Related papers: Deriving SN from PSN: a general proof technique

Normalization methods improve both optimization and generalization of ConvNets. To further boost performance, the recently-proposed switchable normalization (SN) provides a new perspective for deep learning: it learns to select different…

In this article, two types of methods from different perspectives based on spectral normalization are described for ensuring the stability of the system controlled by a neural network. The first one is that the L2 gain of the feedback…

We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…

We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both…

We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of…

Gentzen designed his natural deduction proof system to ``come as close as possible to actual reasoning.'' Indeed, natural deduction proofs closely resemble the static structure of logical reasoning in mathematical arguments. However,…

We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…

In a type-theoretic fibration category in the sense of Shulman (representing a dependent type theory with at least 1, Sigma, Pi, and identity types), we define the type of constant functions from A to B. This involves an infinite tower of…

The theory part of this paper is sketched as follows. Based on column stochastic average matrix $T_n$ selected as a basic substitution matrix, the method of advanced successive difference substitution is established. Then, a set of…

In this paper, we give corrected and improved definitions of the sets $S$ and $\Delta$ compared to [1]. By using these new definitions, we go throughout the proof of the main result in [1], and we correct it.

We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…

Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…

The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived…

It has been observed that linearizability, the prevalent consistency condition for implementing concurrent objects, does not preserve some probability distributions. A stronger condition, called strong linearizability has been proposed, but…

Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…

Why do deep networks generalize well? In contrast to classical generalization theory, we approach this fundamental question by examining not only inputs and outputs, but the evolution of internal features. Our study suggests a phenomenon of…

We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…

We prove that given two cut free nets of linear logic, by means of their relational interpretations one can: 1) first determine whether or not the net obtained by cutting the two nets is strongly normalizable 2) then (in case it is strongly…

In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…

We present a more general (parametric-) homological characterization of the Direct Summand Theorem. Specifically, we state two new conjectures: the Socle-Parameter conjecture (SPC) in its weak and strong forms. We give a proof for the week…