Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Decomposing the QK circuit with Bilinear Sparse Dictionary Learning, published by keith wynroe on July 2, 2024 on LessWrong.
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 attention pattern.
Training Setup
Our training process has two steps:
Step 1: Reconstructing the attention pattern with key- and query- encoder-decoder networks
Step 2: Finding a condensed set of query-key feature pairs by masking
Step 1: Reconstructing the attention pattern with key- and query-transcoders
Architecture
Our first training step involves training two sparse dictionaries in parallel (one for the keys and one for the queries). The dictionaries both take in the layer-normalized residual stream at a given layer (normalised_resid_pre_i) and each output a [n_head * d_head] vector, representing the flattened keys and queries[3].
Figure 1: High-level diagram of our training set-up
Loss functions
However, rather than penalising the reconstruction loss of the keys and queries explicitly, we can use these keys and queries to reconstruct the original model's attention pattern. To train the reconstructed attention pattern, we used several different losses:
KL divergence between the attention pattern (using reconstructed keys and reconstructed queries) and the ground-truth attention pattern produced by the original model.
We also added two auxiliary reconstruction losses both for early-training-run stability, and to ensure our transcoders do not learn to reconstruct the keys and queries with an arbitrary rotation applied (since this would still produce the same attention scores and patterns):
KL divergence between the attention pattern (using reconstructed keys and the original model's queries) and the ground-truth attention pattern produced by the original model.
KL divergence between the attention pattern (using the original models' keys and the reconstructed queries) and the ground-truth atten...

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