Formalize, Don't Optimize: The Heuristic Trap in LLM-Generated Combinatorial Solvers

Large Language Models (LLMs) struggle to solve complex combinatorial problems through direct reasoning, so recent neuro-symbolic systems increasingly use them to synthesize executable solvers. A central design question is how the LLM should represent the solver, and whether it should also attempt to optimize search. We introduce CP-SynC-XL, a benchmark of 100 combinatorial problems (4,577 instances), and evaluate three solver-construction paradigms: native algorithmic search (Python), constraint modeling through a Python solver API (Python + OR-Tools), and declarative constraint modeling (MiniZinc + OR-Tools). We find a consistent representational divergence: Python + OR-Tools attains the highest correctness across LLMs, while MiniZinc + OR-Tools has lower absolute coverage despite using the same OR-Tools back-end. Native Python is the most likely to return a schema-valid solution that fails verification, whereas solver-backed paths preserve higher conditional fidelity. On the heuristic axis, prompting for search optimization yields only small median speed-ups (1.03-1.12x) and a strongly bimodal effect: many instances slow down, and correctness drops sharply on a long tail of problems. A paired code-level audit traces these regressions to a recurring heuristic trap. Under an efficiency-oriented prompt, the LLM may replace complete search with local approximations (Python), inject unverified bounds (Python + OR-Tools), or add redundant declarative machinery that overwhelms or over-constrains the model (MiniZinc + OR-Tools). These findings support a conservative design principle for LLM-generated combinatorial solvers: use the LLM primarily to formalize variables, constraints, and objectives for verified solvers, and separately check any LLM-authored search optimization before use.

Variational Prefix Tuning for Diverse and Accurate Code Summarization Using Pre-trained Language Models

Recent advancements in source code summarization have leveraged transformer-based pre-trained models, including Large Language Models of Code (LLMCs), to automate and improve the generation of code summaries. However, existing methods often focus on generating a single high-quality summary for a given source code, neglecting scenarios where the generated summary might be inadequate and alternative options are needed. In this paper, we introduce Variational Prefix Tuning (VPT), a novel approach that enhances pre-trained models' ability to generate diverse yet accurate sets of summaries, allowing the user to choose the most suitable one for the given source code. Our method integrates a Conditional Variational Autoencoder (CVAE) framework as a modular component into pre-trained models, enabling us to model the distribution of observed target summaries and sample continuous embeddings to be used as prefixes to steer the generation of diverse outputs during decoding. Importantly, we construct our method in a parameter-efficient manner, eliminating the need for expensive model retraining, especially when using LLMCs. Furthermore, we employ a bi-criteria reranking method to select a subset of generated summaries, optimizing both the diversity and the accuracy of the options presented to users. We present extensive experimental evaluations using widely used datasets and current state-of-the-art pre-trained code summarization models to demonstrate the effectiveness of our approach and its adaptability across models.