Related papers: Not All Multi-Valued Partial CFL Functions Are Ref…

Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we…

We develop a functional encoder-decoder approach to supervised meta-learning, where labeled data is encoded into an infinite-dimensional functional representation rather than a finite-dimensional one. Furthermore, rather than directly…

Federated learning (FL) enables collaborative learning across multiple clients. In most FL work, all clients train a single learning task. However, the recent proliferation of FL applications may increasingly require multiple FL tasks to be…

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and…

The partition function of 2d conformal field theory is a modular invariant function. It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function. In this paper,…

Multi-channel Multi-tone Active Noise Equalizers can achieve different user-selected noise spectrum profiles even at different space positions. They can apply a different equalization factor at each noise frequency component and each…

Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design…

To expand a fundamental theory of context-free languages, we equip nondeterministic one-way pushdown automata with additional oracle mechanisms, which naturally induce various nondeterministic reducibilities among formal languages. As a…

For a given function $F$ from $\mathbb F_{p^n}$ to itself, determining whether there exists a function which is CCZ-equivalent but EA-inequivalent to $F$ is a very important and interesting problem. For example, K\"olsch \cite{KOL21} showed…

Reinforcement Learning (RL) uses rewards to guide learning, yet reward design is typically hand-crafted using heuristics that can be difficult to tune. We propose a Control Barrier Function (CBF)-informed reward design for Multi-Agent RL…

In this article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at…

A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…

We propose Sequential Feature Filtering Classifier (FFC), a simple but effective classifier for convolutional neural networks (CNNs). With sequential LayerNorm and ReLU, FFC zeroes out low-activation units and preserves high-activation…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

The Unconstrained Feature Model (UFM) is a mathematical framework that enables closed-form approximations for minimal training loss and related performance measures in deep neural networks (DNNs). This paper leverages the UFM to provide…

Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to…

We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization…

Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting…

Language models trained on large-scale datasets have been shown to learn features that encode abstract concepts such as factuality or intent. Such features are traditionally used for test-time monitoring or steering. We present an…