scripts/nn/layers/conv2d_depthwise.dml - systemds - Git at Google

 #-------------------------------------------------------------
 #
 # Licensed to the Apache Software Foundation (ASF) under one
 # or more contributor license agreements.  See the NOTICE file
 # distributed with this work for additional information
 # regarding copyright ownership.  The ASF licenses this file
 # to you under the Apache License, Version 2.0 (the
 # "License"); you may not use this file except in compliance
 # with the License.  You may obtain a copy of the License at
 #
 #   http://www.apache.org/licenses/LICENSE-2.0
 #
 # Unless required by applicable law or agreed to in writing,
 # software distributed under the License is distributed on an
 # "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 # KIND, either express or implied.  See the License for the
 # specific language governing permissions and limitations
 # under the License.
 #
 #-------------------------------------------------------------

 /*
  * 2D Depthwise Convolutional layer.
  *
  * Utilizes built-in convolution operators for higher performance.
  */
 source("scripts/nn/util.dml") as util

 forward = function(matrix[double] X, matrix[double] W, matrix[double] b,
                    int Hin, int Win, int M, int Hf, int Wf,
                    int strideh, int stridew, int padh, int padw)
     return (matrix[double] out, int Hout, int Wout) {
   /*
    * Computes the forward pass for a 2D depthwise spatial convolutional
    * layer with C*M filters of depth 1.  The input data has N examples,
    * each represented as a 3D volume with C channels unrolled into a
    * single vector.  For each group of M filters, a 2D convolution is
    * applied to 1 unique input channel, yielding M output channels per
    * input channel.  The resulting C groups of M output channels are
    * then concatenated together channel-wise into a single volume of C*M
    * output channels.  This can also be interpreted as C filters of
    * depth 1 that expand each input channel to M output channels, where
    * M is a "depth multiplier".
    *
    * Although there are C*M filters of depth 1, instead of storing W as
    * shape `(C*M, 1*Hf*Wf)`, we reshape it to `(C, M*Hf*Wf)` for
    * performance reasons.
    *
    * Inputs:
    *  - X: Inputs, of shape (N, C*Hin*Win).
    *  - W: Weights, of shape (C, M*Hf*Wf).
    *  - b: Biases, of shape (C*M, 1).
    *  - Hin: Input height.
    *  - Win: Input width.
    *  - M: Number of filters per input channel (i.e. depth multiplier).
    *  - Hf: Filter height.
    *  - Wf: Filter width.
    *  - strideh: Stride over height.
    *  - stridew: Stride over width.
    *  - padh: Padding for top and bottom sides.
    *      For same output height as input, set `padh = (Hf - 1) / 2`,
    *      assuming `strideh = 1`.
    *      More generally, `padh = (Hin*(strideh-1) + Hf - strideh) / 2`
    *      preserves the spatial dimensions of the input.
    *  - padw: Padding for left and right sides.
    *      For same output width as input, set `padw = (Wf - 1) / 2`,
    *      assuming `stridew = 1`.
    *      More generally, `padw = (Win*(stridew-1) + Wf - stridew) / 2`
    *      preserves the spatial dimensions of the input.
    *
    * Outputs:
    *  - out: Outputs, of shape (N, C*M*Hout*Wout).
    *  - Hout: Output height.
    *  - Wout: Output width.
    */
   N = nrow(X)
   C = nrow(W)
   Hout = as.integer(floor((Hin + 2*padh - Hf)/strideh + 1))
   Wout = as.integer(floor((Win + 2*padw - Wf)/stridew + 1))

   # create output volume
   # NOTE: We initialize to 1s vs. 0s to avoid conversions between sparse and dense formats.
   # This is a complete hack until the engine is improved.
   out = matrix(1, rows=N, cols=C*M*Hout*Wout)

   # depthwise convolution
   # TODO: Explore usage of parfor loops more to determine if they can provide a performance
   # benefit.  Initial tests show that they are slower than the regular for loop, likely because
   # they cause a reduction from a multithreaded conv2d op to a singlethreaded version.  For a
   # number of channels >> the number of examples, it's possible that the parfor loop could be
   # faster.
   #parfor (c in 1:C, check=0) {  # each channel
   for (c in 1:C) {  # each channel
     # run conv2d on each input channel separately, each with a different filter
     Xc = X[,((c-1)*Hin*Win + 1):c*Hin*Win]  # shape (N, 1*Hin*Win)
     Wc = matrix(W[c,], rows=M, cols=Hf*Wf)  # shape (M, Hf*Wf)
     outc = conv2d(Xc, Wc, input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf],
                   stride=[strideh,stridew], padding=[padh,padw])  # shape (N, M*Hout*Wout)
     out[,((c-1)*M*Hout*Wout + 1):c*M*Hout*Wout] = outc
   }

