Receptive Fields in Convolutional Networks

Why Location Matters

A convolutional network may detect a useful feature in one part of an image, while the same kind of feature may appear somewhere else. A deep network therefore benefits from depending less on the exact position where a feature was detected. Subsampling helps by combining nearby feature-map values into a lower-resolution representation.

From Four Values to One

A subsampling layer examines local groups in a feature map. For a non-overlapping 2 × 2 receptive field, the group contains four neighboring values. The subsampling unit replaces those four spatially separate values with one average. This output therefore summarizes a region instead of preserving four separate positions.

Tracing Receptive Fields

The word preceding is important. The receptive field is defined relative to the feature map immediately before the subsampling layer. Each output unit summarizes one region of that earlier feature map. Repeating the same operation across the map creates a new, smaller feature map made of regional summaries.

Lower Spatial Resolution

Because each non-overlapping 2 × 2 region becomes one output value, the new feature map contains fewer spatial positions than the preceding feature map. The source describes a first subsampling layer in which each unit in each of six feature maps averages a 2 × 2 receptive field from a feature map produced by the first convolutional layer. The six resulting feature maps have a spatial size of 14 × 14.

This reduction changes how position is represented. The output no longer keeps every value at the original spatial resolution. Instead, each output position summarizes one local region of the earlier map.

Reduced Location Sensitivity

Suppose a useful feature moves within a local region covered by one subsampling receptive field. The subsampling layer combines the nearby feature-map values into one regional summary. Since the result represents the region rather than preserving every separate position, the network response becomes less sensitive to the feature's exact location.

The benefit is not that the network forgets all spatial information. The benefit is that small changes in feature location matter less after nearby values have been combined and represented at lower resolution.

Limits of Invariance

Subsampling makes responses less sensitive to where a feature appears, but the source describes this as reduced sensitivity to small changes in feature location. That wording is different from saying that the response is completely invariant to location. Subsampling addresses local positional variation by combining nearby values; it does not establish that every possible location produces exactly the same response.

Misunderstandings to Avoid

• Treating a subsampling unit as if it received only one preceding feature-map value.

  A subsampling unit receives the values in its receptive field and replaces their local group with an average.

  Fix: Track the full non-overlapping 2 × 2 region that contributes to the unit.

• Assuming subsampling preserves the original spatial resolution.

  Several local positions are replaced by one summary position, producing a lower-resolution feature map.

  Fix: Think in terms of regional summaries and fewer spatial positions.

• Calling lower sensitivity complete spatial invariance.

  The source describes reduced sensitivity to small changes in feature location, not complete independence from location.

  Fix: Say that subsampling reduces dependence on exact local position.

• Focusing on the particular numbers in the averaging example instead of the mechanism.

  Those values illustrate the operation; the important idea is replacing a local group with one average.

  Fix: Focus on the mapping from several nearby values to one regional summary.

Check Your Understanding

Key Takeaways

1. Subsampling replaces local groups of feature-map values with averaged summaries.
2. A receptive field identifies the preceding feature-map values that contribute to one subsampling unit.
3. Non-overlapping 2 × 2 receptive fields reduce spatial resolution by representing each local region with one output value.
4. Lower spatial resolution makes responses less sensitive to small changes in feature location.
5. Reduced location sensitivity is not the same as complete spatial invariance.