ArcMemo: Abstract Reasoning Composition with Lifelong LLM Memory

While inference-time scaling enables LLMs to carry out increasingly long and capable reasoning traces, the patterns and insights uncovered during these traces are immediately discarded once the context window is reset for a new query. External memory is a natural way to persist these discoveries, and recent work has shown clear benefits for reasoning-intensive tasks. We see an opportunity to make such memories more broadly reusable and scalable by moving beyond instance-based memory entries (e.g. exact query/response pairs, or summaries tightly coupled with the original problem context) toward concept-level memory: reusable, modular abstractions distilled from solution traces and stored in natural language. For future queries, relevant concepts are selectively retrieved and integrated into the prompt, enabling test-time continual learning without weight updates. Our design introduces new strategies for abstracting takeaways from rollouts and retrieving entries for new queries, promoting reuse and allowing memory to expand with additional experiences. On the challenging ARC-AGI benchmark, our method yields a 7.5% relative gain over a strong no-memory baseline with performance continuing to scale with inference compute. We find abstract concepts to be the most consistent memory design, outscoring the baseline at all tested inference compute scales. Moreover, we confirm that dynamically updating memory during test-time outperforms an otherwise identical fixed memory setting with additional attempts, supporting the hypothesis that solving more problems and abstracting more patterns to memory enables further solutions in a form of self-improvement. Code available at https://github.com/matt-seb-ho/arc_memo.

GraphIC: A Graph-Based In-Context Example Retrieval Model for Multi-Step Reasoning

In-context learning (ICL) enables large language models (LLMs) to generalize to new tasks by incorporating a few in-context examples (ICEs) directly in the input, without updating parameters. However, the effectiveness of ICL heavily relies on the selection of ICEs, and conventional text-based embedding methods are often inadequate for tasks that require multi-step reasoning, such as mathematical and logical problem solving. This is due to the bias introduced by shallow semantic similarities that fail to capture the deeper reasoning structures required for these tasks. We present GraphIC, a novel approach that leverages graph-based representations of reasoning processes, coupled with Bayesian Networks (BNs) to select ICEs. Graph structures inherently filter out shallow semantics while preserving the core reasoning structure. Importantly, BNs capture the dependency of a node's attributes on its parent nodes, closely mirroring the hierarchical nature of human cognition-where each thought is shaped by preceding ones. This makes BNs particularly well-suited for multi-step reasoning tasks, aligning the process more closely with human-like reasoning. Extensive experiments across three types of reasoning tasks (mathematical reasoning, code generation, and logical reasoning) demonstrate that GraphIC outperforms both training-free and training-based models in selecting ICEs, excelling in terms of both effectiveness and efficiency. We show that GraphIC enhances ICL's performance and interoperability, significantly advancing ICE selection for multi-step reasoning tasks.