On statistical learning of graphs

We study PAC and online learnability of hypothesis classes formed by copies of a countably infinite graph G, where each copy is induced by permuting G's vertices. This corresponds to learning a graph's labeling, knowing its structure and label set. We consider classes where permutations move only finitely many vertices. Our main result shows that PAC learnability of all such finite-support copies implies online learnability of the full isomorphism type of G, and is equivalent to the condition of automorphic triviality. We also characterize graphs where copies induced by swapping two vertices are not learnable, using a relaxation of the extension property of the infinite random graph. Finally, we show that, for all G and k>2, learnability for k-vertex permutations is equivalent to that for 2-vertex permutations, yielding a four-class partition of infinite graphs, whose complexity we also determine using tools coming from both descriptive set theory and computability theory.

PGT-I: Scaling Spatiotemporal GNNs with Memory-Efficient Distributed Training

Spatiotemporal graph neural networks (ST-GNNs) are powerful tools for modeling spatial and temporal data dependencies. However, their applications have been limited primarily to small-scale datasets because of memory constraints. While distributed training offers a solution, current frameworks lack support for spatiotemporal models and overlook the properties of spatiotemporal data. Informed by a scaling study on a large-scale workload, we present PyTorch Geometric Temporal Index (PGT-I), an extension to PyTorch Geometric Temporal that integrates distributed data parallel training and two novel strategies: index-batching and distributed-index-batching. Our index techniques exploit spatiotemporal structure to construct snapshots dynamically at runtime, significantly reducing memory overhead, while distributed-index-batching extends this approach by enabling scalable processing across multiple GPUs. Our techniques enable the first-ever training of an ST-GNN on the entire PeMS dataset without graph partitioning, reducing peak memory usage by up to 89\% and achieving up to a 13.1x speedup over standard DDP with 128 GPUs.

Demystifying Distributed Training of Graph Neural Networks for Link Prediction

Graph neural networks (GNNs) are powerful tools for solving graph-related problems. Distributed GNN frameworks and systems enhance the scalability of GNNs and accelerate model training, yet most are optimized for node classification. Their performance on link prediction remains underexplored. This paper demystifies distributed training of GNNs for link prediction by investigating the issue of performance degradation when each worker trains a GNN on its assigned partitioned subgraph without having access to the entire graph. We discover that the main sources of the issue come from not only the information loss caused by graph partitioning but also the ways of drawing negative samples during model training. While sharing the complete graph information with each worker resolves the issue and preserves link prediction accuracy, it incurs a high communication cost. We propose SpLPG, which effectively leverages graph sparsification to mitigate the issue of performance degradation at a reduced communication cost. Experiment results on several public real-world datasets demonstrate the effectiveness of SpLPG, which reduces the communication overhead by up to about 80% while mostly preserving link prediction accuracy.

Dense Video Captioning using Graph-based Sentence Summarization

Recently, dense video captioning has made attractive progress in detecting and captioning all events in a long untrimmed video. Despite promising results were achieved, most existing methods do not sufficiently explore the scene evolution within an event temporal proposal for captioning, and therefore perform less satisfactorily when the scenes and objects change over a relatively long proposal. To address this problem, we propose a graph-based partition-and-summarization (GPaS) framework for dense video captioning within two stages. For the ``partition" stage, a whole event proposal is split into short video segments for captioning at a finer level. For the ``summarization" stage, the generated sentences carrying rich description information for each segment are summarized into one sentence to describe the whole event. We particularly focus on the ``summarization" stage, and propose a framework that effectively exploits the relationship between semantic words for summarization. We achieve this goal by treating semantic words as nodes in a graph and learning their interactions by coupling Graph Convolutional Network (GCN) and Long Short Term Memory (LSTM), with the aid of visual cues. Two schemes of GCN-LSTM Interaction (GLI) modules are proposed for seamless integration of GCN and LSTM. The effectiveness of our approach is demonstrated via an extensive comparison with the state-of-the-arts methods on the two benchmarks ActivityNet Captions dataset and YouCook II dataset.

EraRAG: Efficient and Incremental Retrieval Augmented Generation for Growing Corpora

Graph-based Retrieval-Augmented Generation (Graph-RAG) enhances large language models (LLMs) by structuring retrieval over an external corpus. However, existing approaches typically assume a static corpus, requiring expensive full-graph reconstruction whenever new documents arrive, limiting their scalability in dynamic, evolving environments. To address these limitations, we introduce EraRAG, a novel multi-layered Graph-RAG framework that supports efficient and scalable dynamic updates. Our method leverages hyperplane-based Locality-Sensitive Hashing (LSH) to partition and organize the original corpus into hierarchical graph structures, enabling efficient and localized insertions of new data without disrupting the existing topology. The design eliminates the need for retraining or costly recomputation while preserving high retrieval accuracy and low latency. Experiments on large-scale benchmarks demonstrate that EraRag achieves up to an order of magnitude reduction in update time and token consumption compared to existing Graph-RAG systems, while providing superior accuracy performance. This work offers a practical path forward for RAG systems that must operate over continually growing corpora, bridging the gap between retrieval efficiency and adaptability. Our code and data are available at https://github.com/EverM0re/EraRAG-Official.

