Inference-Time Code Selection via Symbolic Equivalence Partitioning

"Best-of-N" selection is a popular inference-time scaling method for code generation using Large Language Models (LLMs). However, to reliably identify correct solutions, existing methods often depend on expensive or stochastic external verifiers. In this paper, we propose Symbolic Equivalence Partitioning, a selection framework that uses symbolic execution to group candidate programs by semantic behavior and select a representative from the dominant functional partition. To improve grouping and selection, we encode domain-specific constraints as Satisfiability Modulo Theories (SMT) assumptions during symbolic execution to reduce path explosion and prevent invalid input searches outside the problem domain. At N=10, our method improves average accuracy over Pass@1 from 0.728 to 0.803 on HumanEval+ and from 0.516 to 0.604 on LiveCodeBench, without requiring any additional LLM inference beyond the initial N candidate generations.

SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology

Reinforcement learning has become central to improving large reasoning models, but its success still relies heavily on verifiable rewards or labeled supervision. This limits its applicability to open ended domains where correctness is ambiguous and cannot be verified. Moreover, reasoning trajectories remain largely unconstrained, and optimization towards final answer can favor early exploitation over generalization. In this work, we ask whether general reasoning ability can be improved by teaching models how to think (the structure of reasoning) rather than what to produce (the outcome of reasoning) and extend traditional RLVR to open ended settings. We introduce structure aware reinforcement learning (SARL), a label free framework that constructs a per response Reasoning Map from intermediate thinking steps and rewards its small world topology, inspired by complex networks and the functional organization of the human brain. SARL encourages reasoning trajectories that are both locally coherent and globally efficient, shifting supervision from destination to path. Our experiments on Qwen3-4B show SARL surpasses ground truth based RL and prior label free RL baselines, achieving the best average gain of 9.1% under PPO and 11.6% under GRPO on math tasks and 34.6% under PPO and 30.4% under GRPO on open ended tasks. Beyond good performance, SARL also exhibits lower KL divergence, higher policy entropy, indicating a more stable and exploratory training and generalized reasoning ability.