Symbolic regression (SR) seeks to discover parsimonious mathematical laws from observational data, yet conventional approaches often struggle with the vast combinatorial search space of physically meaningful expressions. We present InsightSR, a framework that embeds Large Language Models (LLMs) as a guiding layer around the PySR genetic programming engine. Rather than relying on LLMs to generate expressions directly, InsightSR uses LLMs to progressively transform the search space itself through two complementary pathways: a Semantic Seed Pathway that proposes dimensionally consistent functional skeletons, and a Structural Feature Pathway that recommends nonlinear feature transformations. These transformations accumulate over iterations, broadening the input space and shifting the symbolic search from constructing deep expression trees over raw variables to assembling shallow trees over a rich, semantically informed feature set. A post-generation feedback loop evaluates candidates, categorizes features by their empirical utility, and refines the guidance for the next iteration, transforming the discovery process from open-ended generation into iterative, self-correcting refinement. Across three benchmarks, InsightSR achieves a 95% exact recovery rate on the Feynman benchmark and 80.18% accuracy on the LLM-SRBench LSR-Transform task, substantially outperforming state-of-the-art genetic programming and neural-symbolic methods while maintaining strong out-of-distribution generalization on real-world datasets.
In dynamic multi-mode project scheduling, activities have alternative execution modes and uncertain durations, while precedence relations and limited resources constrain their execution. Heuristic priority rules support fast online decisions, but their design requires substantial domain expertise. Genetic programming (GP) hyper-heuristics can automatically evolve such rules. Large language models (LLMs), meanwhile, provide a flexible interface for interpreting scheduling information and explaining decisions. However, zero-shot LLM decisions may lack domain knowledge, consume many tokens, and vary across repeated queries. GP-evolved rules therefore provide a potential source of scheduling knowledge for guiding LLM decisions. Unlike existing LLM--GP hybrids that use LLMs to support heuristic evolution, we transfer knowledge in the reverse direction, using knowledge extracted from high-quality GP rules to guide an online LLM decision maker. We extract knowledge from high-quality GP rules and inject it through Feature Selection, Feature Hint, Rule Reference, and Rule Follow. These mechanisms are evaluated in terms of scheduling performance, token consumption, decision stability, and the feature focus expressed in generated rationales. GP-derived guidance generally improves the unguided LLM, but its representation matters. Simplifying the decision context or supplying explicit decision logic is more effective than highlighting important features. Feature Selection offers the best token efficiency, whereas Rule Follow achieves strong performance at greater token cost. Guidance also improves decision stability and changes the features expressed in generated rationales.
Sparse rewards and heterogeneous task sequences remain persistent challenges in Reinforcement Learning (RL), often resulting in slow convergence, weak generalization, and inefficient exploration. We propose Uncertainty-Aware LLM-Guided Policy Shaping (ULPS), a novel framework that integrates a calibrated Large Language Model (LLM) into the RL training loop to provide structured, uncertainty-modulated behavioral guidance. ULPS employs an A*-based oracle to synthesize optimal symbolic trajectories, which are used to fine-tune a BERT-based language model. During training, this model supplies action suggestions whose influence is conditioned on epistemic uncertainty estimated via Monte Carlo (MC) dropout. An entropy-based blending mechanism adaptively balances LLM guidance and the learned policy (via Proximal Policy Optimization, PPO), allowing the agent to prioritize reliable priors while preserving adaptability. We evaluate ULPS on the MiniGridUnlockPickup benchmark and observe consistent improvements in success rate, reward efficiency, and sample complexity over unguided, uncalibrated, and standard RL baselines. ULPS achieves more than 9% improvement in execution accuracy after fine-tuning, requires fewer environment interactions, and yields higher reward AUC. Our results demonstrate that integrating symbolic A* trajectories, pretrained language priors, and uncertainty-aware control offers a principled and effective approach to multi-task reinforcement learning in sparse-reward domains, with potential extensibility to partially observable and multi-agent settings.