Towards Worst-Case Guarantees with Scale-Aware Interpretability
Not on the map. Why?
Abstract (arXiv)
Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and guaranteeing bounds on the influence of fine-grained structure that is discarded as irrelevant noise. We posit that the renormalisation framework from physics can meet this need by offering technical tools that can overcome limitations of current methods. Moreover, relevant work from adjacent fields has now matured to a point where scattered research threads can be synthesized into practical, theory-informed tools. To combine these threads in an AI safety context, we propose a unifying research agenda -- scale-aware interpretability -- to develop formal machinery and interpretability tools that have robustness and faithfulness properties supported by statistical physics.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 85 of its 141 references that are in the map. First posted on arXiv 5 Feb 2026.
Builds on
85 of 141 references.
References · 85
- 2020Denoising Diffusion Probabilistic Modelscited by 20,851
- 2022Scalable Diffusion Models with Transformerscited by 5,931
- 2023Sparse Autoencoders Find Highly Interpretable Features in Language Modelscited by 1,359
- 2016Understanding intermediate layers using linear classifier probescited by 1,279
- 2023Steering Language Models With Activation Engineeringcited by 824
- 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
- 2015Deep Learning and the Information Bottleneck Principlecited by 793
- 2013Exact solutions to the nonlinear dynamics of learning in deep linear neural networkscited by 748
- 2024Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Modelscited by 412
- 2023Finding Neurons in a Haystack: Case Studies with Sparse Probingcited by 328
- 2023Emergent Linear Representations in World Models of Self-Supervised Sequence Modelscited by 313
- 2018Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learningcited by 211
38 more
- 2024Not All Language Model Features Are One-Dimensionally Linearcited by 201
- 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
- 2020Feature Learning in Infinite-Width Neural Networkscited by 182
- 2016Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Reviewcited by 155
- 2019Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processescited by 148
- 2024A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoderscited by 148
- 2023SGD learning on neural networks: leap complexity and saddle-to-saddle dynamicscited by 142
- 2025Learning Multi-Level Features with Matryoshka Sparse Autoencoderscited by 136
- 2025SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretabilitycited by 118
- 2024Automatically Interpreting Millions of Features in Large Language Modelscited by 106
- 2024A Dynamical Model of Neural Scaling Lawscited by 105
- 2022Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networkscited by 104
- 2023Grokking as the Transition from Lazy to Rich Training Dynamicscited by 102
- 2016Why does deep and cheap learning work so well?cited by 100
- 2021Pre-training without Natural Imagescited by 100
- 2021Learning to See by Looking at Noisecited by 92
- 2024A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Datacited by 88
- 2021Continual Learning in the Teacher-Student Setup: Impact of Task Similaritycited by 86
- 2025Sparse Autoencoders Trained on the Same Data Learn Different Featurescited by 86
- 2025Sparse Autoencoders Do Not Find Canonical Units of Analysiscited by 80
- 2023How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Modelcited by 70
- 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
- 2020Neural Networks and Quantum Field Theorycited by 58
- 2025Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometrycited by 58
- 2014An exact mapping between the Variational Renormalization Group and Deep Learningcited by 52
- 2023Grokking as a First Order Phase Transition in Two Layer Networkscited by 48
- 2024From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networkscited by 46
- 2024Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representationscited by 45
- 2025From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuitcited by 45
- 2023Dynamics of Finite Width Kernel and Prediction Fluctuations in Mean Field Neural Networkscited by 42
- 2024Decomposing The Dark Matter of Sparse Autoencoderscited by 42
- 2024Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learningcited by 41
- 2024Loss Landscape Degeneracy and Stagewise Development in Transformerscited by 39
- 2023Stochastic Collapse: How Gradient Noise Attracts SGD Dynamics Towards Simpler Subnetworkscited by 38
- 2024Towards a theory of how the structure of language is acquired by deep neural networkscited by 38
- 2018Caveats for information bottleneck in deterministic scenarioscited by 34
- 2021A self consistent theory of Gaussian Processes captures feature learning effects in finite CNNscited by 33
- 2017Mutual Information, Neural Networks and the Renormalization Groupcited by 32
50 most cited of 85 All 85 (JSON)
Built on by
Citing papers per year: 2026: 3.
3 papers.
- 2026There Will Be a Scientific Theory of Deep Learningcited by 21
- 2026Critical Percolation as a Synthetic Data Model for Interpretabilitycited by 0
- 2026Deep neural networks as lattice gauge theoriescited by 0
- 2026Deep neural networks as lattice gauge theories19 Aug 2026
- 2026Critical Percolation as a Synthetic Data Model for Interpretability18 Jun 2026
- 2026There Will Be a Scientific Theory of Deep Learning23 Apr 2026