# Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition

arXiv: https://arxiv.org/abs/2501.14926 · HTML: https://mlsanity.com/paper/2501.14926/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- First posted on arXiv 24 Jan 2025.

## Placed in

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

## Built on by (most cited first, 27 of 27)

- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [Steering Language Models with Weight Arithmetic](https://mlsanity.com/paper/2511.05408/) (2025)
- [Dense SAE Latents Are Features, Not Bugs](https://mlsanity.com/paper/2506.15679/) (2025)
- [Stochastic Parameter Decomposition](https://mlsanity.com/paper/2506.20790/) (2025)
- [Decomposing Representation Space into Interpretable Subspaces with Unsupervised Learning](https://mlsanity.com/paper/2508.01916/) (2025)
- [Watch the Weights: Unsupervised monitoring and control of fine-tuned LLMs](https://mlsanity.com/paper/2508.00161/) (2025)
- [Subliminal Learning is a LoRA Artifact](https://mlsanity.com/paper/2606.00831/) (2026)
- [Identifying Sparsely Active Circuits Through Local Loss Landscape Decomposition](https://mlsanity.com/paper/2504.00194/) (2025)
- [Towards Interpretability Without Sacrifice: Faithful Dense Layer Decomposition with Mixture of Decoders](https://mlsanity.com/paper/2505.21364/) (2025)
- [Interpreting and Steering State-Space Models via Activation Subspace Bottlenecks](https://mlsanity.com/paper/2602.22719/) (2026)
- [Evaluating Explanations: An Explanatory Virtues Framework for Mechanistic Interpretability -- The Strange Science Part I.ii](https://mlsanity.com/paper/2505.01372/) (2025)
- [Secret mixtures of experts inside your LLM](https://mlsanity.com/paper/2512.18452/) (2025)
- [Compressed Computation is (probably) not Computation in Superposition](https://mlsanity.com/paper/2606.14673/) (2026)
- [Compressed Computation: Dense Circuits in a Toy Model of the Universal-AND Problem](https://mlsanity.com/paper/2507.09816/) (2025)
- [Decomposition of Small Transformer Models](https://mlsanity.com/paper/2511.08854/) (2025)
- [From Mechanistic to Compositional Interpretability](https://mlsanity.com/paper/2605.08934/) (2026)
- [WriteSAE: Sparse Autoencoders for Recurrent State](https://mlsanity.com/paper/2605.12770/) (2026)
- [Sparse Weight Decomposition for Efficient Circuit Extraction](https://mlsanity.com/paper/2608.03913/) (2026)
- [Sparse Readout Prism: Explaining Logit-Lens Scores in Features Instead of Tokens](https://mlsanity.com/paper/2609.01936/) (2026)
- [Distribution-Aware Feature Selection for SAEs](https://mlsanity.com/paper/2508.21324/) (2025)
- [From Weights to Concepts: Data-Free Interpretability of CLIP via Singular Vector Decomposition](https://mlsanity.com/paper/2603.24653/) (2026)
- [AI Engram: In Search of Memory Traces in Artificial Intelligence](https://mlsanity.com/paper/2606.14997/) (2026)
- [Individual Parameters in Weight-Sparse Transformers Appear Interpretable](https://mlsanity.com/paper/2607.02964/) (2026)
- [Compressed Computation under L4 Loss is likely Computation in Superposition](https://mlsanity.com/paper/2607.04800/) (2026)
- [MAxBench: A Multinomial Concept Recovery Benchmark](https://mlsanity.com/paper/2609.13072/) (2026)
- [Neural Dynamics as the Composition of Quantized Units](https://mlsanity.com/paper/2609.32487/) (2026)
- [Weights Read and Write Features: Scalable Parameter Decomposition Grounded in Activation Space](https://mlsanity.com/paper/2609.37731/) (2026)

## Abstract (arXiv)

Mechanistic interpretability aims to understand the internal mechanisms learned by neural networks. Despite recent progress toward this goal, it remains unclear how best to decompose neural network parameters into mechanistic components. We introduce Attribution-based Parameter Decomposition (APD), a method that directly decomposes a neural network's parameters into components that (i) are faithful to the parameters of the original network, (ii) require a minimal number of components to process any input, and (iii) are maximally simple. Our approach thus optimizes for a minimal length description of the network's mechanisms. We demonstrate APD's effectiveness by successfully identifying ground truth mechanisms in multiple toy experimental settings: Recovering features from superposition; separating compressed computations; and identifying cross-layer distributed representations. While challenges remain to scaling APD to non-toy models, our results suggest solutions to several open problems in mechanistic interpretability, including identifying minimal circuits in superposition, offering a conceptual foundation for 'features', and providing an architecture-agnostic framework for neural network decomposition.