A key goal of current mechanistic interpretability research in NLP is to find *linear features* (also called "feature vectors") for transformers: directions in activation space corresponding to concepts that are used by a given model in its computation. Present state-of-the-art methods for finding linear features require large amounts of labelled data -- both laborious to acquire and computationally expensive to utilize. In this work, we introduce a novel method, called "observable propagation" (in short: ObProp), for finding linear features used by transformer language models in computing a given task -- *using almost no data*. Our paradigm centers on the concept of "observables", linear functionals corresponding to given tasks. We then introduce a mathematical theory for the analysis of feature vectors, including a similarity metric between feature vectors called the *coupling coefficient* which estimates the degree to which one feature's output correlates with another's. We use ObProp to perform extensive qualitative investigations into several tasks, including gendered occupational bias, political party prediction, and programming language detection. Our results suggest that ObProp surpasses traditional approaches for finding feature vectors in the low-data regime, and that ObProp can be used to better understand the mechanisms responsible for bias in large language models.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features—such as those found by sparse autoencoders (SAEs)—are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore **transcoders**, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. We then successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the "greater-than circuit" in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits/