CPU-ARC: Agentic Reasoning Caching for on-CPU Reasoning Reuse

Scaling test-time reasoning has substantially improved the problem-solving ability of large language models (LLMs), but standard autoregressive decoding still executes long reasoning traces sequentially, creating severe latency for difficult tasks (up to days and weeks). Parallel reasoning offers a natural remedy. However, prior systems primarily focus on Subtask Parallelism, where the model learns to decompose a high-level task into smaller chunks that can be solved independently. This approach overlooks another pervasive form of parallelism: Trial Parallelism, where multiple speculative attempts explore, verify, and aggregate competing hypotheses in parallel. In this paper, we introduce Parason, which reveals and learns both forms of parallelism in LLM reasoning. Our analysis identifies Trial Parallelism as the majority of parallelizable reasoning computation (65.5% in DeepSeek-V4's reasoning steps in HLE), and it becomes increasingly dominant on hard problems. Guided by this taxonomy, Parason converts sequential reasoning traces into structured parallel trajectories with a context-free grammar, then trains models with Parallelism-Aware Group Relative Policy Optimization (PA-GRPO), whose reward jointly balances accuracy, latency, and the two parallelism ratios. At inference time, Parason executes the learned parallel structure through tool calls, translating theoretical savings to real-world wall-clock acceleration. Experiments on mathematical reasoning benchmarks including AIME24 and AIME25 show that Parason achieves an average acceleration about 1.7$\times$ while maintaining competitive accuracy.

Test-time scaling has emerged as an effective way to improve language models on challenging reasoning tasks. However, most existing methods treat each problem in isolation and do not systematically reuse knowledge from prior reasoning trajectories. In particular, they underutilize procedural knowledge: how to reframe a problem, choose an approach, and verify or backtrack when needed. We introduce Reasoning Memory, a retrieval-augmented generation (RAG) framework for reasoning models that explicitly retrieves and reuses procedural knowledge at scale. Starting from existing corpora of step-by-step reasoning trajectories, we decompose each trajectory into self-contained subquestion-subroutine pairs, yielding a datastore of 32 million compact procedural knowledge entries. At inference time, a lightweight in-thought prompt lets the model verbalize the core subquestion, retrieve relevant subroutines within its reasoning trace, and reason under diverse retrieved subroutines as implicit procedural priors. Across six math, science, and coding benchmarks, Reasoning Memory consistently outperforms RAG with document, trajectory, and template knowledge, as well as a compute-matched test-time scaling baseline. With a higher inference budget, averaged across models and tasks, it improves over no retrieval by 19.5% and over the compute-matched baseline by 8.9%. Ablation studies show that these gains come from two key factors: the broad procedural coverage of the source trajectories and our decomposition and retrieval design, which together enable effective extraction and reuse of procedural knowledge. Our experiment code is available at https://github.com/facebookresearch/reasoning-memory.

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing reasoning from scratch paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.