Continuous FunctionStart learning

Foundation Lab

Tree Search over Thoughts

Makes inference like planning, not text completion

Concept 96 of 100Scaling & AlignmentPhase 13
Open notebook demoAll Foundations
#96MCTS-LLMScaling & Alignment
key equation
a∗=arg⁡max⁡a(Q(s,a)+cln⁡N(s)N(s,a))a^* = \arg\max_a \left( Q(s,a) + c\sqrt{\frac{\ln N(s)}{N(s,a)}} \right)
Reading map and next steps

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 96 of 100MCTS-LLMScaling & Alignment / Phase 13: Cutting-edge 2024-2025 research
Current question

Each node is a partial solution/thought

a∗=arg⁡max⁡a(Q(s,a)+cln⁡N(s)N(s,a))a^* = \arg\max_a \left( Q(s,a) + c\sqrt{\frac{\ln N(s)}{N(s,a)}} \right)
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

  • Makes inference like planning, not text completion
  • Enables systematic exploration of reasoning paths
  • Foundation for o1-style "System 2" thinking

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Each node is a partial solution/thought
  • Verifier provides value estimates for backpropagation
  • Trade-off: exploration (new paths) vs exploitation (best paths)

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
a∗=arg⁡max⁡a(Q(s,a)+cln⁡N(s)N(s,a))a^* = \arg\max_a \left( Q(s,a) + c\sqrt{\frac{\ln N(s)}{N(s,a)}} \right)

MCTS over reasoning states. UCB action selection:

a∗=arg⁡max⁡a(Q(s,a)+cln⁡N(s)N(s,a))a^* = \arg\max_a \left( Q(s,a) + c\sqrt{\frac{\ln N(s)}{N(s,a)}} \right)

Expand with LM policy prior πθ(a∣s)\pi_\theta(a|s). Back up values QQ from rollouts/verifier.

Key insight: Inference becomes planning, not just generation.

Canonical Papers

Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models

Zhou et al.2024ICML
Read paper →

Connections

Prerequisites

💭CoT🧠Test-Time

Next Moves

Choose the next question to carry this object forward.