Organizations: Department of Computer Science University of Bath · Department of Psychology University of Bath
Abstract
We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying on temperature or sampling heuristics to induce diversity, OLLM models variation explicitly: a small latent space parametrizes multiple plausible next-token options which can be selected or searched by a downstream policy. Architecturally, OLLM is a lightweight "plug-in" that inserts two layers: an encoder and a decoder, before the output head, allowing almost any pretrained LLM to be converted with minimal additional parameters. We apply OLLM to a 1.7B-parameter backbone (only 1.56% of parameters trainable) trained on OpenMathReasoning and evaluated on OmniMath. The SOTA LoRA-adapted baselines peak at 51% final answer correctness, while OLLM's option set allows up to ∼70% under optimal latent selection. We then train a compact policy in the latent space that emits latents to control generation. Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses. Our results demonstrate that optionized next-token modeling enhances controllability, robustness, and efficiency in math reasoning, and highlight latent-space policy learning as a promising direction for reinforcement learning in LLMs.
Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.
Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.
Large reasoning models (LRMs) have attracted increasing attention for their ability to solve complex mathematical problems by generating extended reasoning chains. In this work, we focus on two critical yet underexplored aspects of the reasoning process: reasoning transitions capturing the distinct transitions between reasoning steps and answer candidates reflecting the variety of solution paths produced by the model. We collectively define these two aspects as thinking schemata. We observe a correlation between the diversity of thinking schemata and model performance, which motivates us to enhance diversity as a means to further improve reasoning potential. To this end, we propose Diverse Schemata Policy Optimization (DiScO), a framework that first endows the model with schemata awareness, then encourages diversity through reinforcement learning, and further promotes diverse reasoning at inference time. Experiments on multiple mathematical reasoning benchmarks demonstrate that DiScO consistently outperforms standard group relative policy optimization. Beyond accuracy, human-annotated analyses show that DiScO substantially improves the model's ability to recover from erroneous initial attempts. Overall, our work suggests the important role that diversity of the thinking schemata plays and points to scaling along the diversity dimension as a promising research direction.