NeurIPS 2024 Papers

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.

This paper introduces a novel pipeline for long-tail (LT) recognition that diverges from conventional strategies. Instead, it leverages the long-tailed dataset itself to generate a balanced proxy dataset without utilizing external data or model. We deploy a diffusion model trained from scratch on only the long-tailed dataset to create this proxy and verify the effectiveness of the data produced. Our analysis identifies approximately-in-distribution (AID) samples, which slightly deviate from the real data distribution and incorporate a blend of class information, as the crucial samples for enhancing the generative model's performance in long-tail classification. We promote the generation of AID samples during the training of a generative model by utilizing a feature extractor to guide the process and filter out detrimental samples during generation. Our approach, termed Diffusion model for Long-Tail recognition (DiffuLT), represents a pioneer application of generative models in long-tail recognition. DiffuLT achieves state-of-the-art results on CIFAR10-LT, CIFAR100-LT, and ImageNet-LT, surpassing leading competitors by significant margins. Comprehensive ablations enhance the interpretability of our pipeline. Notably, the entire generative process is conducted without relying on external data or pre-trained model weights, which leads to its generalizability to real-world long-tailed scenarios.

Many real-world graphs are large and have some characteristic subgraph patterns, such as triangles in social networks, cliques in web graphs, and cycles in molecular networks. Detecting such subgraph patterns is important in many applications; therefore, establishing graph neural networks (GNNs) that can detect such patterns and run fast on large graphs is demanding. In this study, we propose a new GNN layer, named \emph{graph homomorphism layer}. It enumerates local subgraph patterns that match the predefined set of patterns $\mathcal{P}^\bullet$, applies non-linear transformations to node features, and aggregates them along with the patterns. By stacking these layers, we obtain a deep GNN model called \emph{deep homomorphism network (DHN)}. The expressive power of the DHN is completely characterised by the set of patterns generated from $\mathcal{P}^\bullet$ by graph-theoretic operations; hence, it serves as a useful theoretical tool to analyse the expressive power of many GNN models. Furthermore, the model runs in the same time complexity as the graph homomorphisms, which is fast in many real-word graphs. Thus, it serves as a practical and lightweight model that solves difficult problems using domain knowledge.

Graph Transformers excel in long-range dependency modeling, but generally require quadratic memory complexity in the number of nodes in an input graph, and hence have trouble scaling to large graphs. Sparse attention variants such as Exphormer can help, but may require high-degree augmentations to the input graph for good performance, and do not attempt to sparsify an already-dense input graph. As the learned attention mechanisms tend to use few of these edges, however, such high-degree connections may be unnecessary. We show (empirically and with theoretical backing) that attention scores on graphs are usually quite consistent across network widths, and use this observation to propose a two-stage procedure, which we call Spexphormer: first, train a narrow network on the full augmented graph. Next, use only the active connections to train a wider network on a much sparser graph. We establish theoretical conditions when a narrow network's attention scores can match those of a wide network, and show that Spexphormer achieves good performance with drastically reduced memory requirements on various graph datasets.

Complex logical query answering (CLQA) in knowledge graphs (KGs) goes beyond simple KG completion and aims at answering compositional queries comprised of multiple projections and logical operations. Existing CLQA methods that learn parameters bound to certain entity or relation vocabularies can only be applied to the graph they are trained on which requires substantial training time before being deployed on a new graph. Here we present UltraQuery, the first foundation model for inductive reasoning that can zero-shot answer logical queries on any KG. The core idea of UltraQuery is to derive both projections and logical operations as vocabulary-independent functions which generalize to new entities and relations in any KG. With the projection operation initialized from a pre-trained inductive KG completion model, UltraQuery can solve CLQA on any KG after finetuning on a single dataset. Experimenting on 23 datasets, UltraQuery in the zero-shot inference mode shows competitive or better query answering performance than best available baselines and sets a new state of the art on 15 of them.

Rethink convolution-based graph neural networks (GNN)---they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a simple graph learning module entirely free of convolution operators, coined _random walk with unifying memory_ (RUM) neural network, where an RNN merges the topological and semantic graph features along the random walks terminating at each node. Relating the rich literature on RNN behavior and graph topology, we theoretically show and experimentally verify that RUM attenuates the aforementioned symptoms and is more expressive than the Weisfeiler-Lehman (WL) isomorphism test. On a variety of node- and graph-level classification and regression tasks, RUM not only achieves competitive performance, but is also robust, memory-efficient, scalable, and faster than the simplest convolutional GNNs.

