title: Beyond Scaling Laws: Understanding Transformer Performance with
    Associative Memory
summary: 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.
paper_authors._id: 6644fb26c1a4481c95a34bff
paper_authors.name: Xueyan Niu
paper_authors._id: 6644fb26c1a4481c95a34c00
paper_authors.name: Bo Bai
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-06-11T06:59:48.062Z
paper_authors._id: 6667bdfd215b4c38f7ef17bb
paper_authors.avatarUrl: /avatars/cad66dd576c3261ec5c276ae00e666d1.svg
paper_authors.fullname: Bo Bai
paper_authors.type: user
paper_authors.user: atomistic
paper_authors._id: 6644fb26c1a4481c95a34c01
paper_authors.name: Lei Deng
paper_authors._id: 6644fb26c1a4481c95a34c02
paper_authors.name: Wei Han
paper_title: Beyond Scaling Laws: Understanding Transformer Performance with
    Associative Memory
paper_summary: 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.
paper_ai_keywords: Transformer-based language models associative memories Hopfield networks nearest-neighbor search energy function continuous Hopfield network attention mechanism majorization-minimization technique cross-entropy loss GPT-2 vanilla Transformers