Related papers: The Computational Complexity of Understanding Netw…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…
We consider a model of unreliable or crowdsourced data where there is an underlying set of $n$ binary variables, each evaluator contributes a (possibly unreliable or adversarial) estimate of the values of some subset of $r$ of the…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
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…
Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
This paper discovers that the neural network with lower decision boundary (DB) variability has better generalizability. Two new notions, algorithm DB variability and $(\epsilon, \eta)$-data DB variability, are proposed to measure the…
The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean…
A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The…
We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs…
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…
The paper deals with the interpretability of Graph Neural Networks in the context of Boolean Satisfiability. The goal is to demystify the internal workings of these models and provide insightful perspectives into their decision-making…
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
Linear classifier probes are frequently utilized to better understand how neural networks function. Researchers have approached the problem of determining unit importance in neural networks by probing their learned, internal…
Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit $d^{O(1)}$-variate and degree $d$ polynomial $P_{d}\in VNP$ such that if any depth four circuit $C$ of bounded formal degree $d$ which computes a…
Boolean Petri nets are differentiated by types of nets $\tau$ based on which of the interactions nop, inp, out, set, res, swap, used, and free they apply or spare. The synthesis problem relative to a specific type of nets $\tau$ is to find…