The Nonlinear Library LW - Adam Optimizer Causes Privileged Basis in Transformer Language Models by Diego Caples
Sep 6, 2024
06:59
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: Adam Optimizer Causes Privileged Basis in Transformer Language Models, published by Diego Caples on September 6, 2024 on LessWrong.
Diego Caples (diego@activated-ai.com)
Rob Neuhaus (rob@activated-ai.com)
Introduction
In principle, neuron activations in a transformer-based language model residual stream should be about the same scale. In practice, however the dimensions unexpectedly widely vary in scale. Mathematical theories of the transformer architecture do not predict this. They expect rotational equivariance within a model, where one dimension is no 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 basis.
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
Privileged Bases in the Transformer Residual Stream
Toy Models of Superposition (Privileged Basis Section)
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 the parameter space of a neural network, train it, and then invert the rotation. With Stochastic Gradient Descent (SGD), this process yields the same model as if we hadn't rotated at all. However, with the Adam optimizer, we end up with a different model.
This difference can be explained by the presence/absence a property called rotational equivariance. SGD is rotationally equivariant: optimizer steps are always directly proportional to the gradient of the loss function, regardless of the chosen coordinate system. In contrast, Adam is not rotationally equivariant because it takes steps in ways that are not proportional to the gradient. Updates depend on coordinate-wise gradient statistics.
As we later show, this difference is what leads to privileged basis within LMs.
Kurtosis
Motivated by Anthropic, we use excess kurtosis as a metric for measuring basis privilege.
We encourage the reader to read Anthropic's reasoning for why this is a good metric, but here we aim to demonstrate graphically that excess kurtosis is a reasonable choice for measuring basis privilege.
We plot the middle layer residual stream activations for the last token of string:
"Lilly saw a big red apple!"
as an Adam optimized LM training run progresses....
Diego Caples (diego@activated-ai.com)
Rob Neuhaus (rob@activated-ai.com)
Introduction
In principle, neuron activations in a transformer-based language model residual stream should be about the same scale. In practice, however the dimensions unexpectedly widely vary in scale. Mathematical theories of the transformer architecture do not predict this. They expect rotational equivariance within a model, where one dimension is no 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 basis.
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
Privileged Bases in the Transformer Residual Stream
Toy Models of Superposition (Privileged Basis Section)
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 the parameter space of a neural network, train it, and then invert the rotation. With Stochastic Gradient Descent (SGD), this process yields the same model as if we hadn't rotated at all. However, with the Adam optimizer, we end up with a different model.
This difference can be explained by the presence/absence a property called rotational equivariance. SGD is rotationally equivariant: optimizer steps are always directly proportional to the gradient of the loss function, regardless of the chosen coordinate system. In contrast, Adam is not rotationally equivariant because it takes steps in ways that are not proportional to the gradient. Updates depend on coordinate-wise gradient statistics.
As we later show, this difference is what leads to privileged basis within LMs.
Kurtosis
Motivated by Anthropic, we use excess kurtosis as a metric for measuring basis privilege.
We encourage the reader to read Anthropic's reasoning for why this is a good metric, but here we aim to demonstrate graphically that excess kurtosis is a reasonable choice for measuring basis privilege.
We plot the middle layer residual stream activations for the last token of string:
"Lilly saw a big red apple!"
as an Adam optimized LM training run progresses....