Related papers: Nondeterministic functional transducer inference a…
Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…
Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation…
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the…
Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property---nondeterminism---in nondeterministic finite automata has not been well…
The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…
The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For…
Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…
We study monoidal transducers, transition systems arising as deterministic automata whose transitions also produce outputs in an arbitrary monoid, for instance allowing outputs to commute or to cancel out. We use the categorical framework…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant…
Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…
Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to reactive synthesis, where transformation specifications…
Posterior drift refers to changes in the relationship between responses and covariates while the distributions of the covariates remain unchanged. In this work, we explore functional linear regression under posterior drift with transfer…