Recently, multi-modal entity alignment has emerged as a pivotal endeavor for the integration of Multi-Modal Knowledge Graphs (MMKGs) originating from diverse data sources. Existing works primarily focus on fully depicting entity features by designing various modality encoders or fusion approaches. However, uncertain correspondences between inter-modal or intra-modal cues, such as weak inter-modal associations, description diversity, and modality absence, still severely hinder the effective exploration of aligned entity similarities. To this end, in this paper, we propose a novel Tackling uncertain correspondences method for Multi-modal Entity Alignment (TMEA). Specifically, to handle diverse attribute knowledge descriptions, we design alignment-augmented abstract representation that incorporates the large language model and in-context learning into attribute alignment and filtering for generating and embedding the attribute abstract. In order to mitigate the influence of the modality absence, we propose to unify all modality features into a shared latent subspace and generate pseudo features via variational autoencoders according to existing modal features. Then, we develop an inter-modal commonality enhancement mechanism based on cross-attention with orthogonal constraints, to address weak semantic associations between modalities. Extensive experiments on two real-world datasets validate the effectiveness of TMEA with a clear improvement over competitive baselines.

Personalized Federated Graph Learning (pFGL) facilitates the decentralized training of Graph Neural Networks (GNNs) without compromising privacy while accommodating personalized requirements for non-IID participants. In cross-domain scenarios, structural heterogeneity poses significant challenges for pFGL. Nevertheless, previous pFGL methods incorrectly share non-generic knowledge globally and fail to tailor personalized solutions locally under domain structural shift. We innovatively reveal that the spectral nature of graphs can well reflect inherent domain structural shifts. Correspondingly, our method overcomes it by sharing generic spectral knowledge. Moreover, we indicate the biased message-passing schemes for graph structures and propose the personalized preference module. Combining both strategies, we propose our pFGL framework $\textbf{FedSSP}$ which $\textbf{S}$hares generic $\textbf{S}$pectral knowledge while satisfying graph $\textbf{P}$references. Furthermore, We perform extensive experiments on cross-dataset and cross-domain settings to demonstrate the superiority of our framework. The code is available at https://github.com/OakleyTan/FedSSP.

Molecular learning is pivotal in many real-world applications, such as drug discovery. Supervised learning requires heavy human annotation, which is particularly challenging for molecular data, e.g., the commonly used density functional theory (DFT) is highly computationally expensive. Active learning (AL) automatically queries labels for most informative samples, thereby remarkably alleviating the annotation hurdle. In this paper, we present a principled AL paradigm for molecular learning, where we treat molecules as 3D molecular graphs. Specifically, we propose a new diversity sampling method to eliminate mutual redundancy built on distributions of 3D geometries. We first propose a set of new 3D graph isometries for 3D graph isomorphism analysis. Our method is provably at least as expressive as the Geometric Weisfeiler-Lehman (GWL) test. The moments of the distributions of the associated geometries are then extracted for efficient diversity computing. To ensure our AL paradigm selects samples with maximal uncertainties, we carefully design a Bayesian geometric graph neural network to compute uncertainties specifically for 3D molecular graphs. We pose active sampling as a quadratic programming (QP) problem using the proposed components. Experimental results demonstrate the effectiveness of our AL paradigm, as well as the proposed diversity and uncertainty methods.

We revisit the identification of an $\varepsilon$-optimal policy in average-reward Markov Decision Processes (MDP). In such MDPs, two measures of complexity have appeared in the literature: the diameter, $D$, and the optimal bias span, $H$, which satisfy $H\leq D$. Prior work have studied the complexity of $\varepsilon$-optimal policy identification only when a generative model is available. In this case, it is known that there exists an MDP with $D \simeq H$ for which the sample complexity to output an $\varepsilon$-optimal policy is $\Omega(SAD/\varepsilon^2)$ where $S$ and $A$ are the sizes of the state and action spaces. Recently, an algorithm with a sample complexity of order $SAH/\varepsilon^2$ has been proposed, but it requires the knowledge of $H$. We first show that the sample complexity required to estimate $H$ is not bounded by any function of $S,A$ and $H$, ruling out the possibility to easily make the previous algorithm agnostic to $H$. By relying instead on a diameter estimation procedure, we propose the first algorithm for $(\varepsilon,\delta)$-PAC policy identification that does not need any form of prior knowledge on the MDP. Its sample complexity scales in $SAD/\varepsilon^2$ in the regime of small $\varepsilon$, which is near-optimal. In the online setting, our first contribution is a lower bound which implies that a sample complexity polynomial in $H$ cannot be achieved in this setting. Then, we propose an online algorithm with a sample complexity in $SAD^2/\varepsilon^2$, as well as a novel approach based on a data-dependent stopping rule that we believe is promising to further reduce this bound.

