Continuous FunctionStart learning

Foundation Lab

Process Reward Models

Key to o1-style reasoning: verify each step, not just the answer

Concept 81 of 100Scaling & AlignmentPhase 11
Open notebook demoAll Foundations
#81PRMsScaling & Alignment
key equation
RPRM=∏kP(step k correct)R_{PRM} = \prod_k P(\text{step } k \text{ correct})
Reading map and next steps

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 81 of 100PRMsScaling & Alignment / Phase 11: Frontier research & scaling
Current question

Outcome is sparse feedback; process is dense—better credit assignment

RPRM=∏kP(step k correct)R_{PRM} = \prod_k P(\text{step } k \text{ correct})
PredictionCommit before the demo.

Ask what should change when the equation is manipulated, then use the linked notebook demo to test that expectation.

EvidenceCompare the linked witness and source.

Use the linked notebook demo, this key equation, and canonical papers as separate witnesses for the same object.

InvariantName what survives notation changes.

The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.

Next moveContinue in the newer notebook.

This atlas page has no local demo; the domain notebook carries the interactive witness and the fuller Intuition -> Math -> Code -> Demo sequence.

Open notebook demoInspect equationOpen newer notebookNext foundation

Why It Matters for Modern Models

  • Key to o1-style reasoning: verify each step, not just the answer
  • Better for math/code: catches errors before they compound
  • Enables reliable search over reasoning paths

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Outcome is sparse feedback; process is dense—better credit assignment
  • PRMs need step-level labels—expensive but informative
  • Wrong final answer could mean 1 wrong step or 10; PRM tells you which

Visualization Status

Core Math (Optional Deep Dive)

If you want intuition first, start with the key equation here and the linked notebook demo. Come back here for the full walkthrough.

Key Equation
RPRM=∏kP(step k correct)R_{PRM} = \prod_k P(\text{step } k \text{ correct})

Outcome RM: Score final answer: RORM(y)=P(correct)R_{ORM}(y) = P(\text{correct})

Process RM: Score each step:

RPRM(s1,...,sK)=∏k=1KP(step sk correct)R_{PRM}(s_1, ..., s_K) = \prod_{k=1}^K P(\text{step } s_k \text{ correct})

Best-of-N with PRM: Reject solutions with any incorrect step:

y∗=arg⁡max⁡ymin⁡kRPRM(s1,...,sk)y^* = \arg\max_{y} \min_{k} R_{PRM}(s_1, ..., s_k)

Canonical Papers

Let's Verify Step by Step

Lightman et al.2023arXiv
Read paper →

Connections

Prerequisites

⚖RLHF🧠Test-Time

Next Moves

Choose the next question to carry this object forward.