Introduction

In principle, neuron activations in a transformer-based language model residual stream should be about the same scale. In practice, the dimensions unexpectedly widely vary in scale. Mathematical theories of the transformer architecture do not predict this. They expect no dimension to be more important than any other. Is there something wrong with our reasonably informed intuitions of how transformers work? What explains these outlier channels?

Previously, Anthropic researched the existence of these privileged basis dimensions (dimensions more important / larger than expected) and ruled out several causes. By elimination, they reached the hypothesis that per-channel normalization in the Adam optimizer was the cause of privileged basis. However, they did not prove this was the case.

We conclusively show that Adam causes outlier channels / privileged basis within the transformer residual stream. When replacing the Adam optimizer with SGD, models trained do not have a privileged residual stream.

As a whole, this work improves mechanistic understanding of transformer LM training dynamics and confirms that our mathematical models of transformers are not flawed. Rather, they simply do not take into account the training process.

Our code is open source at the LLM outlier channel exploration GitHub.

Key Results

Training an LM with SGD does not result in a privileged basis, indicating that Adam is the cause of privileged basis in transformer LMs.
Training a 12M parameter model on TinyStories allows us to replicate outlier channel behavior on a small LM, training in less than 15 minutes on an H100.

Background

Recommended Reading

More About Anthropic’s Work

We consider Anthropic’s research on privileged basis the primary motivator for this work. In Anthropic’s Privileged Bases in the Transformer Residual Stream, they demonstrate privileged basis in a 200M parameter LLM, performed some experiments to rule out possible causes, but did not find a definitive cause. They hypothesize that outlier channels are caused by Adam’s lack of rotational equivariance, and suggest that training using SGD could isolate Adam as the cause.

Adam vs SGD, and Rotational Equivariance

Consider an experiment where we rotate...

Erik Garrison

Erik Garrison

Erik Garrison

Erik Garrison

Erik Garrison

Erik Garrison