Study Plan

Apply an AlphaGo Residual Block

Reinforcement LearningComputer VisionNeural Networks

Medium

Apply the two-convolution residual block used in the AlphaGo Zero tower. For input $X$ , convolution weights $W_1$ and $W_2$ , channel scales $\gamma_1$ and $\gamma_2$ , channel shifts $\beta_1$ and $\beta_2$ , and batch normalization $\operatorname{BN}$ over batch and spatial axes, compute

H=\operatorname{ReLU}(\operatorname{BN}(\operatorname{Conv}_{3\times3}(X;W_1);\gamma_1,\beta_1))

Y=\operatorname{ReLU}(X+\operatorname{BN}(\operatorname{Conv}_{3\times3}(H;W_2);\gamma_2,\beta_2))

Here, H is the residual branch activation and Y is the block output. Both convolutions use stride 1, padding 1, and no bias.

For an activation z in one channel, batch normalization is

\operatorname{BN}(z;\gamma,\beta)=\gamma\frac{z-\mu}{\sqrt{\sigma^2+\varepsilon}}+\beta

Here, mu and sigma squared are that channel's mean and population variance over the batch and spatial dimensions. Gamma and beta are its supplied scale and shift, and epsilon is the supplied positive normalization constant.

Return Y as a PyTorch float32 tensor with the same shape and device as x.

Loading visualization...

Examples

Input: x = [[[[2,-1],[0,3]]]], conv1_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale1 = [1], shift1 = [0], conv2_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale2 = [1], shift2 = [0], epsilon = 0.00001

Output: [[[[2.0,0.0],[0.0,3.0]]]]

Explanation: The convolution branch is zero, so the final ReLU acts on the shortcut.

Input: x = [[[[-2]]]], conv1_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale1 = [1], shift1 = [0], conv2_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale2 = [1], shift2 = [0], epsilon = 0.0001

Output: [[[[0.0]]]]

Input: x shape = (2,2,2,2), conv1_weight shape = (2,2,3,3), conv2_weight shape = (2,2,3,3), scale1 = [0.5856,0.6118], shift1 = [-0.0436,-0.0539], scale2 = [0.9551,0.978], shift2 = [0.3145,-0.1452], epsilon = 0.00001

Output: 32-bit floating-point tensor with shape (2,2,2,2)

Hint 1

F.conv2d supports the padding needed to preserve spatial dimensions.

Hint 2

keepdim=True keeps channel statistics broadcastable.

Hint 3

Reshape a channel vector to (1, channels, 1, 1) for broadcasting.

Requirements

Use PyTorch float32 computation and output.
Preserve every input tensor and the input device.

Constraints

Input x is a nonempty floating-point PyTorch tensor of shape (batch, channels, height, width).
Both convolution weights have shape (channels, channels, 3, 3); each scale and shift has shape (channels,).
All supplied tensors are floating-point tensors on the same device; their input dtypes may differ.
Epsilon is a positive finite number.

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Apply an AlphaGo Residual Block

Reinforcement LearningComputer VisionNeural Networks

Medium

H=\operatorname{ReLU}(\operatorname{BN}(\operatorname{Conv}_{3\times3}(X;W_1);\gamma_1,\beta_1))

Y=\operatorname{ReLU}(X+\operatorname{BN}(\operatorname{Conv}_{3\times3}(H;W_2);\gamma_2,\beta_2))

Here, H is the residual branch activation and Y is the block output. Both convolutions use stride 1, padding 1, and no bias.

For an activation z in one channel, batch normalization is

\operatorname{BN}(z;\gamma,\beta)=\gamma\frac{z-\mu}{\sqrt{\sigma^2+\varepsilon}}+\beta

Return Y as a PyTorch float32 tensor with the same shape and device as x.

Loading visualization...

Examples

Input: x = [[[[2,-1],[0,3]]]], conv1_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale1 = [1], shift1 = [0], conv2_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale2 = [1], shift2 = [0], epsilon = 0.00001

Output: [[[[2.0,0.0],[0.0,3.0]]]]

Explanation: The convolution branch is zero, so the final ReLU acts on the shortcut.

Input: x = [[[[-2]]]], conv1_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale1 = [1], shift1 = [0], conv2_weight = [[[[0,0,0],[0,0,0],[0,0,0]]]], scale2 = [1], shift2 = [0], epsilon = 0.0001

Output: [[[[0.0]]]]

Output: 32-bit floating-point tensor with shape (2,2,2,2)

Hint 1

F.conv2d supports the padding needed to preserve spatial dimensions.

Hint 2

keepdim=True keeps channel statistics broadcastable.

Hint 3

Reshape a channel vector to (1, channels, 1, 1) for broadcasting.

Requirements

Use PyTorch float32 computation and output.
Preserve every input tensor and the input device.

Constraints

Input x is a nonempty floating-point PyTorch tensor of shape (batch, channels, height, width).
Both convolution weights have shape (channels, channels, 3, 3); each scale and shift has shape (channels,).
All supplied tensors are floating-point tensors on the same device; their input dtypes may differ.
Epsilon is a positive finite number.

Try Similar Problems

x =

Accepts: array

conv1_weight =

Accepts: array

scale1 =

Accepts: array

shift1 =

Accepts: array

conv2_weight =

Accepts: array

scale2 =

Accepts: array

shift2 =

Accepts: array

epsilon =

Accepts: number