mlsanityData to 7 Oct 2026

Anti Mode-Collapse in Mean-Field Transformer via Auxiliary Variables

arXiv 2605.30229 ↗First posted 28 May 2026cs.LGcited by 0

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Abstract (arXiv)

We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties of self-attention mechanisms has garnered significant attention in recent years due to their ability to comprehensively analyze token interactions. However, analysis of this simple model suggests that mode collapse, where token distributions degenerate to a single point, occurs during long inferences (i.e., many layers), indicating a discrepancy with reality. This study investigates this mean-field transformer model and demonstrates that the introduction of auxiliary variables, such as positional encoding, acts as a counterforce against theoretical mode collapse. Specifically, we show that in the theoretical scheme, the energy-maximizing distribution does not degenerate to a single point; instead, it is characterized by a pushforward of the auxiliary variable distribution, thereby avoiding concentration in the Dirac measure. Our main examples are the positional encoding and the fixed prompt insertion treated as a parallel auxiliary-variable mechanism. Furthermore, we demonstrate that positional encoding and prompt insertion possess universality of representation in the limit, meaning that the limit distribution of inference can exactly represent a wide class of distributions. We also analyze several key properties of positional encoding and metastability, and validate our theoretical results through mathematical experiments.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 32 of its 43 references that are in the map. First posted on arXiv 28 May 2026.

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32 of 43 references.

References · 32

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20 more
  1. 2021Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolationcited by 1,085
  2. 2021P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Taskscited by 686
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  14. 2024On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encodingcited by 28
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  16. 2024Setting the Record Straight on Transformer Oversmoothingcited by 19
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  20. 2026Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformerscited by 1

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