arXiv subjects

Charilaos I. Kanatsoulis

Publications and source records attributed to Charilaos I. Kanatsoulis.

18 recordsLinked to original sources

arXiv2026

Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs

Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing. While MPNNs have a precise definition, there is no widely accepted criterion for what makes a mapping a spectral GNN. Most existing work restricts spectral GNNs to layered architectures based on linear spectral filters. Under this restriction, we show that spectral and spatial GNNs have largely equivalent expressive power. To promote progress in the field, we propose a precise definition of spectral GNNs based on eigenbasis symmetries, in contrast to the definition of MPNNs via neighborhood permutation symmetries. We further argue that the two perspectives offer complementary strengths. MPNNs provide a natural language for discrete structure and expressivity analysis through tools from logic and graph isomorphism, while the spectral perspective offers principled tools for understanding smoothing, bottlenecks, stability, and community structure. Overall, we argue that progress in graph learning will be accelerated by clarifying the similarities and differences between these perspectives and by moving toward a unified theoretical framework.

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arXiv2026

Learning over Positive and Negative Edges with Contrastive Message Passing

Conventional approaches to learning on graphs involve message passing along existing (i.e., positive) edges to update node features. However, these approaches often disregard the potentially valuable information contained in the absence (i.e., negative) of edges. Here, we theoretically analyze the value of negative edges in graph representations and prove that in settings of low label rates, high homophily, and high edge density, access to negative edges provides significant information gain over using only positive edges. Motivated by this insight, we introduce Contrastive Message Passing (CMP), a general message passing architecture that enable graph neural network layers to reason over positive and negative edges. By imposing soft positive semidefinite constraints on the learnable weights, our approach differentially applies similarity-preserving transformations to positively connected nodes and dissimilarity-inducing transformations to negatively connected nodes. Over simulated and real datasets in varying data regimes, CMP consistently outperforms baselines in low-label settings when negative edges are informative.

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arXiv2026

Relational Graph Transformer

Relational Deep Learning (RDL) is a promising approach for building state-of-the-art predictive models on multi-table relational data by representing it as a heterogeneous temporal graph. However, commonly used Graph Neural Network models suffer from fundamental limitations in capturing complex structural patterns and long-range dependencies that are inherent in relational data. While Graph Transformers have emerged as powerful alternatives to GNNs on general graphs, applying them to relational entity graphs presents unique challenges: (i) Traditional positional encodings fail to generalize to massive, heterogeneous graphs; (ii) existing architectures cannot model the temporal dynamics and schema constraints of relational data; (iii) existing tokenization schemes lose critical structural information. Here we introduce the Relational Graph Transformer (RelGT), the first graph transformer architecture designed specifically for relational tables. RelGT employs a novel multi-element tokenization strategy that decomposes each node into five components (features, type, hop distance, time, and local structure), enabling efficient encoding of heterogeneity, temporality, and topology without expensive precomputation. Our architecture combines local attention over sampled subgraphs with global attention to learnable centroids, incorporating both local and database-wide representations. Across 21 tasks from the RelBench benchmark, RelGT consistently matches or outperforms GNN baselines by up to 18%, establishing Graph Transformers as a powerful architecture for Relational Deep Learning.

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arXiv2025

Learning Efficient Positional Encodings with Graph Neural Networks

Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs for graphs poses significant challenges due to the absence of canonical node ordering and the scale of the graph. {In this work, we identify four key properties that graph PEs should satisfy}: stability, expressive power, scalability, and genericness. We find that existing eigenvector-based PE methods often fall short of jointly satisfying these criteria. To address this gap, we introduce PEARL, a novel framework of learnable PEs for graphs. Our primary insight is that message-passing GNNs function as nonlinear mappings of eigenvectors, enabling the design of GNN architectures for generating powerful and efficient PEs. A crucial challenge lies in initializing node attributes in a manner that is both expressive and permutation equivariant. We tackle this by initializing GNNs with random node inputs or standard basis vectors, thereby unlocking the expressive power of message-passing operations, while employing statistical pooling functions to maintain permutation equivariance. Our analysis demonstrates that PEARL approximates equivariant functions of eigenvectors with linear complexity, while rigorously establishing its stability and high expressive power. Experimental evaluations show that PEARL outperforms lightweight versions of eigenvector-based PEs and achieves comparable performance to full eigenvector-based PEs, but with one or two orders of magnitude lower complexity. Our code is available at https://github.com/ehejin/Pearl-PE.

