~/writing/math-foundations-for-reasoning-models $ ls
Structured Neural Architectures
Bridge to Attention
Structured architectures explain locality and recurrence; attention asks which positions should directly interact.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Bridge To Attention
Where We Are
This chapter explained how architecture shapes representation learning.
The progression was:
inductive bias -> fully connected networks -> convolution
Then local structure:
filter -> kernel -> receptive field -> pooling -> feature map
And sequence structure:
recurrence -> hidden state -> sequence modeling -> LSTM -> gates -> GRU
Structured architectures build assumptions into how information flows.
What Structured Architectures Added
Deep representations showed that layers transform information.
Structured architectures showed that the shape of those transformations matters.
Examples:
convolution:
local repeated patterns
recurrence:
ordered state updates
gates:
controlled memory updates
Architecture controls the paths available for representation building.
The Limitation Of Fixed Paths
Convolution uses local neighborhoods.
Recurrence moves through sequences step by step.
These are useful structures, but they also constrain how information moves.
Example:
faraway positions may need many steps to interact
some positions may be more relevant than nearby positions
This raises a new question.
What if the model could choose which positions matter most?
Why Attention Comes Next
Attention is a mechanism for weighting information from different positions.
Instead of only relying on fixed local windows or step-by-step recurrence, attention asks:
for this position, which other positions are relevant?
The model computes weights over information sources.
Attention makes information routing more flexible.
Bridge Question
The next chapter begins with:
what is attention?
That leads to:
self-attention
query
key
value
attention weight
scaled dot-product attention
multi-head attention
positional encoding
transformer block
Attention extends structured representation learning by allowing direct relevance-based interaction.
Final Summary
- Structured architectures encode inductive biases.
- Convolution focuses on local repeated patterns.
- Recurrence processes ordered state updates.
- LSTMs and GRUs use gates to manage sequence memory.
- These architectures shape how information moves.
- Attention asks which positions should directly influence each other.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Attention