Marc E. Canby

Sewoong Lee, Adam Davies, Marc E. Canby et al.

Sparse autoencoders (SAEs) are widely used in mechanistic interpretability research for large language models; however, the state-of-the-art method of using $k$-sparse autoencoders lacks a theoretical grounding for selecting the hyperparameter $k$ that represents the number of nonzero activations, often denoted by $\ell_0$. In this paper, we reveal a theoretical link that the $\ell_2$-norm of the sparse feature vector can be approximated with the $\ell_2$-norm of the dense vector with a closed-form error, which allows sparse autoencoders to be trained without the need to manually determine $\ell_0$. Specifically, we validate two applications of our theoretical findings. First, we introduce a new methodology that can assess the feature activations of pre-trained SAEs by computing the theoretically expected value from the input embedding, which has been overlooked by existing SAE evaluation methods and loss functions. Second, we introduce a novel activation function, top-AFA, which builds upon our formulation of approximate feature activation (AFA). This function enables top-$k$ style activation without requiring a constant hyperparameter $k$ to be tuned, dynamically determining the number of activated features for each input. By training SAEs on three intermediate layers to reconstruct GPT2 hidden embeddings for over 80 million tokens from the OpenWebText dataset, we demonstrate the empirical merits of this approach and compare it with current state-of-the-art $k$-sparse autoencoders. Our code is available at: https://github.com/SewoongLee/top-afa-sae.

Marc E. Canby, Julia Hockenmaier

Transformer-based encoder-decoder models that generate outputs in a left-to-right fashion have become standard for sequence-to-sequence tasks. In this paper, we propose a framework for decoding that produces sequences from the "outside-in": at each step, the model chooses to generate a token on the left, on the right, or join the left and right sequences. We argue that this is more principled than prior bidirectional decoders. Our proposal supports a variety of model architectures and includes several training methods, such as a dynamic programming algorithm that marginalizes out the latent ordering variable. Our model sets state-of-the-art (SOTA) on the 2022 and 2023 shared tasks, beating the next best systems by over 4.7 and 2.7 points in average accuracy respectively. The model performs particularly well on long sequences, can implicitly learn the split point of words composed of stem and affix, and performs better relative to the baseline on datasets that have fewer unique lemmas (but more examples per lemma).