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We develop a theoretical framework for generalization in the interpolating regime of statistical learning. The central question is why highly overparameterized estimators can attain zero empirical risk while still achieving nontrivial predictive accuracy, and how to characterize the boundary between benign and destructive overfitting. We introduce a spectral-transport stability framework in which excess risk is controlled jointly by the spectral geometry of the data distribution, the sensitivity of the learning rule under single-sample replacement, and the alignment structure […]

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Catastrophic forgetting remains a key challenge in Continual Learning (CL). In replay-based CL with severe memory constraints, performance critically depends on the sample selection strategy for the replay buffer. Most existing approaches construct memory buffers using embeddings learned under supervised objectives. However, class-agnostic, self-supervised representations often encode rich, class-relevant semantics that are overlooked. We propose a new method, Multiple Embedding Replay Selection, MERS, which replaces the buffer selection module with a graph-based approach that integrates both supervised and […]

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While numerous machine unlearning (MU) methods have recently been developed with promising results in erasing the influence of forgotten data, classes, or concepts, they are also highly vulnerable-for example, simple fine-tuning can inadvertently reintroduce erased concepts. In this paper, we address this contradiction by examining the internal representations of unlearned models, in contrast to prior work that focuses primarily on output-level behavior. Our analysis shows that many state-of-the-art MU methods appear successful mainly due to a misalignment between […]

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We develop a diagnostic framework for evaluating when LLM self-evaluation can be trusted. The framework’s central results are: (1) under a shared-blind-spot modeling assumption with joint conditional independence of evaluations given the shared failure structure, k rounds of self-critique provide information about correctness bounded by what the shared latent failure variable Z mediates—not by any independent channel—so that confidence accumulated through repeated self-evaluation reflects the shared failure structure rather than independently accumulated evidence; and (2) a selector satisfying […]

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We describe a decimal–hexadecimal block encoding for primality over a finite stored range. Since every prime greater than 5 must lie in one of the residue classes 1, 3, 7, 9 (mod 10), each decimal block of size ten can be encoded by a 4-bit word indicating which of the candidates 10k + 1, 10k + 3, 10k + 7, and 10k + 9 are prime. This yields a nibble-based storage scheme supporting exact primality queries and exact […]

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