~/writing/math-foundations-for-reasoning-models $ ls
Structured Neural Architectures
Sequence Modeling
Sequence modeling learns patterns in ordered data where earlier and later elements can depend on each other.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Sequence Modeling
Definition
Sequence modeling is learning from ordered data.
In a sequence, position matters.
Examples:
words in a sentence
measurements over time
events in a log
audio samples
Sequence modeling focuses on data where order carries information.
Why Order Matters
Changing the order can change the meaning or pattern.
Example:
dog bites man
man bites dog
The same words appear, but the order changes the relationship.
For time series, an earlier event can affect a later event.
Sequence models need to represent order and dependency.
Local And Long Context
Some sequence patterns are local.
nearby elements matter most
Other patterns depend on longer context.
earlier element affects much later element
Architectures differ in how they handle these dependencies.
Sequence modeling must decide how information moves across positions.
Recurrence For Sequences
Recurrent models process sequences step by step.
step 1 -> state 1
step 2 -> state 2
step 3 -> state 3
The hidden state carries information forward.
This gives recurrence a natural connection to sequence modeling.
Recurrence models sequence order through repeated state updates.
Final Summary
- Sequence modeling learns from ordered data.
- Position matters in sequences.
- Earlier and later elements can depend on each other.
- Some dependencies are local; others are long-range.
- Recurrent models process sequences through hidden state updates.
- Sequence architectures differ in how they move information across positions.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
LSTM