Weights Read and Write Features: Scalable Parameter Decomposition Grounded in Activation Space

Mechanistic interpretability aims to uncover how neural networks use their parameters to implement their impressive neural algorithms. Although previous work has uncovered substantial structure in the intermediate representations that networks use, little progress has been made to understand how the parameters and nonlinearities of networks perform computations on those representations. In this work, we present a method that brings us closer to this understanding by decomposing a language model's parameters into subcomponents that each implement only a small part of the model's learned algorithm, while simultaneously requiring only a small fraction of those subcomponents to account for the network's behavior on any input. The method, adVersarial Parameter Decomposition (VPD), optimizes for decompositions of neural network parameters into simple subcomponents that preserve the network's input-output behavior even when many subcomponents are ablated, including under ablations that are adversarially selected to destroy behavior. This encourages learning subcomponents that provide short, mechanistically faithful descriptions of the network's behavior that should aggregate appropriately into more global descriptions of the network's learned algorithm. We study how sequences of interactions between these parameter subcomponents produce the network's output on particular inputs, enabling a new kind of 'circuit' analysis. While more work remains to be done to deepen our understanding of how neural networks use their parameters to compute their behavior, our work suggests an approach to identify a small set of simple, mechanistically faithful subcomponents on which further mechanistic analysis can be based.

Understanding the internal representations of large language models (LLMs) is a central challenge in interpretability research. Existing feature interpretability methods often rely on strong structural assumptions--such as linearity or sparsity--that may not hold in practice. In this work, we introduce InverseScope, an assumption-light and scalable framework for interpreting neural activations via input inversion. Given a target activation, InverseScope characterizes its encoded information by generating natural-language inputs that produce nearby activations, grounding abstract internal states in concrete language. To overcome the prohibitive cost of sampling in high-dimensional activation spaces, we propose a novel control-layer conditioning architecture that substantially improves sample efficiency compared to prior token-prepending approaches. We demonstrate that InverseScope reveals rich geometric structure in LLM representation spaces, including sentence-level linear analogies. The framework scales to state-of-the-art open-source models of up to 14B parameters and generalizes to out-of-distribution inputs, enabling systematic analysis of activation neighborhoods.

Dense pretrained transformers do not naturally expose interpretable units for circuit extraction. Existing approaches obtain such units by learning auxiliary sparse representations or training sparse models, incurring substantial additional computation while potentially introducing a fidelity gap between the representation being analyzed and the original pretrained model. We propose Sparse Weight Decomposition (SWD), which reparameterizes pretrained linear projections by factorizing each weight matrix into two sparse factors whose shared intermediate coordinates serve as individually addressable circuit units. Without training a separate replacement network, this parametric representation supports the same scoring, selection, and ablation circuit extraction workflow used for methods that learn sparse features. Across single-matrix replacements, SWD matches the held-out fidelity achieved by Transcoder and other strong baselines while using less than 1% of the data that those baselines use to train their replacements. For matched replacement fidelity, SWD reaches the same circuit sufficiency and necessity targets with fewer active read/write edges and selected units across tasks on GPT-2, Qwen2.5, and Qwen3.5-27B. We further show that SWD remains effective for full-model replacement of all attention and MLP weight matrices after fine-tuning the nonzero factor values. Finally, SWD also features a zero-data variant, allowing broader use of mechanistic interpretability analysis (e.g., per-step analysis).