LayerTests.swift

// Copyright 2019 The TensorFlow Authors. 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 XCTest

@testable import TensorFlow

fileprivate struct Sigmoid<Scalar: TensorFlowFloatingPoint>: ParameterlessLayer {
  public init() {}

  @differentiable
  public func callAsFunction(_ input: Tensor<Scalar>) -> Tensor<Scalar> {
    sigmoid(input)
  }
}

final class LayerTests: XCTestCase {
  func testConv1D() {
    let filter = Tensor<Float>(ones: [3, 1, 2]) * Tensor<Float>([[[0.5, 1]]])
    let bias = Tensor<Float>([0, 1])
    let layer = Conv1D<Float>(
      filter: filter, bias: bias, activation: identity, stride: 1,
      padding: .valid)
    let input = Tensor<Float>([[0, 1, 2, 3, 4], [10, 11, 12, 13, 14]]).expandingShape(at: 2)
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [2, 3, 2],
      scalars: [1.5, 4, 3, 7, 4.5, 10, 16.5, 34, 18, 37, 19.5, 40])
    XCTAssertEqual(output, expected)

    let layerNoBias = Conv1D<Float>(
      filter: filter, bias: nil, activation: identity, stride: 1,
      padding: .valid)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [2, 3, 2],
      scalars: [1.5, 3, 3, 6, 4.5, 9, 16.5, 33, 18, 36, 19.5, 39])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testConv1DDilation() {
    // Filter shapes.
    let width = 3
    let inputChannels = 1
    let outputChannels = 2

    // Input shapes.
    let inputHeight = 2
    let inputWidth = 5

    let filter = Tensor<Float>(
      shape: [width, inputChannels, outputChannels],
      scalars: [2, 3, 4, 1, 2, 3])
    let bias = Tensor<Float>([0])
    let layer = Conv1D<Float>(
      filter: filter, bias: bias, activation: identity, stride: 1,
      padding: .valid, dilation: 2)
    let input = Tensor<Float>(
      shape: [inputHeight, inputWidth, 1],
      scalars: [0, 1, 2, 3, 4, 10, 11, 12, 13, 14])
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(shape: [2, 1, 2], scalars: [16, 14, 96, 84])
    XCTAssertEqual(output, expected)
  }

  func testConv2D() {
    let filter = Tensor(shape: [1, 2, 2, 1], scalars: (0..<4).map(Float.init))
    let bias = Tensor<Float>([1, 2])
    let layer = Conv2D<Float>(
      filter: filter, bias: bias, activation: identity,
      strides: (2, 2), padding: .valid)
    let input = Tensor(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [2, 1, 1, 2],
      scalars: [15, 16, 63, 64])
    XCTAssertEqual(output, expected)

    let layerNoBias = Conv2D<Float>(
      filter: filter, bias: nil, activation: identity,
      strides: (2, 2), padding: .valid)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [2, 1, 1, 1],
      scalars: [14, 62])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testConv2DGradient() {
    let filter = Tensor(shape: [3, 3, 2, 4], scalars: (0..<72).map(Float.init))
    let bias = Tensor<Float>(zeros: [4])
    let layer = Conv2D<Float>(
      filter: filter,
      bias: bias,
      activation: identity,
      strides: (2, 2),
      padding: .valid)
    let input = Tensor(shape: [2, 4, 4, 2], scalars: (0..<64).map(Float.init))
    let grads = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(64, dtype=tf.float32), [2, 4, 4, 2])
    // filter = tf.reshape(tf.range(72, dtype=tf.float32), [3, 3, 2, 4])
    // bias = tf.zeros([4])
    // with tf.GradientTape() as tape:
    //     tape.watch([x, filter, bias])
    //     y = tf.math.reduce_sum(tf.nn.conv2d(input=x,
    //                                         filters=filter,
    //                                         strides=[1, 2, 2, 1],
    //                                         data_format="NHWC",
    //                                         padding="VALID") + bias)
    // print(tape.gradient(y, [x, filter, bias]))
    // ```
    XCTAssertEqual(
      grads.0,
      [
        [
          [[6, 22], [38, 54], [70, 86], [0, 0]],
          [[102, 118], [134, 150], [166, 182], [0, 0]],
          [[198, 214], [230, 246], [262, 278], [0, 0]],
          [[0, 0], [0, 0], [0, 0], [0, 0]],
        ],
        [
          [[6, 22], [38, 54], [70, 86], [0, 0]],
          [[102, 118], [134, 150], [166, 182], [0, 0]],
          [[198, 214], [230, 246], [262, 278], [0, 0]],
          [[0, 0], [0, 0], [0, 0], [0, 0]],
        ],
      ])
    XCTAssertEqual(
      grads.1.filter,
      [
        [
          [[32, 32, 32, 32], [34, 34, 34, 34]],
          [[36, 36, 36, 36], [38, 38, 38, 38]],
          [[40, 40, 40, 40], [42, 42, 42, 42]],
        ],
        [
          [[48, 48, 48, 48], [50, 50, 50, 50]],
          [[52, 52, 52, 52], [54, 54, 54, 54]],
          [[56, 56, 56, 56], [58, 58, 58, 58]],
        ],
        [
          [[64, 64, 64, 64], [66, 66, 66, 66]],
          [[68, 68, 68, 68], [70, 70, 70, 70]],
          [[72, 72, 72, 72], [74, 74, 74, 74]],
        ],
      ])
    XCTAssertEqual(grads.1.bias, [2, 2, 2, 2])
  }

  func testConv2DDilation() {
    // Input shapes. (Data format = NHWC)
    let batchSize = 2
    let inputHeight = 4
    let inputWidth = 4
    let inputChannels = 1
    let inputSize = batchSize * inputHeight * inputWidth * inputChannels

    // Filter shapes.
    let filterHeight = 2
    let filterWidth = 2
    let outputChannels = 1
    let filterSize = filterHeight * filterWidth * inputChannels * outputChannels

    // Testing.
    let filter = Tensor<Float>(
      shape: [filterHeight, filterWidth, inputChannels, outputChannels],
      scalars: (0..<filterSize).map(Float.init))
    let bias = Tensor<Float>([0])
    let layer = Conv2D<Float>(
      filter: filter, bias: bias, activation: identity, strides: (1, 1),
      padding: .valid, dilations: (2, 2))
    let input = Tensor<Float>(
      shape: [batchSize, inputHeight, inputWidth, inputChannels],
      scalars: (0..<inputSize).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [2, 2, 2, 1],
      scalars: [48, 54, 72, 78, 144, 150, 168, 174])
    XCTAssertEqual(output, expected)
  }

  func testConv3D() {
    let filter = Tensor(shape: [1, 2, 2, 2, 1], scalars: (0..<8).map(Float.init))
    let bias = Tensor<Float>([-1, 1])
    let layer = Conv3D<Float>(
      filter: filter, bias: bias, activation: identity,
      strides: (1, 2, 1), padding: .valid, dilations: (1, 1, 1))
    let input = Tensor(shape: [2, 2, 2, 2, 2], scalars: (0..<32).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [2, 2, 1, 1, 2],
      scalars: [139, 141, 363, 365, 587, 589, 811, 813])
    XCTAssertEqual(output, expected)

    let layerNoBias = Conv3D<Float>(
      filter: filter, bias: nil, activation: identity,
      strides: (1, 2, 1), padding: .valid, dilations: (1, 1, 1))
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [2, 2, 1, 1, 1],
      scalars: [140, 364, 588, 812])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testConv3DGradient() {
    let filter = Tensor(shape: [1, 4, 4, 1, 1], scalars: (0..<16).map(Float.init))
    let bias = Tensor<Float>(ones: [2])
    let layer = Conv3D(
      filter: filter,
      bias: bias,
      activation: identity,
      strides: (2, 2, 2),
      padding: .same)
    let input = Tensor(shape: [1, 4, 4, 4, 1], scalars: (0..<64).map(Float.init))
    let grads = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(64, dtype=tf.float32), [1, 4, 4, 4, 1])
    // filter = tf.reshape(tf.range(72, dtype=tf.float32), [1, 4, 4, 1, 1])
    // bias = tf.ones([2])
    // with tf.GradientTape() as tape:
    //     tape.watch([x, filter, bias])
    //     y = tf.math.reduce_sum(tf.nn.conv3d(input=x,
    //                                         filters=filter,
    //                                         strides=[1, 2, 2, 2, 1],
    //                                         padding="SAME") + bias)
    // print(tape.gradient(y, [x, filter, bias]))
    // ```
    XCTAssertEqual(
      grads.0,
      [
        [
          [
            [[10.0], [20.0], [24.0], [12.0]],
            [[20.0], [40.0], [48.0], [24.0]],
            [[36.0], [72.0], [80.0], [40.0]],
            [[18.0], [36.0], [40.0], [20.0]],
          ],
          [
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
          ],
          [
            [[10.0], [20.0], [24.0], [12.0]],
            [[20.0], [40.0], [48.0], [24.0]],
            [[36.0], [72.0], [80.0], [40.0]],
            [[18.0], [36.0], [40.0], [20.0]],
          ],
          [
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
            [[0.0], [0.0], [0.0], [0.0]],
          ],
        ]
      ])
    XCTAssertEqual(
      grads.1.filter,
      [
        [
          [[[84.0]], [[168.0]], [[176.0]], [[88.0]]],
          [[[168.0]], [[336.0]], [[352.0]], [[176.0]]],
          [[[200.0]], [[400.0]], [[416.0]], [[208.0]]],
          [[[100.0]], [[200.0]], [[208.0]], [[104.0]]],
        ]
      ])
    XCTAssertEqual(grads.1.bias, [8.0, 8.0])
  }

