相关论文: Binary perceptrons capacity via fully lifted rando…

Recent tensor-network samplings of modified Nishimori spin glasses have revealed robust finite-temperature critical transitions in two dimensions, defying the standard Edwards-Anderson lower critical dimension boundary ($d_{l}\approx2.5$).…

The Beta Rank Function (BRF) $x(u) =A(1-u)^b/u^a$, where $u$ is the normalized and continuous rank of an observation $x$, has wide applications in fitting real-world data from social science to biological phenomena. The underlying…

After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order…

We employ the chiral nucleon-nucleon potential derived in ref.[1] to study bound and scattering states in the two-nucleon system. At next-to-leading order, this potential is the sum of renormalized one-pion and two-pion exchange and contact…

We discuss briefly the kappa framework, proposed originally as a test for the Higgs couplings of the Standard Model (SM). Further, we discuss a generalization of this idea in terms of effective field theory. We sketch how to add dimension 6…

We present a rigorous theoretical framework for designing full-space spatial power dividers using metagratings. In our study, the current restrictions of spatial power dividing platforms such as reflection-only performance, operating at…

Doubly charged scalars frequently emerge in many well-motivated extensions of the Standard Model, particularly in frameworks that aim to explain the origin of neutrino masses. Their distinct electric charge and clean leptonic signatures…

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…

In scattering theory, the unitary limit is defined by an infinite scattering-length and a zero effective range, corresponding to a phase-shift \pi/2, independent of energy. This condition is satisfied by a rank-1 separable potential…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We use the replica method of statistical mechanics to examine a typical performance of correctly reconstructing $N$-dimensional sparse vector $bx=(x_i)$ from its linear transformation $by=bF bx$ of $P$ dimensions on the basis of…

We generalize some results on semicomputability by Jockusch \cite{jockusch1968semirecursive} to the setting of $\alpha$-Computability Theory. We define an $\alpha$-Kalimullin pair and show that it is definable in the $\alpha$-enumeration…

In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $\eta^\pi$) attained…

Models based on Universal Extra Dimensions predict Kaluza-Klein (KK) excitations of all Standard Model (SM) particles. We examine the pair production of KK excitations of top- and bottom-quarks at the Large Hadron Collider. Once produced,…

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how…

The main objective of this paper is to derive a new sequential characterization of the Cover and Pombra \cite{cover-pombra1989} characterization of the $n-$finite block or transmission feedback information ($n$-FTFI) capacity, which…

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the…

A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…

We present a new algorithm, Fractional Decomposition Tree (FDT) for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution…

We calculate the multifractal spectrum of the partition of the coupling space of a perceptron induced by random input-output pairs with non-zero mean. From the results we infer the influence of the input and output bias respectively on both…