PENCIL: Long Thoughts with Short Memory

• URL: http://arxiv.org/abs/2503.14337v1
• Date: Tue, 18 Mar 2025 15:14:14 GMT
• Title: PENCIL: Long Thoughts with Short Memory
• Authors: Chenxiao Yang, Nathan Srebro, David McAllester, Zhiyuan Li,
• Abstract summary: We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process.<n> PENCIL significantly reduces the maximal context length required during generation.<n>We demonstrate PENCIL achieves 97% accuracy on the challenging Einstein's puzzle.
• Score: 34.880226179021996
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While recent works (e.g. o1, DeepSeek R1) have demonstrated great promise of using long Chain-of-Thought (CoT) to improve reasoning capabilities of language models, scaling it up during test-time is challenging due to inefficient memory usage -- intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process, allowing the model to recursively clean up intermediate thoughts based on patterns learned from training. With this reduction mechanism, PENCIL significantly reduces the maximal context length required during generation, and thus can generate longer thoughts with limited memory, solving larger-scale problems given more thinking time. For example, we demonstrate PENCIL achieves 97\% accuracy on the challenging Einstein's puzzle -- a task even large models like GPT-4 struggle with -- using only a small 25M-parameter transformer with 2048 context length. Theoretically, we prove PENCIL can perform universal space-efficient computation by simulating Turing machines with optimal time and space complexity, and thus can solve arbitrary computational tasks that would otherwise be intractable given context window constraints.

Related papers

• The Imitation Game: Turing Machine Imitator is Length Generalizable Reasoner [16.32735852049866]
  This paper proposes Turing MAchine Imitation Learning (TAIL) to improve the length generalization ability of large language models.<n>TAIL synthesizes chain-of-thoughts (CoT) data that imitates the execution process of a Turing Machine by computer programs.<n>Without bells and whistles, TAIL significantly improves the length generalization ability as well as the performance of Qwen2.5-7B on various tasks.
  arXiv  Detail & Related papers  (2025-07-17T17:50:07Z)
• Computational Thinking Reasoning in Large Language Models [69.28428524878885]
  Computational Thinking Model (CTM) is a novel framework that incorporates computational thinking paradigms into large language models (LLMs)<n>Live code execution is seamlessly integrated into the reasoning process, allowing CTM to think by computing.<n>CTM outperforms conventional reasoning models and tool-augmented baselines in terms of accuracy, interpretability, and generalizability.
  arXiv  Detail & Related papers  (2025-06-03T09:11:15Z)
• Syzygy of Thoughts: Improving LLM CoT with the Minimal Free Resolution [59.39066657300045]
  Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps.<n>We propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths.<n>SoT captures deeper logical dependencies, enabling more robust and structured problem-solving.
  arXiv  Detail & Related papers  (2025-04-13T13:35:41Z)
• Z1: Efficient Test-time Scaling with Code [26.374317704720234]
  Large Language Models (LLMs) can achieve enhanced complex problem-solving through test-time computing scaling. We propose an efficient test-time scaling method that trains LLMs on code-related reasoning trajectories. We present a novel Shifted Thinking Window to mitigate overthinking overhead.
  arXiv  Detail & Related papers  (2025-04-01T14:01:50Z)
• InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models [44.86868676444545]
  We introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization.<n>By interleaving short reasoning segments with concise progress summaries, our approach enables reasoning depth while maintaining bounded computational costs.
  arXiv  Detail & Related papers  (2025-03-09T16:59:14Z)
• Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching [60.04718679054704]
  Chain-of-Thought prompting elicits step-by-step problem solving, but often at the cost of excessive verbosity in intermediate outputs.<n>We propose Sketch-of-Thought (SoT), a prompting framework that integrates cognitively inspired reasoning paradigms with linguistic constraints.<n>SoT achieves token reductions of up to 78% with minimal accuracy loss across 15 reasoning datasets.
  arXiv  Detail & Related papers  (2025-03-07T06:57:17Z)
• DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Models [31.189242663680695]
  This paper introduces Difficulty-Adaptive Slow-Thinking (DAST), a novel framework that enables models to autonomously adjust the length of Chain-of-Thought(CoT) based on problem difficulty.<n>Experiments on diverse datasets and model scales demonstrate that DAST effectively mitigates overthinking while preserving reasoning accuracy on complex problems.
  arXiv  Detail & Related papers  (2025-03-06T14:23:06Z)
• LightThinker: Thinking Step-by-Step Compression [53.8069487638972]
  We propose LightThinker, a method that enables large language models to dynamically compress intermediate thoughts during reasoning.<n>Inspired by human cognitive processes, LightThinker compresses thought steps into compact representations and discards the original reasoning chains.<n>Experiments show that LightThinker reduces peak memory usage and inference time, while maintaining competitive accuracy.
  arXiv  Detail & Related papers  (2025-02-21T16:57:22Z)
• Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs [76.43407125275202]
  o1-like models can emulate human-like long-time thinking during inference.<n>This paper presents the first comprehensive study on the prevalent issue of overthinking in these models.<n>We propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy.
  arXiv  Detail & Related papers  (2024-12-30T18:55:12Z)
• Markov Chain of Thought for Efficient Mathematical Reasoning [10.678633785012691]
  Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions.<n>We conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT)<n>Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference.
  arXiv  Detail & Related papers  (2024-10-23T07:53:29Z)
• Sparser is Faster and Less is More: Efficient Sparse Attention for Long-Range Transformers [58.5711048151424]
  We introduce SPARSEK Attention, a novel sparse attention mechanism designed to overcome computational and memory obstacles. Our approach integrates a scoring network and a differentiable top-k mask operator, SPARSEK, to select a constant number of KV pairs for each query. Experimental results reveal that SPARSEK Attention outperforms previous sparse attention methods.
  arXiv  Detail & Related papers  (2024-06-24T15:55:59Z)
• Resistive Memory-based Neural Differential Equation Solver for Score-based Diffusion Model [55.116403765330084]
  Current AIGC methods, such as score-based diffusion, are still deficient in terms of rapidity and efficiency. We propose a time-continuous and analog in-memory neural differential equation solver for score-based diffusion. We experimentally validate our solution with 180 nm resistive memory in-memory computing macros.
  arXiv  Detail & Related papers  (2024-04-08T16:34:35Z)
• Tree-of-Mixed-Thought: Combining Fast and Slow Thinking for Multi-hop Visual Reasoning [16.495754104540605]
  Large language models (LLMs) can generate code-like plans for complex inference tasks such as visual reasoning. We propose a hierarchical plan-searching algorithm that integrates the one-stop reasoning (fast) and the Tree-of-thought (slow)
  arXiv  Detail & Related papers  (2023-08-18T16:21:40Z)
• End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking [52.05847268235338]
  We show how machine learning systems can perform logical extrapolation without overthinking problems. We propose a recall architecture that keeps an explicit copy of the problem instance in memory so that it cannot be forgotten. We also employ a progressive training routine that prevents the model from learning behaviors that are specific to number and instead pushes it to learn behaviors that can be repeated indefinitely.
  arXiv  Detail & Related papers  (2022-02-11T18:43:28Z)
• PAC-learning gains of Turing machines over circuits and neural networks [1.4502611532302039]
  We study the potential gains in sample efficiency that can bring in the principle of minimum description length. We use Turing machines to represent universal models and circuits. We highlight close relationships between classical open problems in Circuit Complexity and the tightness of these.
  arXiv  Detail & Related papers  (2021-03-23T17:03:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.