~/writing/math-foundations-for-reasoning-models $ ls
Reasoning Models as Representation Transformation
Chain of Thought
Chain of thought is a visible sequence of intermediate reasoning text, useful as a workspace but not identical to hidden reasoning.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Chain Of Thought
Definition
Chain of thought is a sequence of intermediate reasoning text.
Simple form:
step 1 -> step 2 -> step 3 -> answer
It is a way to externalize parts of a reasoning process.
Chain of thought is written intermediate reasoning.
Why It Can Help
Writing intermediate steps can help structure a task.
Examples:
break problem into parts
track assumptions
hold partial results
avoid skipping steps
make errors easier to inspect
In this sense, chain of thought can act like a scratchpad.
Chain of thought can provide visible structure for multi-step tasks.
Chain Of Thought vs Hidden Reasoning
Chain of thought is visible text.
Hidden reasoning is internal model computation.
These are not the same thing.
visible chain:
what is written
hidden reasoning:
internal representation transformations
A model may have hidden computation that is not fully shown in the visible chain.
Visible reasoning text is not the full internal process.
Faithfulness Problem
A written chain of thought may not always faithfully explain why a model produced an answer.
It may be:
useful
partial
post-hoc
incorrect
incomplete
This is why chain of thought should be treated as an artifact, not perfect transparency.
Chain of thought can help, but it is not guaranteed to be a complete explanation.
Practical Role
In reasoning systems, intermediate text can support:
decomposition
verification
self-correction
tool coordination
human review
The important concept is externalizing useful intermediate structure.
Chain of thought is one form of externalized reasoning workspace.
Final Summary
- Chain of thought is visible intermediate reasoning text.
- It can help structure multi-step tasks.
- It can act like a scratchpad.
- It is not identical to hidden reasoning.
- It is not guaranteed to be a faithful full explanation.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Hidden Reasoning