Unifying over-smoothing and over-squashing in graph neural networks: A physics informed approach and beyond

Graph Neural Networks (GNNs) have emerged as one of the leading approaches for machine learning on graph-structured data. Despite their great success, critical computational challenges such as over-smoothing, over-squashing, and limited expressive power continue to impact the performance of GNNs. In this study, inspired from the time-reversal principle commonly utilized in classical and quantum physics, we reverse the time direction of the graph heat equation. The resulted reversing process yields a class of high pass filtering functions that enhance the sharpness of graph node features. Leveraging this concept, we introduce the Multi-Scaled Heat Kernel based GNN (MHKG) by amalgamating diverse filtering functions' effects on node features. To explore more flexible filtering conditions, we further generalize MHKG into a model termed G-MHKG and thoroughly show the roles of each element in controlling over-smoothing, over-squashing and expressive power. Notably, we illustrate that all aforementioned issues can be characterized and analyzed via the properties of the filtering functions, and uncover a trade-off between over-smoothing and over-squashing: enhancing node feature sharpness will make model suffer more from over-squashing, and vice versa. Furthermore, we manipulate the time again to show how G-MHKG can handle both two issues under mild conditions. Our conclusive experiments highlight the effectiveness of proposed models. It surpasses several GNN baseline models in performance across graph datasets characterized by both homophily and heterophily.

How Curvature Enhance the Adaptation Power of Framelet GCNs

Graph neural network (GNN) has been demonstrated powerful in modeling graph-structured data. However, despite many successful cases of applying GNNs to various graph classification and prediction tasks, whether the graph geometrical information has been fully exploited to enhance the learning performance of GNNs is not yet well understood. This paper introduces a new approach to enhance GNN by discrete graph Ricci curvature. Specifically, the graph Ricci curvature defined on the edges of a graph measures how difficult the information transits on one edge from one node to another based on their neighborhoods. Motivated by the geometric analogy of Ricci curvature in the graph setting, we prove that by inserting the curvature information with different carefully designed transformation function $\zeta$, several known computational issues in GNN such as over-smoothing can be alleviated in our proposed model. Furthermore, we verified that edges with very positive Ricci curvature (i.e., $\kappa_{i,j} \approx 1$) are preferred to be dropped to enhance model's adaption to heterophily graph and one curvature based graph edge drop algorithm is proposed. Comprehensive experiments show that our curvature-based GNN model outperforms the state-of-the-art baselines in both homophily and heterophily graph datasets, indicating the effectiveness of involving graph geometric information in GNNs.

Frameless Graph Knowledge Distillation

Knowledge distillation (KD) has shown great potential for transferring knowledge from a complex teacher model to a simple student model in which the heavy learning task can be accomplished efficiently and without losing too much prediction accuracy. Recently, many attempts have been made by applying the KD mechanism to the graph representation learning models such as graph neural networks (GNNs) to accelerate the model's inference speed via student models. However, many existing KD-based GNNs utilize MLP as a universal approximator in the student model to imitate the teacher model's process without considering the graph knowledge from the teacher model. In this work, we provide a KD-based framework on multi-scaled GNNs, known as graph framelet, and prove that by adequately utilizing the graph knowledge in a multi-scaled manner provided by graph framelet decomposition, the student model is capable of adapting both homophilic and heterophilic graphs and has the potential of alleviating the over-squashing issue with a simple yet effectively graph surgery. Furthermore, we show how the graph knowledge supplied by the teacher is learned and digested by the student model via both algebra and geometry. Comprehensive experiments show that our proposed model can generate learning accuracy identical to or even surpass the teacher model while maintaining the high speed of inference.

Neural 3D Scene Reconstruction from Multiple 2D Images without 3D Supervision

Neural 3D scene reconstruction methods have achieved impressive performance when reconstructing complex geometry and low-textured regions in indoor scenes. However, these methods heavily rely on 3D data which is costly and time-consuming to obtain in real world. In this paper, we propose a novel neural reconstruction method that reconstructs scenes using sparse depth under the plane constraints without 3D supervision. We introduce a signed distance function field, a color field, and a probability field to represent a scene. We optimize these fields to reconstruct the scene by using differentiable ray marching with accessible 2D images as supervision. We improve the reconstruction quality of complex geometry scene regions with sparse depth obtained by using the geometric constraints. The geometric constraints project 3D points on the surface to similar-looking regions with similar features in different 2D images. We impose the plane constraints to make large planes parallel or vertical to the indoor floor. Both two constraints help reconstruct accurate and smooth geometry structures of the scene. Without 3D supervision, our method achieves competitive performance compared with existing methods that use 3D supervision on the ScanNet dataset.

Neural 3D Scene Reconstruction from Multi-view Images without 3D Supervision

Neural scene reconstruction methods have achieved impressive performance in reconstructing complex geometry and low-textured regions in large scenes. However, these methods heavily rely on 3D supervised information which is costly and time-consuming to obtain in the real world. In this paper, we propose a novel neural reconstruction method that reconstructs scenes without 3D supervision. We perform differentiable volume rendering for scene reconstruction by using accessible 2D images as supervision. We impose geometry to improve the reconstruction quality of complex geometry regions in the scenes, and impose plane constraints to improve the reconstruction quality of low-textured regions in the scenes. Specifically, we introduce a signed distance function (SDF) field, a color field, and a probability field to represent the scene, and optimize the fields under the differentiable ray marching to reconstruct the scene. Besides, we impose geometric constraints that project 3D points on the surface to similar-looking regions with similar features in different views. We also impose plane constraints to make large planes keep parallel or vertical to the wall or floor. These two constraints help to reconstruct accurate and smooth geometry structures of the scene. Without 3D supervision information, our method achieves competitive reconstruction compared with some existing methods that use 3D information as supervision on the ScanNet dataset.