When training node embedding models to represent large directed graphs (digraphs), it is impossible to observe all entries of the adjacency matrix during training. As a consequence most methods employ sampling. For very large digraphs, however, this means many (most) entries may be unobserved during training. In general, observing every entry would be necessary to uniquely identify a graph, however if we know the graph has a certain property some entries can be omitted - for example, only half the entries would be required for a symmetric graph. In this work, we develop a novel framework to identify a subset of entries required to uniquely distinguish a graph among all transitively-closed DAGs. We give an explicit algorithm to compute the provably minimal set of entries, and demonstrate empirically that one can train node embedding models with greater efficiency and performance, provided the energy function has an appropriate inductive bias. We achieve robust performance on synthetic hierarchies and a larger real-world taxonomy, observing improved convergence rates in a resource-constrained setting while reducing the set of training examples by as much as 99%.

Expert-designed close-ended benchmarks are indispensable in assessing the knowledge capacity of large language models (LLMs). Despite their widespread use, concerns have mounted regarding their reliability due to limited test scenarios and an unavoidable risk of data contamination. To rectify this, we present PertEval, a toolkit devised for in-depth probing of LLMs' knowledge capacity through **knowledge-invariant perturbations**. These perturbations employ human-like restatement techniques to generate on-the-fly test samples from static benchmarks, meticulously retaining knowledge-critical content while altering irrelevant details. Our toolkit further includes a suite of **response consistency analyses** that compare performance on raw vs. perturbed test sets to precisely assess LLMs' genuine knowledge capacity. Six representative LLMs are re-evaluated using PertEval. Results reveal significantly inflated performance of the LLMs on raw benchmarks, including an absolute 25.8% overestimation for GPT-4. Additionally, through a nuanced response pattern analysis, we discover that PertEval retains LLMs' uncertainty to specious knowledge, and reveals their potential rote memorization to correct options which leads to overestimated performance. We also find that the detailed response consistency analyses by PertEval could illuminate various weaknesses in existing LLMs' knowledge mastery and guide the development of refinement. Our findings provide insights for advancing more robust and genuinely knowledgeable LLMs. Our code is available at https://github.com/aigc-apps/PertEval.

We study the embedding dimension of distance comparison data in two settings: contrastive learning and $k$-nearest neighbors ($k$-NN). In both cases, the goal is to find the smallest dimension $d$ of an $\ell_p$-space in which a given dataset can be represented. We show that the arboricity of the associated graphs plays a key role in designing embeddings. Using this approach, for the most frequently used $\ell_2$-distance, we get matching upper and lower bounds in both settings. In contrastive learning, we are given $m$ labeled samples of the form $(x_i, y_i^+, z_i^-)$ representing the fact that the positive example $y_i$ is closer to the anchor $x_i$ than the negative example $z_i$. We show that for representing such dataset in: - $\ell_2$: $d = \Theta(\sqrt{m})$ is necessary and sufficient. - $\ell_p$ for $p \ge 1$: $d = O(m)$ is sufficient and $d = \tilde \Omega(\sqrt{m})$ is necessary. - $\ell_\infty$: $d = O(m^{2/3})$ is sufficient and $d = \tilde \Omega(\sqrt{m})$ is necessary. We also give results for the more general scenario when $t$ negatives are allowed. In $k$-NN, for each of the $n$ data points we are given an ordered set of the closest $k$ points. We show that for preserving the ordering of the $k$-NN for every point in: - $\ell_2$: $d = \Theta(k)$ is necessary and sufficient. - $\ell_p$ for $p \ge 1$: $d = \tilde O(k^2)$ is sufficient and $d=\tilde \Omega(k)$ is necessary. - $\ell_\infty$ : $d = \tilde \Omega(k)$ is necessary. Furthermore, if the goal is to not just preserve the ordering of the $k$-NN but also keep them as the nearest neighbors then $d = \tilde O (\mathrm{poly}(k))$ suffices in $\ell_p$ for $p \ge 1$.

Interpreting hierarchical structures latent in language is a key limitation of current language models (LMs). While previous research has implicitly leveraged these hierarchies to enhance LMs, approaches for their explicit encoding are yet to be explored. To address this, we introduce a novel approach to re-train transformer encoder-based LMs as Hierarchy Transformer encoders (HiTs), harnessing the expansive nature of hyperbolic space. Our method situates the output embedding space of pre-trained LMs within a Poincaré ball with a curvature that adapts to the embedding dimension, followed by re-training on hyperbolic clustering and centripetal losses. These losses are designed to effectively cluster related entities (input as texts) and organise them hierarchically. We evaluate HiTs against pre-trained LMs, standard fine-tuned LMs, and several hyperbolic embedding baselines, focusing on their capabilities in simulating transitive inference, predicting subsumptions, and transferring knowledge across hierarchies. The results demonstrate that HiTs consistently outperform all baselines in these tasks, underscoring the effectiveness and transferability of our re-trained hierarchy encoders.

