# A Mathematical Philosophy of Explanations in Mechanistic Interpretability -- The Strange Science Part I.i

arXiv: https://arxiv.org/abs/2505.00808 · HTML: https://mlsanity.com/paper/2505.00808/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 54 of its 143 references that are in the map.
- First posted on arXiv 1 May 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 30 of 54)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [Foundational Challenges in Assuring Alignment and Safety of Large Language Models](https://mlsanity.com/paper/2404.09932/) (2024)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Open Problems in Cooperative AI](https://mlsanity.com/paper/2012.08630/) (2020)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)

## Built on by (most cited first, 6 of 6)

- [Mechanistic Indicators of Understanding in Large Language Models](https://mlsanity.com/paper/2507.08017/) (2025)
- [Toward a Theory of Generalizability in LLM Mechanistic Interpretability Research](https://mlsanity.com/paper/2509.22831/) (2025)
- [Position: Don't Just "Fix it in Post": A Science of AI Must Study Training Dynamics](https://mlsanity.com/paper/2606.06533/) (2026)
- [Evaluating Explanations: An Explanatory Virtues Framework for Mechanistic Interpretability -- The Strange Science Part I.ii](https://mlsanity.com/paper/2505.01372/) (2025)
- [From Mechanistic to Compositional Interpretability](https://mlsanity.com/paper/2605.08934/) (2026)
- [A Geometric View for Understanding Concept Learning and Neuron Interpretation in Sparse Autoencoders](https://mlsanity.com/paper/2606.07007/) (2026)

## Abstract (arXiv)

Mechanistic Interpretability aims to understand neural networks through causal explanations. We argue for the Explanatory View Hypothesis: that Mechanistic Interpretability research is a principled approach to understanding models because neural networks contain implicit explanations which can be extracted and understood. We hence show that Explanatory Faithfulness, an assessment of how well an explanation fits a model, is well-defined. We propose a definition of Mechanistic Interpretability (MI) as the practice of producing Model-level, Ontic, Causal-Mechanistic, and Falsifiable explanations of neural networks, allowing us to distinguish MI from other interpretability paradigms and detail MI's inherent limits. We formulate the Principle of Explanatory Optimism, a conjecture which we argue is a necessary precondition for the success of Mechanistic Interpretability.