{"ID":2843407,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08243","arxiv_id":"2511.08243","title":"A Unified Geometric Field Theory Framework for Transformers: From Manifold Embeddings to Kernel Modulation","abstract":"The Transformer architecture has achieved tremendous success in natural language processing, computer vision, and scientific computing through its self-attention mechanism. However, its core components-positional encoding and attention mechanisms-have lacked a unified physical or mathematical interpretation. This paper proposes a structural theoretical framework that integrates positional encoding, kernel integral operators, and attention mechanisms for in-depth theoretical investigation. We map discrete positions (such as text token indices and image pixel coordinates) to spatial functions on continuous manifolds, enabling a field-theoretic interpretation of Transformer layers as kernel-modulated operators acting over embedded manifolds.","short_abstract":"The Transformer architecture has achieved tremendous success in natural language processing, computer vision, and scientific computing through its self-attention mechanism. However, its core components-positional encoding and attention mechanisms-have lacked a unified physical or mathematical interpretation. This paper...","url_abs":"https://arxiv.org/abs/2511.08243","url_pdf":"https://arxiv.org/pdf/2511.08243v2","authors":"[\"Xianshuai Shi\",\"Jianfeng Zhu\",\"Leibo Liu\"]","published":"2025-11-11T13:41:01Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Transformer\"]","has_code":false}