@tensorflow/tfjs-core
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Hardware-accelerated JavaScript library for machine intelligence
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JavaScript
/**
* @license
* Copyright 2018 Google LLC. All Rights Reserved.
* Licensed 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.
* =============================================================================
*/
import * as tf from '../index';
import { ALL_ENVS, describeWithFlags } from '../jasmine_util';
import { expectArraysClose } from '../test_util';
describeWithFlags('RMSPropOptimizer', ALL_ENVS, () => {
it('basic', async () => {
const learningRate = 0.1;
const moment = 0.1;
const rho = 0.95;
const optimizer = tf.train.rmsprop(learningRate, rho, moment);
const x = tf.tensor1d([1, 2]).variable();
const f = () => x.square().sum();
let numTensors = tf.memory().numTensors;
let cost = optimizer.minimize(f, /* returnCost */ true);
// Cost & 2 accumulators should be the only additional arrays.
expect(tf.memory().numTensors).toBe(numTensors + 3);
// epsilon = 1e-8
// newAccumulatedMeanSquare =
// rho * accumulatedMeanSquare + (1 - rho) * grad ^ 2 = (0.2)
// newAccumulatedMoments = momentum * accumulatedMoments +
// learning_rate * gradient / sqrt(newAccumulatedMeanSquare +
// epsilon) = 0.1 * 0 + ((0.1 * 2) / sqrt(0.2 + 1e-8)) = 0.44721
// x -= learningRate * newAccumulatedMoments
//
// de/dx = [2, 4]
// accumulatedMeanSquare = [0, 0]
// newAccumulatedMeanSquare = [.2, .8]
// accumulatedMoments = [0, 0]
// newAccumulatedMoments = [0.44721, 0.44721]
// x = [0.55279, 1.55279]
expectArraysClose(await x.data(), [0.55279, 1.55279]);
cost.dispose();
numTensors = tf.memory().numTensors;
cost = optimizer.minimize(f, /* returnCost */ false);
// x = [0.55279, 1.55279]
// de/dx = [1.10558, 3.10558]
// accumulatedMeanSquare = [0.2, 0.8]
// newAccumulatedMeanSquare = [0.25105125, 1.242231]
// accumulatedMoments = [0.44721, 0.44721]
// newAccumulatedMoments = [0.26534, 0.32336]
// x = [0.28745, 1.22943]
// TODO: Fix numerical precision.
expectArraysClose(await x.data(), [0.28745, 1.222943], 1e-2);
// There should be no new additional Tensors.
expect(tf.memory().numTensors).toBe(numTensors);
expect(cost).toBe(null);
x.dispose();
optimizer.dispose();
// The only tensor remaining is the argument to variable().
expect(tf.memory().numTensors).toBe(1);
});
it('gradient with centered momentum', async () => {
const learningRate = 0.1;
const moment = 0.1;
const rho = 0.95;
const eps = 1e-8;
const optimizer = tf.train.rmsprop(learningRate, rho, moment, eps, true);
const x = tf.tensor1d([1, 2]).variable();
const f = () => x.square().sum();
let numTensors = tf.memory().numTensors;
let cost = optimizer.minimize(f, /* returnCost */ true);
// Cost & 3 accumulators should be the only additional arrays.
expect(tf.memory().numTensors).toBe(numTensors + 4);
// epsilon = 1e-8
// newAccumulatedMeanSquare =
// rho * accumulatedMeanSquare + (1 - rho) * grad ^ 2 = [.2, .8]
// newAccumulatedMeanGrad =
// rho * accumulatedMeanGrad + (1 - rho) * grad = [0.1, 0.2]
// newAccumulatedMoments = momentum * accumulatedMoments +
// learning_rate * gradient / sqrt(newAccumulatedMeanSquare
// - newAccumulatedMeanGrad * 2 +
// epsilon) = 0.1 * 0 + ((0.1 * 2)
// / sqrt(0.2 - 0.01 + 1e-8)) = 0.458831
// x -= learningRate * newAccumulatedMoments
//
// de/dx = [2, 4]
// accumulatedMeanSquare = [0, 0]
// newAccumulatedMeanSquare = [.2, .8]
// newAccumulatedMeanGrad = [.1, .2]
// accumulatedMoments = [0, 0]
// newAccumulatedMoments = [0.45883, 0.458831]
// x = [0.54117, 1.541169]
expectArraysClose(await x.data(), [0.54117, 1.541169]);
cost.dispose();
numTensors = tf.memory().numTensors;
cost = optimizer.minimize(f, /* returnCost */ false);
// x = [0.54117, 1.541169]
// de/dx = [1.08234, 3.082338]
// accumulatedMeanSquare = [0.2, 0.8]
// accumulatedMeanGrad = [.1, .2]
// newAccumulatedMeanSquare = [0.248572, 1.235040]
// newAccumulatedMeanGrad = [0.149117, 0.3441169]
// accumulatedMoments = [0.45883, 0.458831]
// newAccumulatedMoments = [0.273385, 0.3375766]
// x = [0.267785, 1.2035924]
// TODO: Fix numerical precision.
