Recent advances toward foundation models for routing problems have shown great potential of a unified deep model for various VRP variants. However, they overlook the complex real-world customer distributions. In this work, we advance the Multi-Task VRP (MTVRP) setting to the more realistic yet challenging Multi-Task Multi-Distribution VRP (MTMDVRP) setting, and introduce SHIELD, a novel model that leverages both sparsity and hierarchy principles. Building on a deeper decoder architecture, we first incorporate the Mixture-of-Depths (MoD) technique to enforce sparsity. This improves both efficiency and generalization by allowing the model to dynamically select nodes to use or skip each decoder layer, providing the needed capacity to adaptively allocate computation for learning the task/distribution specific and shared representations. We also develop a context-based clustering layer that exploits the presence of hierarchical structures in the problems to produce better local representations. These two designs inductively bias the network to identify key features that are common across tasks and distributions, leading to significantly improved generalization on unseen ones. Our empirical results demonstrate the superiority of our approach over existing methods on 9 real-world maps with 16 VRP variants each.

We investigate Graph Neural Networks (GNNs) on heterophilous graphs for node classification. To address the scarcity of useful local information in heterophilous neighborhood, it is often essential to explore global interactions. However, many existing methods in this endeavor are computationally expensive and may suffer from issues like oversquashing. In addition, earlier studies show that GNNs can be outperformed by Multi-Layer Perceptrons on heterophilous graphs, indicating insufficient exploitation of node feature information. To address these limitations, we propose Prototype Mediated GNN (PM-GNN), a novel framework which efficiently captures global feature information using class prototypes. PM-GNN learns multiple class prototypes for each class from raw node features with a soft k-means clustering mechanism. These prototypes are then transferred onto node embeddings via explicit message passing, bypassing local neighborhoods and mitigating oversquashing. PM-GNN can scale to large graphs, outperforming strong baselines on multiple heterophilous datasets.

This paper addresses the challenge of object-centric lay-out generation under spatial constraints, seen in multi-ple domains including floorplan design process. The de-sign process typically involves specifying a set of spa-tial constraints that include object attributes like size and inter-object relations such as relative positioning. Existing works, which typically represent objects as single nodes, lack the granularity to accurately model complex interactions between objects. For instance, often only certain parts of an object, like a room's right wall, interact with adjacent objects. To address this gap, we introduce a factor graph based approach with four latent variable nodes for each room, and a factor node for each constraint. The factor nodes represent dependencies among the variables to which they are connected, effectively capturing constraints that are potentially of a higher order. We then develop message-passing on the bipartite graph, forming a factor graph neu-ral network that is trained to produce a floorplan that aligns with the desired requirements. Our approach is simple and generates layouts faithful to the user requirements, demon-strated by a large improvement in IOU scores over existing methods. Additionally, our approach, being inferential and accurate, is well-suited to the practical human-in-the-loop design process where specifications evolve iteratively, offering a practical and powerful tool for AI-guided design.

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been demonstrated on entirely random problem instances that inadequately capture real-world scenarios. In this paper, we introduce realistic Traveling Salesman Problem (TSP) scenarios relevant to industrial settings and derive the following insights: (1) The optimal next node (or city) to visit often lies within proximity to the current node, suggesting the potential benefits of biasing choices based on current locations. (2) Effectively solving the TSP requires robust tracking of unvisited nodes and warrants succinct grouping strategies. Building upon these insights, we propose integrating a learnable choice layer inspired by Hypernetworks to prioritize choices based on the current location, and a learnable approximate clustering algorithm inspired by the Expectation-Maximization algorithm to facilitate grouping the unvisited cities. Together, these two contributions form a hierarchical approach towards solving the realistic TSP by considering both immediate local neighbourhoods and learning an intermediate set of node representations. Our hierarchical approach yields superior performance compared to both classical and recent transformer models, showcasing the efficacy of the key designs.

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, 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 1 .

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.

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.