Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes

Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous graphs, many real-world graphs exhibit heterogeneous patterns where nodes and edges have multiple types. This paper fills this gap by introducing the first approach for heterogeneous graph structure learning (HGSL). To this end, we first propose a novel statistical model for the data-generating process (DGP) of heterogeneous graph data, namely hidden Markov networks for heterogeneous graphs (H2MN). Then we formalize HGSL as a maximum a-posterior estimation problem parameterized by such DGP and derive an alternating optimization method to obtain a solution together with a theoretical justification of the optimization conditions. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate that our proposed method excels in learning structure on heterogeneous graphs in terms of edge type identification and edge weight recovery.

Judge a Book by its Cover: Investigating Multi-Modal LLMs for Multi-Page Handwritten Document Transcription

Handwritten text recognition (HTR) remains a challenging task, particularly for multi-page documents where pages share common formatting and contextual features. While modern optical character recognition (OCR) engines are proficient with printed text, their performance on handwriting is limited, often requiring costly labeled data for fine-tuning. In this paper, we explore the use of multi-modal large language models (MLLMs) for transcribing multi-page handwritten documents in a zero-shot setting. We investigate various configurations of commercial OCR engines and MLLMs, utilizing the latter both as end-to-end transcribers and as post-processors, with and without image components. We propose a novel method, '+first page', which enhances MLLM transcription by providing the OCR output of the entire document along with just the first page image. This approach leverages shared document features without incurring the high cost of processing all images. Experiments on a multi-page version of the IAM Handwriting Database demonstrate that '+first page' improves transcription accuracy, balances cost with performance, and even enhances results on out-of-sample text by extrapolating formatting and OCR error patterns from a single page.

Are We There Yet? Revealing the Risks of Utilizing Large Language Models in Scholarly Peer Review

Scholarly peer review is a cornerstone of scientific advancement, but the system is under strain due to increasing manuscript submissions and the labor-intensive nature of the process. Recent advancements in large language models (LLMs) have led to their integration into peer review, with promising results such as substantial overlaps between LLM- and human-generated reviews. However, the unchecked adoption of LLMs poses significant risks to the integrity of the peer review system. In this study, we comprehensively analyze the vulnerabilities of LLM-generated reviews by focusing on manipulation and inherent flaws. Our experiments show that injecting covert deliberate content into manuscripts allows authors to explicitly manipulate LLM reviews, leading to inflated ratings and reduced alignment with human reviews. In a simulation, we find that manipulating 5% of the reviews could potentially cause 12% of the papers to lose their position in the top 30% rankings. Implicit manipulation, where authors strategically highlight minor limitations in their papers, further demonstrates LLMs' susceptibility compared to human reviewers, with a 4.5 times higher consistency with disclosed limitations. Additionally, LLMs exhibit inherent flaws, such as potentially assigning higher ratings to incomplete papers compared to full papers and favoring well-known authors in single-blind review process. These findings highlight the risks of over-reliance on LLMs in peer review, underscoring that we are not yet ready for widespread adoption and emphasizing the need for robust safeguards.

Scalable Message Passing Neural Networks: No Need for Attention in Large Graph Representation Learning

We propose Scalable Message Passing Neural Networks (SMPNNs) and demonstrate that, by integrating standard convolutional message passing into a Pre-Layer Normalization Transformer-style block instead of attention, we can produce high-performing deep message-passing-based Graph Neural Networks (GNNs). This modification yields results competitive with the state-of-the-art in large graph transductive learning, particularly outperforming the best Graph Transformers in the literature, without requiring the otherwise computationally and memory-expensive attention mechanism. Our architecture not only scales to large graphs but also makes it possible to construct deep message-passing networks, unlike simple GNNs, which have traditionally been constrained to shallow architectures due to oversmoothing. Moreover, we provide a new theoretical analysis of oversmoothing based on universal approximation which we use to motivate SMPNNs. We show that in the context of graph convolutions, residual connections are necessary for maintaining the universal approximation properties of downstream learners and that removing them can lead to a loss of universality.

Synthesizing Post-Training Data for LLMs through Multi-Agent Simulation

Post-training is essential for enabling large language models (LLMs) to follow human instructions. Inspired by the recent success of using LLMs to simulate human society, we leverage multi-agent simulation to automatically generate diverse text-based scenarios, capturing a wide range of real-world human needs. We propose MATRIX, a multi-agent simulator that creates realistic and scalable scenarios. Leveraging these outputs, we introduce a novel scenario-driven instruction generator MATRIX-Gen for controllable and highly realistic data synthesis. Extensive experiments demonstrate that our framework effectively generates both general and domain-specific data. Notably, on AlpacaEval 2 and Arena-Hard benchmarks, Llama-3-8B-Base, post-trained on datasets synthesized by MATRIX-Gen with just 20K instruction-response pairs, outperforms Meta's Llama-3-8B-Instruct model, which was trained on over 10M pairs; see our project at https://github.com/ShuoTang123/MATRIX-Gen.

