Credit assignment for trained neural networks based on Koopman operator theory

1 Introduction Artificial neural networks(ANNs,also NNs)have recently emerged as leading candidate models for deep learning,popularly used in various areas[1–3].Behind the enormous success,ANNs are generally with complicated structures,there being an intricate data flow through multiple linear or nonlinear components between the input layer and the output layer.Consequently,it is pressing to evaluate how much a specific component contributes to the final output,termed the Credit Assignment Problem(CAP)[4]in this paper.

Towards robust neural networks via a global and monotonically decreasing robustness training strategy

Robustness of deep neural networks(DNNs)has caused great concerns in the academic and industrial communities,especially in safety-critical domains.Instead of verifying whether the robustness property holds or not in certain neural networks,this paper focuses on training robust neural networks with respect to given perturbations.State-of-the-art training methods,interval bound propagation(IBP)and CROWN-IBP,perform well with respect to small perturbations,but their performance declines significantly in large perturbation cases,which is termed“drawdown risk”in this paper.Specifically,drawdown risk refers to the phenomenon that IBPfamily training methods cannot provide expected robust neural networks in larger perturbation cases,as in smaller perturbation cases.To alleviate the unexpected drawdown risk,we propose a global and monotonically decreasing robustness training strategy that takes multiple perturbations into account during each training epoch(global robustness training),and the corresponding robustness losses are combined with monotonically decreasing weights(monotonically decreasing robustness training).With experimental demonstrations,our presented strategy maintains performance on small perturbations and the drawdown risk on large perturbations is alleviated to a great extent.It is also noteworthy that our training method achieves higher model accuracy than the original training methods,which means that our presented training strategy gives more balanced consideration to robustness and accuracy.

Salivary microbiota may predict the presence of esophageal squamous cell carcinoma

The aim is to explore the predictive value of salivary bacteria for the presence of esophageal squamous cell carcinoma (ESCC). Saliva samples were obtained from 178 patients with ESCC and 101 healthy controls, and allocated to screening and verification cohorts, respectively. In the screening phase, after saliva DNA was extracted, 16S rRNA V4 regions of salivary bacteria were amplified by polymerase chain reaction (PCR) with high-throughput sequencing. Highly expressed target bacteria were screened by Operational Taxonomic Units clustering, species annotation and microbial diversity assessment. In the verification phase, the expression levels of target bacteria identified in the screening phase were verified by absolute quantitative PCR (Q-PCR). Receiver operating characteristic (ROC) curves were plotted to investigate the predictive value of target salivary bacteria. LEfSe analysis revealed higher proportions of Fusobacterium, Streptococcus and Porphyromonas, and Q-PCR assay showed significantly higher numbers of Streptococcus salivarius, Fusobacterium nucleatum and Porphyromonas gingivalis in patients with ESCC, when compared with healthy controls (all P < 0.05). The areas under the ROC curves for Streptococcus salivarius, Fusobacterium nucleatum, Porphyromonas gingivalis and the combination of the three bacteria for predicting patients with ESCC were 69%, 56.5%, 61.8% and 76.4%, respectively. The sensitivities corresponding to cutoff value were 69.3%, 22.7%, 35.2% and 86.4%, respectively, and the matched specificity were 78.4%, 96.1%, 90.2% and 58.8%, respectively. These highly expressed Streptococcus salivarius, Fusobacterium nucleatum and Porphyromonas gingivalis in the saliva, alone or in combination, indicate their predictive value for ESCC.

Towards Connecting Discrete Mathematics and Software Engineering

To enhance training in software development,we argue that students of software engineering should be exposed to software development activities early in the curriculum.This entails meeting the challenge of engaging students in software development before they take the software engineering course.In this paper,we propose a method to connect courses in the software engineering curriculum by setting comprehensive development projects to students in prerequisite courses for software development.Using the Discrete Mathematics(DM)course as an example,we describe the implementation of the proposed method and teaching practices using several practical and comprehensive projects derived from topics in discrete mathematics.Detailed descriptions of the sample projects,their application,and training results are given.Results and lessons learned from applying these practices show that it is a promising way to connect courses in the software engineering curriculum.

An Axiom System of Probabilistic Mu-Calculus

Mu-calculus(a.k.a.μTL)is built up from modal/dynamic logic via adding the least fixpoint operatorμ.This type of logic has attracted increasing attention since Kozen’s seminal work.PμTL is a succinct probabilistic extension of the standardμTL obtained by making the modal operators probabilistic.Properties of this logic,such as expressiveness and satisfiability decision,have been studied elsewhere.We consider another important problem:the axiomatization of that logic.By extending the approaches of Kozen and Walukiewicz,we present an axiom system for PμTL.In addition,we show that the axiom system is complete for aconjunctive formulas.

Probabilistic synthesis against GR(1) winning condition

Reactive synthesis is a technique for automatic generation of a reactive system from a high level specification.The system is reactive in the sense that it reacts to the inputs from the environment.The specification is in general given as a linear temporal logic(LTL)formula.The behaviour of the system interacting with the environment can be represented as a game in which the system plays against the environment.Thus,a problem of reactive synthesis is commonly treated as solving such a game with the specification as the winning condition.Reactive synthesis has been thoroughly investigated for more two decades.A well-known challenge is to deal with the complex uncertainty of the environment.We understand that a major issue is due to the lack of a sufficient treatment of probabilistic properties in the traditional models.For example,a two-player game defined by a standard Kriple structure does not consider probabilistic transitions in reaction to the uncertain physical environment;and a Markov Decision Process(MDP)in general does not explicitly separate the system from its environment and it does not describe the interaction between system and the environment.In this paper,we propose a new and more general model which combines the two-player game and the MDP.Furthermore,we study probabilistic reactive synthesis for the games of General Reactivity of Rank 1(i.e.,GR(1))defined in this model.More specifically,we present an algorithm,which for given model,a location and a GR(1)specification,determines the strategy for each player how to maximize/minimize the probabilities of the satisfaction of at location.We use an example to describe the model of probabilistic games and demonstrate our algorithm.

Software testing without the oracle correctness assumption

1 Introduction When testing programs,the oracle correctness assumption(OCA)implies that there are no errors in the test oracles,such as the expected outputs are always correctly designed and written in unit testing assertions.Guo's work[1]is the first piece of work that investigated the influences on fault localization caused by errors in test oracles and proposed a method to identify potential incorrect oracles.However,no systematic discussions are availed.