Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization methods are used to transform higher-order problems into QUBOs. However, quadratization methods for complex problems involving Machine Learning (ML) remain largely unknown. In these problems, strong nonlinearity and dense interactions prevent conventional methods from being applied. Therefore, we model target functions by the sum of rectified linear unit bases, which not only have the ability of universal approximation, but also have an equivalent quadratic-polynomial representation. In this study, the proof of concept is verified both numerically and analytically. In addition, by combining QA with the proposed quadratization, we design a new black-box optimization scheme, in which ML surrogate regressors are inputted to QA after the quadratization process.

In recent years, advanced U-like networks have demonstrated remarkable performance in medical image segmentation tasks. However, their drawbacks, including excessive parameters, high computational complexity, and slow inference speed, pose challenges for practical implementation in scenarios with limited computational resources. Existing lightweight U-like networks have alleviated some of these problems, but they often have pre-designed structures and consist of inseparable modules, limiting their application scenarios. In this paper, we propose three plug-and-play decoders by employing different discretization methods of the neural memory Ordinary Differential Equations (nmODEs). These decoders integrate features at various levels of abstraction by processing information from skip connections and performing numerical operations on upward path. Through experiments on the PH2, ISIC2017, and ISIC2018 datasets, we embed these decoders into different U-like networks, demonstrating their effectiveness in significantly reducing the number of parameters and FLOPs while maintaining performance. In summary, the proposed discretized nmODEs decoders are capable of reducing the number of parameters by about 20% ~ 50% and FLOPs by up to 74%, while possessing the potential to adapt to all U-like networks. Our code is available at https://github.com/nayutayuki/Lightweight-nmODE-Decoders-For-U-like-networks.

Q-learning is widely recognized as an effective approach for synthesizing controllers to achieve specific goals. However, handling challenges posed by continuous state-action spaces remains an ongoing research focus. This paper presents a systematic analysis that highlights a major drawback in space discretization methods. To address this challenge, the paper proposes a symbolic model that represents behavioral relations, such as alternating simulation from abstraction to the controlled system. This relation allows for seamless application of the synthesized controller based on abstraction to the original system. Introducing a novel Q-learning technique for symbolic models, the algorithm yields two Q-tables encoding optimal policies. Theoretical analysis demonstrates that these Q-tables serve as both upper and lower bounds on the Q-values of the original system with continuous spaces. Additionally, the paper explores the correlation between the parameters of the space abstraction and the loss in Q-values. The resulting algorithm facilitates achieving optimality within an arbitrary accuracy, providing control over the trade-off between accuracy and computational complexity. The obtained results provide valuable insights for selecting appropriate learning parameters and refining the controller. The engineering relevance of the proposed Q-learning based symbolic model is illustrated through two case studies.

Machine learning (ML) has employed various discretization methods to partition numerical attributes into intervals. However, an effective discretization technique remains elusive in many ML applications, such as association rule mining. Moreover, the existing discretization techniques do not reflect best the impact of the independent numerical factor on the dependent numerical target factor. This research aims to establish a benchmark approach for numerical attribute partitioning. We conduct an extensive analysis of human perceptions of partitioning a numerical attribute and compare these perceptions with the results obtained from our two proposed measures. We also examine the perceptions of experts in data science, statistics, and engineering by employing numerical data visualization techniques. The analysis of collected responses reveals that $68.7\%$ of human responses approximately closely align with the values generated by our proposed measures. Based on these findings, our proposed measures may be used as one of the methods for discretizing the numerical attributes.

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the proposed design. In each equation, a deep neural network is used to approximate the unknown function. Three forms of fractional differential equations have been examined to highlight the method's versatility: a fractional ordinary differential equation, a fractional order integrodifferential equation, and a fractional order partial differential equation. The results show that the proposed architecture solves different forms of fractional differential equations with excellent precision.

We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization methods. Particularly, this strategy can be used to efficiently train neural network surrogate models of partial differential equations by (i) leveraging the accuracy and convergence properties of advanced numerical methods, solvers, and preconditioners, as well as (ii) better scalability to higher order PDEs by strictly limiting optimization to first order automatic differentiation. The presented neural bootstrapping method (hereby dubbed NBM) is based on evaluation of the finite discretization residuals of the PDE system obtained on implicit Cartesian cells centered on a set of random collocation points with respect to trainable parameters of the neural network. Importantly, the conservation laws and symmetries present in the bootstrapped finite discretization equations inform the neural network about solution regularities within local neighborhoods of training points. We apply NBM to the important class of elliptic problems with jump conditions across irregular interfaces in three spatial dimensions. We show the method is convergent such that model accuracy improves by increasing number of collocation points in the domain and predonditioning the residuals. We show NBM is competitive in terms of memory and training speed with other PINN-type frameworks. The algorithms presented here are implemented using \texttt{JAX} in a software package named \texttt{JAX-DIPS} (https://github.com/JAX-DIPS/JAX-DIPS), standing for differentiable interfacial PDE solver. We open sourced \texttt{JAX-DIPS} to facilitate research into use of differentiable algorithms for developing hybrid PDE solvers.

