~/writing/math-foundations-for-reasoning-models $ ls
Reasoning Models as Representation Transformation
Search
Search is the exploration of possible states, steps, plans, or answers before choosing a path forward.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Search
Definition
Search is the exploration of possible options.
Simple form:
current state -> possible next states -> selected path
In reasoning models, search can apply to answers, plans, tool calls, or intermediate steps.
Search explores possible paths before choosing one.
Why Search Is Needed
Some tasks have many possible paths.
Examples:
multiple solution strategies
many possible tool calls
different interpretations
several candidate answers
The model or system may need to compare alternatives.
Search helps when the next step is not obvious.
Search Space
The search space is the set of possible options being explored.
Examples:
possible answers
possible plans
possible actions
possible program edits
possible proof steps
A larger search space can be more powerful but also more expensive.
Search space defines what can be considered.
Search Is Not Always Exhaustive
A reasoning model usually cannot explore every possible path.
It may use limited search.
Examples:
consider a few candidates
sample alternatives
rank likely options
use heuristics
This makes search practical but imperfect.
Search often explores enough to help, not everything possible.
Search And Verification
Search produces candidates.
Verification checks candidates.
Simple flow:
generate options -> evaluate options -> choose or revise
This combination is stronger than generation alone.
Search is more useful when paired with evaluation.
Final Summary
- Search explores possible paths.
- It can apply to answers, plans, steps, or tool calls.
- The search space defines available options.
- Search is usually limited, not exhaustive.
- Search works best with verification.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Verification