Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fréchet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256 × 256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph directly; instead, noisy and indirect measurements of these properties are available. These scenarios are coined as Graph Inverse Problems (GRIPs). In this work, we introduce a framework leveraging GNNs to solve GRIPs. The framework is based on a combination of likelihood and prior terms, which are used to find a solution that fits the data while adhering to learned prior information. Specifically, we propose to combine recent deep learning techniques that were developed for inverse problems, together with GNN architectures, to formulate and solve GRIPs. We study our approach on a number of representative problems that demonstrate the effectiveness of the framework.

We investigate a link between Graph Neural Networks (GNNs) and Quadratic Unconstrained Binary Optimization (QUBO) problems, laying the groundwork for GNNs to approximate solutions for these computationally challenging tasks. By analyzing the sensitivity of QUBO formulations, we frame the solution of QUBO problems as a heterophilic node classification task. We then propose QUBO-GNN, an architecture that integrates graph representation learning techniques with QUBO-aware features to approximate solutions efficiently. Additionally, we introduce a self-supervised data generation mechanism to enable efficient and scalable training data acquisition even for large-scale QUBO instances. Experimental evaluations of QUBO-GNN across diverse QUBO problem sizes demonstrate its superior performance compared to exhaustive search and heuristic methods. Finally, we discuss open challenges in the emerging intersection between QUBO optimization and GNN-based learning.

Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we propose a novel GNN architecture inspired by Advection-Diffusion-Reaction systems, called ADR-GNN. Advection models feature transportation, while diffusion captures the local smoothing of features, and reaction represents the non-linear transformation between feature channels. We provide an analysis of the qualitative behavior of ADR-GNN, that shows the benefit of combining advection, diffusion, and reaction. To demonstrate its efficacy, we evaluate ADR-GNN on real-world node classification and spatio-temporal datasets, and show that it improves or offers competitive performance compared to state-of-the-art networks.

Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs), which leverage principles from continuous dynamical systems to model information flow on graphs with built-in properties such as feature smoothing or preservation. However, existing DE-GNNs rely on first or second-order temporal dependencies. In this paper, we propose a neural extension to those pre-defined temporal dependencies. We show that our model, called TDE-GNN, can capture a wide range of temporal dynamics that go beyond typical first or second-order methods, and provide use cases where existing temporal models are challenged. We demonstrate the benefit of learning the temporal dependencies using our method rather than using pre-defined temporal dynamics on several graph benchmarks.

Graph Neural Networks (GNNs) are prominent in handling sparse and unstructured data efficiently and effectively. Specifically, GNNs were shown to be highly effective for node classification tasks, where labelled information is available for only a fraction of the nodes. Typically, the optimization process, through the objective function, considers only labelled nodes while ignoring the rest. In this paper, we propose novel objective terms for the training of GNNs for node classification, aiming to exploit all the available data and improve accuracy. Our first term seeks to maximize the mutual information between node and label features, considering both labelled and unlabelled nodes in the optimization process. Our second term promotes anisotropic smoothness in the prediction maps. Lastly, we propose a cross-validating gradients approach to enhance the learning from labelled data. Our proposed objectives are general and can be applied to various GNNs, and require no architectural modifications. Extensive experiments demonstrate our approach using popular GNNs like Graph Convolutional Networks (e.g., GCN and GCNII), and Graph Attention Networks (e.g., GAT), reading a consistent and significant accuracy improvement on 10 real-world node classification datasets.

Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of these problems typically combine Convolution Neural Networks (CNN) architecture with a time prediction mechanism. However, oftentimes, such approaches underperform in the long-range propagation of information and lack explainability. In this work, we introduce a physically inspired architecture for the solution of such problems. Namely, we propose to augment CNNs with advection by designing a novel semi-Lagrangian push operator. We show that the proposed operator allows for the non-local transformation of information compared with standard convolutional kernels. We then complement it with Reaction and Diffusion neural components to form a network that mimics the Reaction-Advection-Diffusion equation, in high dimensions. We demonstrate the effectiveness of our network on a number of spatio-temporal datasets that show their merit. Our code is available at https://github.com/Siddharth-Rout/deepADRnet.

In this paper, we introduce neural network accelerated implicit filtering (NNAIF), a novel family of methods for solving noisy derivative free (i.e. black box, zeroth order) optimization problems. NNAIF intelligently combines the established literature on implicit filtering (IF) optimization methods with a neural network (NN) surrogate model of the objective function, resulting in accelerated derivative free methods for unconstrained optimization problems. The NN surrogate model consists of a fixed number of parameters, which can be as few as $\approx 1.3 \times 10^{4}$, that are updated as NNAIF progresses. We show that NNAIF directly inherits the convergence properties of IF optimization methods, and thus NNAIF is guaranteed to converge towards a critical point of the objective function under appropriate assumptions. Numerical experiments with $31$ noisy problems from the CUTEst optimization benchmark set demonstrate the benefits and costs associated with NNAIF. These benefits include NNAIF’s ability to minimize structured functions of several thousand variables much more rapidly than well-known alternatives, such as Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and finite difference based variants of gradient descent (GD) and BFGS, as well as its namesake IF.