SViP: Sequencing Bimanual Visuomotor Policies with Object-Centric Motion Primitives

Imitation learning (IL), particularly when leveraging high-dimensional visual inputs for policy training, has proven intuitive and effective in complex bimanual manipulation tasks. Nonetheless, the generalization capability of visuomotor policies remains limited, especially when small demonstration datasets are available. Accumulated errors in visuomotor policies significantly hinder their ability to complete long-horizon tasks. To address these limitations, we propose SViP, a framework that seamlessly integrates visuomotor policies into task and motion planning (TAMP). SViP partitions human demonstrations into bimanual and unimanual operations using a semantic scene graph monitor. Continuous decision variables from the key scene graph are employed to train a switching condition generator. This generator produces parameterized scripted primitives that ensure reliable performance even when encountering out-of-the-distribution observations. Using only 20 real-world demonstrations, we show that SViP enables visuomotor policies to generalize across out-of-distribution initial conditions without requiring object pose estimators. For previously unseen tasks, SViP automatically discovers effective solutions to achieve the goal, leveraging constraint modeling in TAMP formulism. In real-world experiments, SViP outperforms state-of-the-art generative IL methods, indicating wider applicability for more complex tasks. Project website: https://sites.google.com/view/svip-bimanual

GCN-Driven Reinforcement Learning for Probabilistic Real-Time Guarantees in Industrial URLLC

Ensuring packet-level communication quality is vital for ultra-reliable, low-latency communications (URLLC) in large-scale industrial wireless networks. We enhance the Local Deadline Partition (LDP) algorithm by introducing a Graph Convolutional Network (GCN) integrated with a Deep Q-Network (DQN) reinforcement learning framework for improved interference coordination in multi-cell, multi-channel networks. Unlike LDP's static priorities, our approach dynamically learns link priorities based on real-time traffic demand, network topology, remaining transmission opportunities, and interference patterns. The GCN captures spatial dependencies, while the DQN enables adaptive scheduling decisions through reward-guided exploration. Simulation results show that our GCN-DQN model achieves mean SINR improvements of 179.6\%, 197.4\%, and 175.2\% over LDP across three network configurations. Additionally, the GCN-DQN model demonstrates mean SINR improvements of 31.5\%, 53.0\%, and 84.7\% over our previous CNN-based approach across the same configurations. These results underscore the effectiveness of our GCN-DQN model in addressing complex URLLC requirements with minimal overhead and superior network performance.

Decoupled Classifier-Free Guidance for Counterfactual Diffusion Models

Counterfactual image generation aims to simulate realistic visual outcomes under specific causal interventions. Diffusion models have recently emerged as a powerful tool for this task, combining DDIM inversion with conditional generation via classifier-free guidance (CFG). However, standard CFG applies a single global weight across all conditioning variables, which can lead to poor identity preservation and spurious attribute changes - a phenomenon known as attribute amplification. To address this, we propose Decoupled Classifier-Free Guidance (DCFG), a flexible and model-agnostic framework that introduces group-wise conditioning control. DCFG builds on an attribute-split embedding strategy that disentangles semantic inputs, enabling selective guidance on user-defined attribute groups. For counterfactual generation, we partition attributes into intervened and invariant sets based on a causal graph and apply distinct guidance to each. Experiments on CelebA-HQ, MIMIC-CXR, and EMBED show that DCFG improves intervention fidelity, mitigates unintended changes, and enhances reversibility, enabling more faithful and interpretable counterfactual image generation.

Relaxation-Free Min-k-Partition for PCI Assignment in 5G Networks

Physical Cell Identity (PCI) is a critical parameter in 5G networks. Efficient and accurate PCI assignment is essential for mitigating mod-3 interference, mod-30 interference, collisions, and confusions among cells, which directly affect network reliability and user experience. In this paper, we propose a novel framework for PCI assignment by decomposing the problem into Min-3-Partition, Min-10-Partition, and a graph coloring problem, leveraging the Chinese Remainder Theorem (CRT). Furthermore, we develop a relaxation-free approach to the general Min-$k$-Partition problem by reformulating it as a quadratic program with a norm-equality constraint and solving it using a penalized mirror descent (PMD) algorithm. The proposed method demonstrates superior computational efficiency and scalability, significantly reducing interference while eliminating collisions and confusions in large-scale 5G networks. Numerical evaluations on real-world datasets show that our approach reduces computational time by up to 20 times compared to state-of-the-art methods, making it highly practical for real-time PCI optimization in large-scale networks. These results highlight the potential of our method to improve network performance and reduce deployment costs in modern 5G systems.

Learning to Collaborate Over Graphs: A Selective Federated Multi-Task Learning Approach

We present a novel federated multi-task learning method that leverages cross-client similarity to enable personalized learning for each client. To avoid transmitting the entire model to the parameter server, we propose a communication-efficient scheme that introduces a feature anchor, a compact vector representation that summarizes the features learned from the client's local classes. This feature anchor is shared with the server to account for local clients' distribution. In addition, the clients share the classification heads, a lightweight linear layer, and perform a graph-based regularization to enable collaboration among clients. By modeling collaboration between clients as a dynamic graph and continuously updating and refining this graph, we can account for any drift from the clients. To ensure beneficial knowledge transfer and prevent negative collaboration, we leverage a community detection-based approach that partitions this dynamic graph into homogeneous communities, maximizing the sum of task similarities, represented as the graph edges' weights, within each community. This mechanism restricts collaboration to highly similar clients within their formed communities, ensuring positive interaction and preserving personalization. Extensive experiments on two heterogeneous datasets demonstrate that our method significantly outperforms state-of-the-art baselines. Furthermore, we show that our method exhibits superior computation and communication efficiency and promotes fairness across clients.