Convolutional Feature Maps
Subsampling replaces local groups of feature-map values with averaged summaries. The result has fewer spatial positions and is less sensitive to small changes in feature location.
Why Subsample Feature Maps
A convolutional network may detect a useful feature in one part of an image, but the same kind of feature can also appear somewhere else. If later layers depend too strongly on the exact position of the detection, the network becomes less useful when that feature shifts slightly. Subsampling addresses this by combining nearby feature-map values into lower-resolution summaries.
Subsampling replaces local groups of feature-map values with averaged summaries. The result has fewer spatial positions and is less sensitive to small changes in feature location.
From Receptive Fields to Summaries
A receptive field identifies which preceding units contribute to one unit in the subsampling layer. With non-overlapping 2 × 2 receptive fields, each subsampling unit receives four nearby values from a feature map produced by the preceding convolutional layer. It averages those four values and stores the result as one value in the new feature map.
The diagram shows the essential mapping: four neighboring positions in the earlier feature map contribute to one position in the subsampled map. A different, non-overlapping group contributes to the neighboring output position. The output therefore describes regions rather than preserving every original position separately.
Averaging One Local Region
One 2 × 2 Receptive Field
A 2 × 2 receptive field contains the values 2, 4, 6, and 8. What value does the subsampling unit produce?
- 1Collect the local values
The receptive field supplies four values: 2, 4, 6, and 8.
- 2Combine the values
The subsampling unit averages the four values rather than keeping them as four separate spatial values.
- 3Interpret the result
The resulting summary value is 5. It represents the local region with one value.
The subsampling unit produces the average value 5.
The important point is not the particular numbers. Repeating this operation across non-overlapping local regions creates a smaller feature map. Each output position summarizes one receptive field from the preceding map.
How Resolution Decreases
Replacing each non-overlapping 2 × 2 group with one value reduces the number of spatial positions in both dimensions. This is why the output has lower spatial resolution. In the first subsampling layer described in the source, each unit in each of six feature maps averages a 2 × 2 receptive field from a feature map produced by the first convolutional layer, and the six resulting feature maps have a spatial size of 14 × 14.
Subsampling does not create more spatial detail. It trades separate local positions for averaged regional summaries.
Location Sensitivity After Averaging
A feature that moves slightly within the region covered by the same receptive field can still contribute to the same averaged summary. Because nearby values are combined, the response depends less on the feature's exact position than it would if every position were kept separately. This gives the network reduced sensitivity to small changes in feature location.
| Spatial information | Effect of subsampling |
|---|---|
| Regional response | Preserved as an averaged summary |
| Exact position within a receptive field | Less influential because nearby values are combined |
| Every original spatial position | Not preserved as a separate output position |
| Small feature-location changes | Responses become less sensitive to them |
Subsampling reduces dependence on exact position by replacing local groups with summaries.
Common Misunderstandings
Common mistake Treating a receptive field as one input value
What it looks likeDescribing a subsampling unit as if it reads only one position from the preceding feature map.
Why it failsA receptive field defines the group of preceding units that contribute to one subsampling unit. With a 2 × 2 receptive field, four nearby values contribute.
Do this insteadTrace the complete local group before describing the output value.
Common mistake Assuming subsampling keeps the same spatial resolution
What it looks likeExpecting every original feature-map position to remain as a separate position in the output.
Why it failsNon-overlapping 2 × 2 groups are replaced by one average each, producing a lower-resolution feature map.
Do this insteadCount local groups and remember that each group maps to one output summary.
Common mistake Calling subsampling complete location invariance
What it looks likeClaiming that the network will respond identically regardless of where a feature appears.
Why it failsThe source describes reduced sensitivity to exact position and small changes in feature location, not the preservation of all responses as identical.
Do this insteadUse the more precise description: subsampling makes responses less sensitive to feature location.
Common mistake Thinking averaging preserves all local detail
What it looks likeInterpreting the average of four values as four independently available output values.
Why it failsThe local group is represented by one summary value rather than four separate spatial values.
Do this insteadDistinguish the regional summary from the original individual positions.
Check Your Understanding
Explain, in your own words, how a non-overlapping 2 × 2 receptive field changes a feature map. Include what happens to the four local values, what happens to spatial resolution, and why the resulting response is less sensitive to a small shift within that local region.
Hints
- Start by identifying the four preceding values that contribute to one subsampling unit.
- State that the four values are replaced by one averaged summary.
- Connect the smaller number of output positions to lower spatial resolution.
- Explain that nearby feature locations can contribute to the same regional summary.
Key Takeaways
- A subsampling layer averages local groups of values from a preceding feature map.
- A receptive field specifies which preceding units contribute to one subsampling unit.
- Non-overlapping 2 × 2 receptive fields replace four local positions with one summary and reduce spatial resolution.
- Averaging nearby values makes responses less sensitive to small changes in feature location.
- Reduced sensitivity to position is not the same as complete location invariance or preservation of every original spatial detail.