This paper develops a novel, computationally efficient method to quantify the uncertainty in wide neural network predictions by characterizing the limiting random fluctuations using stochastic evoluti…

The paper reformulates nonreversible perturbations of Fokker--Planck dynamics as gauge fields, providing a unified operator viewpoint to analyze relaxation processes and develop methods for learning o…

This paper establishes an exact mathematical correspondence between training and inference in deep learning and the solution of Hamilton-Jacobi partial differential equations, unifying multiple theore…

This paper develops a perturbation theory for spherical Hellinger-Kantorovich (SHK) gradient flows, providing explicit, time-dependent bounds on divergence metrics to guarantee differential privacy fo…

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

The paper introduces a Jacobian-based spectral audit to evaluate neural operators, demonstrating that standard prediction error metrics fail to capture crucial local dynamical structures and operator…

The paper analyzes the algorithmic complexity of finding collisions in single-layer binary neural networks, establishing that the collision resistance depends critically on the activation function's t…

The paper introduces the $\alpha$-Wasserstein mechanism to achieve Rényi Pufferfish Privacy using Laplace and Gaussian noise, demonstrating that it generalizes existing privacy frameworks and reduces…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

The study finds that specific, interpretable neuron populations (Rosetta Neurons) exhibit predictable, scale-dependent changes in selectivity and specialization as neural models grow larger.

The paper introduces Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes deep learning training in non-smooth loss landscapes by dynamically damping updates based on local geometric ins…

This paper demonstrates that the Euston secure inference framework, which uses SVD-based matrix transmission to save bandwidth, leaks private input data by exploiting subspace leakage of random masks.

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

This paper investigates the phenomenon of 'copying' in Distribution Matching Distillation (DMD), finding that high-dimensional distillation causes student models to spontaneously reproduce the teacher…

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

The paper establishes that the training process of fully connected deep neural networks (DNNs) on exponential family data is mathematically equivalent to performing a Renormalization Group (RG) calcul…

The paper analyzes the expressivity of padded transformers, proving that their computational power is primarily determined by model depth and numeric precision, rather than attention type or width.