# Stochastic Parameter Decomposition arXiv: https://arxiv.org/abs/2506.20790 ยท HTML: https://mlsanity.com/paper/2506.20790/ ## Key facts - Cited by 16 papers in the map (data through 14 Oct 2026). - Builds on 25 of its 41 references that are in the map. - First posted on arXiv 25 Jun 2025. ## Builds on (most cited first, 25 of 25) - [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017) - [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013) - [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023) - [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022) - [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018) - [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023) - [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017) - [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024) - [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021) - [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023) - [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023) - [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024) - [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023) - [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024) - [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021) - [Are Neural Nets Modular? Inspecting Functional Modularity Through Differentiable Weight Masks](https://mlsanity.com/paper/2010.02066/) (2020) - [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025) - [Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?](https://mlsanity.com/paper/2106.02890/) (2021) - [Low-Complexity Probing via Finding Subnetworks](https://mlsanity.com/paper/2104.03514/) (2021) - [Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient](https://mlsanity.com/paper/2410.02984/) (2024) - [Mathematical Models of Computation in Superposition](https://mlsanity.com/paper/2408.05451/) (2024) - [Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition](https://mlsanity.com/paper/2501.14926/) (2025) - [Missed Causes and Ambiguous Effects: Counterfactuals Pose Challenges for Interpreting Neural Networks](https://mlsanity.com/paper/2407.04690/) (2024) - [Identifying Sparsely Active Circuits Through Local Loss Landscape Decomposition](https://mlsanity.com/paper/2504.00194/) (2025) - [Uncovering Model Processing Strategies with Non-Negative Per-Example Fisher Factorization](https://mlsanity.com/paper/2310.04649/) (2023) ## Built on by (most cited first, 16 of 16) - [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (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) - [Bi-Orthogonal Factor Decomposition for Vision Transformers](https://mlsanity.com/paper/2601.05328/) (2026) - [From Memorization to Reasoning in the Spectrum of Loss Curvature](https://mlsanity.com/paper/2510.24256/) (2025) - [Hedonic Neurons: A Mechanistic Mapping of Latent Coalitions in Transformer MLPs](https://mlsanity.com/paper/2509.23684/) (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) - [Targeted Recovery of Weight-Space Mechanisms From Neural Networks](https://mlsanity.com/paper/2607.13047/) (2026) - [Sparse Weight Decomposition for Efficient Circuit Extraction](https://mlsanity.com/paper/2608.03913/) (2026) - [Matryoshka attribution: Learning to attribute language model outputs to representations and weights](https://mlsanity.com/paper/2609.25518/) (2026) - [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) - [Weights Read and Write Features: Scalable Parameter Decomposition Grounded in Activation Space](https://mlsanity.com/paper/2609.37731/) (2026) ## Abstract (arXiv) A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce textitStochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd/tree/spd-paper.