scripts.nn.layers.cross_entropy_loss.dml Maven / Gradle / Ivy
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Declarative Machine Learning
#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
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# 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
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# http://www.apache.org/licenses/LICENSE-2.0
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# 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.
#
#-------------------------------------------------------------
/*
* Cross-Entropy loss function.
*/
forward = function(matrix[double] pred, matrix[double] y)
return (double loss) {
/*
* Computes the forward pass for a cross-entropy loss function. The
* inputs consist of N examples, each with K dimensions corresponding
* to normalized probabilities of K classes.
*
* ```
* L_i = -y_i^T * log(pred_i)
* L = (1/N) sum(L_i) for i=1 to N
* ```
*
* In these equations, `L` is the total loss, `L_i` is the loss for
* example `i`, `y_i` is the K-dimensional vector of target class
* probabilities, `pred_i` is K-dimensional vector of predicted
* class probabilities, and `N` is the number of examples.
*
* This can be interpreted as the negative log-likelihood assuming
* a Bernoulli distribution generalized to K dimensions, or a
* Multinomial with one observation.
*
* Inputs:
* - pred: Predictions, of shape (N, K).
* - y: Targets, of shape (N, K).
*
* Outputs:
* - loss: Average loss.
*/
N = nrow(y)
eps = 1e-10 # numerical stability to avoid log(0)
losses = rowSums(-y * log(pred+eps))
loss = sum(losses) / N
}
backward = function(matrix[double] pred, matrix[double] y)
return (matrix[double] dpred) {
/*
* Computes the backward pass of a cross-entropy loss function. The
* inputs consist of N examples, each with K dimensions corresponding
* to normalized probabilities of K classes.
*
* Inputs:
* - pred: Predictions, of shape (N, K).
* - y: Targets, of shape (N, K).
*
* Outputs:
* - dpred: Gradient wrt `pred`, of shape (N, K).
*/
N = nrow(y)
eps = 1e-10 # numerical stability to avoid divide-by-zero
dpred = (1/N) * -y * (1/(pred+eps))
}