Related papers: Extracting Formulae in Many-Valued Logic from Deep…
Deep ReLU neural networks admit nontrivial functional symmetries: vastly different architectures and parameters (weights and biases) can realize the same function. We address the complete identification problem -- given a function f,…
Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive…
We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…
Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…
This work describes a methodology that combines logic-based systems and connectionist systems. Our approach uses finite truth-valued {\L}ukasiewicz logic, wherein every connective can be defined by a neuron in an artificial network. This…
In this paper we present some results on the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, Rational {\L}ukasiewicz logic…
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
Deep ReLU Networks can be decomposed into a collection of linear models, each defined in a region of a partition of the input space. This paper provides three results extending this theory. First, we extend this linear decompositions to…
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g.,…
We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries…
It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Knowledge extraction is used to convert neural networks into symbolic descriptions with the objective of producing more comprehensible learning models. The central challenge is to find an explanation which is more comprehensible than the…
Deep learning models are favored in many research and industry areas and have reached the accuracy of approximating or even surpassing human level. However they've long been considered by researchers as black-box models for their…
We propose an open-source end-to-end logic optimization framework for large-scale boolean network with reinforcement learning.
We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and we show that, unlike standard MLNs with real-valued weights, complex MLNs are fully expressive. We then observe that…
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…
We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean cost in the input layer, and under the assumption that the weights are, in…
Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural…
Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these…