org.nd4j.linalg.learning.regularization.L2Regularization Maven / Gradle / Ivy
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.schedule.FixedSchedule;
import org.nd4j.linalg.schedule.ISchedule;
import org.nd4j.shade.jackson.annotation.JsonProperty;
/**
* L2 regularization: very similar to {@link WeightDecay}, but is applied before the updater is applied, not after.
*
*
* Implements updating as follows:
* {@code L = loss + l2 * 0.5 * sum_i w[i]^2}
* {@code w[i] -= updater(gradient[i] + l2 * w[i])
* That is, L2 regularization is applied before the updater (Adam/Nesterov/etc) is applied to the gradients. This differs
* from {@link WeightDecay} mainly in that WeightDecay is applied after the updater.
*
* See also: {@link WeightDecay} which should generally be preferred in practice.
* See https://www.fast.ai/2018/07/02/adam-weight-decay/
* for further details
*
* @author Alex Black
*/
@Data
public class L2Regularization implements Regularization {
protected final ISchedule l2;
/**
* @param l2 L2 regularization coefficient
*/
public L2Regularization(double l2) {
this(new FixedSchedule(l2));
}
/**
* @param l2 L2 regularization coefficient (schedule)
*/
public L2Regularization(@JsonProperty("l2") @NonNull ISchedule l2) {
this.l2 = l2;
}
@Override
public ApplyStep applyStep(){
return ApplyStep.BEFORE_UPDATER;
}
@Override
public void apply(INDArray param, INDArray gradView, double lr, int iteration, int epoch) {
//L = loss + l2 * 0.5 * sum_i x[i]^2
//dL/dx[i] = dloss/dx[i] + l2 * x[i]
double coeff = l2.valueAt(iteration, epoch);
Nd4j.exec(new Axpy(param, gradView, gradView, coeff)); //Gradient = scale * param + gradient
}
@Override
public double score(INDArray param, int iteration, int epoch) {
//Score: L = 0.5 * sum_i x[i]^2
double norm2 = param.norm2Number().doubleValue(); //Norm2 is sqrt(sum_i x[i]^2)
return l2.valueAt(iteration, epoch) * 0.5 * norm2 * norm2;
}
@Override
public Regularization clone() {
return new L2Regularization(l2.clone());
}
}