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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.
The paper adapts classical statistical estimators to deep learning for tracing epistemic uncertainty into aleatoric and data-scarcity sources, leveraging approximate Fisher Information Matrices for scalability.
The paper proposes a verifiable label-free reward for training calibrated probabilistic forecasters using reinforcement learning, avoiding the calibration degradation that occurs when rewarding single outcomes. Applied to NFL win probability, a 7B model trained with this reward achieves calibration comparable to the betting market.