  func testDepthwiseConv2D() {
    let filter = Tensor(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
    let bias = Tensor<Float>([1, 2, 3, 4])
    let layer = DepthwiseConv2D<Float>(
      filter: filter, bias: bias, activation: identity,
      strides: (2, 2), padding: .same)
    let input = Tensor(shape: [1, 1, 8, 2], scalars: (0..<16).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 1, 4, 4],
      scalars: [
        9, 12, 23, 28, 25, 36, 55, 68, 41, 60, 87, 108,
        57, 84, 119, 148,
      ])
    XCTAssertEqual(output, expected)

    let channelMultiplier = 4
    let multiplierLayer = DepthwiseConv2D<Float>(
      filterShape: (2, 2, input.shape[3], channelMultiplier),
      filterInitializer: glorotUniform(),
      biasInitializer: zeros())
    let multiplierOutput = multiplierLayer.inferring(from: input)
    XCTAssertEqual(multiplierOutput.shape[3], input.shape[3] * channelMultiplier)
  }

  func testDepthwiseConv2DGradient() {
    let filter = Tensor(shape: [2, 1, 2, 2], scalars: (0..<8).map(Float.init))
    let bias = Tensor<Float>(ones: [4])
    let layer = DepthwiseConv2D<Float>(
      filter: filter,
      bias: bias,
      activation: identity,
      strides: (1, 1),
      padding: .same)
    let input = Tensor(shape: [2, 1, 2, 2], scalars: (0..<8).map(Float.init))
    let grads = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // input = tf.reshape(tf.range(8, dtype=tf.float32), [2, 1, 2, 2])
    // filter = tf.reshape(tf.range(8, dtype=tf.float32), [2, 1, 2, 2])
    // bias = tf.ones([4])
    // with tf.GradientTape() as tape:
    //     tape.watch([x, filter, bias])
    //     y = tf.math.reduce_sum(tf.nn.depthwise_conv2d(input=x,
    //                                                   filters=filter,
    //                                                   strides=[1, 1, 1, 1],
    //                                                   data_format="NHWC",
    //                                                   padding="SAME") + bias)
    // print(tape.gradient(y, [x, filter, bias]))
    // ```
    XCTAssertEqual(
      grads.0,
      [
        [[[1, 5], [1, 5]]],
        [[[1, 5], [1, 5]]],
      ])
    XCTAssertEqual(
      grads.1.filter,
      [
        [[[12, 12], [16, 16]]],
        [[[0, 0], [0, 0]]],
      ])
    XCTAssertEqual(grads.1.bias, [4, 4, 4, 4])
  }

  func testTransposedConv1D() {
    let filter = Tensor(shape: [4, 1, 1], scalars: (0..<4).map(Float.init))
    let bias = Tensor<Float>([8])
    let layer = TransposedConv1D(
      filter: filter, bias: bias, activation: identity,
      stride: 1, padding: .same)
    let input = Tensor(shape: [1, 4, 1], scalars: (0..<4).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 1, 4, 1],
      scalars: [8, 9, 12, 18])
    XCTAssertEqual(output, expected)

    let layerNoBias = TransposedConv1D(
      filter: filter, bias: nil, activation: identity,
      stride: 1, padding: .same)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [1, 1, 4, 1],
      scalars: [0, 1, 4, 10])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testTransposedConv2D() {
    let filter = Tensor(shape: [4, 2, 1, 1], scalars: (0..<8).map(Float.init))
    let bias = Tensor<Float>([8])
    let layer = TransposedConv2D(
      filter: filter, bias: bias, activation: identity,
      strides: (1, 1), padding: .same)
    let input = Tensor(shape: [1, 4, 2, 1], scalars: (0..<8).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 4, 2, 1],
      scalars: [8, 12, 12, 28, 24, 64, 48, 112])
    XCTAssertEqual(output, expected)

    let layerNoBias = TransposedConv2D(
      filter: filter, bias: nil, activation: identity,
      strides: (1, 1), padding: .same)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [1, 4, 2, 1],
      scalars: [0, 4, 4, 20, 16, 56, 40, 104])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testTransposedConv2DGradient() {
    let filter = Tensor(shape: [3, 3, 2, 4], scalars: (0..<72).map(Float.init))
    let bias = Tensor<Float>(zeros: [2])
    let layer = TransposedConv2D<Float>(
      filter: filter,
      bias: bias,
      activation: identity,
      strides: (2, 2),
      padding: .same)
    let input = Tensor(shape: [2, 2, 2, 4], scalars: (0..<32).map(Float.init))
    let grads = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(32, dtype=tf.float32), [2, 2, 2, 4])
    // filter = tf.reshape(tf.range(72, dtype=tf.float32), [3, 3, 2, 4])
    // bias = tf.zeros([2])
    // with tf.GradientTape() as tape:
    //     tape.watch([x, filter, bias])
    //     y = tf.math.reduce_sum(tf.nn.conv2d_transpose(input=x,
    //                                                   filters=filter,
    //                                                   output_shape=[2, 4, 4, 2],
    //                                                   strides=[1, 2, 2, 1],
    //                                                   data_format="NHWC",
    //                                                   padding="SAME") + bias)
    // print(tape.gradient(y, [x, filter, bias]))
    // ```
    XCTAssertEqual(
      grads.0,
      [
        [
          [[612, 630, 648, 666], [360, 372, 384, 396]],
          [[264, 276, 288, 300], [144, 152, 160, 168]],
        ],
        [
          [[612, 630, 648, 666], [360, 372, 384, 396]],
          [[264, 276, 288, 300], [144, 152, 160, 168]],
        ],
      ])
    XCTAssertEqual(
      grads.1.filter,
      [
        [
          [[112, 120, 128, 136], [112, 120, 128, 136]],
          [[112, 120, 128, 136], [112, 120, 128, 136]],
          [[48, 52, 56, 60], [48, 52, 56, 60]],
        ],
        [
          [[112, 120, 128, 136], [112, 120, 128, 136]],
          [[112, 120, 128, 136], [112, 120, 128, 136]],
          [[48, 52, 56, 60], [48, 52, 56, 60]],
        ],
        [
          [[40, 44, 48, 52], [40, 44, 48, 52]],
          [[40, 44, 48, 52], [40, 44, 48, 52]],
          [[16, 18, 20, 22], [16, 18, 20, 22]],
        ],
      ])
    XCTAssertEqual(grads.1.bias, [32, 32])
  }

  func testTransposedConv3D() {
    let filter = Tensor(shape: [2, 2, 2, 1, 1], scalars: (0..<8).map(Float.init))
    let bias = Tensor<Float>([8])
    let layer = TransposedConv3D(
      filter: filter, bias: bias, activation: identity,
      strides: (1, 1, 1), padding: .same)
    let input = Tensor(shape: [1, 2, 2, 2, 1], scalars: (0..<8).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 2, 2, 2, 1],
      scalars: [8, 8, 8, 12, 8, 16, 24, 64])
    XCTAssertEqual(output, expected)

    let layerNoBias = TransposedConv3D(
      filter: filter, bias: nil, activation: identity,
      strides: (1, 1, 1), padding: .same)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [1, 2, 2, 2, 1],
      scalars: [0, 0, 0, 4, 0, 8, 16, 56])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testSeparableConv1D() {
    let depthwiseFilter = Tensor(shape: [2, 2, 2], scalars: (0..<8).map(Float.init))
    let pointwiseFilter = Tensor(shape: [1, 4, 1], scalars: (0..<4).map(Float.init))
    let bias = Tensor<Float>([4])
    let layer = SeparableConv1D<Float>(
      depthwiseFilter: depthwiseFilter,
      pointwiseFilter: pointwiseFilter,
      bias: bias,
      activation: identity,
      stride: 1,
      padding: .same)
    let input = Tensor(shape: [2, 2, 2], scalars: (0..<8).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(shape: [2, 2, 1], scalars: [17, 45, 73, 101])
    XCTAssertEqual(output, expected)

    let layerNoBias = SeparableConv1D<Float>(
      depthwiseFilter: depthwiseFilter,
      pointwiseFilter: pointwiseFilter,
      bias: nil,
      activation: identity,
      stride: 1,
      padding: .same)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(shape: [2, 2, 1], scalars: [13, 41, 69, 97])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testSeparableConv2D() {
    let depthwiseFilter = Tensor(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
    let pointwiseFilter = Tensor(shape: [1, 1, 4, 1], scalars: (0..<4).map(Float.init))
    let bias = Tensor<Float>([4])
    let layer = SeparableConv2D<Float>(
      depthwiseFilter: depthwiseFilter,
      pointwiseFilter: pointwiseFilter,
      bias: bias,
      activation: identity,
      strides: (2, 2),
      padding: .valid)
    let input = Tensor(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [2, 1, 1, 1],
      scalars: [1016, 2616])
    XCTAssertEqual(output, expected)

    let layerNoBias = SeparableConv2D<Float>(
      depthwiseFilter: depthwiseFilter,
      pointwiseFilter: pointwiseFilter,
      bias: nil,
      activation: identity,
      strides: (2, 2),
      padding: .valid)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>(
      shape: [2, 1, 1, 1],
      scalars: [1012, 2612])
    XCTAssertEqual(outputNoBias, expectedNoBias)
  }

