Spatial Channel Aggregation (Easy) — Practice with Code Visualizer

In modern convolutional neural networks, spatial channel aggregation is a crucial dimension reduction technique that transforms multi-dimensional feature maps into compact, channel-wise representations. This operation computes the arithmetic mean of all spatial positions within each feature channel, effectively summarizing the spatial information into a single value per channel.

Given a 3D tensor X of shape (H, W, C) where:

H represents the height (number of rows)
W represents the width (number of columns)
C represents the number of channels (feature maps)

The spatial channel aggregation produces a 1D output vector y of length C, where each element yₖ is computed as:

$$y_k = \frac{1}{H \times W} \sum_{i=1}^{H} \sum_{j=1}^{W} X_{i,j,k}$$

This means for each channel k, we sum all H × W spatial values and divide by the total number of spatial positions to obtain the average.

Key Properties:

Translation Invariance: The output is independent of where features are located spatially, making the representation robust to positional shifts in the input
Dimensionality Reduction: Reduces the spatial dimensions (H × W) to a single value per channel, dramatically decreasing parameter count
Regularization Effect: By averaging over spatial positions, this operation inherently reduces overfitting compared to fully-connected layers

Your Task: Write a Python function that performs spatial channel aggregation on a 3D feature map. The function should:

Accept a 3D array of shape (height, width, channels)
Return a 1D list of length C containing the average value across all spatial positions for each channel
Round each output value to 4 decimal places

The input is a 2×2×3 tensor (height=2, width=2, channels=3).

Channel 0: Values are [1.0, 4.0, 7.0, 10.0] Average = (1.0 + 4.0 + 7.0 + 10.0) / 4 = 22.0 / 4 = 5.5

Channel 1: Values are [2.0, 5.0, 8.0, 11.0] Average = (2.0 + 5.0 + 8.0 + 11.0) / 4 = 26.0 / 4 = 6.5

Channel 2: Values are [3.0, 6.0, 9.0, 12.0] Average = (3.0 + 6.0 + 9.0 + 12.0) / 4 = 30.0 / 4 = 7.5

The output is the 1D vector [5.5, 6.5, 7.5].

The input is a 2×2×2 tensor (height=2, width=2, channels=2).

Channel 0: Values are [1.0, 3.0, 5.0, 7.0] Average = (1.0 + 3.0 + 5.0 + 7.0) / 4 = 16.0 / 4 = 4.0

Channel 1: Values are [2.0, 4.0, 6.0, 8.0] Average = (2.0 + 4.0 + 6.0 + 8.0) / 4 = 20.0 / 4 = 5.0

The output is [4.0, 5.0].

The input is a 2×2×1 tensor (height=2, width=2, channels=1).

Channel 0: All spatial values are [10.0, 20.0, 30.0, 40.0] Average = (10.0 + 20.0 + 30.0 + 40.0) / 4 = 100.0 / 4 = 25.0

With only one channel, the output is a single-element list [25.0].