# Towards Interpretability Without Sacrifice: Faithful Dense Layer Decomposition with Mixture of Decoders

arXiv: https://arxiv.org/abs/2505.21364 · HTML: https://mlsanity.com/paper/2505.21364/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 104 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 30 of 64)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [Manipulating and Measuring Model Interpretability](https://mlsanity.com/paper/1802.07810/) (2018)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [LLMs instead of Human Judges? A Large Scale Empirical Study across 20 NLP Evaluation Tasks](https://mlsanity.com/paper/2406.18403/) (2024)
- [Bridging Language and Items for Retrieval and Recommendation: Benchmarking LLMs as Semantic Encoders](https://mlsanity.com/paper/2403.03952/) (2024)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)

## Built on by (most cited first, 5 of 5)

- [Towards Intrinsic Interpretability of Large Language Models:A Survey of Design Principles and Architectures](https://mlsanity.com/paper/2604.16042/) (2026)
- [PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decoding](https://mlsanity.com/paper/2602.01322/) (2026)
- [Toward Structural Multimodal Representations: Specialization, Selection, and Sparsification via Mixture-of-Experts](https://mlsanity.com/paper/2605.03348/) (2026)
- [fmxcoders: Factorized Masked Crosscoders for Cross-Layer Feature Discovery](https://mlsanity.com/paper/2605.09438/) (2026)
- [Faithful by Definition: Emotion Analysis via Natural Semantic Metalanguage Explications](https://mlsanity.com/paper/2607.00661/) (2026)

## Abstract (arXiv)

Multilayer perceptrons (MLPs) are an integral part of large language models, yet their dense representations render them difficult to understand, edit, and steer. Recent methods learn interpretable approximations via neuron-level sparsity, yet fail to faithfully reconstruct the original mapping--significantly increasing model's next-token cross-entropy loss. In this paper, we advocate for moving to layer-level sparsity to overcome the accuracy trade-off in sparse layer approximation. Under this paradigm, we introduce Mixture of Decoders (MxDs). MxDs generalize MLPs and Gated Linear Units, expanding pre-trained dense layers into tens of thousands of specialized sublayers. Through a flexible form of tensor factorization, each sparsely activating MxD sublayer implements a linear transformation with full-rank weights--preserving the original decoders' expressive capacity even under heavy sparsity. Experimentally, we show that MxDs significantly outperform state-of-the-art methods (e.g., Transcoders) on the sparsity-accuracy frontier in language models with up to 3B parameters. Further evaluations on sparse probing and feature steering demonstrate that MxDs learn similarly specialized features of natural language--opening up a promising new avenue for designing interpretable yet faithful decompositions. Our code is included at: https://github.com/james-oldfield/MxD/.