mlsanityData to 14 Oct 2026

Learning to Reason in 13 Parameters

arXiv 2602.04118 ↗First posted 4 Feb 2026cs.LGcited by 14

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Recent research has shown that language models can learn to textitreason, often via reinforcement learning. Some work even trains low-rank parameterizations for reasoning, but conventional LoRA cannot scale below the model dimension. We question whether even rank=1 LoRA is necessary for learning to reason and propose TinyLoRA, a method for scaling low-rank adapters to sizes as small as one parameter. Within our new parameterization, we are able to train the 8B parameter size of Qwen2.5 to 91% accuracy on GSM8K with only 13 trained parameters in bf16 (26 total bytes). We find this trend holds in general: we are able to recover 90% of performance improvements while training 1000x fewer parameters across a suite of more difficult learning-to-reason benchmarks such as AIME, AMC, and MATH500. Notably, we are only able to achieve such strong performance with RL: models trained using SFT require 100-1000x larger updates to reach the same performance.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 41 of its 49 references that are in the map. First posted on arXiv 4 Feb 2026.

Builds on

41 of 49 references.

References · 41

  1. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  4. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  5. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  6. 2024Qwen2.5 Technical Reportcited by 4,942
  7. 2021Prefix-Tuning: Optimizing Continuous Prompts for Generationcited by 3,915
  8. 2023QLoRA: Efficient Finetuning of Quantized LLMscited by 3,418
  9. 2024HybridFlow: A Flexible and Efficient RLHF Frameworkcited by 2,057
  10. 2022Solving Quantitative Reasoning Problems with Language Modelscited by 1,392
  11. 2021BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-modelscited by 1,245
  12. 2024OpenAI o1 System Cardcited by 1,244
29 more
  1. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
  2. 2025SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-trainingcited by 672
  3. 2020Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuningcited by 671
  4. 2025SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wildcited by 511
  5. 2025LIMO: Less is More for Reasoningcited by 498
  6. 2018Measuring the Intrinsic Dimension of Objective Landscapescited by 370
  7. 2023AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuningcited by 357
  8. 2024LoRA Learns Less and Forgets Lesscited by 328
  9. 2025OpenThoughts: Data Recipes for Reasoning Modelscited by 304
  10. 2023VeRA: Vector-based Random Matrix Adaptationcited by 300
  11. 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 295
  12. 2024When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Methodcited by 204
  13. 2023Evaluating the Performance of Large Language Models on GAOKAO Benchmarkcited by 186
  14. 2025RL's Razor: Why Online Reinforcement Learning Forgets Lesscited by 176
  15. 2024LoRA vs Full Fine-tuning: An Illusion of Equivalencecited by 109
  16. 2025Retaining by Doing: The Role of On-Policy Data in Mitigating Forgettingcited by 94
  17. 2023Punica: Multi-Tenant LoRA Servingcited by 83
  18. 2025Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contaminationcited by 82
  19. 2024LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameterscited by 76
  20. 2024VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Bankscited by 52
  21. 2025Reinforcement Learning Finetunes Small Subnetworks in Large Language Modelscited by 49
  22. 2024LoRA-drop: Efficient LoRA Parameter Pruning based on Output Evaluationcited by 38
  23. 2025Scalpel vs. Hammer: GRPO Amplifies Existing Capabilities, SFT Replaces Themcited by 15
  24. 2024NoRA: Nested Low-Rank Adaptation for Efficient Fine-Tuning Large Modelscited by 13
  25. 2025Evaluating Parameter Efficient Methods for RLVRcited by 12
  26. 2018Playing Atari with Six Neuronscited by 11
  27. 2024ShareLoRA: Parameter Efficient and Robust Large Language Model Fine-tuning via Shared Low-Rank Adaptationcited by 11
  28. 2025Uni-LoRA: One Vector is All You Needcited by 7
  29. 2025WeightLoRA: Keep Only Necessary Adapterscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 14.

14 papers.

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  1. 2026Neural Thickets: Diverse Task Experts Are Dense Around Pretrained Weightscited by 28
  2. 2026Operationalising the Superficial Alignment Hypothesis via Task Complexitycited by 4
  3. 2026Consolidating Rewarded Perturbations for LLM Post-Trainingcited by 3
  4. 2026Spectral Rewiring for Exploration, Purification, and Model Mergingcited by 1
  5. 2026Non-vacuous Generalization Bounds for Reinforcement Learning with Verifiable Rewardscited by 1
  6. 2026How Much Can a LoRA Adapter Memorize? Measuring Adapter Capacity in Bitscited by 1
  7. 2026BoostLoRA: Growing Effective Rank by Boosting Adapterscited by 0
  8. 2026Not How Many, But Which: Parameter Placement in Low-Rank Adaptationcited by 0
  9. 2026PreFT: Prefill-only finetuning for efficient inferencecited by 0
  10. 2026Super Weights in LLMs and the Failure of Selective Trainingcited by 0
  11. 2026Can Bayesian Optimization Efficiently Find a Strong Single Expert in Neural Thickets?cited by 0
  12. 2026Understanding and Exploiting Anisotropy in Post-Trainingcited by 0
2 more
  1. 2026The Low-Rank Structure of VLA Reinforcement Learningcited by 0
  2. 2026How Low Can You Go: Fine-Tuning LLMs with Bayesian Optimization (LlMBO)cited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Tina: Tiny Reasoning Models via LoRA
  2. 2025Making Small Language Models Efficient Reasoners: Intervention, Supervision, Reinforcement
  3. 2026Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge
  4. 2025Rank-1 LoRAs Encode Interpretable Reasoning Signals
  5. 2025Effective Learning for Small Reasoning Models: An Empirical Study on 0.5B Reasoning LLMs
  6. 2025TinyV: Reducing False Negatives in Verification Improves RL for LLM Reasoning
  7. 2025General-Reasoner: Advancing LLM Reasoning Across All Domains
  8. 2025Training Language Models to Reason Efficiently