma: scale parameter
beta_updates: gradient update for beta (updated)
gamma_updates: gradient update for gamma (updated)
"""
gamma_updates[:] = self.ng.sum(xhat * error, axis=1)
beta_updates[:] = self.ng.sum(error, axis=1)
xhat[:] = (xhat * gamma_updates + beta_updates) / float(xhat.shape[1])
error[:] = xvar * gamma * (error - xhat)