   # add bias term to each output filter
   out = bias_add(out, b)
 }

 backward = function(matrix[double] dout, int Hout, int Wout,
                     matrix[double] X, matrix[double] W, matrix[double] b,
                     int Hin, int Win, int M, int Hf, int Wf,
                     int strideh, int stridew, int padh, int padw)
     return (matrix[double] dX, matrix[double] dW, matrix[double] db) {
   /*
    * Computes the backward pass for a 2D depthwise spatial convolutional
    * layer with C*M filters of depth 1.
    *
    * Inputs:
    *  - dout: Gradient wrt `out` from upstream, of
    *      shape (N, C*M*Hout*Wout).
    *  - Hout: Output height.
    *  - Wout: Output width.
    *  - X: Inputs, of shape (N, C*Hin*Win).
    *  - W: Weights, of shape (C, M*Hf*Wf).
    *  - b: Biases, of shape (C*M, 1).
    *  - Hin: Input height.
    *  - Win: Input width.
    *  - M: Num filters per input channel (i.e. depth multiplier).
    *  - Hf: Filter height.
    *  - Wf: Filter width.
    *  - strideh: Stride over height.
    *  - stridew: Stride over width.
    *  - padh: Padding for top and bottom sides.
    *  - padw: Padding for left and right sides.
    *
    * Outputs:
    *  - dX: Gradient wrt `X`, of shape (N, C*Hin*Win).
    *  - dW: Gradient wrt `W`, of shape (C, M*Hf*Wf).
    *  - db: Gradient wrt `b`, of shape (C*M, 1).
    */
   N = nrow(X)
   C = nrow(W)

   # create gradient volumes
   # NOTE: We initialize to 1s vs. 0s to avoid conversions between sparse and dense formats.
   # This is a complete hack until the engine is improved.
   dX = matrix(1, rows=N, cols=C*Hin*Win)
   dW = matrix(1, rows=C, cols=M*Hf*Wf)
   db = matrix(1, rows=C*M, cols=1)

   # partial derivatives for depthwise convolution
   for (c in 1:C) {  # all examples
     # extract channel c
     doutc = dout[,((c-1)*M*Hout*Wout + 1):c*M*Hout*Wout]  # (N,M*Hout*Wout)
     Xc = X[,((c-1)*Hin*Win + 1):c*Hin*Win]  # shape (N, 1*Hin*Win)
     Wc = matrix(W[c,], rows=M, cols=Hf*Wf)  # shape (M, 1*Hf*Wf)

     # compute gradients for channel c
     dWc = conv2d_backward_filter(Xc, doutc, stride=[strideh,stridew], padding=[padh,padw],
                                  input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf])
     dXc = conv2d_backward_data(Wc, doutc, stride=[strideh,stridew], padding=[padh,padw],
                                input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf])

     # store
     dX[,((c-1)*Hin*Win + 1):c*Hin*Win] = dXc
     dW[c,] = matrix(dWc, rows=1, cols=M*Hf*Wf)
   }

   # partial derivatives for bias vector
   db = util::channel_sums(dout, C*M, Hout, Wout)
 }

 init = function(int C, int M, int Hf, int Wf)
     return (matrix[double] W, matrix[double] b) {
   /*
    * Initialize the parameters of this layer.
    *
    * Note: This is just a convenience function, and parameters
    * may be initialized manually if needed.
    *
    * We use the heuristic by He et al., which limits the magnification
    * of inputs/gradients during forward/backward passes by scaling
    * unit-Gaussian weights by a factor of sqrt(2/n), under the
    * assumption of relu neurons.
    *  - http://arxiv.org/abs/1502.01852
    *
    * Inputs:
    *  - C: Number of input channels (dimensionality of depth).
    *  - M: Number of filters per input channel (i.e. depth multiplier).
    *  - Hf: Filter height.
    *  - Wf: Filter width.
    *
    * Outputs:
    *  - W: Weights, of shape (C, M*Hf*Wf).
    *  - b: Biases, of shape (C*M, 1).
    */
   # Note: Each filter is applied to a volume of depth 1, so we only use Hf*Wf in the scaling factor.
   W = rand(rows=C, cols=M*Hf*Wf, pdf="normal") * sqrt(2.0/(Hf*Wf))
   b = matrix(0, rows=C*M, cols=1)
 }
	#-------------------------------------------------------------
	#
	# Licensed to the Apache Software Foundation (ASF) under one
	# or more contributor license agreements. See the NOTICE file
	# distributed with this work for additional information
	# regarding copyright ownership. The ASF licenses this file
	# to you under the Apache License, Version 2.0 (the
	# "License"); you may not use this file except in compliance
	# with the License. You may obtain a copy of the License at
	#
	# http://www.apache.org/licenses/LICENSE-2.0
	#
	# Unless required by applicable law or agreed to in writing,
	# software distributed under the License is distributed on an
	# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	# KIND, either express or implied. See the License for the
	# specific language governing permissions and limitations
	# under the License.
	#
	#-------------------------------------------------------------