Communication is crucial in multi-agent reinforcement learning when agents are not able to observe the full state of the environment. The most common approach to allow learned communication between agents is the use of a differentiable communication channel that allows gradients to flow between agents as a form of feedback. However, this is challenging when we want to use discrete messages to reduce the message size, since gradients cannot flow through a discrete communication channel. Previous work proposed methods to deal with this problem. However, these methods are tested in different communication learning architectures and environments, making it hard to compare them. In this paper, we compare several state-of-the-art discretization methods as well as a novel approach. We do this comparison in the context of communication learning using gradients from other agents and perform tests on several environments. In addition, we present COMA-DIAL, a communication learning approach based on DIAL and COMA extended with learning rate scaling and adapted exploration. Using COMA-DIAL allows us to perform experiments on more complex environments. Our results show that the novel ST-DRU method, proposed in this paper, achieves the best results out of all discretization methods across the different environments. It achieves the best or close to the best performance in each of the experiments and is the only method that does not fail on any of the tested environments.

IoT device identification is the process of recognizing and verifying connected IoT devices to the network. This is an essential process for ensuring that only authorized devices can access the network, and it is necessary for network management and maintenance. In recent years, machine learning models have been used widely for automating the process of identifying devices in the network. However, these models are vulnerable to adversarial attacks that can compromise their accuracy and effectiveness. To better secure device identification models, discretization techniques enable reduction in the sensitivity of machine learning models to adversarial attacks contributing to the stability and reliability of the model. On the other hand, Ensemble methods combine multiple heterogeneous models to reduce the impact of remaining noise or errors in the model. Therefore, in this paper, we integrate discretization techniques and ensemble methods and examine it on model robustness against adversarial attacks. In other words, we propose a discretization-based ensemble stacking technique to improve the security of our ML models. We evaluate the performance of different ML-based IoT device identification models against white box and black box attacks using a real-world dataset comprised of network traffic from 28 IoT devices. We demonstrate that the proposed method enables robustness to the models for IoT device identification.

Recently, many improved naive Bayes methods have been developed with enhanced discrimination capabilities. Among them, regularized naive Bayes (RNB) produces excellent performance by balancing the discrimination power and generalization capability. Data discretization is important in naive Bayes. By grouping similar values into one interval, the data distribution could be better estimated. However, existing methods including RNB often discretize the data into too few intervals, which may result in a significant information loss. To address this problem, we propose a semi-supervised adaptive discriminative discretization framework for naive Bayes, which could better estimate the data distribution by utilizing both labeled data and unlabeled data through pseudo-labeling techniques. The proposed method also significantly reduces the information loss during discretization by utilizing an adaptive discriminative discretization scheme, and hence greatly improves the discrimination power of classifiers. The proposed RNB+, i.e., regularized naive Bayes utilizing the proposed discretization framework, is systematically evaluated on a wide range of machine-learning datasets. It significantly and consistently outperforms state-of-the-art NB classifiers.

In many classification models, data is discretized to better estimate its distribution. Existing discretization methods often target at maximizing the discriminant power of discretized data, while overlooking the fact that the primary target of data discretization in classification is to improve the generalization performance. As a result, the data tend to be over-split into many small bins since the data without discretization retain the maximal discriminant information. Thus, we propose a Max-Dependency-Min-Divergence (MDmD) criterion that maximizes both the discriminant information and generalization ability of the discretized data. More specifically, the Max-Dependency criterion maximizes the statistical dependency between the discretized data and the classification variable while the Min-Divergence criterion explicitly minimizes the JS-divergence between the training data and the validation data for a given discretization scheme. The proposed MDmD criterion is technically appealing, but it is difficult to reliably estimate the high-order joint distributions of attributes and the classification variable. We hence further propose a more practical solution, Max-Relevance-Min-Divergence (MRmD) discretization scheme, where each attribute is discretized separately, by simultaneously maximizing the discriminant information and the generalization ability of the discretized data. The proposed MRmD is compared with the state-of-the-art discretization algorithms under the naive Bayes classification framework on 45 machine-learning benchmark datasets. It significantly outperforms all the compared methods on most of the datasets.