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arXiv2024

T-GAE: Transferable Graph Autoencoder for Network Alignment

Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form. Existing optimization algorithms do not scale up as the size of the graphs increases. While being able to reduce the matching complexity, current GNN approaches fit a deep neural network on each graph and requires re-train on unseen samples, which is time and memory inefficient. To tackle both challenges we propose T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining. We prove that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods. Our experiments on real-world benchmarks demonstrate that T-GAE outperforms the state-of-the-art optimization method and the best GNN approach by up to 38.7% and 50.8%, respectively, while being able to reduce 90% of the training time when matching out-of-distribution large scale networks. We conduct ablation studies to highlight the effectiveness of the proposed encoder architecture and training objective in enhancing the expressiveness of GNNs to match perturbed graphs. T-GAE is also proved to be flexible to utilize matching algorithms of different complexities. Our code is available at https://github.com/Jason-Tree/T-GAE.

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arXiv2024

Generalizability of Graph Neural Networks for Decentralized Unlabeled Motion Planning

Unlabeled motion planning involves assigning a set of robots to target locations while ensuring collision avoidance, aiming to minimize the total distance traveled. The problem forms an essential building block for multi-robot systems in applications such as exploration, surveillance, and transportation. We address this problem in a decentralized setting where each robot knows only the positions of its $k$-nearest robots and $k$-nearest targets. This scenario combines elements of combinatorial assignment and continuous-space motion planning, posing significant scalability challenges for traditional centralized approaches. To overcome these challenges, we propose a decentralized policy learned via a Graph Neural Network (GNN). The GNN enables robots to determine (1) what information to communicate to neighbors and (2) how to integrate received information with local observations for decision-making. We train the GNN using imitation learning with the centralized Hungarian algorithm as the expert policy, and further fine-tune it using reinforcement learning to avoid collisions and enhance performance. Extensive empirical evaluations demonstrate the scalability and effectiveness of our approach. The GNN policy trained on 100 robots generalizes to scenarios with up to 500 robots, outperforming state-of-the-art solutions by 8.6\% on average and significantly surpassing greedy decentralized methods. This work lays the foundation for solving multi-robot coordination problems in settings where scalability is important.

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arXiv2024

Solving Large-scale Spatial Problems with Convolutional Neural Networks

Over the past decade, deep learning research has been accelerated by increasingly powerful hardware, which facilitated rapid growth in the model complexity and the amount of data ingested. This is becoming unsustainable and therefore refocusing on efficiency is necessary. In this paper, we employ transfer learning to improve training efficiency for large-scale spatial problems. We propose that a convolutional neural network (CNN) can be trained on small windows of signals, but evaluated on arbitrarily large signals with little to no performance degradation, and provide a theoretical bound on the resulting generalization error. Our proof leverages shift-equivariance of CNNs, a property that is underexploited in transfer learning. The theoretical results are experimentally supported in the context of mobile infrastructure on demand (MID). The proposed approach is able to tackle MID at large scales with hundreds of agents, which was computationally intractable prior to this work.

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arXiv2023

Multi-Target Tracking with Transferable Convolutional Neural Networks

Multi-target tracking (MTT) is a classical signal processing task, where the goal is to estimate the states of an unknown number of moving targets from noisy sensor measurements. In this paper, we revisit MTT from a deep learning perspective and propose a convolutional neural network (CNN) architecture to tackle it. We represent the target states and sensor measurements as images and recast the problem as an image-to-image prediction task. Then we train a fully convolutional model at small tracking areas and transfer it to much larger areas with numerous targets and sensors. This transfer learning approach enables MTT at a large scale and is also theoretically supported by our novel analysis that bounds the generalization error. In practice, the proposed transferable CNN architecture outperforms random finite set filters on the MTT task with 10 targets and transfers without re-training to a larger MTT task with 250 targets with a 29% performance improvement.

