mlsanityData to 14 Oct 2026

From Memorization to Reasoning in the Spectrum of Loss Curvature

arXiv 2510.24256 ↗First posted 28 Oct 2025cs.CL cs.LGcited by 2

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

We characterize how memorization is represented in transformer models and show that it can be disentangled in the weights of both language models (LMs) and vision transformers (ViTs) using a decomposition based on the loss landscape curvature. This insight is based on prior theoretical and empirical work showing that the curvature for memorized training points is much sharper than non memorized, meaning ordering weight components from high to low curvature can reveal a distinction without explicit labels. This motivates a weight editing procedure that suppresses far more recitation of untargeted memorized data more effectively than a recent unlearning method (BalancedSubnet), while maintaining lower perplexity. Since the basis of curvature has a natural interpretation for shared structure in model weights, we analyze the editing procedure extensively on its effect on downstream tasks in LMs, and find that fact retrieval and arithmetic are specifically and consistently negatively affected, even though open book fact retrieval and general logical reasoning is conserved. We posit these tasks rely heavily on specialized directions in weight space rather than general purpose mechanisms, regardless of whether those individual datapoints are memorized. We support this by showing a correspondence between task data's activation strength with low curvature components that we edit out, and the drop in task performance after the edit. Our work enhances the understanding of memorization in neural networks with practical applications towards removing it, and provides evidence for idiosyncratic, narrowly-used structures involved in solving tasks like math and fact retrieval.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 43 of its 49 references that are in the map. First posted on arXiv 28 Oct 2025.

Builds on

43 of 49 references.

References · 43

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  12. 2021Knowledge Neurons in Pretrained Transformerscited by 601
31 more
  1. 2024GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projectioncited by 463
  2. 20242 OLMo 2 Furiouscited by 340
  3. 2019An Investigation into Neural Net Optimization via Hessian Eigenvalue Densitycited by 292
  4. 2023Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Modelscited by 243
  5. 2023Linearity of Relation Decoding in Transformer Language Modelscited by 200
  6. 2023Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solvecited by 178
  7. 2023The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reductioncited by 123
  8. 2023Copyright Violations and Large Language Modelscited by 108
  9. 2024OLMES: A Standard for Language Model Evaluationscited by 106
  10. 2023Language Models Implement Simple Word2Vec-style Vector Arithmeticcited by 98
  11. 2024Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristicscited by 97
  12. 2025Language Models Use Trigonometry to Do Additioncited by 70
  13. 2023Can Neural Network Memorization Be Localized?cited by 69
  14. 2023Compressing LLMs: The Truth is Rarely Pure and Never Simplecited by 62
  15. 2025How much do language models memorize?cited by 61
  16. 2024Demystifying Verbatim Memorization in Large Language Modelscited by 56
  17. 2024Localizing Paragraph Memorization in Language Modelscited by 31
  18. 2024Approaching Deep Learning through the Spectral Dynamics of Weightscited by 31
  19. 2023Do Localization Methods Actually Localize Memorized Data in LLMs? A Tale of Two Benchmarkscited by 29
  20. 2023Memorization Through the Lens of Curvature of Loss Function Around Samplescited by 27
  21. 2024From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applicationscited by 25
  22. 2025On Linear Representations and Pretraining Data Frequency in Language Modelscited by 23
  23. 2024Differential learning kinetics govern the transition from memorization to generalization during in-context learningcited by 21
  24. 2025Stochastic Parameter Decompositioncited by 16
  25. 2024Measuring Non-Adversarial Reproduction of Training Data in Large Language Modelscited by 14
  26. 2025Analyzing Memorization in Large Language Models through the Lens of Model Attributioncited by 14
  27. 2024Using Degeneracy in the Loss Landscape for Mechanistic Interpretabilitycited by 13
  28. 2025Structural Inference: Interpreting Small Language Models with Susceptibilitiescited by 13
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  30. 2025Precise In-Parameter Concept Erasure in Large Language Modelscited by 11
  31. 2024Unveiling Privacy, Memorization, and Input Curvature Linkscited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Contribution Weights: A Geometrical Analysis of Self-Attention Transformerscited by 0
  2. 2026Fisher information and the geometry of memorization in neural networkscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Too Big to Think: Capacity, Memorization, and Generalization in Pre-Trained Transformers
  2. 2025An Analysis for Reasoning Bias of Language Models with Small Initialization
  3. 2025Disentangling Recall and Reasoning in Transformer Models through Layer-wise Attention and Activation Analysis
  4. 2026MemoReason: Evaluating the Effect of Parametric Memory on Contextual Reasoning in LLMs
  5. 2026Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models
  6. 2026Dual-Latent Memory Routing for Vision-Language Reasoning
  7. 2025Analyzing the Power of Chain of Thought through Memorization Capabilities
  8. 2023Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models