Proposal: Implement CoRT (Code-integrated Reasoning within Thinking) Approach

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Proposal: Implement CoRT (Code-integrated Reasoning within Thinking) Approach

Summary

Implement a new approach inspired by the CoRT paper that combines our existing thinkdeeper and z3 capabilities to create more efficient mathematical reasoning with strategic code integration.

Background

The CoRT paper demonstrates that Large Reasoning Models can be significantly improved by strategically integrating code execution within their thinking process, rather than treating code execution as a separate step. The key insight is using "hint-engineering" to guide models on when and how to use computational tools efficiently.

Proposal

Create a new cort approach that combines our existing capabilities:

Core Implementation Strategy

1. Base Framework: Use thinkdeeper as the foundation since it already implements thinking with <think> tags and reasoning patterns

2. Strategic Z3 Integration: Instead of using z3 as a separate approach, integrate Z3 calls within the thinking process by:

   • Detecting when the model attempts complex mathematical operations manually
   • Inserting strategic hints like "This looks tedious, let's use Z3 to solve this systematically"
   • Automatically triggering Z3 solver for appropriate mathematical/logical problems

3. Hint-Engineering Logic: Implement detection patterns for:

   • Delayed computation: When model starts manual calculation of complex math
   • Result distrust: When model wants to verify computational results manually
   • Insert appropriate hints to redirect to Z3 usage

4. Trust Enhancement: Add hints like "We don't need to doubt the accuracy of Z3 calculations" to prevent unnecessary manual verification

Expected Benefits

Based on the CoRT paper results:

• Performance: 4-8% accuracy improvements on mathematical reasoning tasks
• Efficiency: 30-50% token reduction by avoiding redundant manual calculations
• Better Code Usage: More strategic use of computational tools vs. verification-heavy patterns

Implementation Plan

1. Create basic cort.py module that wraps thinkdeeper with Z3 integration points
2. Implement mathematical operation detection and hint insertion logic
3. Add result trust mechanisms and optimize hint placement
4. Testing and optimization on mathematical reasoning benchmarks

Integration with Existing Code

The approach would:

1. Use thinkdeeper's thinking framework
2. Monitor the thinking process for mathematical operations
3. Strategically insert Z3 solver calls with appropriate hints
4. Prevent unnecessary manual verification of computational results

Technical Considerations

• Leverage existing thinkdeeper.py configuration system for thinking parameters
• Reuse z3_solver.py Z3SymPySolverSystem for mathematical problem solving
• Add new hint detection and insertion logic specific to mathematical reasoning
• Maintain compatibility with existing optillm plugin architecture

Rationale

This approach would be novel because:

• Synergy: Combines reasoning-focused thinking with precise computation in a integrated way
• Efficiency: Addresses the core inefficiencies identified in the CoRT paper
• Leverages Existing: Builds on our already implemented thinkdeeper and z3 capabilities
• Strategic: Uses hints to guide optimal tool usage rather than naive integration