~/tedtes/writing/math-foundations-for-reasoning-models

~/writing/math-foundations-for-reasoning-models $ ls

Structured Neural Architectures

Feature Map

A feature map records where and how strongly a learned filter responds across an input.

~/writing/math-foundations-for-reasoning-models $ cat topic.md

Feature Map

Definition

A feature map is the output produced by applying a filter across an input.

Basic pattern:

input -> filter -> feature map

Each value in the feature map is a response.

A feature map shows where a learned pattern appears.


What Values Mean

A feature map value measures how strongly the filter responded at a position.

Example:

high value -> strong match
low value -> weak match

The feature map keeps this response across many positions.

Feature maps preserve pattern strength by location.


Multiple Feature Maps

A convolutional layer usually has multiple filters.

Each filter produces its own feature map.

Example:

filter 1 -> feature map 1
filter 2 -> feature map 2
filter 3 -> feature map 3

Together, these maps represent multiple learned signals.

Multiple feature maps store multiple pattern responses.


Feature Map As Representation

A feature map is an internal representation.

It is not the final answer by itself.

It gives later layers structured information.

input -> feature maps -> later layers -> output

Later layers can combine feature maps into more task-relevant representations.

Feature maps are intermediate structured representations.


Final Summary

  • A feature map is produced by applying a filter across an input.
  • It stores response strength at positions.
  • High values mean stronger filter response.
  • Multiple filters produce multiple feature maps.
  • Feature maps are internal representations.
  • Later layers combine feature maps into higher-level signals.

~/writing/math-foundations-for-reasoning-models $ open

Continue the series.

Recurrence