Related papers: The Consequences of Eliminating NP Solutions
This paper presents an anlysis of the NP-hard minimization problem $\min \{\|b - Ax\|_2: \ x \in [0,1]^n, | \text{supp}(x) | \leq \sigma\}$, where $\text{supp}(x) = \{i \in [n]: x_i \neq 0\}$ and $\sigma$ is a positive integer. The object…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
We investigate regularization of scalar one-loop integrals in the Pauli- Villars subtraction scheme. The results depend on the number of sub- tractions, in particular the finite terms that survive after the diver- gences have been absorbed…
Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
A problem is \emph{downward self-reducible} if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that…
The increasing size of recently proposed Neural Networks makes it hard to implement them on embedded devices, where memory, battery and computational power are a non-trivial bottleneck. For this reason during the last years network…
Hardness magnification reduces major complexity separations (such as $\mathsf{\mathsf{EXP}} \nsubseteq \mathsf{NC}^1$) to proving lower bounds for some natural problem $Q$ against weak circuit models. Several recent works [OS18, MMW19,…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Patterns provide a concise, syntactic way of describing a set of strings, but their expressive power comes at a price: a number of fundamental decision problems concerning (erasing) pattern languages, such as the membership problem and…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
In recent years, many neural network models have been proposed for pattern classification, function approximation and regression problems. This paper presents an approach for classifying patterns from simplified NNs. Although the predictive…
The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
Artificial intelligence and machine learning algorithms have become ubiquitous. Although they offer a wide range of benefits, their adoption in decision-critical fields is limited by their lack of interpretability, particularly with textual…
In recent years, continual learning, a prediction setting in which the problem environment may evolve over time, has become an increasingly popular research field due to the framework's gearing towards complex, non-stationary objectives.…
The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular…
The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete,…