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.

We present AS-CDG, a novel automatic scalable system for data-driven coverage-directed generation. The goal of AS-CDG is to find the test templates that maximize the probability of hitting uncovered events. The system contains two phases, one for a coarse-grained search that finds relevant parameters and the other for a fine-grained search for the settings of these parameters. To overcome the lack of evidence in the search, we replace the real target with an approximated target induced by neighboring events, for which we have evidence. Usage results on real-life units of high-end processors illustrate the ability of the proposed system to automatically find the desired test-templates and hit the previously uncovered target events.

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional neural networks, deep graph networks do not necessarily yield better performance than shallow graph networks. This behavior usually stems from the over-smoothing phenomenon. In this work, we propose a family of architecturesto control this behavior by design. Our networks are motivated by numerical methods for solving Partial Differential Equations (PDEs) on manifolds, and as such, their behavior can be explained by similar analysis. Moreover, as we demonstrate using an extensive set of experiments, our PDE-motivated networks can generalize and be effective for various types of problems from different fields. Our architectures obtain better or on par with the current state-of-the-art results for problems that are typically approached using different architectures.

Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use. These challenges include improving the network’s robustness to perturbations of the input image and the limited “field of view” of convolution operators. We introduce the IMEXnet that addresses these challenges by adapting semi-implicit methods for partial differential equations. Compared to similar explicit networks, such as residual networks, our network is more stable, which has recently shown to reduce the sensitivity to small changes in the input features and improve generalization. The addition of an implicit step connects all pixels in each channel of the image and therefore addresses the field of view problem while still being comparable to standard convolutions in terms of the number of parameters and computational complexity. We also present a new dataset for semantic segmentation and demonstrate the effectiveness of our architecture using the NYU Depth dataset.

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep residual networks as ordinary differential equations (ODEs), which have long been studied in mathematics and physics with rich theoretical and empirical success. From this interpretation, we develop a theoretical framework on stability and reversibility of deep neural networks, and derive three reversible neural network architectures that can go arbitrarily deep in theory. The reversibility property allows a memory-efficient implementation, which does not need to store the activations for most hidden layers. Together with the stability of our architectures, this enables training deeper networks using only modest computational resources. We provide both theoretical analyses and empirical results. Experimental results demonstrate the efficacy of our architectures against several strong baselines on CIFAR-10, CIFAR-100 and STL-10 with superior or on-par state-of-the-art performance. Furthermore, we show our architectures yield superior results when trained using fewer training data.

In this work, we establish the relation between optimal control and training deep Convolution Neural Networks (CNNs). We show that the forward propagation in CNNs can be interpreted as a time-dependent nonlinear differential equation and learning can be seen as controlling the parameters of the differential equation such that the network approximates the data-label relation for given training data. Using this continuous interpretation, we derive two new methods to scale CNNs with respect to two different dimensions. The first class of multiscale methods connects low-resolution and high-resolution data using prolongation and restriction of CNN parameters inspired by algebraic multigrid techniques. We demonstrate that our method enables classifying high-resolution images using CNNs trained with low-resolution images and vice versa and warm-starting the learning process. The second class of multiscale methods connects shallow and deep networks and leads to new training strategies that gradually increase the depths of the CNN while re-using parameters for initializations.

Mineral prospectivity mapping is an emerging application for machine learning algorithms which presents a series of practical difficulties. The goal is to learn the mapping function which can predict the existence or absence of economic mineralization from a compilation of geoscience datasets (ie: bedrock type, magnetic signature, geochemical response etc). The challenges include sparse, imbalanced labels (mineralization occurrences), varied label reliability, and a wide range in data quality and uncertainty. In order to address these issues an algorithm was developed based on total least squares and support vector machine regression which incorporates both data and label uncertainty into the objective function. This was done without losing sparsity in the residuals, thus maintaining minimal support vectors. Mineral prospectivity mapping is an application for machine learning which presents a series of practical difficulties. The goal is to learn the mapping function which can predict the existence of mineralization from a compilation of geoscience datasets. Challenges include sparse, imbalanced labels, varied label reliability, and a wide range in data uncertainty. To address this, an algorithm was developed based on TLS and SVM which incorporates both data and label uncertainty into the objective function.

Detection of fire and smoke in video is of practical and theoretical interest. In this paper, we propose the use of optimal mass transport (OMT) optical flow as a low-dimensional descriptor of these complex processes. The detection process is posed as a supervised Bayesian classification problem with spatio-temporal neighborhoods of pixels;feature vectors are composed of OMT velocities and R,G,B color channels. The classifier is implemented as a single-hidden-layer neural network. Sample results show probability of pixels belonging to fire or smoke. In particular, the classifier successfully distinguishes between smoke and similarly colored white wall, as well as fire from a similarly colored background.