	/*
	* 2D Depthwise Convolutional layer.
	*
	* Utilizes built-in convolution operators for higher performance.
	*/
	source("scripts/nn/util.dml") as util

	forward = function(matrix[double] X, matrix[double] W, matrix[double] b,
	int Hin, int Win, int M, int Hf, int Wf,
	int strideh, int stridew, int padh, int padw)
	return (matrix[double] out, int Hout, int Wout) {
	/*
	* Computes the forward pass for a 2D depthwise spatial convolutional
	* layer with C*M filters of depth 1. The input data has N examples,
	* each represented as a 3D volume with C channels unrolled into a
	* single vector. For each group of M filters, a 2D convolution is
	* applied to 1 unique input channel, yielding M output channels per
	* input channel. The resulting C groups of M output channels are
	* then concatenated together channel-wise into a single volume of C*M
	* output channels. This can also be interpreted as C filters of
	* depth 1 that expand each input channel to M output channels, where
	* M is a "depth multiplier".
	*
	* Although there are C*M filters of depth 1, instead of storing W as
	* shape `(CM, 1HfWf)`, we reshape it to `(C, MHf*Wf)` for
	* performance reasons.
	*
	* Inputs:
	* - X: Inputs, of shape (N, CHinWin).
	* - W: Weights, of shape (C, MHfWf).
	* - b: Biases, of shape (C*M, 1).
	* - Hin: Input height.
	* - Win: Input width.
	* - M: Number of filters per input channel (i.e. depth multiplier).
	* - Hf: Filter height.
	* - Wf: Filter width.
	* - strideh: Stride over height.
	* - stridew: Stride over width.
	* - padh: Padding for top and bottom sides.
	* For same output height as input, set `padh = (Hf - 1) / 2`,
	* assuming `strideh = 1`.
	* More generally, `padh = (Hin*(strideh-1) + Hf - strideh) / 2`
	* preserves the spatial dimensions of the input.
	* - padw: Padding for left and right sides.
	* For same output width as input, set `padw = (Wf - 1) / 2`,
	* assuming `stridew = 1`.
	* More generally, `padw = (Win*(stridew-1) + Wf - stridew) / 2`
	* preserves the spatial dimensions of the input.
	*
	* Outputs:
	* - out: Outputs, of shape (N, CMHout*Wout).
	* - Hout: Output height.
	* - Wout: Output width.
	*/
	N = nrow(X)
	C = nrow(W)
	Hout = as.integer(floor((Hin + 2*padh - Hf)/strideh + 1))
	Wout = as.integer(floor((Win + 2*padw - Wf)/stridew + 1))

	# create output volume
	# NOTE: We initialize to 1s vs. 0s to avoid conversions between sparse and dense formats.
	# This is a complete hack until the engine is improved.
	out = matrix(1, rows=N, cols=CMHout*Wout)

	# depthwise convolution
	# TODO: Explore usage of parfor loops more to determine if they can provide a performance
	# benefit. Initial tests show that they are slower than the regular for loop, likely because
	# they cause a reduction from a multithreaded conv2d op to a singlethreaded version. For a
	# number of channels >> the number of examples, it's possible that the parfor loop could be
	# faster.
	#parfor (c in 1:C, check=0) { # each channel
	for (c in 1:C) { # each channel
	# run conv2d on each input channel separately, each with a different filter
	Xc = X[,((c-1)HinWin + 1):cHinWin] # shape (N, 1HinWin)
	Wc = matrix(W[c,], rows=M, cols=HfWf) # shape (M, HfWf)
	outc = conv2d(Xc, Wc, input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf],
	stride=[strideh,stridew], padding=[padh,padw]) # shape (N, MHoutWout)
	out[,((c-1)MHoutWout + 1):cMHoutWout] = outc
	}

