Expanding LLM Reasoning

Many LLMs plan before they act, yet planning and execution are often still entangled in one long generation trace, enforced only through prompts, or split across separate components. We argue that these two stages call for different computation: planning benefits from diversity and breadth, whereas execution demands precision and faithful adherence to a chosen strategy. Treating them as a single undifferentiated chain wastes tokens on routine derivation and makes it costly to explore alternative strategies at test time. We present the \textbf{Explore-Execute Chain (E\textsuperscript{2}C)}, which keeps both stages in one model but separates them structurally: a stochastic \textit{Exploration} phase drafts a concise high-level plan, and a deterministic \textit{Execution} phase carries it out. Causal SFT and RL train this split so that exploration stays informative and execution remains plan-faithful. Once plans are short yet decisive, extra inference compute can be directed to exploration rather than to repeatedly decoding full solutions. On AIME'2024 at $K{=}32$, \textbf{E\textsuperscript{2}C-ReAct Loop} reaches 53.3% accuracy with only 12.4k tokens, outperforming Tree-of-Thoughts ($N{=}32$: 50.0%, 71.3k). The same structure also supports lightweight domain adaptation: \textbf{Exploration-Focused SFT (EF-SFT)} updates only the planning phase, uses 3.5% of the tokens required by standard SFT, and improves medical benchmark accuracy by up to 14.5%.

Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid proof itself, requiring a reasoning procedure in which intermediate inferences are correct. Specifically, we investigate whether LLMs can learn to generate correct and efficient proofs with guidance from A* search -- an algorithm that guarantees an optimally efficient path to a goal. We explore two training techniques: supervised fine-tuning on execution traces from A* and reinforcement learning with A*-informed process reward models. Empirically, we find that Llama-3.2 models in the 1B--3B range benefit substantially from A* post training, going from near-zero accuracy to outperforming DeepSeek-V3.2 -- a much larger model. Our analysis uncovers a trade-off: while simple correctness rewards maximize accuracy, A*-informed signals strike a balance between accuracy and efficiency. Furthermore, we find that on larger search spaces, models trained with imperfect heuristics exhibit superior accuracy. Our results demonstrate a promising direction towards reasoning guided by principles derived from classical search algorithms.