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arXiv2023

Representation Power of Graph Neural Networks: Improved Expressivity via Algebraic Analysis

Despite the remarkable success of Graph Neural Networks (GNNs), the common belief is that their representation power is limited and that they are at most as expressive as the Weisfeiler-Lehman (WL) algorithm. In this paper, we argue the opposite and show that standard GNNs, with anonymous inputs, produce more discriminative representations than the WL algorithm. Our novel analysis employs linear algebraic tools and characterizes the representation power of GNNs with respect to the eigenvalue decomposition of the graph operators. We prove that GNNs are able to generate distinctive outputs from white uninformative inputs, for, at least, all graphs that have different eigenvalues. We also show that simple convolutional architectures with white inputs, produce equivariant features that count the closed paths in the graph and are provably more expressive than the WL representations. Thorough experimental analysis on graph isomorphism and graph classification datasets corroborates our theoretical results and demonstrates the effectiveness of the proposed approach.

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arXiv2023

Transferability of Convolutional Neural Networks in Stationary Learning Tasks

Recent advances in hardware and big data acquisition have accelerated the development of deep learning techniques. For an extended period of time, increasing the model complexity has led to performance improvements for various tasks. However, this trend is becoming unsustainable and there is a need for alternative, computationally lighter methods. In this paper, we introduce a novel framework for efficient training of convolutional neural networks (CNNs) for large-scale spatial problems. To accomplish this we investigate the properties of CNNs for tasks where the underlying signals are stationary. We show that a CNN trained on small windows of such signals achieves a nearly performance on much larger windows without retraining. This claim is supported by our theoretical analysis, which provides a bound on the performance degradation. Additionally, we conduct thorough experimental analysis on two tasks: multi-target tracking and mobile infrastructure on demand. Our results show that the CNN is able to tackle problems with many hundreds of agents after being trained with fewer than ten. Thus, CNN architectures provide solutions to these problems at previously computationally intractable scales.

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arXiv2022

GAGE: Geometry Preserving Attributed Graph Embeddings

Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes, in the form of features or time-series data. Modern representation learning techniques employ both the connectivity and attribute information of the nodes to produce embeddings in an unsupervised manner. In this context, deriving embeddings that preserve the geometry of the network and the attribute vectors would be highly desirable, as they would reflect both the topological neighborhood structure and proximity in feature space. While this is fairly straightforward to maintain when only observing the connectivity or attribute information of the network, preserving the geometry of both types of information is challenging. A novel tensor factorization approach for node embedding in attributed networks is proposed in this paper, that preserves the distances of both the connections and the attributes. Furthermore, an effective and lightweight algorithm is developed to tackle the learning task and judicious experiments with multiple state-of-the-art baselines suggest that the proposed algorithm offers significant performance improvements in downstream tasks.

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arXiv2022

Space-Time Graph Neural Networks

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators. We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.

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arXiv2020

TeX-Graph: Coupled tensor-matrix knowledge-graph embedding for COVID-19 drug repurposing

Knowledge graphs (KGs) are powerful tools that codify relational behaviour between entities in knowledge bases. KGs can simultaneously model many different types of subject-predicate-object and higher-order relations. As such, they offer a flexible modeling framework that has been applied to many areas, including biology and pharmacology -- most recently, in the fight against COVID-19. The flexibility of KG modeling is both a blessing and a challenge from the learning point of view. In this paper we propose a novel coupled tensor-matrix framework for KG embedding. We leverage tensor factorization tools to learn concise representations of entities and relations in knowledge bases and employ these representations to perform drug repurposing for COVID-19. Our proposed framework is principled, elegant, and achieves 100% improvement over the best baseline in the COVID-19 drug repurposing task using a recently developed biological KG.

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arXiv2020

PREMA: Principled Tensor Data Recovery from Multiple Aggregated Views

Multidimensional data have become ubiquitous and are frequently encountered in situations where the information is aggregated over multiple data atoms. The aggregation can be over time or other features, such as geographical location. We often have access to multiple aggregated views of the same data, each aggregated in one or more dimensions, especially when data are collected or measured by different agencies. For instance, item sales can be aggregated temporally, and over groups of stores based on their location or affiliation. However, data mining and machine learning models benefit from detailed data for personalized analysis and prediction. Thus, data disaggregation algorithms are becoming increasingly important in various domains. The goal of this paper is to reconstruct finer-scale data from multiple coarse views, aggregated over different (subsets of) dimensions. The proposed method, called PREMA, leverages low-rank tensor factorization tools to fuse the multiple views and provide recovery guarantees under certain conditions. PREMA can tackle challenging scenarios, such as missing or partially observed data, double aggregation, and even blind disaggregation (without knowledge of the aggregation patterns) using a variant of PREMA called B-PREMA. To showcase the effectiveness of PREMA, the paper includes extensive experiments using real data from different domains: retail sales, crime counts, and weather observations.

