Upon increasing the depth, the over-smoothing issue arises: a GCN's

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption).

Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences and algebraic multigrid frameworks. We form a parameterized convolution kernel based on discretized differential operators, leveraging the graph mass, gradient and Laplacian. This way, the parameterization does not depend on the graph structure, only on the meaning of the network convolutions as differential operators. To allow hierarchical representations of the input, we propose pooling and unpooling operations that are based on algebraic multigrid methods, which are mainly used to solve partial differential equations on unstructured grids. To motivate and explain our method, we compare it to standard convolutional neural networks, and show their similarities and relations in the case of a regular grid. Our proposed method is demonstrated in various experiments like classification and part-segmentation, achieving on par or better than state of the art results. We also analyze the computational cost of our method compared to other GCNs.

Graphs arise across diverse domains, from biology and chemistry to social and information networks, as well as in transportation and logistics. Inference on graph-structured data requires methods that are permutation-invariant, scalable across varying sizes and sparsities, and capable of capturing complex long-range dependencies, making posterior estimation on graph parameters particularly challenging. Amortized Bayesian Inference (ABI) is a simulation-based framework that employs generative neural networks to enable fast, likelihood-free posterior inference. We adapt ABI to graph data to address these challenges to perform inference on node-, edge-, and graph-level parameters. Our approach couples permutation-invariant graph encoders with flexible neural posterior estimators in a two-module pipeline: a summary network maps attributed graphs to fixed-length representations, and an inference network approximates the posterior over parameters. In this setting, several neural architectures can serve as the summary network. In this work we evaluate multiple architectures and assess their performance on controlled synthetic settings and two real-world domains -- biology and logistics -- in terms of recovery and calibration.

Graph Neural Networks (GNNs) are powerful tools for learning from graph-structured data, but their application to large graphs is hindered by computational costs. The need to process every neighbor for each node creates memory and computational bottlenecks. To address this, we introduce BLISS, a Bandit Layer Importance Sampling Strategy. It uses multi-armed bandits to dynamically select the most informative nodes at each layer, balancing exploration and exploitation to ensure comprehensive graph coverage. Unlike existing static sampling methods, BLISS adapts to evolving node importance, leading to more informed node selection and improved performance. It demonstrates versatility by integrating with both Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs), adapting its selection policy to their specific aggregation mechanisms. Experiments show that BLISS maintains or exceeds the accuracy of full-batch training.

In recent years, several results in the supervised learning setting suggested that classical statistical learning-theoretic measures, such as VC dimension, do not adequately explain the performance of deep learning models which prompted a slew of work in the infinite-width and iteration regimes. However, there is little theoretical explanation for the success of neural networks beyond the supervised setting. In this paper we argue that, under some distributional assumptions, classical learning-theoretic measures can sufficiently explain generalization for graph neural networks in the transductive setting. In particular, we provide a rigorous analysis of the performance of neural networks in the context of transductive inference, specifically by analysing the generalisation properties of graph convolutional networks for the problem of node classification. While VC-dimension does result in trivial generalisation error bounds in this setting as well, we show that transductive Rademacher complexity can explain the generalisation properties of graph convolutional networks for stochastic block models. We further use the generalisation error bounds based on transductive Rademacher complexity to demonstrate the role of graph convolutions and network architectures in achieving smaller generalisation error and provide insights into when the graph structure can help in learning.

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This allows us to overcome the difficulties of dealing with discrete notions such as isomorphisms on very large graphs, by considering instead more natural geometric aspects. We first study the convergence of GCNs to their continuous counterpart as the number of nodes grows. Our results are fully non-asymptotic and are valid for relatively sparse graphs with an average degree that grows logarithmically with the number of nodes. We then analyze the stability of GCNs to small deformations of the random graph model. In contrast to previous studies of stability in discrete settings, our continuous setup allows us to provide more intuitive deformation-based metrics for understanding stability, which have proven useful for explaining the success of convolutional representations on Euclidean domains.

Potential-based reward shaping provides an approach for designing good reward functions, with the purpose of speeding up learning. However, automatically finding potential functions for complex environments is a difficult problem (in fact, of the same difficulty as learning a value function from scratch). We propose a new framework for learning potential functions by leveraging ideas from graph representation learning. Our approach relies on Graph Convolutional Networks which we use as a key ingredient in combination with the probabilistic inference view of reinforcement learning. More precisely, we leverage Graph Convolutional Networks to perform message passing from rewarding states. The propagated messages can then be used as potential functions for reward shaping to accelerate learning. We verify empirically that our approach can achieve considerable improvements in both small and high-dimensional control problems.

Human-object interaction segmentation is a fundamental task of daily activity understanding, which plays a crucial role in applications such as assistive robotics, healthcare, and autonomous systems. Most existing learning-based methods excel in closed-world action segmentation, they struggle to generalize to open-world scenarios where novel actions emerge. Collecting exhaustive action categories for training is impractical due to the dynamic diversity of human activities, necessitating models that detect and segment out-of-distribution actions without manual annotation. To address this issue, we formally define the open-world action segmentation problem and propose a structured framework for detecting and segmenting unseen actions. Our framework introduces three key innovations: 1) an Enhanced Pyramid Graph Convolutional Network (EPGCN) with a novel decoder module for robust spatiotemporal feature upsampling. 2) Mixup-based training to synthesize out-of-distribution data, eliminating reliance on manual annotations. 3) A novel Temporal Clustering loss that groups in-distribution actions while distancing out-of-distribution samples. We evaluate our framework on two challenging human-object interaction recognition datasets: Bimanual Actions and 2 Hands and Object (H2O) datasets. Experimental results demonstrate significant improvements over state-of-the-art action segmentation models across multiple open-set evaluation metrics, achieving 16.9% and 34.6% relative gains in open-set segmentation (F1@50) and out-of-distribution detection performances (AUROC), respectively. Additionally, we conduct an in-depth ablation study to assess the impact of each proposed component, identifying the optimal framework configuration for open-world action segmentation.

Abstract-- Accurate temporal segmentation of human actions is critical for intelligent robots in collaborative settin gs, where a precise understanding of sub-activity labels and their tem poral structure is essential. However, the inherent noise in both human pose estimation and object detection often leads to over-segmentation errors, disrupting the coherence of act ion sequences. T o address this, we propose a Multi-Modal Graph Convolutional Network (MMGCN) that integrates low-frame-rate (e.g., 1 fps) visual data with high-frame-rate (e.g., 3 0 fps) motion data (skeleton and object detections) to mitiga te fragmentation. Our framework introduces three key contributions. First, a sinusoidal encoding strategy that maps 3D skeleton coordinates into a continuous sin-cos space to enh ance spatial representation robustness. Second, a temporal gra ph fusion module that aligns multi-modal inputs with differin g resolutions via hierarchical feature aggregation, Third, inspired by the smooth transitions inherent to human actions, we desi gn SmoothLabelMix, a data augmentation technique that mixes i n-put sequences and labels to generate synthetic training exa mples with gradual action transitions, enhancing temporal consi stency in predictions and reducing over-segmentation artifacts. Extensive experiments on the Bimanual Actions Dataset, a public benchmark for human-object interaction understand ing, demonstrate that our approach outperforms state-of-the-a rt methods, especially in action segmentation accuracy, achi eving F1@10: 94.5% and F1@25: 92.8%. I. INTRODUCTION Human action segmentation, the task of temporally decomposing continuous activities into coherent sub-action uni ts, is a cornerstone of intelligent robotic systems operating in collaborative environments.