Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard combinatorial optimization problems in the form of binary variables. The Hamiltonian function is often used to formulate QUBO problems where it is used as the objective function in the context of optimization. Recently, PI-GNN, a generic scalable framework, has been proposed to address the Combinatorial Optimization (CO) problems over graphs based on a simple Graph Neural Network (GNN) architecture. Their novel contribution was a generic QUBO-formulated Hamiltonian-inspired loss function that was optimized using GNN. In this study, we address a crucial issue related to the aforementioned setup especially observed in denser graphs. The reinforcement learning-based paradigm has also been widely used to address numerous CO problems. Here we also formulate and empirically evaluate the compatibility of the QUBO-formulated Hamiltonian as the generic reward function in the Reinforcement Learning paradigm to directly integrate the actual node projection status during training as the form of rewards. In our experiments, we observed up to 44% improvement in the RL-based setup compared to the PI-GNN algorithm. Our implementation can be found in //github.com/rizveeredwan/learning-graph-structure.
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The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this equation numerically is challenging due to the need to discretize complicated integral operators which increase the computational costs. These complexities are exacerbated by nonlinear source terms, nonsmooth data and irregular domains. In this study, we propose a second order Exponential Time Differencing Finite Element Method (ETD-RDP-FEM) to efficiently solve nonlinear FDE, posed in irregular domains. This approach discretizes matrix exponentials using a rational function with real and distinct poles, resulting in an L-stable scheme that damps spurious oscillations caused by non-smooth initial data. The method is shown to outperform existing second-order methods for FDEs with a higher accuracy and faster computational time.
Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of encoder architectures only perform dimension reduction on single streamlines as opposed to a full bundle of streamlines. This is a severe limitation of the encoder architecture that completely disregards the global geometric structure of streamlines at the expense of individual fibers. Moreover, the latent space may not be well structured which leads to doubt into their interpretability. In this paper we propose a novel Differentiable Vector Quantized Variational Autoencoder, which are engineered to ingest entire bundles of streamlines as single data-point and provides reliable trustworthy encodings that can then be later used to analyze streamlines in the latent space. Comparisons with several state of the art Autoencoders demonstrate superior performance in both encoding and synthesis.
Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods often face challenges in consistently achieving satisfactory performance and lack interpretability, which hinders our understanding of anomaly detection decisions. In this paper, we propose a novel approach to graph anomaly detection that leverages the power of interpretability to enhance performance. Specifically, our method extracts an attention map derived from gradients of graph neural networks, which serves as a basis for scoring anomalies. In addition, we conduct theoretical analysis using synthetic data to validate our method and gain insights into its decision-making process. To demonstrate the effectiveness of our method, we extensively evaluate our approach against state-of-the-art graph anomaly detection techniques. The results consistently demonstrate the superior performance of our method compared to the baselines.
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however, while these methods have demonstrated state-of-the-art performance in both accuracy and computational efficiency, a significant challenge remains in their interpretability. Most existing methodologies prioritize predictive accuracy over clarity in the underlying mechanisms driving the model's decisions. Interpretability is crucial for trustworthiness and broader applicability, especially in scientific and engineering domains where neural PDE solvers might see the most impact. In this context, a notable gap in current research is the integration of symbolic frameworks (such as symbolic regression) into these solvers. Symbolic frameworks have the potential to distill complex neural operations into human-readable mathematical expressions, bridging the divide between black-box predictions and solutions.
Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for parameterized non-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find a global minimizer reliably and quickly by using convex optimization algorithms.
Wireless capsule endoscopy (WCE) is a non-invasive method for visualizing the gastrointestinal (GI) tract, crucial for diagnosing GI tract diseases. However, interpreting WCE results can be time-consuming and tiring. Existing studies have employed deep neural networks (DNNs) for automatic GI tract lesion detection, but acquiring sufficient training examples, particularly due to privacy concerns, remains a challenge. Public WCE databases lack diversity and quantity. To address this, we propose a novel approach leveraging generative models, specifically the diffusion model (DM), for generating diverse WCE images. Our model incorporates semantic map resulted from visualization scale (VS) engine, enhancing the controllability and diversity of generated images. We evaluate our approach using visual inspection and visual Turing tests, demonstrating its effectiveness in generating realistic and diverse WCE images.
Spiking Neural Network (SNN) is known as the most famous brain-inspired model, but the non-differentiable spiking mechanism makes it hard to train large-scale SNNs. To facilitate the training of large-scale SNNs, many training methods are borrowed from Artificial Neural Networks (ANNs), among which deep residual learning is the most commonly used. But the unique features of SNNs make prior intuition built upon ANNs not available for SNNs. Although there are a few studies that have made some pioneer attempts on the topology of Spiking ResNet, the advantages of different connections remain unclear. To tackle this issue, we analyze the merits and limitations of various residual connections and empirically demonstrate our ideas with extensive experiments. Then, based on our observations, we abstract the best-performing connections into densely additive (DA) connection, extend such a concept to other topologies, and propose four architectures for training large-scale SNNs, termed DANet, which brings up to 13.24% accuracy gain on ImageNet. Besides, in order to present a detailed methodology for designing the topology of large-scale SNNs, we further conduct in-depth discussions on their applicable scenarios in terms of their performance on various scales of datasets and demonstrate their advantages over prior architectures. At a low training expense, our best-performing ResNet-50/101/152 obtain 73.71%/76.13%/77.22% top-1 accuracy on ImageNet with 4 time steps. We believe that this work shall give more insights for future works to design the topology of their networks and promote the development of large-scale SNNs. The code will be publicly available.
Reinforcement Learning (RL) is an emerging approach to control many dynamical systems for which classical control approaches are not applicable or insufficient. However, the resultant policies may not generalize to variations in the parameters that the system may exhibit. This paper presents a powerful yet simple algorithm in which collaboration is facilitated between RL agents that are trained independently to perform the same task but with different system parameters. The independency among agents allows the exploitation of multi-core processing to perform parallel training. Two examples are provided to demonstrate the effectiveness of the proposed technique. The main demonstration is performed on a quadrotor with slung load tracking problem in a real-time experimental setup. It is shown that integrating the developed algorithm outperforms individual policies by reducing the RMSE tracking error. The robustness of the ensemble is also verified against wind disturbance.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.
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