  func testSeparableConv2DGradient() {
    let depthwiseFilter = Tensor(shape: [2, 1, 2, 2], scalars: (0..<8).map(Float.init))
    let pointwiseFilter = Tensor(shape: [1, 1, 4, 1], scalars: (0..<4).map(Float.init))
    let bias = Tensor<Float>([1, 1])
    let layer = SeparableConv2D<Float>(
      depthwiseFilter: depthwiseFilter,
      pointwiseFilter: pointwiseFilter,
      bias: bias,
      activation: identity,
      strides: (1, 1),
      padding: .same)
    let input = Tensor(shape: [2, 1, 2, 2], scalars: (0..<8).map(Float.init))
    let grads = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [2, 1, 2, 2])
    // depthwiseFilter = tf.reshape(tf.range(8, dtype=tf.float32), [2, 1, 2, 2])
    // pointwiseFilter = tf.reshape(tf.range(4, dtype=tf.float32), [1, 1, 4, 1])
    // bias = tf.ones([2])
    // with tf.GradientTape() as tape:
    //     tape.watch([x, depthwiseFilter, pointwiseFilter, bias])
    //     y = tf.math.reduce_sum(tf.nn.separable_conv2D(input,
    //                                                   depthwiseFilter,
    //                                                   pointwiseFilter
    //                                                   strides=[1, 1, 1, 1],
    //                                                   padding="SAME") + bias)
    // print(tape.gradient(y, [x, depthwiseFilter, pointwiseFilter, bias])
    // ```
    XCTAssertEqual(
      grads.0,
      [
        [[[2.0, 26.0], [2.0, 26.0]]],
        [[[2.0, 26.0], [2.0, 26.0]]],
      ])
    XCTAssertEqual(
      grads.1.depthwiseFilter,
      [
        [[[0.0, 24.0], [64.0, 96.0]]],
        [[[0.0, 0.0], [0.0, 0.0]]],
      ])
    XCTAssertEqual(grads.1.bias, [4.0, 4.0])
  }

  func testZeroPadding1D() {
    let input = Tensor<Float>(shape: [1, 3, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding1D<Float>(padding: 2)
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 7, 1],
      scalars: [0.0, 0.0, 0.0, 1.0, 2.0, 0.0, 0.0])
    XCTAssertEqual(output, expected)
  }

  func testZeroPadding1DGradient() {
    let x = Tensor<Float>(shape: [1, 3, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding1D<Float>(padding: 2)
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.constant([0.0, 1.0, 2.0]), [1, 3, 1])
    // layer = tf.keras.layers.ZeroPadding1D(2)
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.reduce_sum(layer(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>(onesLike: x)
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testZeroPadding2D() {
    let input = Tensor<Float>(shape: [1, 3, 1, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding2D<Float>(padding: ((0, 0), (0, 1)))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(
      shape: [1, 3, 2, 1],
      scalars: [0.0, 0.0, 1.0, 0.0, 2.0, 0.0])
    XCTAssertEqual(output, expected)
  }

  func testZeroPadding2DGradient() {
    let x = Tensor<Float>(shape: [1, 3, 1, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding2D<Float>(padding: ((0, 0), (0, 1)))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.constant([0.0, 1.0, 2.0]), [1, 3, 1, 1])
    // layer = tf.keras.layers.ZeroPadding2D(((0, 0), (0, 1)))
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.reduce_sum(layer(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>(onesLike: x)
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testZeroPadding3D() {
    let input = Tensor<Float>(shape: [1, 3, 1, 1, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding3D<Float>(padding: ((0, 0), (0, 1), (0, 0)))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>(shape: [1, 3, 2, 1, 1], scalars: [0, 0, 1, 0, 2, 0])
    XCTAssertEqual(output, expected)
  }

  func testZeroPadding3DGradient() {
    let x = Tensor<Float>(shape: [1, 3, 1, 1, 1], scalars: [0.0, 1.0, 2.0])
    let layer = ZeroPadding3D<Float>(padding: ((0, 0), (0, 1), (0, 0)))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.constant([0.0, 1.0, 2.0]), [1, 3, 1, 1, 1])
    // layer = tf.keras.layers.ZeroPadding3D(((0, 0), (0, 1), (0, 0)))
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.reduce_sum(layer(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>(onesLike: x)
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testMaxPool1D() {
    let layer = MaxPool1D<Float>(poolSize: 3, stride: 1, padding: .valid)
    let input = Tensor<Float>([[0, 1, 2, 3, 4], [10, 11, 12, 13, 14]]).expandingShape(at: 2)
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[2], [3], [4]], [[12], [13], [14]]])
    XCTAssertEqual(output, expected)
  }

  func testMaxPool1DGradient() {
    let layer = MaxPool1D<Float>(poolSize: 2, stride: 1, padding: .valid)
    let x = Tensor<Float>(shape: [1, 4, 4], scalars: (0..<16).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // maxpool1D = tf.keras.layers.MaxPool1D()
    // x = tf.reshape(tf.range(16, dtype=tf.float32), [1, 4, 4])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(maxpool1D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [0, 0, 0, 0],
        [1, 1, 1, 1],
        [1, 1, 1, 1],
        [1, 1, 1, 1],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testMaxPool2D() {
    let layer = MaxPool2D<Float>(poolSize: (2, 2), strides: (1, 1), padding: .valid)
    let input = Tensor(shape: [1, 2, 2, 1], scalars: (0..<4).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[[3]]]])
    XCTAssertEqual(output, expected)
  }

  func testMaxPool2DGradient() {
    let layer = MaxPool2D<Float>(poolSize: (2, 2), strides: (2, 2), padding: .valid)
    let x = Tensor(shape: [1, 4, 4, 1], scalars: (0..<16).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // maxpool2D = tf.keras.layers.MaxPool2D(strides=(2, 2))
    // x = tf.reshape(tf.range(16, dtype=tf.float32), [1, 4, 4, 1])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(maxpool2D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [[0], [0], [0], [0]],
        [[0], [1], [0], [1]],
        [[0], [0], [0], [0]],
        [[0], [1], [0], [1]],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testMaxPool3D() {
    let layer = MaxPool3D<Float>(poolSize: (2, 2, 2), strides: (1, 1, 1), padding: .valid)
    let input = Tensor(shape: [1, 2, 2, 2, 1], scalars: (0..<8).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[[[7]]]]])
    XCTAssertEqual(output, expected)
  }

  func testMaxPool3DGradient() {
    let layer = MaxPool3D<Float>(poolSize: (2, 2, 2), strides: (1, 1, 1), padding: .valid)
    let x = Tensor(shape: [1, 2, 2, 2, 1], scalars: (0..<8).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // maxpool3D = tf.keras.layers.MaxPool3D(strides=(1, 1, 1))
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [1, 2, 2, 2, 1])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(maxpool3D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [
          [[0], [0]],
          [[0], [0]],
        ],
        [
          [[0], [0]],
          [[0], [1]],
        ],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testAvgPool1D() {
    let layer = AvgPool1D<Float>(poolSize: 3, stride: 1, padding: .valid)
    let input = Tensor<Float>([[0, 1, 2, 3, 4], [10, 11, 12, 13, 14]]).expandingShape(at: 2)
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[1], [2], [3]], [[11], [12], [13]]])
    XCTAssertEqual(output, expected)
  }

  func testAvgPool1DGradient() {
    let layer = AvgPool1D<Float>(poolSize: 2, stride: 1, padding: .valid)
    let x = Tensor(shape: [1, 4, 4], scalars: (0..<16).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // avgpool1D = tf.keras.layers.AvgPool1D(strides=1)
    // x = tf.reshape(tf.range(16, dtype=tf.float32), [1, 4, 4])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(avgpool1D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [0.5, 0.5, 0.5, 0.5],
        [1.0, 1.0, 1.0, 1.0],
        [1.0, 1.0, 1.0, 1.0],
        [0.5, 0.5, 0.5, 0.5],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testAvgPool2D() {
    let layer = AvgPool2D<Float>(poolSize: (2, 5), strides: (1, 1), padding: .valid)
    let input = Tensor(shape: [1, 2, 5, 1], scalars: (0..<10).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[[4.5]]]])
    XCTAssertEqual(output, expected)
  }

  func testAvgPool2DGradient() {
    let layer = AvgPool2D<Float>(poolSize: (2, 2), strides: (1, 1), padding: .valid)
    let x = Tensor(shape: [1, 4, 4, 2], scalars: (0..<32).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // avgpool2D = tf.keras.layers.AvgPool2D(strides=(1, 1))
    // x = tf.reshape(tf.range(32, dtype=tf.float32), [1, 4, 4, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(avgpool2D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [[0.25, 0.25], [0.50, 0.50], [0.50, 0.50], [0.25, 0.25]],
        [[0.50, 0.50], [1.00, 1.00], [1.00, 1.00], [0.50, 0.50]],
        [[0.50, 0.50], [1.00, 1.00], [1.00, 1.00], [0.50, 0.50]],
        [[0.25, 0.25], [0.50, 0.50], [0.50, 0.50], [0.25, 0.25]],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testAvgPool3D() {
    let layer = AvgPool3D<Float>(poolSize: (2, 4, 5), strides: (1, 1, 1), padding: .valid)
    let input = Tensor(shape: [1, 2, 4, 5, 1], scalars: (0..<40).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[[[19.5]]]]])
    XCTAssertEqual(output, expected)
  }

  func testAvgPool3DGradient() {
    let layer = AvgPool3D<Float>(poolSize: (2, 2, 2), strides: (1, 1, 1), padding: .valid)
    let x = Tensor(shape: [1, 2, 2, 2, 1], scalars: (0..<8).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // avgpool3D = tf.keras.layers.AvgPool3D(strides=(1, 1, 1))
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [1, 2, 2, 2, 1])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(avgpool3D(x))
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>(repeating: 0.125, shape: [1, 2, 2, 2, 1])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testGlobalAvgPool1D() {
    let layer = GlobalAvgPool1D<Float>()
    let input = Tensor(shape: [2, 5, 1], scalars: (0..<10).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[2], [7]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalAvgPool1DGradient() {
    let layer = GlobalAvgPool1D<Float>()
    let input = Tensor(shape: [2, 2, 2], scalars: (0..<8).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // globalAvgPool1D = tf.keras.layers.GlobalAveragePooling1D()
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [2, 2, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalAvgPool1D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [0.5, 0.5],
          [0.5, 0.5],
        ],
        [
          [0.5, 0.5],
          [0.5, 0.5],
        ],
      ])
  }

