This work was produced as part of Lee Sharkey's stream in the ML Alignment & Theory Scholars Program - Winter 2023-24 Cohort Intro and Motivation Sparse dictionary learning (SDL) has attracted a lot of attention recently as a method for interpreting transformer activations. They demonstrate that model activations can often be explained using a sparsely-activating, overcomplete set of human-interpretable directions. However, despite its success for explaining many components, applying SDL to interpretability is relatively nascent and have yet to be applied to some model activations. In particular, intermediate activations of attention blocks have yet to be studied, and provide challenges for standard SDL methods. The first challenge is bilinearity: SDL is usually applied to individual vector spaces at individual layers, so we can simply identify features as a direction in activation space. But the QK circuits of transformer attention layers are different: They involve a bilinear form followed by a softmax. Although simply applying sparse encoders to the keys and queries[1] could certainly help us understand the “concepts” being used by a given attention layer, this approach would fail to explain how the query-features and key-features interact bilinearly. We need to understand which keys matter to which queries. The second challenge is attention-irrelevant variance: A lot of the variance in the attention scores is irrelevant to the attention pattern because it is variance in low scores which are softmaxed to zero; this means that most of the variability in the keys and queries is irrelevant for explaining downstream behaviour[2]. The standard method of reconstructing keys and queries would therefore waste capacity on what is effectively functionally irrelevant noise. To tackle these two problems (bilinearity and attention-irrelevant variance), we propose a training setup which only reconstructs the dimensions of the keys and queries that most affect the atten