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.
Semantic tube prediction: Beating llm data efficiency with jepa
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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.
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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Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
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.