expectArraysClose(await x.data(), [0.267785, 1.2035924], 1e-2);
// There should be no new additional Tensors.
expect(tf.memory().numTensors).toBe(numTensors);
expect(cost).toBe(null);
x.dispose();
optimizer.dispose();
// The only tensor remaining is the argument to variable().
expect(tf.memory().numTensors).toBe(1);
});
it('Save and load weights: centered = false', async () => {
const learningRate = 0.1;
const moment = 0.1;
const rho = 0.95;
const optimizer1 = tf.train.rmsprop(learningRate, rho, moment);
const x = tf.tensor1d([1, 2]).variable();
const f = () => x.square().sum();
let cost = optimizer1.minimize(f, /* returnCost */ true);
expectArraysClose(await cost.data(), 5);
expectArraysClose(await x.data(), [0.5527865, 1.5527864]);
const weights = await optimizer1.getWeights();
// An iteration variable and two optimizer state variables.
expect(weights.length).toEqual(3);
const optimizer2 = tf.train.rmsprop(learningRate, rho, moment);
await optimizer2.setWeights(weights);
cost = optimizer2.minimize(f, /* returnCost */ true);
expectArraysClose(await cost.data(), 2.7167187);
expectArraysClose(await x.data(), [0.2874418, 1.2294267]);
expect(optimizer2.iterations).toEqual(2);
});
it('Save, load weights and continue training: centered = true', async () => {
const learningRate = 0.1;
const moment = 0.1;
const rho = 0.95;
const epsilon = undefined;
const centered = true;
const optimizer1 = tf.train.rmsprop(learningRate, rho, moment, epsilon, centered);
const x = tf.tensor1d([1, 2]).variable();
const f = () => x.square().sum();
let cost = optimizer1.minimize(f, /* returnCost */ true);
expectArraysClose(await cost.data(), 5);
expectArraysClose(await x.data(), [0.5411684, 1.5411685]);
const weights = await optimizer1.getWeights();
// An iteration variable and three optimizer state variables.
expect(weights.length).toEqual(4);
const optimizer2 = tf.train.rmsprop(learningRate, rho, moment, epsilon, centered);
await optimizer2.setWeights(weights);
cost = optimizer2.minimize(f, /* returnCost */ true);
expectArraysClose(await cost.data(), 2.668063);
expectArraysClose(await x.data(), [0.2677834, 1.2035918]);
expect(optimizer2.iterations).toEqual(2);
const optimizer3 = tf.train.rmsprop(learningRate, rho, moment, epsilon, centered);
await optimizer3.setWeights(await optimizer2.getWeights());
cost = optimizer3.minimize(f, /* returnCost */ true);
expectArraysClose(await cost.data(), 1.520341);
expect(optimizer3.iterations).toEqual(3);
});
it('serialization round-trip', () => {
const originalOpt = tf.train.rmsprop(0.1, 0.5, 0.1, 1e-7, true);
const reserialized = tf.RMSPropOptimizer.fromConfig(tf.RMSPropOptimizer, originalOpt.getConfig());
expect(reserialized.getConfig()).toEqual(originalOpt.getConfig());
});
it('must define learning rate', () => {
const learningRate = undefined;
expect(() => tf.train.rmsprop(learningRate))
.toThrowError(/learningRate for RMSPropOptimizer must be defined./);
});
});
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