  func testGlobalAvgPool2D() {
    let layer = GlobalAvgPool2D<Float>()
    let input = Tensor(shape: [2, 6, 2, 1], scalars: (0..<24).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[5.5], [17.5]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalAvgPool2DGradient() {
    let layer = GlobalAvgPool2D<Float>()
    let input = Tensor(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // globalAvgPool2D = tf.keras.layers.GlobalAveragePooling2D()
    // x = tf.reshape(tf.range(16, dtype=tf.float32), [2, 2, 2, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalAvgPool2D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [[0.25, 0.25], [0.25, 0.25]],
          [[0.25, 0.25], [0.25, 0.25]],
        ],
        [
          [[0.25, 0.25], [0.25, 0.25]],
          [[0.25, 0.25], [0.25, 0.25]],
        ],
      ])
  }

  func testGlobalAvgPool3D() {
    let layer = GlobalAvgPool3D<Float>()
    let input = Tensor<Float>(shape: [2, 6, 2, 1, 1], scalars: (0..<24).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[5.5], [17.5]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalAvgPool3DGradient() {
    let layer = GlobalAvgPool3D<Float>()
    let input = Tensor(shape: [1, 3, 2, 3, 1], scalars: (0..<18).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // globalAvgPool3D = tf.keras.layers.GlobalAveragePooling3D()
    // x = tf.reshape(tf.range(18, dtype=tf.float32), [1, 3, 2, 2, 1])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalAvgPool3D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [
            [[0.055555556], [0.055555556], [0.055555556]],
            [[0.055555556], [0.055555556], [0.055555556]],
          ],
          [
            [[0.055555556], [0.055555556], [0.055555556]],
            [[0.055555556], [0.055555556], [0.055555556]],
          ],
          [
            [[0.055555556], [0.055555556], [0.055555556]],
            [[0.055555556], [0.055555556], [0.055555556]],
          ],
        ]
      ])
  }

  func testGlobalMaxPool1D() {
    let layer = GlobalMaxPool1D<Float>()
    let input = Tensor(shape: [1, 10, 1], scalars: (0..<10).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[9]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalMaxPool1DGradient() {
    let layer = GlobalMaxPool1D<Float>()
    let input = Tensor(shape: [2, 2, 2], scalars: (0..<8).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // globalMaxPool1D = tf.keras.layers.GlobalMaxPooling1D()
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [2, 2, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalMaxPool1D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [0.0, 0.0],
          [1.0, 1.0],
        ],
        [
          [0.0, 0.0],
          [1.0, 1.0],
        ],
      ])
  }

  func testGlobalMaxPool2D() {
    let layer = GlobalMaxPool2D<Float>()
    let input = Tensor(shape: [1, 2, 10, 1], scalars: (0..<20).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[19]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalMaxPool2DGradient() {
    let layer = GlobalMaxPool2D<Float>()
    let input = Tensor(shape: [2, 3, 3, 2], scalars: (0..<36).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    //import tensorflow as tf
    // globalMaxPool2D = tf.keras.layers.GlobalMaxPooling2D()
    // x = tf.reshape(tf.range(36, dtype=tf.float32), [2, 3, 3, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalMaxPool2D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
          [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
          [[0.0, 0.0], [0.0, 0.0], [1.0, 1.0]],
        ],
        [
          [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
          [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]],
          [[0.0, 0.0], [0.0, 0.0], [1.0, 1.0]],
        ],
      ])
  }

  func testGlobalMaxPool3D() {
    let layer = GlobalMaxPool3D<Float>()
    let input = Tensor<Float>(shape: [1, 2, 3, 5, 1], scalars: (0..<30).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[29]])
    XCTAssertEqual(output, expected)
  }

  func testGlobalMaxPool3DGradient() {
    let layer = GlobalMaxPool3D<Float>()
    let input = Tensor(shape: [2, 2, 2, 2, 2], scalars: (0..<32).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // globalMaxPool3D = tf.keras.layers.GlobalMaxPooling3D()
    // x = tf.reshape(tf.range(32, dtype=tf.float32), [2, 2, 2, 2, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(globalMaxPool3D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [
            [[0.0, 0.0], [0.0, 0.0]],
            [[0.0, 0.0], [0.0, 0.0]],
          ],
          [
            [[0.0, 0.0], [0.0, 0.0]],
            [[0.0, 0.0], [1.0, 1.0]],
          ],
        ],
        [
          [
            [[0.0, 0.0], [0.0, 0.0]],
            [[0.0, 0.0], [0.0, 0.0]],
          ],
          [
            [[0.0, 0.0], [0.0, 0.0]],
            [[0.0, 0.0], [1.0, 1.0]],
          ],
        ],
      ])
  }

  func testFractionalMaxPool2D() {
    let layer = FractionalMaxPool2D<Float>(poolingRatio: (1.4, 1.5), pseudoRandom: false)
    let input = Tensor(shape: [1, 2, 2, 1], scalars: (0..<4).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[[[3]]]])
    XCTAssertEqual(output, expected)
  }

  func testFractionalMaxPool2DGradient() {
    let layer = FractionalMaxPool2D<Float>(poolingRatio: (1.4, 1.5), pseudoRandom: false)
    let x = Tensor(shape: [1, 2, 2, 1], scalars: (0..<4).map(Float.init))
    let computedGradient = gradient(at: x, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(4, dtype=tf.float32), [1, 2, 2, 1])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(tf.nn.fractional_max_pool(x, pooling_ratio=[1, 1.4, 1.5, 1], pseudo_random=False)[0])
    // print(tape.gradient(y, x))
    // ```
    let expectedGradient = Tensor<Float>([
      [
        [
          [0.0],
          [0.0],
        ],
        [
          [0.0],
          [1.0],
        ],
      ]
    ])
    XCTAssertEqual(computedGradient.0, expectedGradient)
  }

  func testUpSampling1D() {
    let size = 6
    let layer = UpSampling1D<Float>(size: size)
    let input = Tensor<Float>(shape: [1, 10, 1], scalars: (0..<10).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = TensorShape([1, input.shape[1] * size, 1])
    XCTAssertEqual(output.shape, expected)
  }

  func testUpSampling1DGradient() {
    let layer = UpSampling1D<Float>(size: 3)
    let input = Tensor(shape: [2, 2, 2], scalars: (0..<8).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // upSampling1D = tf.keras.layers.UpSampling1D(size = 3)
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [2, 2, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(upSampling1D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [3.0, 3.0],
          [3.0, 3.0],
        ],
        [
          [3.0, 3.0],
          [3.0, 3.0],
        ],
      ])
  }

  func testUpSampling2D() {
    let size = 6
    let layer = UpSampling2D<Float>(size: size)
    let input = Tensor<Float>(shape: [1, 3, 5, 1], scalars: (0..<15).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = TensorShape([1, input.shape[1] * size, input.shape[2] * size, 1])
    XCTAssertEqual(output.shape, expected)
  }

  func testUpSampling2DGradient() {
    let layer = UpSampling2D<Float>(size: 3)
    let input = Tensor(shape: [1, 3, 4, 2], scalars: (0..<24).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // upSampling2D = tf.keras.layers.UpSampling2D(size = 3)
    // x = tf.reshape(tf.range(24, dtype=tf.float32), [1, 3, 4, 2])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(upSampling2D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [[9.0, 9.0], [9.0, 9.0], [9.0, 9.0], [9.0, 9.0]],
          [[9.0, 9.0], [9.0, 9.0], [9.0, 9.0], [9.0, 9.0]],
          [[9.0, 9.0], [9.0, 9.0], [9.0, 9.0], [9.0, 9.0]],
        ]
      ])
  }

  func testUpSampling3D() {
    let size = 6
    let layer = UpSampling3D<Float>(size: size)
    let input = Tensor<Float>(shape: [1, 4, 3, 2, 1], scalars: (0..<24).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = TensorShape(
      [1, input.shape[1] * size, input.shape[2] * size, input.shape[3] * size, 1])
    XCTAssertEqual(output.shape, expected)
    XCTAssertEqual(output.shape, expected)
  }

  func testUpSampling3DGradient() {
    let layer = UpSampling3D<Float>(size: 3)
    let input = Tensor(shape: [1, 2, 2, 2, 4], scalars: (0..<32).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // upSampling3D = tf.keras.layers.UpSampling3D(size = 3)
    // x = tf.reshape(tf.range(32, dtype=tf.float32), [1, 2, 2, 2, 4])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(upSampling3D(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [
            [[27.0, 27.0, 27.0, 27.0], [27.0, 27.0, 27.0, 27.0]],
            [[27.0, 27.0, 27.0, 27.0], [27.0, 27.0, 27.0, 27.0]],
          ],
          [
            [[27.0, 27.0, 27.0, 27.0], [27.0, 27.0, 27.0, 27.0]],
            [[27.0, 27.0, 27.0, 27.0], [27.0, 27.0, 27.0, 27.0]],
          ],
        ]
      ])
  }

  func testReshape() {
    let layer = Reshape<Float>(shape: [10, 2, 1])
    let input = Tensor(shape: [20, 1], scalars: (0..<20).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = TensorShape([10, 2, 1])
    XCTAssertEqual(output.shape, expected)
  }

  func testReshapeGradient() {
    let layer = Reshape<Float>(shape: [10, 2, 1])
    let input = Tensor(shape: [1, 5, 4], scalars: (0..<20).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // reshape = tf.keras.layers.Reshape(target_shape = (10, 2, 1))
    // x = tf.reshape(tf.range(20, dtype=tf.float32), [1, 5, 4])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(reshape(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
        ]
      ])
  }

