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Latent Semantic Manifolds in Large Language Models

arXiv:2603.22301v1 Announce Type: new Abstract: Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens — a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that interprets LLM hidden states…

Scaling Attention via Feature Sparsity

arXiv:2603.22300v1 Announce Type: new Abstract: Scaling Transformers to ultra-long contexts is bottlenecked by the $O(n^2 d)$ cost of self-attention. Existing methods reduce this cost along the sequence axis through local windows, kernel approximations, or token-level sparsity, but these approaches consistently…

Learning dynamically inspired bases for Koopman and transfer operator approximation

arXiv:2505.05085v3 Announce Type: replace-cross Abstract: Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide important insights into system…

Full waveform inversion method based on diffusion model

arXiv:2603.22307v1 Announce Type: new Abstract: Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process getting trapped in local…