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arXiv2020

Generalized Canonical Correlation Analysis: A Subspace Intersection Approach

Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding `common' random variables that are strongly correlated across multiple feature representations (views) of the same set of entities. CCA and to a lesser extent GCCA have been studied from the statistical and algorithmic points of view, but not as much from the standpoint of linear algebra. This paper offers a fresh algebraic perspective of GCCA based on a (bi-)linear generative model that naturally captures its essence. It is shown that from a linear algebra point of view, GCCA is tantamount to subspace intersection; and conditions under which the common subspace of the different views is identifiable are provided. A novel GCCA algorithm is proposed based on subspace intersection, which scales up to handle large GCCA tasks. Synthetic as well as real data experiments are provided to showcase the effectiveness of the proposed approach.

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arXiv2019

Tensor Completion from Regular Sub-Nyquist Samples

Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the maximum frequency present in the signal. Unfortunately a large number of signals of interest are far from being band-limited. This motivated research on reconstruction from sub-Nyquist samples, which mainly hinges on the use of random / incoherent sampling procedures. However, uniform or regular sampling is more appealing in practice and from the system design point of view, as it is far simpler to implement, and often necessary due to system constraints. In this work, we study regular sampling and reconstruction of three- or higher-dimensional signals (tensors). We show that reconstructing a tensor signal from regular samples is feasible. Under the proposed framework, the sample complexity is determined by the tensor rank---rather than the signal bandwidth. This result offers new perspectives for designing practical regular sampling patterns and systems for signals that are naturally tensors, e.g., images and video. For a concrete application, we show that functional magnetic resonance imaging (fMRI) acceleration is a tensor sampling problem, and design practical sampling schemes and an algorithmic framework to handle it. Numerical results show that our tensor sampling strategy accelerates the fMRI sampling process significantly without sacrificing reconstruction accuracy.

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arXiv2018

Structured SUMCOR Multiview Canonical Correlation Analysis for Large-Scale Data

The sum-of-correlations (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is considered arguably the most natural extension of classical two-view CCA to the multiview case, and thus has numerous applications in signal processing and data analytics. Recent work has proposed effective algorithms for handling the SUMCOR problem at very large scale. However, the existing scalable algorithms cannot incorporate structural regularization and prior information -- which are critical for good performance in real-world applications. In this work, we propose a new computational framework for large-scale SUMCOR GCCA that can easily incorporate a suite of structural regularizers which are frequently used in data analytics. The updates of the proposed algorithm are lightweight and the memory complexity is also low. In addition, the proposed algorithm can be readily implemented in a parallel fashion. We show that the proposed algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the regularized SUMCOR problem. Judiciously designed simulations and real-data experiments are employed to demonstrate the effectiveness of the proposed algorithm.

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arXiv2018

Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Hyperspectral super-resolution refers to the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that has fine spatial and spectral resolution. State-of-the-art methods approach the problem via low-rank matrix approximations to the matricized HSI and MSI. These methods are effective to some extent, but a number of challenges remain. First, HSIs and MSIs are naturally third-order tensors (data "cubes") and thus matricization is prone to loss of structural information--which could degrade performance. Second, it is unclear whether or not these low-rank matrix-based fusion strategies can guarantee identifiability or exact recovery of the SRI. However, identifiability plays a pivotal role in estimation problems and usually has a significant impact on performance in practice. Third, the majority of the existing methods assume that there are known (or easily estimated) degradation operators applied to the SRI to form the corresponding HSI and MSI--which is hardly the case in practice. In this work, we propose to tackle the super-resolution problem from a tensor perspective. Specifically, we utilize the multidimensional structure of the HSI and MSI to propose a coupled tensor factorization framework that can effectively overcome the aforementioned issues. The proposed approach guarantees the identifiability of the SRI under mild and realistic conditions. Furthermore, it works with little knowledge of the degradation operators, which is clearly an advantage over the existing methods. Semi-real numerical experiments are included to show the effectiveness of the proposed approach.

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