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This paper introduces a geometric framework using the average kernel size to derive deterministic, model-independent bounds on empirical error and accuracy for regression and classification in metric-space settings, highlighting an accuracy–stability trade-off and an empirical error floor caused by data ambiguity.
Presents a continuous geometric framework modeling Transformer operations as integro-differential equations on a semantic fiber bundle, validated across multiple architectures.
Introduces a geometric framework to identify 'AI engrams' – memory traces in deep neural networks – formalizing neuroscientific criteria into a closed-form estimator, enabling surgical memory manipulation in models from MLPs to LLMs.
This paper presents a geometric framework to analyze the instability of feature composition in Sparse Autoencoders, revealing that non-linearities cause a ratchet effect leading to compositional collapse beyond a critical density.