~/writing/math-foundations-for-reasoning-models $ ls
Structured Neural Architectures
Receptive Field
A receptive field is the part of the input that can affect a particular hidden value or output value.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Receptive Field
Definition
A receptive field is the part of the input that can influence a particular value in the network.
Example:
one hidden value depends on a small local region
that local region is its receptive field
A receptive field defines what input region a computed value can see.
Local Receptive Fields
In convolution, each output value often depends on a local input region.
Example:
output at position 5
depends on input positions 4, 5, and 6
That local input region is the receptive field.
Convolution gives each output a local view of the input.
Receptive Field Can Grow
Stacking layers can increase the effective receptive field.
Example:
layer 1 sees small local regions
layer 2 combines layer 1 outputs
layer 2 indirectly sees a larger input region
This lets deeper layers combine broader context.
Depth can expand how much input context later values depend on.
Why It Matters
Some tasks need local information.
Some tasks need wider context.
The receptive field affects what information a layer can use.
small receptive field -> local detail
large receptive field -> broader context
Receptive field controls the scope of information available to a value.
Final Summary
- A receptive field is the input region that affects a computed value.
- Convolution often creates local receptive fields.
- Deeper layers can have larger effective receptive fields.
- Small receptive fields focus on local detail.
- Larger receptive fields capture broader context.
- Architecture affects what each value can see.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Pooling