  func testFlatten() {
    let layer = Flatten<Float>()
    let input = Tensor(shape: [10, 2, 2], scalars: (0..<40).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = TensorShape([10, 4])
    XCTAssertEqual(output.shape, expected)
  }

  func testFlattenGradient() {
    let layer = Flatten<Float>()
    let input = Tensor(shape: [1, 4, 4], scalars: (0..<16).map(Float.init))
    let computedGradient = gradient(at: input, layer) { $1($0).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // flatten = tf.keras.layers.Flatten()
    // x = tf.reshape(tf.range(16, dtype=tf.float32), [1, 4, 4])
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = tf.math.reduce_sum(flatten(x))
    // print(tape.gradient(y, x))
    // ```
    XCTAssertEqual(
      computedGradient.0,
      [
        [
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
          [1.0, 1.0, 1.0, 1.0],
        ]
      ])
  }

  func testEmbedding() {
    var layer = Embedding<Float>(vocabularySize: 3, embeddingSize: 5)
    var input = Tensor<Int32>(shape: [2, 3], scalars: [0, 1, 2, 1, 2, 2])
    var output = layer(input)
    let expectedShape = TensorShape([2, 3, 5])
    XCTAssertEqual(output.shape, expectedShape)

    let pretrained = Tensor<Float>(shape: [2, 2], scalars: [0.4, 0.3, 0.2, 0.1])
    layer = Embedding<Float>(embeddings: pretrained)
    input = Tensor<Int32>(shape: [2, 2], scalars: [0, 1, 1, 1])
    output = layer(input)
    let expected = Tensor<Float>([[[0.4, 0.3], [0.2, 0.1]], [[0.2, 0.1], [0.2, 0.1]]])
    XCTAssertEqual(output, expected)
  }

  func testEmbeddingGradient() {
    let embeddings = Tensor<Float>([
      [0.0, 0.2, 0.1],
      [0.1, 0.7, 0.5],
      [0.2, 0.4, 0.6],
      [0.3, 0.2, 0.3],
    ])
    let layer = Embedding<Float>(embeddings: embeddings)
    let indices = Tensor<Int32>(shape: [2, 3], scalars: [0, 1, 2, 1, 2, 2])
    let grad = gradient(at: layer) { $0(indices).sum() }
    // The expected value of the gradient was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // indices = tf.constant([0, 1, 2, 1, 2, 2], dtype=tf.int32)
    // embeddings = tf.constant([
    //      [0.0, 0.2, 0.1],
    //      [0.1, 0.7, 0.5],
    //      [0.2, 0.4, 0.6],
    //      [0.3, 0.2, 0.3]])
    // layer = tf.keras.layers.Embedding(4, 3, weights=[embeddings])
    // with tf.GradientTape() as tape:
    //     tape.watch(layer.weights)
    //     y = tf.reduce_sum(layer(indices))
    // grad_slice = tape.gradient(y, layer.weights)[0]  # IndexedSlice
    // grad = tf.zeros_like(embeddings).numpy()
    // for index in grad_slice.indices:
    //     grad[index] += grad_slice.values[index].numpy()
    // print(grad)
    // ```
    let expected = Tensor<Float>([
      [1, 1, 1],
      [2, 2, 2],
      [3, 3, 3],
      [0, 0, 0],
    ])
    XCTAssertEqual(grad.embeddings, expected)
  }

  func testBasicRNNCell() {
    let weight = Tensor<Float>(ones: [7, 5]) * Tensor<Float>([0.3333, 1, 0.3333, 1, 0.3333])
    let bias = Tensor<Float>(ones: [5])
    var cell = BasicRNNCell<Float>(inputSize: 2, hiddenSize: 5)
    cell.weight = weight
    cell.bias = bias
    let state = Tensor<Float>(ones: [1, 5]) * Tensor<Float>([1, 0.2, 0.5, 2, 0.6])
    let input = Tensor<Float>(ones: [1, 2]) * Tensor<Float>([0.3, 0.7])
    let output = cell(input: input, state: state).state
    let expected = Tensor<Float>([[0.9921227, 0.9999934, 0.9921227, 0.9999934, 0.9921227]])
    XCTAssertEqual(output, expected)
  }

  func testDense() {
    let weight = Tensor<Float>(shape: [3, 2], scalars: (0..<6).map(Float.init))
    let bias = Tensor<Float>([[1.0, 2.0]])
    let layer = Dense<Float>(weight: weight, bias: bias, activation: identity)
    let input = Tensor<Float>(shape: [1, 3], scalars: (0..<3).map(Float.init))
    let output = layer.inferring(from: input)
    let expected = Tensor<Float>([[11.0, 15.0]])
    XCTAssertEqual(output, expected)
    XCTAssertFalse(layer.batched)

    let layerNoBias = Dense<Float>(weight: weight, bias: nil, activation: identity)
    let outputNoBias = layerNoBias.inferring(from: input)
    let expectedNoBias = Tensor<Float>([[10.0, 13.0]])
    XCTAssertEqual(outputNoBias, expectedNoBias)
    XCTAssertFalse(layerNoBias.batched)

    let weightBatched = Tensor<Float>(shape: [2, 2, 3], scalars: (0..<12).map(Float.init))
    let biasBatched = Tensor<Float>([[1.0, 2.0, 3.0]])
    let layerBatched = Dense<Float>(
      weight: weightBatched,
      bias: biasBatched,
      activation: identity)
    let inputBatched = Tensor<Float>(shape: [2, 2], scalars: (0..<4).map(Float.init))
    let outputBatched = layerBatched.inferring(from: inputBatched)
    let expectedBatched = Tensor<Float>([[4.0, 6.0, 8.0], [40.0, 46.0, 52.0]])
    XCTAssertEqual(outputBatched, expectedBatched)
    XCTAssertTrue(layerBatched.batched)

    let layerBatchedNoBias = Dense<Float>(
      weight: weightBatched,
      bias: nil,
      activation: identity)
    let outputBatchedNoBias = layerBatchedNoBias.inferring(from: inputBatched)
    let expectedBatchedNoBias = Tensor<Float>([[3.0, 4.0, 5.0], [39.0, 44.0, 49.0]])
    XCTAssertEqual(outputBatchedNoBias, expectedBatchedNoBias)
    XCTAssertTrue(layerBatchedNoBias.batched)
  }

  func testDenseGradient() {
    let weight = Tensor<Float>(shape: [4, 8], scalars: (0..<32).map(Float.init))
    let bias = Tensor<Float>(shape: [1, 8], scalars: (0..<8).map(Float.init))

    // Test `Dense.init` derivative.
    let denseInitPullback = pullback(at: weight) { weight in
      Dense(weight: weight, bias: bias, activation: identity)
    }
    let weightGrad = denseInitPullback(.init(weight: Tensor(100), bias: Tensor(1)))
    XCTAssertEqual(Tensor(100), weightGrad)

    // Test `Dense.callAsFunction` derivative.
    let layer = Dense<Float>(weight: weight, bias: bias, activation: identity)
    let x = Tensor<Float>(shape: [2, 4], scalars: (0..<8).map(Float.init))
    let grad = gradient(at: x, layer) { $1($0).squared().sum() }
    let value = layer(x)
    // The expected values and gradients were computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(8, dtype=tf.float32), [2, 4])
    // kernel_value = np.arange(32.0).reshape([4, 8])
    // bias_value = np.arange(8.0)
    // kernel_initializer = tf.compat.v2.constant_initializer(kernel_value)
    // bias_initializer = tf.compat.v2.constant_initializer(bias_value)
    // layer = tf.keras.layers.Dense(8,
    //                               kernel_initializer=kernel_initializer,
    //                               bias_initializer=bias_initializer)
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = layer(x)
    //     z = tf.math.reduce_sum(tf.math.square(y))
    // print(y, tape.gradient(z, [x] + layer.trainable_variables))
    // ```
    assertEqual(
      value,
      [
        [112.0, 119.0, 126.0, 133.0, 140.0, 147.0, 154.0, 161.0],
        [304.0, 327.0, 350.0, 373.0, 396.0, 419.0, 442.0, 465.0],
      ],
      accuracy: 1e-5)
    assertEqual(
      grad.0,
      [
        [8232.0, 25704.0, 43176.0, 60648.0],
        [23464.0, 72680.0, 121896.0, 171112.0],
      ],
      accuracy: 1e-5)
    assertEqual(
      grad.1.weight,
      [
        [2432.0, 2616.0, 2800.0, 2984.0, 3168.0, 3352.0, 3536.0, 3720.0],
        [3264.0, 3508.0, 3752.0, 3996.0, 4240.0, 4484.0, 4728.0, 4972.0],
        [4096.0, 4400.0, 4704.0, 5008.0, 5312.0, 5616.0, 5920.0, 6224.0],
        [4928.0, 5292.0, 5656.0, 6020.0, 6384.0, 6748.0, 7112.0, 7476.0],
      ],
      accuracy: 1e-5)
    assertEqual(
      grad.1.bias,
      [[832.0, 892.0, 952.0, 1012.0, 1072.0, 1132.0, 1192.0, 1252.0]],
      accuracy: 1e-5)
  }

