HoPE replaces RoPE's sine/cosine rotations with hyperbolic functions plus an exponential damping term to enforce monotonic attention decay, but the claimed consistent superiority and the 'RoPE as special case' theorem are not supported.
An Elementary Introduction to Groups and Representations
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abstract
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the exponential mapping, the basics of representations theory, the Baker-Campbell-Hausdorff formula, a detailed study of the representations of SU(3), and a brief survey of the representation theory of general semisimple groups.
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2025 1verdicts
REJECT 1representative citing papers
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HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Models
HoPE replaces RoPE's sine/cosine rotations with hyperbolic functions plus an exponential damping term to enforce monotonic attention decay, but the claimed consistent superiority and the 'RoPE as special case' theorem are not supported.