This paper studies approximating the partition function of the anti-ferromagnetic multi-state Potts model at low temperature on random regular bipartite graphs, and shows that single-site Glauber dyna…

This paper presents the first application of thermodynamic computing to mRNA codon optimization in pharmaceutical R&D, achieving significant energy savings compared to conventional GPUs.

The paper introduces an improved PULSE method to efficiently estimate the thermodynamic properties of chemically disordered compounds by sampling and estimating the system's partition function, demons…

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 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.

Chen et al. prove a Poincaré inequality for Glauber dynamics of hard-core model on random regular graphs using Bochner--Bakry--Émery approach.

This paper shows that shallow circuits cannot prepare near-optimal states for random quantum $p$-spin glasses, and proves depth lower bounds for such preparations.

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…

The paper presents black box algorithms for constructing standard generators and performing membership testing in Suzuki groups, with no false positives.

This paper presents a method for identifying probabilistic structures from empirical probability tensors using algebraic statistics and Kronecker-stack class of configuration matrices.

The paper proposes a semi-relaxed Gromov-Wasserstein objective to estimate the latent connectivity structure of large-scale networks, achieving statistically consistent and efficient recovery of the u…

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

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

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 proposes a method to describe dynamical systems using molecular and reaction concepts, making three key decisions: number of places, species determination, and transitions.

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…