Related papers: Not All Multi-Valued Partial CFL Functions Are Ref…
This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…
While transformers have proven enormously successful in a range of tasks, their fundamental properties as models of computation are not well understood. This paper contributes to the study of the expressive capacity of transformers,…
This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the…
We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
Conventional deep networks rely on one-way backpropagation that overlooks reconciling high-level predictions with lower-level representations. We propose \emph{Contextual Feedback Loops} (CFLs), a lightweight mechanism that re-injects…
Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics.…
Multivariable, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We examine the geometry of this space of matrices and conclude that the best notion…
Machine learning classifiers' capability is largely dependent on the scale of available training data and limited by the model overfitting in data-scarce learning tasks. To address this problem, this work proposes a novel framework of Meta…
In this paper we study the problem of learning from multiple modal data for purpose of document classification. In this problem, each document is composed two different modals of data, i.e., an image and a text. Cross-modal factor analysis…
We study the problem of synthesizing non-smooth control barrier functions (CBFs) for continuous-time switched affine systems. Switched affine systems are defined by a set of affine dynamical modes, wherein the control consists of a…
In the standard model of computing multi-output functions in logspace ($\mathsf{FL}$), we are given a read-only tape holding $x$ and a logarithmic length worktape, and must print $f(x)$ to a dedicated write-only tape. However, there has…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
Boolean functional synthesis is the process of constructing a Boolean function from a Boolean specification that relates input and output variables. Despite significant recent developments in synthesis algorithms, Boolean functional…
Despite recent successes in Reinforcement Learning, value-based methods often suffer from high variance hindering performance. In this paper, we illustrate this in a continuous control setting where state of the art methods perform poorly…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…