HilbNets define convolutions via Hilbert bundle connection Laplacians, prove that sampled Hilbert cellular sheaf Laplacians converge to the continuous operator, and show that discretized networks are consistent and transferable across samplings.
Ranganath Krishnan, Piyush Khanna, and Omesh Tickoo
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2026 6representative citing papers
Applying STP at consecutive semantic reasoning steps achieves 168x more accurate multi-step latent prediction on ProcessBench than frozen baselines, with trajectories forming smooth curves best captured by non-linear predictors.
Contextual curvature of LLM representational trajectories correlates with and causally modulates next-token entropy.
An empirical audit of 22 JEPA-style training auxiliaries on Llama-3.2-1B fine-tuning for regex generation finds no statistically significant task improvement after multiple-testing correction, even when auxiliaries visibly alter hidden-state geometry.
Transformers face a topological limitation in dynamic state tracking because their feedforward architecture pushes evolving state representations deeper into layers until depth is exhausted, requiring a shift to recurrent architectures for implicit activation dynamics.
AI's compositional reasoning failures originate in psychological learning paradigms that shaped its architectures, and the ReSynth trimodular framework is proposed to embed systematicity structurally.
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Representational Curvature Modulates Behavioral Uncertainty in Large Language Models
Contextual curvature of LLM representational trajectories correlates with and causally modulates next-token entropy.