Related papers: CORN: Correlation-Driven Nonparametric Learning Ap…
We introduce a logical language for reasoning about quantized aggregate-combine graph neural networks with global readout (ACR-GNNs). We provide a logical characterization and use it to prove that verification tasks for quantized GNNs with…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
We introduce a new categorical and constructive foundation for analytic approximation based on a Contextual Choice Principle (CCP), which enforces locality and compatibility in the construction of mathematical objects. Central to our…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Networks are hard to configure correctly, and misconfigurations occur frequently, leading to outages or security breaches. Formal verification techniques have been applied to guarantee the correctness of network configurations, thereby…
We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.
The fixed-point index of a homeomorphism of Jordan curves measures the number of fixed-points, with multiplicity, of the extension of the homeomorphism to the full Jordan domains in question. The now-classical Circle Index Lemma says that…
Is there any theoretical guarantee for the approximation ability of neural networks? The answer to this question is the "Universal Approximation Theorem for Neural Networks". This theorem states that a neural network is dense in a certain…
We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
We prove universality for cokernels of random integral matrices with symmetries via an approach different from the classical surjection moment method introduced by Wood (arXiv:1402.5149). In the symmetric case, we reprove Hodges'…
This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by…
For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…
Bibliometrics is useful to analyze the research impact for measuring the research quality. Different bibliographic databases like Scopus, Web of Science, Google Scholar etc. are accessed for evaluating the trend of publications and…
We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.
Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…