Flatten Feature Map

easyPROCNNsDeep LearningCV: Deep Learning

Implement a function to transform a 3D feature map into a 1D vector, a crucial step in Convolutional Neural Networks (CNNs). This process enables the connection of convolutional layers to fully connected layers.

In CNNs, a feature map is a 3D array of size $C \times H \times W$ , where $C$ is the number of channels, $H$ is the height, and $W$ is the width. To feed this data into a fully connected layer, it must be flattened into a 1D vector.

The values must appear in channel, then row, then column order: all of channel 1 comes before channel 2, within a channel row 1 comes before row 2, and within a row the values keep their left-to-right order. Return the result as a flat Python list of length $C \cdot H \cdot W$ .

\text{Flattened Vector} = [x_{1,1,1}, x_{1,1,2},..., x_{C,H,W}]

This technique is widely used in image classification tasks.

Example

Input

flatten([[[1,2],[3,4]], [[5,6],[7,8]]])

Output

[1,2,3,4,5,6,7,8]

Reasoning

Input: a nested list with $C = 2$ channels, each an $H \times W = 2 \times 2$ grid. Channel 1 holds $\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and channel 2 holds $\begin{bmatrix}5&6\\7&8\end{bmatrix}$ .
Output size: the vector has $C \cdot H \cdot W = 2 \cdot 2 \cdot 2 = 8$ entries, one per value, none added or dropped.
Where each value lands: counting from 0, entry $x_{c,h,w}$ goes to position $p = c \cdot HW + h \cdot W + w = 4c + 2h + w$ . So $6$ (channel $c=1$ , row $h=0$ , column $w=1$ ) lands at $p = 4 + 0 + 1 = 5$ , and $7$ ( $c=1, h=1, w=0$ ) lands at $p = 6$ .
Result: positions 0 to 3 are channel 1 read row by row (1, 2, 3, 4), positions 4 to 7 are channel 2 (5, 6, 7, 8), giving [1,2,3,4,5,6,7,8].
Notice that the column index changes fastest and the channel index slowest. Reading columns first would give $1, 3, 2, 4$ for channel 1 instead.

Constraints

Return flattened list in C, H, W order

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Concept primerPREVIEW

1. Background Knowledge

In Convolutional Neural Networks (CNNs), convolutional layers extract hierarchical feature maps from input images. These are typically 3D tensors with dimensions C × H × W, where C is the number of channels (feature depth), H is height, and W is width. Each channel captures specific patterns like edges or textures, preserving spatial relationships critical for tasks like object detection.

Flattening transforms this 3D structure into a 1D vector of size C × H × W, enabling connection to fully connected (FC) layers for classification. This bridge is essential in classic CNN architectures (e.g., AlexNet, VGG), as FC layers perform global reasoning but require fixed-size inputs. Modern alternatives like Global Average Pooling reduce parameters, but flattening remains fundamental for understanding CNN-FC transitions.

2. Algorithm/Approach

The core pattern is tensor reshaping: treat the 3D feature map as a contiguous block of elements and collapse spatial (H, W) and channel (C) dimensions into a single vector. This is a view operation in frameworks like PyTorch or TensorFlow, preserving all values without copying data.

# Conceptual PyTorch pattern (not exact solution)
feature_map = torch.randn(C, H, W) # 3D input
flattened = feature_map.view(-1) # Shape: (C*H*W,)

Maintain memory layout (e.g., channel-major or row-major) to ensure correct indexing for downstream FC weights.

3. Step-by-Step Strategy

PRO

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