	# add bias term to each output filter
	out = bias_add(out, b)
	}

	backward = function(matrix[double] dout, int Hout, int Wout,
	matrix[double] X, matrix[double] W, matrix[double] b,
	int Hin, int Win, int M, int Hf, int Wf,
	int strideh, int stridew, int padh, int padw)
	return (matrix[double] dX, matrix[double] dW, matrix[double] db) {
	/*
	* Computes the backward pass for a 2D depthwise spatial convolutional
	* layer with C*M filters of depth 1.
	*
	* Inputs:
	* - dout: Gradient wrt `out` from upstream, of
	* shape (N, CMHout*Wout).
	* - Hout: Output height.
	* - Wout: Output width.
	* - X: Inputs, of shape (N, CHinWin).
	* - W: Weights, of shape (C, MHfWf).
	* - b: Biases, of shape (C*M, 1).
	* - Hin: Input height.
	* - Win: Input width.
	* - M: Num filters per input channel (i.e. depth multiplier).
	* - Hf: Filter height.
	* - Wf: Filter width.
	* - strideh: Stride over height.
	* - stridew: Stride over width.
	* - padh: Padding for top and bottom sides.
	* - padw: Padding for left and right sides.
	*
	* Outputs:
	* - dX: Gradient wrt `X`, of shape (N, CHinWin).
	* - dW: Gradient wrt `W`, of shape (C, MHfWf).
	* - db: Gradient wrt `b`, of shape (C*M, 1).
	*/
	N = nrow(X)
	C = nrow(W)

	# create gradient volumes
	# NOTE: We initialize to 1s vs. 0s to avoid conversions between sparse and dense formats.
	# This is a complete hack until the engine is improved.
	dX = matrix(1, rows=N, cols=CHinWin)
	dW = matrix(1, rows=C, cols=MHfWf)
	db = matrix(1, rows=C*M, cols=1)

	# partial derivatives for depthwise convolution
	for (c in 1:C) { # all examples
	# extract channel c
	doutc = dout[,((c-1)MHoutWout + 1):cMHoutWout] # (N,MHoutWout)
	Xc = X[,((c-1)HinWin + 1):cHinWin] # shape (N, 1HinWin)
	Wc = matrix(W[c,], rows=M, cols=HfWf) # shape (M, 1Hf*Wf)

	# compute gradients for channel c
	dWc = conv2d_backward_filter(Xc, doutc, stride=[strideh,stridew], padding=[padh,padw],
	input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf])
	dXc = conv2d_backward_data(Wc, doutc, stride=[strideh,stridew], padding=[padh,padw],
	input_shape=[N,1,Hin,Win], filter_shape=[M,1,Hf,Wf])

	# store
	dX[,((c-1)HinWin + 1):cHinWin] = dXc
	dW[c,] = matrix(dWc, rows=1, cols=MHfWf)
	}

	# partial derivatives for bias vector
	db = util::channel_sums(dout, C*M, Hout, Wout)
	}

	init = function(int C, int M, int Hf, int Wf)
	return (matrix[double] W, matrix[double] b) {
	/*
	* Initialize the parameters of this layer.
	*
	* Note: This is just a convenience function, and parameters
	* may be initialized manually if needed.
	*
	* We use the heuristic by He et al., which limits the magnification
	* of inputs/gradients during forward/backward passes by scaling
	* unit-Gaussian weights by a factor of sqrt(2/n), under the
	* assumption of relu neurons.
	* - http://arxiv.org/abs/1502.01852
	*
	* Inputs:
	* - C: Number of input channels (dimensionality of depth).
	* - M: Number of filters per input channel (i.e. depth multiplier).
	* - Hf: Filter height.
	* - Wf: Filter width.
	*
	* Outputs:
	* - W: Weights, of shape (C, MHfWf).
	* - b: Biases, of shape (C*M, 1).
	*/
	# Note: Each filter is applied to a volume of depth 1, so we only use Hf*Wf in the scaling factor.
	W = rand(rows=C, cols=MHfWf, pdf="normal") * sqrt(2.0/(Hf*Wf))
	b = matrix(0, rows=C*M, cols=1)
	}