Planning and Problem-Solving with General, Scalable Neuro-Symbolic Models

Abstract

Autonomous systems, including physical robots and digital agents, must reason over long horizons, satisfy complex geometric and temporal constraints, and operate robustly in dynamic, uncertain environments. Although Large Language Models (LLMs) capture broad commonsense knowledge and exhibit strong generalization, they struggle with combinatorial search, precise constraint satisfaction, and formal verification—capabilities that are essential for reliable planning in both embodied and virtual domains. This thesis argues that scalable autonomy requires tightly integrating foundation models with symbolic planning and computation-based search. This work develops a general neuro-symbolic framework that augments LLMs with formal planners, code-based reasoning, and unified learning-and-search strategies. First, it introduces methods that translate natural language instructions into formal planning abstractions, enabling models to interface with algorithmic planners and verification tools. Systems such as AutoTAMP and NL2TL convert language into temporal logic and structured planning representations that can be solved and formally checked. This approach enables robots to handle geometric and temporal constraints in task and motion planning, while allowing digital agents to solve complex scheduling and travel planning problems with rigorous guarantees. Second, it proposes Code-as-Symbolic-Planner, a scalable paradigm in which models generate executable code that functions as planners, constraint checkers, and optimization modules. Instead of relying solely on predefined solvers, agents synthesize task-specific planning logic through code, combining symbolic computation with high-level reasoning. Systems including CodeSteer, R1-Code-Interpreter, and TUMIX are developed to enable models to dynamically coordinate textual reasoning, code execution, and external tool use. These methods substantially improve success rates, efficiency, and generalization across robotic task and motion planning, multi-step digital agent planning, and complex reasoning tasks. Third, it unifies training-based adaptation with test-time search and multi-agent coordination to improve robustness and scalability. By combining supervised learning, reinforcement learning, curriculum strategies, and search-based optimization, these approaches enable both robots and digital agents to self-correct errors, refine intermediate plans, and flexibly allocate computation as task complexity grows. These methods are validated across robotic task and motion planning, multi-robot collaboration, long-horizon embodied tasks, and real-world digital planning benchmarks. Together, this thesis advances scalable neuro-symbolic agents that integrate language understanding, formal reasoning, and structured search, moving toward autonomous systems capable of robust planning, reasoning, and generalization across both physical and digital environments.