This paper uses ergodic theory to study statistical properties of smooth sequences over the odd alphabet {1,3}, defining a notion of type for those sequences and proving unique ergodicity for subshift…

This paper measures the lower bound for the shortest program generating a sequence, proving a conservation law and providing a deterministic engine to recover generating programs for certain sequences…

This paper introduces a novel algorithm for generating k Hamming weight binary words in linear time while minimizing random bit consumption.

This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

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 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…

The paper analyzes the phase transitions of the noisy transformer model on the unit sphere, proving a sharp global-minimizer dichotomy that depends on the dimension and coupling strength.

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

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…

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…

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

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 proposes using distributional Reinforcement Learning (RL) to stabilize learning in chaotic dynamical systems by optimizing the smooth evolution of the return distribution rather than individ…

Stochastic Lifting is a novel technique that enhances the modeling of stochastic physical systems by introducing independent random labels to state transitions, allowing a single network to generate d…

This paper completely characterizes cyclic equalizability for two words over any finite alphabet by proving that the words must share the same Parikh vector.

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 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 proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.

The paper introduces PRAXIS, a novel algorithm that efficiently approximates the computation of 'Rashomon sets' for decision trees, significantly reducing memory and runtime complexity.

This paper provides a focused, preparatory introduction to sheaves and topoi, establishing the necessary structural background to understand the advanced sheaf-theoretic framework used in cryptographi…