Knowledge in materials science is widely dispersed across extensive scientific literature, posing significant challenges for efficient discovery and integration of new materials. Traditional methods, often reliant on costly and time-consuming experimental approaches, further complicate rapid innovation. Addressing these challenges, the integration of artificial intelligence with materials science has opened avenues for accelerating the discovery process, though it also demands precise annotation, data extraction, and traceability of information. To tackle these issues, this article introduces the Materials Knowledge Graph (MKG), which utilizes advanced natural language processing techniques, integrated with large language models to extract and systematically organize a decade's worth of high-quality research into structured triples, contains 162,605 nodes and 731,772 edges. MKG categorizes information into comprehensive labels such as Name, Formula, and Application, structured around a meticulously designed ontology, thus enhancing data usability and integration. By implementing network-based algorithms, MKG not only facilitates efficient link prediction but also significantly reduces reliance on traditional experimental methods. This structured approach not only streamlines materials research but also lays the groundwork for more sophisticated materials knowledge graphs.

Class-incremental learning (CIL) aims to continually learn a sequence of tasks, with each task consisting of a set of unique classes. Graph CIL (GCIL) follows the same setting but needs to deal with graph tasks (e.g., node classification in a graph). The key characteristic of CIL lies in the absence of task identifiers (IDs) during inference, which causes a significant challenge in separating classes from different tasks (i.e., inter-task class separation). Being able to accurately predict the task IDs can help address this issue, but it is a challenging problem. In this paper, we show theoretically that accurate task ID prediction on graph data can be achieved by a Laplacian smoothing-based graph task profiling approach, in which each graph task is modeled by a task prototype based on Laplacian smoothing over the graph. It guarantees that the task prototypes of the same graph task are nearly the same with a large smoothing step, while those of different tasks are distinct due to differences in graph structure and node attributes. Further, to avoid the catastrophic forgetting of the knowledge learned in previous graph tasks, we propose a novel graph prompting approach for GCIL which learns a small discriminative graph prompt for each task, essentially resulting in a separate classification model for each task. The prompt learning requires the training of a single graph neural network (GNN) only once on the first task, and no data replay is required thereafter, thereby obtaining a GCIL model being both replay-free and forget-free. Extensive experiments on four GCIL benchmarks show that i) our task prototype-based method can achieve 100% task ID prediction accuracy on all four datasets, ii) our GCIL model significantly outperforms state-of-the-art competing methods by at least 18% in average CIL accuracy, and iii) our model is fully free of forgetting on the four datasets.

The practical utility of machine learning models in the sciences often hinges on their interpretability. It is common to assess a model's merit for scientific discovery, and thus novel insights, by how well it aligns with already available domain knowledge - a dimension that is currently largely disregarded in the comparison of neural network models. While pruning can simplify deep neural network architectures and excels in identifying sparse models, as we show in the context of gene regulatory network inference, state-of-the-art techniques struggle with biologically meaningful structure learning. To address this issue, we propose DASH, a generalizable framework that guides network pruning by using domain-specific structural information in model fitting and leads to sparser, better interpretable models that are more robust to noise. Using both synthetic data with ground truth information, as well as real-world gene expression data, we show that DASH, using knowledge about gene interaction partners within the putative regulatory network, outperforms general pruning methods by a large margin and yields deeper insights into the biological systems being studied.

Transformer architectures have become a dominant paradigm for domains like language modeling but suffer in many inference settings due to their quadratic-time self-attention. Recently proposed subquadratic architectures, such as Mamba, have shown promise, but have been pretrained with substantially less computational resources than the strongest Transformer models. In this work, we present a method that is able to distill a pretrained Transformer architecture into alternative architectures such as state space models (SSMs). The key idea to our approach is that we can view both Transformers and SSMs as applying different forms of mixing matrices over the token sequences. We can thus progressively distill the Transformer architecture by matching different degrees of granularity in the SSM: first matching the mixing matrices themselves, then the hidden units at each block, and finally the end-to-end predictions. Our method, called MOHAWK, is able to distill a Mamba-2 variant based on the Phi-1.5 architecture (Phi-Mamba) using only 3B tokens. Despite using less than 1% of the training data typically used to train models from scratch, Phi-Mamba boasts substantially stronger performance compared to all past open-source non-Transformer models. MOHAWK allows models like SSMs to leverage computational resources invested in training Transformer-based architectures, highlighting a new avenue for building such models.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular *low displacement rank*) for integrating tensor fields defined on weighted trees. Several applications of the resulting *fast tree-field integrators* (FTFIs) are presented, including: (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) *Topological Transformers* (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as **three** extra learnable parameters per Transformer layer, leading to **1.0-1.5\%+** accuracy gains. Importantly, most of FTFIs are **exact** methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide **5.7-13x** speedups. We also provide an extensive theoretical analysis of our methods.