  func testRNN() {
    let x = Tensor<Float>(rangeFrom: 0.0, to: 0.4, stride: 0.1).rankLifted()
    let inputs: [Tensor<Float>] = Array(repeating: x, count: 4)
    let rnn = BasicRNN<Float>(BasicRNNCell(inputSize: 4, hiddenSize: 4, seed: (0xFeed, 0xBeef)))
    withTensorLeakChecking {
      let (outputs, pullback) = valueWithPullback(at: rnn, inputs) { rnn, inputs in
        return rnn(inputs)
      }
      assertEqual(
        outputs.map { $0 }[0],
        [
          [0.20775771, 0.20080023, -0.13768704, -0.18534681],
          [0.22666009, 0.30019346, -0.19720285, -0.14683801],
          [0.23758979, 0.32101023, -0.20359215, -0.1787096],
          [0.24337786, 0.3389194, -0.21143384, -0.1675081],
        ],
        accuracy: 1e-6)
      let (𝛁rnn, _) = pullback(.init(inputs))
      // TODO: Verify that RNN gradients are correct using a reference implementation.
      XCTAssertEqual(
        𝛁rnn.cell.weight,
        [
          [0.0, 0.0, 0.0, 0.0],
          [-0.014372801, 0.03128201, 0.07844338, 0.08569162],
          [-0.028745603, 0.06256402, 0.15688676, 0.17138325],
          [-0.043118402, 0.09384604, 0.2353301, 0.25707486],
          [-0.019920545, 0.05355064, 0.13140751, 0.15169607],
          [-0.024906494, 0.06562942, 0.15947133, 0.18506715],
          [0.016476292, -0.042923313, -0.10459379, -0.12082438],
          [0.013913135, -0.040882945, -0.100636974, -0.11757788],
        ])
      XCTAssertEqual(𝛁rnn.cell.bias, [-0.14372802, 0.31282014, 0.78443366, 0.8569162])
    }
  }

  func testLSTM() {
    // Data generated by "Tools/ReferenceImplementations/lstm.py".
    // BEGIN GENERATED CODE
    let kernel = Tensor<Float>(
      [
        [
          0.4545238, 0.17410219, 0.07151973, -0.043370485, -0.08141422, -0.23986903,
          0.2063713, 0.17585361, 0.4534099, -0.5096329, 0.2199418, -0.2149244,
          0.23440659, 0.43826634, -0.13891399, -0.17842606,
        ],
        [
          -0.3797379, 0.079282284, -0.10015741, -0.3239718, -0.27132228, 0.39218837,
          -0.43364745, -0.34852988, 0.2132551, -0.5461597, -0.048002183, 0.26265675,
          -0.18781787, -0.41067505, -0.051611483, 0.4885484,
        ],
        [
          -0.06933203, 0.54473567, -0.21874839, -0.49106207, -0.071650594, -0.08455315,
          0.5346174, 0.057993293, -0.13344201, -0.48908734, -0.058430463, -0.15182033,
          0.03391558, 0.009597003, 0.273346, -0.49635035,
        ],
        [
          -0.07164055, 0.37893647, -0.108646095, 0.07596207, 0.31213146, -0.3623113,
          -0.20532963, -0.302337, -0.26968825, 0.4479969, -0.085390985, 0.2579115,
          0.2743805, -0.21505526, -0.31751555, -0.44200268,
        ],
      ]
    )
    let recurrentKernel = Tensor<Float>(
      [
        [
          0.001444459, -0.44615534, 0.17120321, 0.028076064, -0.36675194, -0.37769908,
          -0.038331404, -0.3308463, 0.18919824, 0.21540813, 0.21875387, -0.17696984,
          0.24726436, -0.2989273, 0.26229933, 0.045673575,
        ],
        [
          -0.0060651056, -0.010614913, -0.41048288, -0.16720156, -0.042991478,
          -0.034523666, -0.22591552, -0.46458426, -0.15950868, 0.0032770582,
          0.02271657, 0.26582226, -0.38004795, 0.21254668, 0.35087258, 0.35231543,
        ],
        [
          -0.2352461, -0.12130469, -0.19648746, 0.29172993, 0.10191456, -0.2919168,
          -0.1870388, 0.2183716, 0.34960067, -0.24624759, 0.3270614, 0.4467347,
          0.11563631, 0.2551108, 0.06388308, -0.2366966,
        ],
        [
          -0.36797202, 0.21800567, -0.06400205, 0.43761855, 0.1086247, 0.3239568,
          -0.23723324, -0.07836083, -0.10523385, 0.34244883, 0.11385839, -0.15765572,
          0.42096126, 0.08826415, 0.10015068, 0.28478572,
        ],
      ]
    )
    let bias = Tensor<Float>(
      [0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
    )
    let x = Tensor<Float>(
      [
        [
          [-0.6346513, -0.43788078, -0.40050998, -0.35219777],
          [-0.59232813, -0.728384, -0.22974151, 0.3288936],
          [0.5766824, -0.5468713, 0.16438323, 0.6741958],
          [-0.47952235, -0.24399251, 0.8553043, 0.8588342],
        ]
      ]
    )
    let initialStateHidden = Tensor<Float>(
      [[0.9577427, -0.7377565, 0.35953724, -0.5784317]]
    )
    let initialStateCell = Tensor<Float>(
      [[-0.905442, -0.95177335, -0.05345559, -1.0015926]]
    )
    let expectedStates = Tensor<Float>(
      [
        [
          [-0.24107721, -0.17449945, 0.037506927, -0.30990827],
          [-0.26881245, -0.00634476, -0.019400658, -0.2071909],
          [-0.2842662, 0.032890536, -0.015112571, -0.13682269],
          [-0.31182146, 0.08775673, -0.072591506, -0.07358349],
        ]
      ]
    )
    let expectedOutput = Tensor<Float>(
      [[-0.7036462, 0.19863679, -0.14904207, -0.25543863]]
    )
    let expectedGradKernel = Tensor<Float>(
      [
        [
          0.0805003, -0.08275342, 0.03522955, -0.030312482, 0.11720966, 0.07540316,
          -0.0023639323, 0.10740622, -0.2532557, -0.16903767, -0.5353516, -0.3493193,
          0.016285714, 0.008904671, -0.003577555, -0.006157878,
        ],
        [
          0.08940101, -0.095668815, 0.032129567, -0.013392258, 0.17761931, 0.071601115,
          -0.000029361108, 0.17159097, -0.78527546, -0.5366851, -0.898436, -0.68411684,
          0.05064467, 0.0044404613, 0.0010539321, 0.022477672,
        ],
        [
          -0.124524735, 0.014374042, -0.065310925, 0.04207304, -0.018112179,
          0.054847445, -0.0053864224, -0.044751726, 0.12626463, 0.57195514, 0.0789956,
          0.21590737, 0.010621901, 0.0052103405, -0.0023645863, -0.00021189498,
        ],
        [
          -0.1812453, 0.07054679, -0.08742681, 0.046577554, -0.10540785, 0.021182634,
          -0.002338124, -0.14174302, 0.6233163, 0.88522494, 0.5829264, 0.6225763,
          -0.026014743, 0.0054547004, -0.0054682456, -0.018445207,
        ],
      ]
    )
    let expectedGradRecurrentKernel = Tensor<Float>(
      [
        [
          0.109804794, -0.006917909, 0.06479619, -0.02927, -0.07282017, -0.06949664,
          -0.007851637, -0.0064141527, 0.01585731, -0.27055892, 0.18191284,
          -0.036890596, 0.00081066974, -0.012041213, 0.008538903, 0.004745292,
        ],
        [
          -0.022427287, -0.037062988, -0.021642044, 0.009100201, 0.113654904,
          0.07015832, 0.00417687, 0.073882714, -0.31279865, -0.057589047, -0.4670751,
          -0.2540243, 0.019137694, 0.008957855, -0.004623856, 0.005064313,
        ],
        [
          0.015348908, 0.013859384, 0.012477149, -0.0050131185, -0.050523866,
          -0.031698443, -0.0024695867, -0.0299116, 0.12353469, 0.012106655, 0.19668634,
          0.0989304, -0.0068828184, -0.0043967483, 0.0024977797, -0.001459891,
        ],
        [
          0.024811182, -0.05493941, 0.0018467754, -0.001980858, 0.1320867, 0.06232968,
          0.0034385736, 0.10646886, -0.46687102, -0.2663457, -0.5953469, -0.4029197,
          0.02738668, 0.0066831633, -0.0024504992, 0.010666027,
        ],
      ]
    )
    let expectedGradBias = Tensor<Float>(
      [
        -0.2057409, 0.18275242, -0.07681093, 0.042995583, -0.3810982, -0.12361911,
        -0.008955841, -0.3550135, 1.5545796, 1.3119538, 1.8124579, 1.4128002,
        -0.08343395, -0.010454425, 0.0008502216, -0.038896702,
      ]
    )
    let expectedGradX = Tensor<Float>(
      [
        [
          [0.21591075, 0.11293747, -0.13014226, -0.022586256],
          [0.08480768, 0.13718912, -0.12702335, 0.077232406],
          [0.01666388, 0.0068455637, -0.35854548, 0.1287557],
          [-0.2761167, -0.088074416, -0.415294, 0.32159615],
        ]
      ]
    )
    let expectedGradInitialStateHidden = Tensor<Float>(
      [[0.25400645, 0.07120966, 0.36865664, -0.05423181]]
    )
    let expectedGradInitialStateCell = Tensor<Float>(
      [[0.48873883, 0.23135301, 0.6608742, 0.37556332]]
    )
    // END GENERATED CODE

