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This paper explores optimization landscapes in complex neural networks using Kähler geometry and information manifolds, providing theoretical guarantees on descent paths and analyzing effects of Calabi-Yau metrics.
A second-order early warning signal for multi-turn prompt injection is introduced, based on information geometry and a statistical manifold. The method uses a meta rate derived from the second derivative of the stability parameter to predict adversarial trajectories before threshold crossing, providing proactive detection.
Introduces CuBAS, an information-geometric framework for adaptive data selection in supervised classification that uses local curvature of the data manifold to identify informative samples, achieving improved accuracy across 30 benchmark datasets.
This paper introduces the degeneracy distillery, a method that automatically detects and resolves degenerate parameter combinations in physical models by estimating and flattening the Fisher information matrix, reducing the simulation budget required for neural posterior estimation while providing physical insight.
CoreMem proposes a resource-efficient edge-cloud memory architecture for dialogue agents, using Riemannian retrieval with a Fisher-Rao metric and Fisher-guided discrete token distillation to achieve strong accuracy improvements within an 8 GB VRAM budget.
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 studies generalization in learning through the lens of bounded-rational decision theory, where the learner's response law induces a tradeoff between training loss and sample dependence. The authors show that this tradeoff is governed by an f-divergence regularizer and that generalization can be certified from the learner's hedging behavior.