Neural Spacetimes for DAG Representation Learning

We propose a class of trainable deep learning-based geometries called Neural Spacetimes (NSTs), which can universally represent nodes in weighted directed acyclic graphs (DAGs) as events in a spacetime manifold. While most works in the literature focus on undirected graph representation learning or causality embedding separately, our differentiable geometry can encode both graph edge weights in its spatial dimensions and causality in the form of edge directionality in its temporal dimensions. We use a product manifold that combines a quasi-metric (for space) and a partial order (for time). NSTs are implemented as three neural networks trained in an end-to-end manner: an embedding network, which learns to optimize the location of nodes as events in the spacetime manifold, and two other networks that optimize the space and time geometries in parallel, which we call a neural (quasi-)metric and a neural partial order, respectively. The latter two networks leverage recent ideas at the intersection of fractal geometry and deep learning to shape the geometry of the representation space in a data-driven fashion, unlike other works in the literature that use fixed spacetime manifolds such as Minkowski space or De Sitter space to embed DAGs. Our main theoretical guarantee is a universal embedding theorem, showing that any $k$-point DAG can be embedded into an NST with $1+\mathcal{O}(\log(k))$ distortion while exactly preserving its causal structure. The total number of parameters defining the NST is sub-cubic in $k$ and linear in the width of the DAG. If the DAG has a planar Hasse diagram, this is improved to $\mathcal{O}(\log(k)) + 2)$ spatial and 2 temporal dimensions. We validate our framework computationally with synthetic weighted DAGs and real-world network embeddings; in both cases, the NSTs achieve lower embedding distortions than their counterparts using fixed spacetime geometries.

Separation Power of Equivariant Neural Networks

The separation power of a machine learning model refers to its capacity to distinguish distinct inputs, and it is often employed as a proxy for its expressivity. In this paper, we propose a theoretical framework to investigate the separation power of equivariant neural networks with point-wise activations. Using the proposed framework, we can derive an explicit description of inputs indistinguishable by a family of neural networks with given architecture, demonstrating that it remains unaffected by the choice of non-polynomial activation function employed. We are able to understand the role played by activation functions in separability. Indeed, we show that all non-polynomial activations, such as ReLU and sigmoid, are equivalent in terms of expressivity, and that they reach maximum discrimination capacity. We demonstrate how assessing the separation power of an equivariant neural network can be simplified to evaluating the separation power of minimal representations. We conclude by illustrating how these minimal components form a hierarchy in separation power.

Rough Transformers: Lightweight Continuous-Time Sequence Modelling with Path Signatures

Time-series data in real-world settings typically exhibit long-range dependencies and are observed at non-uniform intervals. In these settings, traditional sequence-based recurrent models struggle. To overcome this, researchers often replace recurrent architectures with Neural ODE-based models to account for irregularly sampled data and use Transformer-based architectures to account for long-range dependencies. Despite the success of these two approaches, both incur very high computational costs for input sequences of even moderate length. To address this challenge, we introduce the Rough Transformer, a variation of the Transformer model that operates on continuous-time representations of input sequences and incurs significantly lower computational costs. In particular, we propose \textit{multi-view signature attention}, which uses path signatures to augment vanilla attention and to capture both local and global (multi-scale) dependencies in the input data, while remaining robust to changes in the sequence length and sampling frequency and yielding improved spatial processing. We find that, on a variety of time-series-related tasks, Rough Transformers consistently outperform their vanilla attention counterparts while obtaining the representational benefits of Neural ODE-based models, all at a fraction of the computational time and memory resources.

Bundle Neural Networks for message diffusion on graphs

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited node-level expressivity. To address these limitations we propose Bundle Neural Networks (BuNN), a new type of GNN that operates via message diffusion over flat vector bundles - structures analogous to connections on Riemannian manifolds that augment the graph by assigning to each node a vector space and an orthogonal map. A BuNN layer evolves the features according to a diffusion-type partial differential equation. When discretized, BuNNs are a special case of Sheaf Neural Networks (SNNs), a recently proposed MPNN capable of mitigating over-smoothing. The continuous nature of message diffusion enables BuNNs to operate on larger scales of the graph and, therefore, to mitigate over-squashing. Finally, we prove that BuNN can approximate any feature transformation over nodes on any (potentially infinite) family of graphs given injective positional encodings, resulting in universal node-level expressivity. We support our theory via synthetic experiments and showcase the strong empirical performance of BuNNs over a range of real-world tasks, achieving state-of-the-art results on several standard benchmarks in transductive and inductive settings.

Bayesian Optimization of Functions over Node Subsets in Graphs

We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various algorithms have been introduced in the literature, most are either task-specific or computationally inefficient and only utilize information about the graph structure without considering the characteristics of the function. To address these limitations, we utilize Bayesian Optimization (BO), a sample-efficient black-box solver, and propose a novel framework for combinatorial optimization on graphs. More specifically, we map each $k$-node subset in the original graph to a node in a new combinatorial graph and adopt a local modeling approach to efficiently traverse the latter graph by progressively sampling its subgraphs using a recursive algorithm. Extensive experiments under both synthetic and real-world setups demonstrate the effectiveness of the proposed BO framework on various types of graphs and optimization tasks, where its behavior is analyzed in detail with ablation studies.