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 * Copyright (c) 2015-2019 Skymind, Inc.
 *
 * This program and the accompanying materials are made available under the
 * terms of the Apache License, Version 2.0 which is available at
 * https://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
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 * under the License.
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 * SPDX-License-Identifier: Apache-2.0
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package org.nd4j.linalg.learning.regularization;

import lombok.Data;
import lombok.NonNull;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.ops.impl.transforms.pairwise.arithmetic.Axpy;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.linalg.ops.transforms.Transforms;
import org.nd4j.linalg.schedule.FixedSchedule;
import org.nd4j.linalg.schedule.ISchedule;
import org.nd4j.shade.jackson.annotation.JsonProperty;

/**
 * L1 regularization: Implements updating as follows:
* {@code L = loss + l1 * sum_i abs(w[i])}
* {@code w[i] -= updater(gradient[i] + l1 * sign(w[i])) - where sign(w[i]) is +/- 1
* Note that L1 regularization is applied before the updater (Adam/Nesterov/etc) is applied. * * @author Alex Black */ @Data public class L1Regularization implements Regularization { protected final ISchedule l1; /** * @param l1 l1 regularization coefficient */ public L1Regularization(double l1) { this(new FixedSchedule(l1)); } /** * @param l1 L1 regularization coefficient (schedule) */ public L1Regularization(@JsonProperty("l1") @NonNull ISchedule l1) { this.l1 = l1; } @Override public ApplyStep applyStep(){ return ApplyStep.BEFORE_UPDATER; } @Override public void apply(INDArray param, INDArray gradView, double lr, int iteration, int epoch) { //L = loss + l1 * sum_i abs(x[i]) //dL/dx[i] = dloss/dx[i] + l1 * sign(x[i]) //where sign(x[i]) is -1 or 1 double coeff = l1.valueAt(iteration, epoch); INDArray sign = Transforms.sign(param, true); Nd4j.exec(new Axpy(sign, gradView, gradView, coeff)); //Gradient = l1 * sign(param) + gradient } @Override public double score(INDArray param, int iteration, int epoch) { return l1.valueAt(iteration, epoch) * param.norm1Number().doubleValue(); } @Override public Regularization clone() { return new L1Regularization(l1.clone()); } }




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