Parameter decomposition (PD) decomposes neural networks into interpretable computational components that faithfully reflect the original network's operations. However, scaling PD to large models requires vast compute, making it a costly and risky endeavor. Here we propose targeted PD (tPD), which identifies only the components that process specific inputs of interest -- from isolated prompts to large subtasks -- by introducing a high-rank catch-all component that handles all non-target data. We validate tPD on toy models and on transformer language models trained on The Pile, where it recovers reproducible, mechanistically faithful circuits. We extract a CSS-only submodel of a 4-block transformer using 7% of the FLOPs of its published decomposition, and in a 12-block transformer we surgically ablate and rewire memorized sequences, with negligible side effects on other inputs.
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).
A central goal of mechanistic interpretability is to understand how neural networks work and what each individual component does. Dominant circuit-finding approaches focus on a specific behavior and reverse-engineer the role of components on the associated sub-distribution. However, past work has shown that components can have different functions that are active on different subsets of the input distribution. In this work we ask whether a single weight can be understood globally across the full training distribution by characterizing when it matters (the inputs on which ablating it changes the model's predictions). We introduce an automated LLM pipeline that writes a short, human-readable description of when a weight matters and verifies it on held-out text, crediting a weight only if its description generalizes. Across two sparse and two dense transformers, the fraction of weights that are interpretable (in this sense) is higher in sparse transformers than in dense ones, a gap that widens once unreliable descriptions are discarded. Our results show that a meaningful fraction of a sparse transformer model's weights can be interpreted: 12 to 31% of weights have a single short description that identifies what the weight is used for.
A longstanding goal of research on interpretable deep learning is to replace opaque neural computations with human-meaningful symbolic descriptions. In this paper, we propose an approach for approximating the behavior of components of deep networks with executable programs. We focus on attention heads in transformer language models. For a given head, we first compute its associated attention matrices on a collection of randomly selected training examples. Next, we prompt a pre-trained language model with a summary of these matrices, and instruct it to generate a set of Python programs that can reproduce the associated attention patterns given only text from the input sentence. Finally, we re-rank programs according to how well our final set of programs predict behavior on held-out inputs. We demonstrate that a set of fewer than 1,000 such generated programs can reproduce the attention patterns of heads in GPT-2, TinyLlama-1.1B, and Llama-3B, achieving an average Intersection-over-Union similarity above 75% on TinyStories. Moreover, the best-fit programs can replace neural attention heads without substantially affecting model behavior: replacing 25% of attention heads with programmatic surrogates across the three models incurs only a 16% average perplexity increase, while maintaining performance on a variety of downstream question answering benchmarks. This work contributes a scalable pipeline for reverse-engineering attention heads in transformer models using human-readable, executable code, advancing a path toward symbolic transparency in neural models.