Beyond Scaling Laws: Understanding Transformer Performance with
  Associative Memory
Increasing the size of a Transformer model does not always lead to enhanced
performance. This phenomenon cannot be explained by the empirical scaling laws.
Furthermore, improved generalization ability occurs as the model memorizes the
training samples. We present a theoretical framework that sheds light on the
memorization process and performance dynamics of transformer-based language
models. We model the behavior of Transformers with associative memories using
Hopfield networks, such that each transformer block effectively conducts an
approximate nearest-neighbor search. Based on this, we design an energy
function analogous to that in the modern continuous Hopfield network which
provides an insightful explanation for the attention mechanism. Using the
majorization-minimization technique, we construct a global energy function that
captures the layered architecture of the Transformer. Under specific
conditions, we show that the minimum achievable cross-entropy loss is bounded
from below by a constant approximately equal to 1. We substantiate our
theoretical results by conducting experiments with GPT-2 on various data sizes,
as well as training vanilla Transformers on a dataset of 2M tokens.
6644fb26c1a4481c95a34bff
Xueyan Niu
extracted_confirmed
2025-09-02T02:27:21.058Z
68b65343dd7f21b75891e446
https://cdn-avatars.huggingface.co/v1/production/uploads/68b65343dd7f21b75891e446/g4dtudmiuSBZY63eLFxJ8.jpeg
Xueyan Niu
user
niuxueyan
6644fb26c1a4481c95a34c00
Bo Bai
claimed_verified
2024-06-11T06:59:48.062Z
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Bo Bai
user
atomistic
6644fb26c1a4481c95a34c01
Lei Deng
6644fb26c1a4481c95a34c02
Wei Han
Beyond Scaling Laws: Understanding Transformer Performance with
  Associative Memory
Increasing the size of a Transformer model does not always lead to enhanced
performance. This phenomenon cannot be explained by the empirical scaling laws.
Furthermore, improved generalization ability occurs as the model memorizes the
training samples. We present a theoretical framework that sheds light on the
memorization process and performance dynamics of transformer-based language
models. We model the behavior of Transformers with associative memories using
Hopfield networks, such that each transformer block effectively conducts an
approximate nearest-neighbor search. Based on this, we design an energy
function analogous to that in the modern continuous Hopfield network which
provides an insightful explanation for the attention mechanism. Using the
majorization-minimization technique, we construct a global energy function that
captures the layered architecture of the Transformer. Under specific
conditions, we show that the minimum achievable cross-entropy loss is bounded
from below by a constant approximately equal to 1. We substantiate our
theoretical results by conducting experiments with GPT-2 on various data sizes,
as well as training vanilla Transformers on a dataset of 2M tokens.
A theoretical framework using Hopfield networks explains memorization and performance dynamics in Transformer-based language models, showing bounds on achievable cross-entropy loss.
Transformer model Hopfield networks associative memories nearest-neighbor search attention mechanism energy function majorization-minimization technique cross-entropy loss GPT-2 vanilla Transformers