David O. Wipf

Qitian Wu, David Wipf, Junchi Yan

Learning representations for structured data with certain geometries (e.g., observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper, inspired by physical systems, we propose an energy-constrained diffusion model, which integrates the inductive bias of diffusion on manifolds with layer-wise constraints of energy minimization. We identify that the diffusion operators have a one-to-one correspondence with the energy functions implicitly descended by the diffusion process, and the finite-difference iteration for solving the energy-constrained diffusion system induces the propagation layers of various types of MPNNs operating on observed or latent structures. This leads to a unified mathematical framework for common neural architectures whose computational flows can be cast as message passing (or its special case), including MLPs, GNNs, and Transformers. Building on these insights, we devise a new class of neural message passing models, dubbed diffusion-inspired Transformers (DIFFormer), whose global attention layers are derived from the principled energy-constrained diffusion framework. Across diverse datasets ranging from real-world networks to images, texts, and physical particles, we demonstrate that the new model achieves promising performance in scenarios where the data structures are observed (as a graph), partially observed, or entirely unobserved.

Ning Li, Kounianhua Du, Han Zhang et al.

Relational databases (RDBs) have become the industry standard for storing massive and heterogeneous data. However, despite the widespread use of RDBs across various fields, the inherent structure of relational databases hinders their ability to benefit from flourishing deep learning methods. Previous research has primarily focused on exploiting the unary dependency among multiple tables in a relational database using the primary key - foreign key relationships, either joining multiple tables into a single table or constructing a graph among them, which leaves the implicit composite relations among different tables and a substantial potential of improvement for predictive modeling unexplored. In this paper, we propose SRP, a unified predictive modeling framework that synthesizes features using the unary dependency, retrieves related information to capture the composite dependency, and propagates messages across a constructed graph to learn adjacent patterns for prediction on relation databases. By introducing a new retrieval mechanism into RDB, SRP is designed to fully capture both the unary and the composite dependencies within a relational database, thereby enhancing the receptive field of tabular data prediction. In addition, we conduct a comprehensive analysis on the components of SRP, offering a nuanced understanding of model behaviors and practical guidelines for future applications. Extensive experiments on five real-world datasets demonstrate the effectiveness of SRP and its potential applicability in industrial scenarios. The code is released at https://github.com/NingLi670/SRP.

Chenxiao Yang, Cai Zhou, David Wipf et al.

Diffusion language models have recently emerged as a competitive alternative to autoregressive language models. Beyond next-token generation, they are more efficient and flexible by enabling parallel and any-order token generation. However, despite empirical successes, their computational power and fundamental limitations remain poorly understood. In this paper, we formally study whether non-autoregressive generation in Masked Diffusion Models (MDM) enables solving problems beyond the reach of Auto-Regressive Models (ARM). Our results show that MDM with sufficiently large context length is computationally universal with decoding steps matching the optimal parallel time complexity in PRAM. However, when controlling for other factors, MDM's flexibility to generate in any-order does not expand what ARM can already solve. To address this, we propose a new form of generation called any-process generation, which extends MDM with capabilities to remask, insert and delete tokens, allowing self-correction, length-variable editing, and adaptive parallelism. Theoretically and empirically, we demonstrate these capabilities enable scalability to significantly harder reasoning problems that are otherwise intractable for ARM and vanilla MDM. Additionally, they prove essential for generation tasks where objects naturally evolve through non-sequential processes, crucial for extending current LLMs beyond natural language to domains such as coding and science.