Related papers: Instruction sequence size complexity of parity
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
Test suites assess natural language processing models' performance on specific functionalities: cases of interest involving model robustness, fairness, or particular linguistic capabilities. This paper introduces specification instructions:…
Single-pass instruction sequences under execution are considered to produce behaviours to be controlled by some execution environment. Threads as considered in thread algebra model such behaviours: upon each action performed by a thread, a…
We investigate explainability via short Boolean formulas in the data model based on unary relations. As an explanation of length k, we take a Boolean formula of length k that minimizes the error with respect to the target attribute to be…
An increasing number of scientific applications are making use of irregular data access patterns. An important class of such patterns involve subscripted-subscripts, wherein an array value appears in the index expression of another array.…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
Given a Boolean formula and a satisfying assignment, a flip is an operation that changes the value of a variable in the assignment so that the resulting assignment remains satisfying. We study the problem of computing the shortest sequence…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
We consider the problem of representing Boolean functions exactly by "sparse" linear combinations (over $\mathbb{R}$) of functions from some "simple" class ${\cal C}$. In particular, given ${\cal C}$ we are interested in finding…
Static verification techniques leverage Boolean formula satisfiability solvers such as SAT and SMT solvers that operate on conjunctive normal form and first order logic formulae, respectively, to validate programs. They force bounds on…
Message passing programs commonly use buffers to avoid unnecessary synchronizations and to improve performance by overlapping communication with computation. Unfortunately, using buffers makes the program no longer portable, potentially…
Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as…
Continual learning aims to enable a single model to learn a sequence of tasks without catastrophic forgetting. Top-performing methods usually require a rehearsal buffer to store past pristine examples for experience replay, which, however,…
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…
$ \newcommand{\cclass}[1]{{\normalfont\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there…
The increasing complexity of modern deep neural network models and the expanding sizes of datasets necessitate the development of optimized and scalable training methods. In this white paper, we addressed the challenge of efficiently…
The alignment of biological sequences such as DNA, RNA, and proteins, is one of the basic tools that allow to detect evolutionary patterns, as well as functional/structural characterizations between homologous sequences in different…
Many operations on sensory data -- comparison, memory, retrieval, and reasoning -- are naturally expressed over discrete symbolic structures. In language this interface is given by tokens; in audio, it must be learned. Existing audio…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…