Related papers: Bisimulations for Neural Network Reduction
In this paper, we propose a concept of approximate bisimulation relation for feedforward neural networks. In the framework of approximate bisimulation relation, a novel neural network merging method is developed to compute the approximate…
Artificial neural networks have diverged far from their early inspiration in neurology. In spite of their technological and commercial success, they have several shortcomings, most notably the need for a large number of training examples…
Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions…
The paper provides a method to approximate a large-scale finite-valued network by a smaller model called the aggregated simulation, which is a combination of aggregation and (bi-)simulation. First, the algebraic state space representation…
This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of $\varepsilon$-perturbed bisimulation…
Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, computation time for inference can be reduced in most practical cases by exploiting domain knowledge and by making approximations in the knowledge…
This paper exploits bisimulation relations, generated by extracting the concept of morphisms between algebraic structures, to analyze set stabilization of Boolean control networks with lower complexity. First, for two kinds of bisimulation…
Simulation-based inference methods have been shown to be inaccurate in the data-poor regime, when training simulations are limited or expensive. Under these circumstances, the inference network is particularly prone to overfitting, and…
Neural networks have been extensively applied to a variety of tasks, achieving astounding results. Applying neural networks in the scientific field is an important research direction that is gaining increasing attention. In scientific…
We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…
Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
Step net bisimulation is a coinductive behavioral relation for finite Petri nets, which is a smooth generalization of the definition of standard step bisimulation \cite{NT84} on finite Petri nets. Its induced equivalence offers an…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is…
Establishing equivalences between programs or systems is crucial both for verifying correctness of programs, by establishing that two implementations are equivalent, and for justifying optimisations and program transformations, by…
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…
This paper presents methods to compare networks where relationships between pairs of nodes in a given network are defined. We define such network distance by searching for the optimal method to embed one network into another network, prove…