    // Swaps the columns corresponding to "forget" and "update" gates.
    //
    // This translates between the keras ordering
    //   [input | forget | update | output]
    // and the swift-apis ordering
    //   [input | update | forget | output]
    func swapForgetUpdate(_ t: Tensor<Float>) -> Tensor<Float> {
      var split = t.split(count: 4, alongAxis: -1)
      split.swapAt(1, 2)
      return Tensor(concatenating: split, alongAxis: -1)
    }

    withTensorLeakChecking {
      var lstm = LSTM<Float>(LSTMCell(inputSize: 4, hiddenSize: 4))
      lstm.cell.fusedWeight =
        swapForgetUpdate(Tensor(concatenating: [kernel, recurrentKernel]))
      lstm.cell.fusedBias = swapForgetUpdate(bias)

      let inputs = x.squeezingShape(at: 0).unstacked().map { $0.rankLifted() }
      let initialState = LSTMCell<Float>.State(
        cell: initialStateCell,
        hidden: initialStateHidden)

      let outputs = lstm(inputs, initialState: initialState)
      assertEqual(
        Tensor(concatenating: outputs.map { $0.hidden }),
        expectedStates,
        accuracy: 1e-6)
      assertEqual(
        outputs.last!.cell,
        expectedOutput,
        accuracy: 1e-6)

      let (gradLSTM, gradInputs, gradInitialState) =
        gradient(at: lstm, inputs, initialState) { lstm, inputs, initialState in
          lstm.lastOutput(from: inputs, initialState: initialState).cell.sum()
        }
      assertEqual(
        gradLSTM.cell.fusedWeight,
        swapForgetUpdate(
          Tensor(concatenating: [expectedGradKernel, expectedGradRecurrentKernel])),
        accuracy: 1e-6)
      assertEqual(
        gradLSTM.cell.fusedBias,
        swapForgetUpdate(expectedGradBias),
        accuracy: 1e-6)
      assertEqual(
        Tensor(concatenating: gradInputs.map { $0 }),
        expectedGradX,
        accuracy: 1e-6)
      assertEqual(
        gradInitialState.cell,
        expectedGradInitialStateCell,
        accuracy: 1e-6)
      assertEqual(
        gradInitialState.hidden,
        expectedGradInitialStateHidden,
        accuracy: 1e-6)

    }
  }

  func testGRU() {
    let x = Tensor<Float>(rangeFrom: 0.0, to: 0.4, stride: 0.1).rankLifted()
    let inputs: [Tensor<Float>] = Array(repeating: x, count: 4)
    let gru = GRU<Float>(
      GRUCell(
        inputSize: 4,
        hiddenSize: 4,
        weightInitializer: glorotUniform(seed: (0xFeed, 0xBeef)),
        biasInitializer: zeros())
    )
    withTensorLeakChecking {
      let (outputs, pullback) = valueWithPullback(at: gru, inputs) { gru, inputs in
        return gru(inputs)
      }
      assertEqual(
        outputs.map { $0 }[0],
        [
          [0.1193780, 0.1193780, 0.1193780, 0.1193780],
          [0.1887644, 0.1887644, 0.1887644, 0.1887644],
          [0.2230835, 0.2230835, 0.2230835, 0.2230835],
          [0.2383619, 0.2383619, 0.2383619, 0.2383619],
        ],
        accuracy: 1e-5)
      // TODO: Verify that GRU gradients are correct using a reference implementation.
      let (𝛁gru, _) = pullback(.init(inputs))
      assertEqual(
        𝛁gru.cell.updateWeight1,
        [[0.0], [-0.040293925], [-0.08058785], [-0.12088178]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.updateWeight2,
        [[-0.056792725], [-0.056792725], [-0.056792725], [-0.056792725]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.resetWeight1,
        [[0.0], [0.0039126356], [0.007825271], [0.011737906]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.resetWeight2,
        [[0.0069182813], [0.0069182813], [0.0069182813], [0.0069182813]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.outputWeight1,
        [[0.0], [0.1221647], [0.2443294], [0.3664941]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.outputWeight2,
        [[0.08078343], [0.08078343], [0.08078343], [0.08078343]],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.updateBias,
        [-0.016739635, -0.04493352, -0.13216142, -0.20910467],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.resetBias,
        [0.023218961, -0.024303729, 0.010057628, 0.030153492],
        accuracy: 1e-5)
      assertEqual(
        𝛁gru.cell.outputBias,
        [0.06667276, 0.115095116, 0.39864573, 0.6412333],
        accuracy: 1e-5)
    }
  }

  func testFunction() {
    let tanhLayer = Function<Tensor<Float>, Tensor<Float>>(tanh)
    let input = Tensor(shape: [5, 1], scalars: (0..<5).map(Float.init))
    let output = tanhLayer.inferring(from: input)
    let expected = Tensor<Float>([[0.0], [0.7615942], [0.9640276], [0.9950547], [0.9993292]])
    XCTAssertEqual(output, expected)
  }

  func testBatchNorm() {
    let x = Tensor<Float>([
      [-1.0474433, -0.11914538, -0.08634827, 0.15446888, 1.0572497],
      [1.5165012, 0.3753972, -0.30856386, -0.3100725, -1.9584457],
      [0.006384419, 1.4424847, 0.91568077, 0.66328526, -1.0794537],
      [1.056803, 0.14263044, -1.8308276, 0.4189805, 0.6933893],
      [0.30175626, -0.16121633, -0.4191958, -0.53092813, -0.029484272],
    ])
    let bnLayer = BatchNorm<Float>(featureCount: 5, axis: 0)
    Context.local.learningPhase = .training
    withTensorLeakChecking {
      let output = bnLayer(x)
      let grad = gradient(at: x, bnLayer) { $1($0).squared().sum() }
      // The expected values and gradients were computed using the following Python code:
      // ```
      // import tensorflow as tf
      // x = tf.constant(
      //        [[  -1.0474433,  -0.11914538,  -0.08634827,   0.15446888,    1.0572497],
      //         [   1.5165012,    0.3753972,  -0.30856386,   -0.3100725,   -1.9584457],
      //         [ 0.006384419,    1.4424847,   0.91568077,   0.66328526,   -1.0794537],
      //         [    1.056803,   0.14263044,   -1.8308276,    0.4189805,    0.6933893],
      //         [  0.30175626,  -0.16121633,   -0.4191958,  -0.53092813, -0.029484272]])
      // scale = tf.reshape(tf.constant([1., 1., 1., 1., 1.]), [5, 1])
      // offset = tf.reshape(tf.constant([0., 0., 0., 0., 0.]), [5, 1])
      // (mean, var) = tf.nn.moments(x, axes=1, keepdims=True)
      // bn = tf.nn.batch_normalization(x, mean, var, offset=offset, scale=scale,
      //                                variance_epsilon=0.001)
      // scaled = tf.reduce_sum(tf.square(bn))
      // g = tf.gradients(scaled, [x, offset, scale])
      // init = tf.initialize_all_variables()
      // with tf.Session() as sess:
      //     sess.run(init)
      //     print(sess.run([bn, g]))
      // ```
      assertEqual(
        output,
        [
          [-1.5439795, -0.16477099, -0.11604305, 0.24174842, 1.5830451],
          [1.4639764, 0.45368853, -0.15186328, -0.15319899, -1.6126028],
          [-0.44139984, 1.2124169, 0.60574806, 0.3150888, -1.6918538],
          [0.9507547, 0.04595902, -1.9072568, 0.31947452, 0.5910686],
          [1.5834246, 0.02224666, -0.8476793, -1.2244489, 0.46645695],
        ],
        accuracy: 1e-5)
      assertEqual(
        grad.0,
        [
          [-1.0127544e-02, -1.0807812e-03, -7.6115131e-04, 1.5857220e-03, 1.0383606e-02],
          [2.0323221e-03, 6.2976527e-04, -2.1077941e-04, -2.1265696e-04, -2.2384699e-03],
          [-1.3483668e-03, 3.7030075e-03, 1.8500184e-03, 9.6232636e-04, -5.1673558e-03],
          [1.8438101e-03, 8.9146197e-05, -3.6990643e-03, 6.1964989e-04, 1.1463165e-03],
          [1.2142579e-01, 1.7060755e-03, -6.5005139e-02, -9.3897656e-02, 3.5770576e-02],
        ],
        accuracy: 1e-5)
      assertEqual(grad.1.offset, [0.0, 0.0, 0.0, 0.0, 0.0], accuracy: 1e-5)
      assertEqual(
        grad.1.scale,
        [9.977925, 9.992161, 9.986738, 9.990202, 9.886292],
        accuracy: 1e-5)
    }
  }

  func testBatchNormInference() {
    Context.local.learningPhase = .inference
    // This tests for a specific failure that had impacted the MiniGo model.
    let miniGoTensor = Tensor<Float>(randomUniform: [2, 19, 19, 256])
    let miniGoBatchNorm = BatchNorm<Float>(featureCount: 256, momentum: 0.95, epsilon: 1e-5)
    let miniGoResult = miniGoBatchNorm(miniGoTensor)
    XCTAssertEqual(miniGoTensor.shape, miniGoResult.shape)

    let x = Tensor<Float>(rangeFrom: 0, to: 20, stride: 1).reshaped(to: [4, 5])
    let epsilon: Float = 0.001
    let bnLayer = BatchNorm<Float>(featureCount: 5, axis: 1, epsilon: epsilon)
    // Test inference before any training.
    assertEqual(bnLayer.inferring(from: x), x / TensorFlow.sqrt(1 + epsilon), accuracy: 1e-5)
    // Perform one training step, updating the running mean and variance.
    Context.local.learningPhase = .training
    _ = bnLayer(x)  // This line is important and cannot be removed.
    // Test inference after training step.
    // The expected value was computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.reshape(tf.range(20, dtype=tf.float32), [4,5])
    // bn = tf.nn.batch_normalization(x, mean, var, offset=offset, scale=scale,
    //                                variance_epsilon=0.001)
    // y_train = bnLayer(x, training=True)
    // y = bnLayer(x, training=False)
    // print(y)
    // ```
    assertEqual(
      bnLayer.inferring(from: x),
      [
        [-0.06569097, 0.8014299, 1.6685508, 2.5356717, 3.4027927],
        [4.3137074, 5.180828, 6.0479493, 6.91507, 7.7821913],
        [8.693106, 9.560227, 10.427347, 11.294469, 12.16159],
        [13.072505, 13.939626, 14.806746, 15.673867, 16.540987],
      ],
      accuracy: 1e-5)
  }

