Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND

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}.

Toward Explainable and Fine-Grained 3D Grounding through Referring Textual Phrases

Recent progress on 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, thus ignoring fine-grained relationships between contexts and non-target ones. In this paper, we extend 3DVG to a more reliable and explainable task, called 3D Phrase Aware Grounding (3DPAG). The 3DPAG task aims to localize the target object in the 3D scenes by explicitly identifying all phrase-related objects and then conducting reasoning according to contextual phrases. To tackle this problem, we label about 400K phrase-level annotations from 170K sentences in available 3DVG datasets, i.e., Nr3D, Sr3D and ScanRefer. By tapping on these developed datasets, we propose a novel framework, i.e., PhraseRefer, which conducts phrase-aware and object-level representation learning through phrase-object alignment optimization as well as phrase-specific pre-training. In our setting, we extend previous 3DVG methods to the phrase-aware scenario and provide metrics to measure the explainability of the 3DPAG task. Extensive results confirm that 3DPAG effectively boosts the 3DVG, and PhraseRefer achieves state-of-the-arts across three datasets, i.e., 63.0%, 54.4% and 55.5% overall accuracy on Sr3D, Nr3D and ScanRefer, respectively.