PF-GNN: Differentiable particle filtering based approximation of universal graph representations

Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to extract structural features from the graph. In this work, we propose to make GNNs universal by guiding the learning process with exact isomorphism solver techniques which operate on the paradigm of Individualization and Refinement (IR), a method to artificially introduce asymmetry and further refine the coloring when 1-WL stops. Isomorphism solvers generate a search tree of colorings whose leaves uniquely identify the graph. However, the tree grows exponentially large and needs hand-crafted pruning techniques which are not desirable from a learning perspective. We take a probabilistic view and approximate the search tree of colorings (i.e. embeddings) by sampling multiple paths from root to leaves of the search tree. To learn more discriminative representations, we guide the sampling process with particle filter updates, a principled approach for sequential state estimation. Our algorithm is end-to-end differentiable, can be applied with any GNN as backbone and learns richer graph representations with only linear increase in runtime. Experimental evaluation shows that our approach consistently outperforms leading GNN models on both synthetic benchmarks for isomorphism detection as well as real-world datasets.Comment: Published as a conference paper at ICLR 202

Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience over-smoothing issues, or exhibit suboptimal convergence and generalization properties, potentially hindering their practical performance. To tackle these issues, we introduce a geometric framework for designing implicit graph diffusion layers based on a parameterized graph Laplacian operator. Our framework allows learning the metrics of vertex and edge spaces, as well as the graph diffusion strength from data. We show how implicit GNN layers can be viewed as the fixed-point equation of a Dirichlet energy minimization problem and give conditions under which it may suffer from over-smoothing during training (OST) and inference (OSI). We further propose a new implicit GNN model to avoid OST and OSI. We establish that with an appropriately chosen hyperparameter greater than the largest eigenvalue of the parameterized graph Laplacian, DIGNN guarantees a unique equilibrium, quick convergence, and strong generalization bounds. Our models demonstrate better performance than most implicit and explicit GNN baselines on benchmark datasets for both node and graph classification tasks.Comment: 57 page

Factor Graph Neural Networks

In recent years, we have witnessed a surge of Graph Neural Networks (GNNs), most of which can learn powerful representations in an end-to-end fashion with great success in many real-world applications. They have resemblance to Probabilistic Graphical Models (PGMs), but break free from some limitations of PGMs. By aiming to provide expressive methods for representation learning instead of computing marginals or most likely configurations, GNNs provide flexibility in the choice of information flowing rules while maintaining good performance. Despite their success and inspirations, they lack efficient ways to represent and learn higher-order relations among variables/nodes. More expressive higher-order GNNs which operate on k-tuples of nodes need increased computational resources in order to process higher-order tensors. We propose Factor Graph Neural Networks (FGNNs) to effectively capture higher-order relations for inference and learning. To do so, we first derive an efficient approximate Sum-Product loopy belief propagation inference algorithm for discrete higher-order PGMs. We then neuralize the novel message passing scheme into a Factor Graph Neural Network (FGNN) module by allowing richer representations of the message update rules; this facilitates both efficient inference and powerful end-to-end learning. We further show that with a suitable choice of message aggregation operators, our FGNN is also able to represent Max-Product belief propagation, providing a single family of architecture that can represent both Max and Sum-Product loopy belief propagation. Our extensive experimental evaluation on synthetic as well as real datasets demonstrates the potential of the proposed model.Comment: Accepted by JML

Tell2Design: A Dataset for Language-Guided Floor Plan Generation

We consider the task of generating designs directly from natural language descriptions, and consider floor plan generation as the initial research area. Language conditional generative models have recently been very successful in generating high-quality artistic images. However, designs must satisfy different constraints that are not present in generating artistic images, particularly spatial and relational constraints. We make multiple contributions to initiate research on this task. First, we introduce a novel dataset, \textit{Tell2Design} (T2D), which contains more than $80k$ floor plan designs associated with natural language instructions. Second, we propose a Sequence-to-Sequence model that can serve as a strong baseline for future research. Third, we benchmark this task with several text-conditional image generation models. We conclude by conducting human evaluations on the generated samples and providing an analysis of human performance. We hope our contributions will propel the research on language-guided design generation forward.Comment: Paper published in ACL2023; Area Chair Award; Best Paper Nominatio

ALGORITHMIC INDUCTIVE BIASES FOR GRAPH REPRESENTATION LEARNING

Ph.DDOCTOR OF PHILOSOPHY (SOC

Visual Relationship Detection with Low Rank Non-Negative Tensor Decomposition

We address the problem of Visual Relationship Detection (VRD) which aims to describe the relationships between pairs of objects in the form of triplets of (subject, predicate, object). We observe that given a pair of bounding box proposals, objects often participate in multiple relations implying the distribution of triplets is multimodal. We leverage the strong correlations within triplets to learn the joint distribution of triplet variables conditioned on the image and the bounding box proposals, doing away with the hitherto used independent distribution of triplets. To make learning the triplet joint distribution feasible, we introduce a novel technique of learning conditional triplet distributions in the form of their normalized low rank non-negative tensor decompositions. Normalized tensor decompositions take form of mixture distributions of discrete variables and thus are able to capture multimodality. This allows us to efficiently learn higher order discrete multimodal distributions and at the same time keep the parameter size manageable. We further model the probability of selecting an object proposal pair and include a relation triplet prior in our model. We show that each part of the model improves performance and the combination outperforms state-of-the-art score on the Visual Genome (VG) and Visual Relationship Detection (VRD) datasets