# ConvMem: Convolutional Memory for Long-Context Reasoning

arXiv: https://arxiv.org/abs/2609.10441 · HTML: https://mlsanity.com/paper/2609.10441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 21 of 21)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Mem0: Building Production-Ready AI Agents with Scalable Long-Term Memory](https://mlsanity.com/paper/2504.19413/) (2025)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [MemAgent: Reshaping Long-Context LLM with Multi-Conv RL-based Memory Agent](https://mlsanity.com/paper/2507.02259/) (2025)
- [Memory-R1: Enhancing Large Language Model Agents to Manage and Utilize Memories via Reinforcement Learning](https://mlsanity.com/paper/2508.19828/) (2025)
- [MIRIX: Multi-Agent Memory System for LLM-Based Agents](https://mlsanity.com/paper/2507.07957/) (2025)
- [Mem-α: Learning Memory Construction via Reinforcement Learning](https://mlsanity.com/paper/2509.25911/) (2025)
- [Coarse-to-Fine Grounded Memory for LLM Agent Planning](https://mlsanity.com/paper/2508.15305/) (2025)
- [Self-Guided Function Calling in Large Language Models via Stepwise Experience Recall](https://mlsanity.com/paper/2508.15214/) (2025)

## Abstract (arXiv)

While Large Language Models (LLMs) have demonstrated impressive capabilities, they often struggle with extremely long contexts due to fixed context limits. To address this, sequential approaches like MemAgent extend the effective context by reading text in segments and iteratively updating a fixed-size memory. However, this sequential paradigm suffers from high latency and requires costly reinforcement learning (RL) training, which can lead to overfitting on specific datasets. To overcome these limitations, we propose ConvMem, a training-free, highly parallelizable framework that reformulates long-context reasoning as a hierarchical convolution. Inspired by CNNs, ConvMem treats an LLM prompted with a specific query as a convolutional kernel. This kernel summarizes text segments hierarchically, shortening the reasoning path from a linear chain into a logarithmic tree. Specifically, ConvMem integrates textitConfigurable Strides and textitSkip Connections to ensure robust evidence capture and propagation, while employing textitMulti-Kernel Convolution to decompose complex queries into disentangled semantic channels. This design not only mitigates error accumulation but also enables massive parallelization across both text segments and reasoning threads. Experiments on RULER-HotpotQA and RULER-2WikiMultiHopQA demonstrate that ConvMem outperforms training-free baselines and avoids the risk of overfitting to parametric priors often observed in RL-trained models on out-of-distribution tasks.