Unifying Neural and Symbolic Decision Making

Key Challenges with LLMs

• Difficulty with tasks requiring complex planning (e.g., travel itineraries, meeting schedules).
• Performance declines with increasing task complexity (e.g., more cities, people, or constraints).

Three Proposed Solutions

1. Scaling Law
   • Increase data, compute, and model size.
   • Limitation: High costs and diminishing returns for reasoning/planning tasks.
2. Hybrid Systems
   • Combine deep learning models with symbolic solvers. Symbolic reasoning refers to the process of solving problems and making decisions using explicit symbols, rules, and logic. It is a method where reasoning is based on clearly defined relationships and representations, often following formal logic or mathematical principles.
   • Approaches:
     • End-to-End Integration: Unified deep model and symbolic system.
     • Data Augmentation: Neural models provide structured data for solvers.
     • Tool Use: LLMs act as interfaces for external solvers.
   • Notable Examples:
     • MILP Solvers: For travel planning with constraints.
     • Searchformer: Transformers trained to emulate A* search.
     • DualFormer: Switches dynamically between fast (heuristic) and slow (deliberative) reasoning.
     • SurCo: Combines combinatorial optimization with latent space representations.
3. Emerging Symbolic Structures
   • Exploration of symbolic reasoning emerging in neural networks.
   • Findings:
     • Neural networks exhibit Fourier-like patterns in arithmetic tasks.
     • Gradient descent produces solutions aligned with algebraic constructs.
     • Emergent ring homomorphisms and symbolic efficiency in complex tasks.

Research Implications

• Neural networks naturally learn symbolic abstractions, offering potential for improved reasoning.
• Hybrid systems might represent the optimal balance between adaptability (neural) and precision (symbolic).
• Advanced algebraic techniques could eventually replace gradient descent.

Overall Takeaway

The future of decision-making AI lies in leveraging both neural adaptability and symbolic rigor. Hybrid approaches appear most promising for solving tasks requiring both perception and structured reasoning.