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We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.

We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \url{https://github.com/zknus/ICLR2024-FROND}., Comment: The Twelfth International Conference on Learning Representations

Recent progress in 3D scene understanding has explored visual grounding (3DVG) to localize a target object through a language description. However, existing methods only consider the dependency between the entire sentence and the target object, ignoring fine-grained relationships between contexts and non-target ones. In this paper, we extend 3DVG to a more fine-grained and interpretable task, called 3D Phrase Aware Grounding (3DPAG). The 3DPAG task aims to localize the target objects in a 3D scene by explicitly identifying all phrase-related objects and then conducting the reasoning according to contextual phrases. To tackle this problem, we manually labeled about 227K phrase-level annotations using a self-developed platform, from 88K sentences of widely used 3DVG datasets, i.e., Nr3D, Sr3D and ScanRefer. By tapping on our datasets, we can extend previous 3DVG methods to the fine-grained phrase-aware scenario. It is achieved through the proposed novel phrase-object alignment optimization and phrase-specific pre-training, boosting conventional 3DVG performance as well. Extensive results confirm significant improvements, i.e., previous state-of-the-art method achieves 3.9%, 3.5% and 4.6% overall accuracy gains on Nr3D, Sr3D and ScanRefer respectively., Comment: New dataset for 3D visual grounding is available at https://yanx27.github.io/phraserefer/