Methods · Interpretability-by-Design Methods for Intrinsic Interpretability
Sparse Mixture of Linear Transforms (MOLT)
Survey sections: §6.10.4 Modifications of Computational Primitives: MOLT
Summary The sparse mixture of linear transforms (MOLT) reconsiders what the computational primitives should be, shifting from extracting features to extracting the transformations a model applies to its activations.
A recent example is the sparse mixture of linear transforms (MOLT), which represents a conceptual shift from feature extraction towards transformation extraction (Lindsey et al., 2025b).
Assumptions and requirements
To achieve this, MOLT replaces the MLP with a sparse mixture of learned linear transformation matrices. The basic unit of analysis becomes transformations applied to model activations rather than features.
Intended applications
The basic unit of analysis becomes transformations applied to model activations rather than features. For example, in a modular arithmetic task, MOLT can represent the concept of addition with a learned rotation matrix, which relates more directly to the underlying algorithm than a collection of state-specific features.
More broadly, approaches that represent computational operations explicitly, as MOLT does, may facilitate the development of interpretable representations for tasks governed by systematic operations.
Related methods
Key papers
Cited in §6.10.4.
- James Oldfield, Shawn Im, Sharon Li, Mihalis Nicolaou, Ioannis Patras, and Grigorios Chrysos. Towards interpretability without sacrifice: Faithful dense layer decomposition with mixture of decoders. In The Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025. URL https://openreview.net/forum?id=jcvX8XFNqX.
- Jungwoo Park, Ahn Young Jin, Kee-Eung Kim, and Jaewoo Kang. Monet: Mixture of monosemantic experts for transformers. In The Thirteenth International Conference on Learning Representations, 2025.
- PreprintDan Braun, Lucius Bushnaq, Stefan Heimersheim, Jake Mendel, and Lee Sharkey. Interpretability in parameter space: Minimizing mechanistic description length with attribution-based parameter decomposition, 2025. URL https://arxiv.org/abs/2501.14926.
- PreprintLucius Bushnaq, Dan Braun, and Lee Sharkey. Stochastic parameter decomposition, 2025. URL https://arxiv.org/abs/2506.20790.
- PreprintJack Lindsey, Brian Chen, Adam Pearce, Sasha Hydrie, Thomas Conerly, and Jeff Wu. Sparse mixtures of linear transforms. https://transformer-circuits.pub/2025/bulk-update/index.html, 2025b.
Also discussed in: §5.2 Architectural Responses to Superposition
Other methods in Interpretability-by-Design Methods for Intrinsic Interpretability
Weight-Sparse Training (Weight-Sparse Transformer) · Attention-Sparse Training (SPARTAN) · Softmax Linear Units (SoLU) · Kolmogorov–Arnold Networks (KANs)