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This paper rethinks the linguistic notion of 'state' as a systemic morphosyntactic mechanism across synthetic languages, formalizing it as a set-valued function over grammatical templates within a Template-Based Modular Cognitive framework and offering a unified computational learning theory account.
This paper analyzes language generation in the limit, introducing a precision notion to study the recall-precision trade-off. It shows that allowing infinitely many hallucinations (with diminishing frequency) can increase recall when the adversary withholds much of the target language.
This paper develops a Fourier analysis framework to study data augmentation under group invariances, showing that partial augmentation can achieve the same minimax rates as full augmentation up to a vanishing approximation error, while also proving that exact invariance requires full group averaging.
Introduces Fisher width, a Riemannian analogue of Gaussian width for statistical manifolds, which captures local statistical curvature and is invariant under reparameterization. The paper develops its theory, proves generalization bounds for Fisher-Lipschitz classes, and demonstrates computable estimators on MNIST.
This paper proposes using pairwise queries to improve selective classification for binary classification, particularly where confidence estimates are inconsistent, as in LLM in-context learning. Theoretical conditions and experiments on synthetic and real datasets show that pairwise query-based algorithms achieve better accuracy-cost tradeoffs than raw confidence estimates.
This paper proposes a unified theoretical framework for phase transitions in deep learning (grokking, emergent capabilities) and non-equilibrium chemistry, describing both as driven informational systems governed by two gradient fields.
This paper provides the first non-asymptotic sample complexity bounds for learning exponential families of polynomials with score matching, showing polynomial dependence on model dimension.