Why a One-Pixel Shift Can Change a CNN Prediction

Same part. Same defect. One pixel to the right—and a different prediction.

A CNN can behave this way without anything random happening. One reason is how it downsamples its feature maps.

The sampling grid matters

Stride-one convolution is translation-equivariant away from image boundaries: move the input, and the feature map moves with it. That is different from invariance, where the output stays unchanged.

Downsampling complicates this. Consider a toy feature-map row, keeping every second position:

Original:       [0, 0, 1, 0, 0, 0] → [0, 1, 0]
Shifted right:  [0, 0, 0, 1, 0, 0] → [0, 0, 0]

The peak still exists. It simply falls between the retained positions.

This illustrates the sampling step, not a complete CNN. But strided convolutions and pooling contain this step—and learned filters are not guaranteed to prevent aliasing. Zhang, 2019.

Filter before downsampling

Anti-aliasing applies a low-pass filter before reducing spatial resolution. It suppresses rapid spatial variations that the coarser grid cannot reliably represent.

For max-pooling, the BlurPool approach separates the operations: evaluate the maximum at stride one, blur the resulting feature map, then subsample. This can improve prediction consistency under small shifts. BlurPool paper.

It is not a guarantee. Nonlinearities such as ReLU can still turn small differences into different outputs, while padding creates separate boundary effects. Excessive smoothing can also sacrifice useful detail. Chaman & Dokmanić, 2021.

What I’d test in an inspection system

Before changing the architecture, I’d compare predictions across small horizontal and vertical shifts:

• Keep the defect fully visible; document cropping and padding.

• Measure score changes and pass/fail disagreements.

• Check tiny defects separately when evaluating anti-aliasing.

A consistent prediction can still be consistently wrong, so stability must be checked alongside accuracy.

A one-pixel shift is a small input change—not automatically a small computational change.