MILES: Modular Instruction Memory with Learnable Selection for Self-Improving LLM Reasoning

To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby conflates internal computation with external communication. In contrast, human cognition can use working memory to hold and manipulate information internally without the need to externalize intermediate thoughts. Drawing on this principle, we introduce Reasoning in Memory (RiM), a latent reasoning method that replaces the autoregressive generation of reasoning steps with memory blocks. These memory blocks are fixed sequences of special tokens that unlock the working-memory capacity of large language models. Since they are fixed rather than generated, they can be processed in a single forward pass, enabling compute-efficient latent reasoning. To operationalize these memory blocks, we employ a two-stage curriculum. First, we ground them by predicting explicit reasoning steps after each memory block. Second, we discard this step-level supervision and iteratively refine the final answer after each memory block. Our experiments on reasoning benchmarks show that, across language models of different families and sizes, RiM matches or exceeds existing latent reasoning methods while avoiding the autoregressive generation of thoughts. These results demonstrate that large language models can be trained to use working memory as an effective mechanism for latent reasoning.

Large language models achieve strong reasoning performance by scaling inference-time compute, yet remain fundamentally stateless, discarding the rich, self-produced reasoning traces generated during this process. We investigate whether models can instead learn online from this experience, converting transient computation (reasoning traces) into persistent reusable knowledge, and without external supervision or access to future data. We show that In-Context Learning (ICL) over raw reasoning traces fails to generalize, reflecting a fundamental limitation of token-level reuse: individual traces lack the abstraction needed for transfer, even after refinement (e.g. self-reflection). In contrast, drawing inspiration from recent works on unsupervised reinforcement learning, we find that lightweight per-instance training with self-generated test-time signals (majority voting) as rewards yields substantial gains, often surpassing full-dataset offline training, motivating a shift from raw traces to learned latent representations. Building on this insight, we propose an online method that distills inference-time compute spent on encountered problems into compact modular latent memories capturing the underlying reasoning structure. These memories are stored and retrieved for future inputs, enabling continual improvement while avoiding catastrophic forgetting through modular design. Importantly, our method is highly efficient, parametrized as extremely lightweight soft prompt memories (~0.001% of model parameters) and trained with only a few gradient steps, yet achieving performance competitive with full parametric updates and offline training. Across challenging mathematical reasoning benchmarks, our approach significantly outperforms zero-shot and raw data ICL baselines, while transferring effectively across datasets.

Test-time scaling improves LLM reasoning by using additional inference compute, but wider sampling alone can suffer from diminishing returns: new rollouts often repeat existing answer patterns instead of adding useful reasoning diversity. Verifier-based selection offers an alternative, but its performance depends on the calibration of an external reward model. We propose a verifier-free breadth--depth refinement framework that uses test-time compute to both explore and improve candidate solutions. The method samples multiple independent reasoning rollouts, refines each rollout through iterative self-critique and self-correction, and aggregates the refined answers by majority voting. Breadth preserves diverse initial attempts, while depth repairs local reasoning errors before aggregation. Across AIME24, AIME25, AMC, OlympiadBench, and MATH500, our method consistently improves over greedy decoding, majority voting, verifier-based best-of-$N$, beam search, and lookahead decoding across multiple open-weight models. For instance, with Qwen2.5-1.5B, accuracy increases from the strongest verifier-based baseline to $58.0\%$ on MATH500, and from $25.0\%$ to $32.5\%$ on AMC. These results show that test-time compute can be more effective when used to refine sampled trajectories rather than only to sample more candidates or rely on verifier-guided selection.