Riemannian Attention Mechanisms for Transformers: A Theoretical Framework and Architecture Design
All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al. (2021) proved causes representational rank to decay doubly exponentially with depth in pure self-attention stacks. We develop a theoretical framework that targets this structural limitation at the mathematical level by replacing the flat Euclidean metric with learned per-token Riemannian metrics. Our contributions are threefold. (1) We prove that Riemannian attention scores with heterogeneous per-token metrics are non-Gram---they cannot be factorized as QK^T with factorization dimension O(d). We are explicit that this is a structural observation, not a pr...
| Authors | Sen Song |
|---|---|
| Primary category | cs.LG |
| Published | 2 August 2026 |
| Last updated at source | 26 August 2026 |
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