Revisiting Generalized p-Laplacian Regularized Framelet GCNs: Convergence, Energy Dynamic and Training with Non-Linear Diffusion

This work presents a comprehensive theoretical analysis of graph p-Laplacian based framelet network (pL-UFG) to establish a solid understanding of its properties. We begin by conducting a convergence analysis of the p-Laplacian based implicit layer integrated after the framelet convolution, providing insights into the asymptotic behavior of pL-UFG. By exploring the generalized Dirichlet energy of pL-UFG, we demonstrate that the Dirichlet energy remains non-zero, ensuring the avoidance of over-smoothing issues in pL-UFG as it approaches convergence. Furthermore, we elucidate the dynamic energy perspective through which the implicit layer in pL-UFG synergizes with graph framelets, enhancing the model's adaptability to both homophilic and heterophilic data. Remarkably, we establish that the implicit layer can be interpreted as a generalized non-linear diffusion process, enabling training using diverse schemes. These multifaceted analyses lead to unified conclusions that provide novel insights for understanding and implementing pL-UFG, contributing to advancements in the field of graph-based deep learning.

A Study of Generative Large Language Model for Medical Research and Healthcare

There is enormous enthusiasm and concerns in using large language models (LLMs) in healthcare, yet current assumptions are all based on general-purpose LLMs such as ChatGPT. This study develops a clinical generative LLM, GatorTronGPT, using 277 billion words of mixed clinical and English text with a GPT-3 architecture of 20 billion parameters. GatorTronGPT improves biomedical natural language processing for medical research. Synthetic NLP models trained using GatorTronGPT generated text outperform NLP models trained using real-world clinical text. Physicians Turing test using 1 (worst) to 9 (best) scale shows that there is no significant difference in linguistic readability (p = 0.22; 6.57 of GatorTronGPT compared with 6.93 of human) and clinical relevance (p = 0.91; 7.0 of GatorTronGPT compared with 6.97 of human) and that physicians cannot differentiate them (p < 0.001). This study provides insights on the opportunities and challenges of LLMs for medical research and healthcare.

Contextualized Medication Information Extraction Using Transformer-based Deep Learning Architectures

Objective: To develop a natural language processing (NLP) system to extract medications and contextual information that help understand drug changes. This project is part of the 2022 n2c2 challenge. Materials and methods: We developed NLP systems for medication mention extraction, event classification (indicating medication changes discussed or not), and context classification to classify medication changes context into 5 orthogonal dimensions related to drug changes. We explored 6 state-of-the-art pretrained transformer models for the three subtasks, including GatorTron, a large language model pretrained using >90 billion words of text (including >80 billion words from >290 million clinical notes identified at the University of Florida Health). We evaluated our NLP systems using annotated data and evaluation scripts provided by the 2022 n2c2 organizers. Results:Our GatorTron models achieved the best F1-scores of 0.9828 for medication extraction (ranked 3rd), 0.9379 for event classification (ranked 2nd), and the best micro-average accuracy of 0.9126 for context classification. GatorTron outperformed existing transformer models pretrained using smaller general English text and clinical text corpora, indicating the advantage of large language models. Conclusion: This study demonstrated the advantage of using large transformer models for contextual medication information extraction from clinical narratives.

SODA: A Natural Language Processing Package to Extract Social Determinants of Health for Cancer Studies

Objective: We aim to develop an open-source natural language processing (NLP) package, SODA (i.e., SOcial DeterminAnts), with pre-trained transformer models to extract social determinants of health (SDoH) for cancer patients, examine the generalizability of SODA to a new disease domain (i.e., opioid use), and evaluate the extraction rate of SDoH using cancer populations. Methods: We identified SDoH categories and attributes and developed an SDoH corpus using clinical notes from a general cancer cohort. We compared four transformer-based NLP models to extract SDoH, examined the generalizability of NLP models to a cohort of patients prescribed with opioids, and explored customization strategies to improve performance. We applied the best NLP model to extract 19 categories of SDoH from the breast (n=7,971), lung (n=11,804), and colorectal cancer (n=6,240) cohorts. Results and Conclusion: We developed a corpus of 629 cancer patients notes with annotations of 13,193 SDoH concepts/attributes from 19 categories of SDoH. The Bidirectional Encoder Representations from Transformers (BERT) model achieved the best strict/lenient F1 scores of 0.9216 and 0.9441 for SDoH concept extraction, 0.9617 and 0.9626 for linking attributes to SDoH concepts. Fine-tuning the NLP models using new annotations from opioid use patients improved the strict/lenient F1 scores from 0.8172/0.8502 to 0.8312/0.8679. The extraction rates among 19 categories of SDoH varied greatly, where 10 SDoH could be extracted from >70% of cancer patients, but 9 SDoH had a low extraction rate (<70% of cancer patients). The SODA package with pre-trained transformer models is publicly available at https://github.com/uf-hobiinformatics-lab/SDoH_SODA.