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How Reasoning Models Work

By Kai Bergin

Reasoning chat
Visible chat
User

Explain how photosynthesis works in simple terms.

Assistant

Photosynthesis is how plants make food. They use sunlight, water, and carbon dioxide to make sugar, and they release oxygen as a by-product.

The demo currently compares 4 candidate paths and verifies the clearest explanation.

Model work area
Reasoning controller Medium reasoning effort
56 reasoning tokens 4 candidate paths 82% chance at least one path is useful
Reasoning-token budget
Candidate paths sampled

How the chat becomes reasoning

The visible answer comes from a path-selection loop

The chat prompt starts the process, the model work area creates and checks candidate paths, and the math below explains why sampling several diverse routes can improve the chance of finding a useful one.

Candidate-path math

Why More Candidate Paths Help

A single sampled path can be correct, incomplete, or misleading. If one candidate path has probability p of being useful, the probability that it fails is 1 - p. With n candidate paths, this simplified model treats each path as an independent chance to find a useful route.

The chance that all candidate paths fail is (1 - p)n. Therefore the chance that at least one path is useful is:

1 - (1 - p)n

In real models, paths are not perfectly independent. The formula is a teaching approximation: diversity plus verification is what makes extra reasoning useful.

Change either value and the chat demo above updates: more routes appear, the probability label changes, and the candidate path cards rebalance.

At least one useful path: 82% 1 - (1 - 0.35)^4 = 0.82

Verification still matters: extra paths only help when the system can identify which candidate is accurate, relevant, and clear.

How Reasoning Models Work

Reasoning paths, search, and verification

Step 2: Generate Reasoning Paths

How token-by-token generation creates multiple candidate solutions

1

Tokenise
the prompt

Prompt:

"Explain how photosynthesis works in simple terms."

Explainhowphotosynthesis worksinsimpleterms.

(tokens)

2

Predict next-token
probabilities

Next-token candidates

3

Sample or choose
a token

Selected token

It

Path A begins with this token.

4

Extend
the sequence

Sequence grows token by token

5

Create multiple
reasoning paths

Different token sequences become different paths

  • Tokens are the model's basic units.
  • Each next token is predicted from previous context.
  • Different token sequences become different reasoning paths.

Step 3: Search / Explore

The model explores alternative token continuations and solution routes

1

Start from
current context

User question

Explainhowphotosynthesisworkssimply

"Explain how photosynthesis works in simple terms."

2

Expand possible
next tokens

Candidate next tokens

PlantsSunlightWaterSugarOxygen

Several likely continuations remain available instead of choosing only one.

3

Branch into
continuations

Token paths

Click a path to see how the route reader evaluates it.

4

Explore promising
routes

Selected route

Explore promising routes

This branch explains how chlorophyll captures sunlight, a useful route for the photosynthesis answer.

route score 0.84
5

Keep diverse
options alive

Completion stays grounded

Photosynthesis is how plants make food.

The selected path keeps sunlight, water, carbon dioxide, sugar, and oxygen together in the final answer.

  • Search tests different continuations.
  • Branches represent different reasoning routes.
  • Diversity helps the model avoid getting stuck.

Step 4: Verify

Candidate completions are checked against facts, prompt constraints, and tests

1

Extract the final answer

2

Run checks or tests

Plants use sunlight, water, and carbon dioxide to make sugar, releasing oxygen.

Candidate completion under test.

3

Compare with rules or facts

Science factsOK
Required inputsOK
Outputs namedOK
Misconception testOK
Simple wordingOK
4

Mark pass or fail

PASS
5

Assign a score or reward

1.00 High
  • Verification checks the outcome, not just the wording.
  • Clear tests make reasoning measurable.
  • Scores tell the model which paths worked.

Step 5: Select Best Answer

The highest-quality verified path is chosen for the final response

1

Collect candidates

Gather the candidate photosynthesis completions.

2

Compare verification scores

4

Choose the best verified path

Path A has the strongest verified photosynthesis answer.

5

Return final answer

Plants use sunlight, water, and carbon dioxide to make sugar, releasing oxygen.

Chosen from Path A (score: 1.00)

  • The model may generate many candidates.
  • Verification helps identify the strongest one.
  • The selected path becomes the final answer.

Step 6: Learn from Success

Offline post-training uses feedback to improve future model versions

During normal use: search, verify, select — no weight updates during one query
During post-training: feedback can update a future model version
1

Collect outcomes

Save examples from many tasks, including the photosynthesis answer.

Successful sunlightwaterCO2sugar
Weak eat sunlightsoil foodmissing oxygen
2

Score or verify

Use verifiers, preference data, or benchmark scoring.

✓ correct science ✓ simple wording × misconception
reward = 1 if useful, 0 otherwise
3

Update model weights

Offline training adjusts the model. This does not happen inside the user query.

4

Create improved version

Useful patterns become more likely; weak patterns become less likely.

Probability up
Weak patterns down
5

Deploy and improve future reasoning

Later model versions are more likely to keep the correct photosynthesis pattern.

sunlightwaterCO2sugaroxygen
offline loop 0

What happens during a single query

QuestionSearchVerifyAnswer

The current answer can improve through reasoning, but the model does not permanently learn here.

How labs improve models over time

Fast loop prompts and tools Medium loop preference data and fine-tuning Slow loop new base-model training runs
  • Reasoning models usually do not reward themselves during normal operation.
  • Weight updates happen in offline post-training loops.
  • User interactions can inform later model updates, not instant learning.