Reasoning for Math and Optimization

Model training and evaluation for mathematical reasoning, automated optimization modeling, code-integrated thinking, and video reasoning.

Reasoning systems
MathScale ORLM CALM/STORM CoRT Video-R1
Reasoning and optimization award signal

The reasoning line studies how models solve problems when correctness can be checked: math, optimization modeling, medical reasoning, code-integrated thinking, critique, and multimodal video reasoning.

Research Storyline

Math
Start with verifiable answers

MathScale and outcome-supervised verifiers use problems where correctness can be checked, giving reasoning models sharper feedback than preference alone.

Optimize
Translate language into executable models

ORLM asks models to formulate optimization problems with formal constraints, objectives, and solver-ready structure.

Compute
Let code enter the thinking loop

CoRT treats computation as part of reasoning, making intermediate steps more inspectable and less dependent on hidden mental arithmetic.

See
Extend reasoning to video and medicine

Video-R1 and HuatuoGPT-o1 show the same verifiable-reasoning idea in multimodal and medical settings.

Research Threads

MathScale and verifiers

Scaling instruction tuning and outcome-supervised verifiers for mathematical reasoning and planning.

ORLM and CALM/STORM

Large models for automated optimization modeling, where outputs must match formal constraints and executable optimization structure.

CoRT and code-integrated reasoning

Models reason with code inside the thinking process, making intermediate computation more explicit and testable.

Video-R1 and multimodal reasoning

Reinforcement-style training for video reasoning in multimodal LLMs, extending verifiable reasoning beyond text-only math.

Display Figures

Paper Trail

Math
MathScale: Scaling Instruction Tuning for Mathematical Reasoning

Studies scaling and verifier-style feedback for mathematical reasoning.

Paper
OR
ORLM: Training Large Models for Automated Optimization Modeling

Turns natural language problem descriptions into formal optimization models and solver-ready structure.

Repository
Code
CoRT: Code-integrated Reasoning within Thinking

Uses executable computation inside the reasoning process to improve reliability and inspectability.

Repository
Video
Video-R1: Reinforcing Video Reasoning in MLLMs

Transfers reasoning-style training into video understanding and multimodal LLMs.

Repository

Why It Matters

  • Reasoning models become more trustworthy when they can be trained and evaluated against verifiable constraints.
  • Optimization modeling is a bridge from natural language to executable decision-making systems.
  • Code and video reasoning show that "thinking" is not a single modality; it can involve computation, perception, and action.

Resource Map

ORLM

Customizable framework for training large models for automated optimization modeling.

Repository
CoRT

Code-integrated reasoning within thinking for models that can use computation as part of the reasoning process.

Repository
Video-R1

Reinforcing video reasoning in multimodal LLMs.

Repository