  func testLayerNorm() {
    let x = Tensor<Float>([
      [2.736876, -0.8932728, -0.11240143, 1.252899, -0.35648823],
      [-0.43356904, -0.5147881, 0.8055815, 0.97228354, 1.4561518],
      [0.56300443, -0.87069905, -0.20677163, 1.1823419, 1.0455104],
      [-0.8246169, 1.4249208, 1.2131604, 1.1445689, -0.94032115],
    ])
    let lnLayer = LayerNorm<Float>(featureCount: 5, axis: 1)
    let value = lnLayer(x)
    let grad = gradient(at: x, lnLayer) { $1($0).squared().sum() }
    // The expected values and gradients were computed using the following Python code:
    // ```
    // import tensorflow as tf
    // x = tf.constant([[ 2.736876  , -0.8932728 , -0.11240143,  1.252899  , -0.35648823],
    //                  [-0.43356904, -0.5147881 ,  0.8055815 ,  0.97228354,  1.4561518 ],
    //                  [ 0.56300443, -0.87069905, -0.20677163,  1.1823419 ,  1.0455104 ],
    //                  [-0.8246169 ,  1.4249208 ,  1.2131604 ,  1.1445689 , -0.94032115]])
    // lnLayer = tf.keras.layers.LayerNormalization(axis=1, epsilon=0.001)
    // with tf.GradientTape() as tape:
    //     tape.watch(x)
    //     y = lnLayer(x)
    //     z = tf.math.reduce_sum(tf.math.square(y))
    // print(y, tape.gradient(z, [x] + lnLayer.trainable_variables))
    // ```
    assertEqual(
      value,
      [
        [1.6839857, -1.0804383, -0.4857906, 0.5539104, -0.6716671],
        [-1.1261504, -1.228839, 0.44055927, 0.6513276, 1.2631025],
        [0.28318238, -1.5595294, -0.70619607, 1.079205, 0.9033381],
        [-1.1639192, 0.96795416, 0.7672701, 0.70226634, -1.2735714],
      ],
      accuracy: 1e-5)
    assertEqual(
      grad.0,
      [
        [0.00148721, -0.00095408, -0.00042902, 0.00048913, -0.00059323],
        [-0.00455132, -0.00496664, 0.00178061, 0.00263247, 0.00510535],
        [0.0012024, -0.00662184, -0.00299847, 0.00458241, 0.00383568],
        [-0.0019815, 0.00164783, 0.00130618, 0.00119543, -0.00216818],
      ],
      accuracy: 1e-5)
    assertEqual(
      grad.1.offset,
      [-0.645803, -5.8017054, 0.03168535, 5.973418, 0.44240427],
      accuracy: 1e-5)
    assertEqual(
      grad.1.scale,
      [11.077844, 12.092919, 3.0350027, 4.7778125, 8.969137],
      accuracy: 1e-5)
  }

  func testLayerNormInference() {
    Context.local.learningPhase = .inference
    // This tests for a specific failure that had impacted the Transformer model.
    let transformerTensor = Tensor<Float>(randomUniform: [1, 1, 768])
    let transformerLayerNorm = LayerNorm<Float>(featureCount: 768, axis: -1, epsilon: 1e-5)
    let transformerResult = transformerLayerNorm(transformerTensor)
    XCTAssertEqual(transformerTensor.shape, transformerResult.shape)
  }
  
  func testGaussianNoise() {
    Context.local.learningPhase = .inference
    let gaussianNoise = GaussianNoise<Float>(standardDeviation: 1.0)
    let x = Tensor<Float>(repeating: 1.0, shape: [5, 5])
    XCTAssertEqual(gaussianNoise(x), x)
    withLearningPhase(LearningPhase.inference) {
      XCTAssertEqual(gaussianNoise(x), x)
      withLearningPhase(LearningPhase.training) {
        XCTAssertNotEqual(gaussianNoise(x), x)
      }
      XCTAssertEqual(gaussianNoise(x), x)
    }
    XCTAssertEqual(gaussianNoise(x), x)
  }

  func testGaussianDropout() {
    Context.local.learningPhase = .inference
    let dropout = GaussianDropout<Float>(probability: 0.5)
    let x = Tensor<Float>(repeating: 1.0, shape: [5, 5])
    XCTAssertEqual(dropout(x), x)
    withLearningPhase(LearningPhase.inference) {
      XCTAssertEqual(dropout(x), x)
      withLearningPhase(LearningPhase.training) {
        XCTAssertNotEqual(dropout(x), x)
      }
      XCTAssertEqual(dropout(x), x)
    }
    XCTAssertEqual(dropout(x), x)
  }

  func testAlphaDropout() {
    Context.local.learningPhase = .inference
    let dropout = AlphaDropout<Float>(probability: 0.5)
    let x = Tensor<Float>(repeating: 1.0, shape: [4, 4])
    XCTAssertEqual(dropout(x), x)
    withLearningPhase(LearningPhase.inference) {
      XCTAssertEqual(dropout(x), x)
      withLearningPhase(LearningPhase.training) {
        XCTAssertNotEqual(dropout(x), x)
      }
      XCTAssertEqual(dropout(x), x)
    }
    XCTAssertEqual(dropout(x), x)
  }

  static var allTests = [
    ("testConv1D", testConv1D),
    ("testConv1DDilation", testConv1DDilation),
    ("testConv2D", testConv2D),
    ("testConv2DGradient", testConv2DGradient),
    ("testConv2DDilation", testConv2DDilation),
    ("testConv3D", testConv3D),
    ("testConv3DGradient", testConv3DGradient),
    ("testTransposedConv1D", testTransposedConv1D),
    ("testTransposedConv2D", testTransposedConv2D),
    ("testTransposedConv2DGradient", testTransposedConv2DGradient),
    ("testTransposedConv3D", testTransposedConv3D),
    ("testDepthwiseConv2D", testDepthwiseConv2D),
    ("testDepthwiseConv2DGradient", testDepthwiseConv2DGradient),
    ("testSeparableConv1D", testSeparableConv1D),
    ("testSeparableConv2D", testSeparableConv2D),
    ("testSeparableConv2DGradient", testSeparableConv2DGradient),
    ("testZeroPadding1D", testZeroPadding1D),
    ("testZeroPadding1DGradient", testZeroPadding1DGradient),
    ("testZeroPadding2D", testZeroPadding2D),
    ("testZeroPadding2DGradient", testZeroPadding2DGradient),
    ("testZeroPadding3D", testZeroPadding3D),
    ("testZeroPadding3DGradient", testZeroPadding3DGradient),
    ("testMaxPool1D", testMaxPool1D),
    ("testMaxPool1DGradient", testMaxPool1DGradient),
    ("testMaxPool2D", testMaxPool2D),
    ("testMaxPool2DGradient", testMaxPool2DGradient),
    ("testMaxPool3D", testMaxPool3D),
    ("testMaxPool3DGradient", testMaxPool3DGradient),
    ("testAvgPool1D", testAvgPool1D),
    ("testAvgPool1DGradient", testAvgPool1DGradient),
    ("testAvgPool2D", testAvgPool2D),
    ("testAvgPool2DGradient", testAvgPool2DGradient),
    ("testAvgPool3D", testAvgPool3D),
    ("testAvgPool3DGradient", testAvgPool3DGradient),
    ("testGlobalAvgPool1D", testGlobalAvgPool1D),
    ("testGlobalAvgPool1DGradient", testGlobalAvgPool1DGradient),
    ("testGlobalAvgPool2D", testGlobalAvgPool2D),
    ("testGlobalAvgPool2DGradient", testGlobalAvgPool2DGradient),
    ("testGlobalAvgPool3D", testGlobalAvgPool3D),
    ("testGlobalAvgPool3DGradient", testGlobalAvgPool3DGradient),
    ("testGlobalMaxPool1D", testGlobalMaxPool1D),
    ("testGlobalMaxPool1DGradient", testGlobalMaxPool1DGradient),
    ("testGlobalMaxPool2D", testGlobalMaxPool2D),
    ("testGlobalMaxPool2DGradient", testGlobalMaxPool2DGradient),
    ("testGlobalMaxPool3D", testGlobalMaxPool3D),
    ("testGlobalMaxPool3DGradient", testGlobalMaxPool3DGradient),
    ("testFractionalMaxPool2D", testFractionalMaxPool2D),
    ("testFractionalMaxPool2DGradient", testFractionalMaxPool2DGradient),
    ("testUpSampling1D", testUpSampling1D),
    ("testUpSampling1DGradient", testUpSampling1DGradient),
    ("testUpSampling2D", testUpSampling2D),
    ("testUpSampling2DGradient", testUpSampling2DGradient),
    ("testUpSampling3D", testUpSampling3D),
    ("testUpSampling3DGradient", testUpSampling3DGradient),
    ("testReshape", testReshape),
    ("testReshapeGradient", testReshapeGradient),
    ("testFlatten", testFlatten),
    ("testFlattenGradient", testFlattenGradient),
    ("testEmbedding", testEmbedding),
    ("testEmbeddingGradient", testEmbeddingGradient),
    ("testBasicRNNCell", testBasicRNNCell),
    ("testDense", testDense),
    ("testDenseGradient", testDenseGradient),
    ("testRNN", testRNN),
    ("testLSTM", testLSTM),
    ("testGRU", testGRU),
    ("testFunction", testFunction),
    ("testBatchNorm", testBatchNorm),
    ("testBatchNormInference", testBatchNormInference),
    ("testLayerNorm", testLayerNorm),
    ("testLayerNormInference", testLayerNormInference),
    ("testGaussianNoise", testGaussianNoise),
    ("testGaussianDropout", testGaussianDropout),
    ("testAlphaDropout", testAlphaDropout),
  ]
}