Researchy Questions: A Dataset of Multi-Perspective, Decompositional Questions for LLM Web Agents

Existing question answering (QA) datasets are no longer challenging to most powerful Large Language Models (LLMs). Traditional QA benchmarks like TriviaQA, NaturalQuestions, ELI5 and HotpotQA mainly study ``known unknowns'' with clear indications of both what information is missing, and how to find it to answer the question. Hence, good performance on these benchmarks provides a false sense of security. A yet unmet need of the NLP community is a bank of non-factoid, multi-perspective questions involving a great deal of unclear information needs, i.e. ``unknown uknowns''. We claim we can find such questions in search engine logs, which is surprising because most question-intent queries are indeed factoid. We present Researchy Questions, a dataset of search engine queries tediously filtered to be non-factoid, ``decompositional'' and multi-perspective. We show that users spend a lot of ``effort'' on these questions in terms of signals like clicks and session length, and that they are also challenging for GPT-4. We also show that ``slow thinking'' answering techniques, like decomposition into sub-questions shows benefit over answering directly. We release $\sim$ 100k Researchy Questions, along with the Clueweb22 URLs that were clicked.

inGRASS: Incremental Graph Spectral Sparsification via Low-Resistance-Diameter Decomposition

This work presents inGRASS, a novel algorithm designed for incremental spectral sparsification of large undirected graphs. The proposed inGRASS algorithm is highly scalable and parallel-friendly, having a nearly-linear time complexity for the setup phase and the ability to update the spectral sparsifier in $O(\log N)$ time for each incremental change made to the original graph with $N$ nodes. A key component in the setup phase of inGRASS is a multilevel resistance embedding framework introduced for efficiently identifying spectrally-critical edges and effectively detecting redundant ones, which is achieved by decomposing the initial sparsifier into many node clusters with bounded effective-resistance diameters leveraging a low-resistance-diameter decomposition (LRD) scheme. The update phase of inGRASS exploits low-dimensional node embedding vectors for efficiently estimating the importance and uniqueness of each newly added edge. As demonstrated through extensive experiments, inGRASS achieves up to over $200 \times$ speedups while retaining comparable solution quality in incremental spectral sparsification of graphs obtained from various datasets, such as circuit simulations, finite element analysis, and social networks.

SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds

Modern graph neural networks (GNNs) can be sensitive to changes in the input graph structure and node features, potentially resulting in unpredictable behavior and degraded performance. In this work, we introduce a spectral framework known as SAGMAN for examining the stability of GNNs. This framework assesses the distance distortions that arise from the nonlinear mappings of GNNs between the input and output manifolds: when two nearby nodes on the input manifold are mapped (through a GNN model) to two distant ones on the output manifold, it implies a large distance distortion and thus a poor GNN stability. We propose a distance-preserving graph dimension reduction (GDR) approach that utilizes spectral graph embedding and probabilistic graphical models (PGMs) to create low-dimensional input/output graph-based manifolds for meaningful stability analysis. Our empirical evaluations show that SAGMAN effectively assesses the stability of each node when subjected to various edge or feature perturbations, offering a scalable approach for evaluating the stability of GNNs, extending to applications within recommendation systems. Furthermore, we illustrate its utility in downstream tasks, notably in enhancing GNN stability and facilitating adversarial targeted attacks.

A Topology-aware Graph Coarsening Framework for Continual Graph Learning

Continual learning on graphs tackles the problem of training a graph neural network (GNN) where graph data arrive in a streaming fashion and the model tends to forget knowledge from previous tasks when updating with new data. Traditional continual learning strategies such as Experience Replay can be adapted to streaming graphs, however, these methods often face challenges such as inefficiency in preserving graph topology and incapability of capturing the correlation between old and new tasks. To address these challenges, we propose TA$\mathbb{CO}$, a (t)opology-(a)ware graph (co)arsening and (co)ntinual learning framework that stores information from previous tasks as a reduced graph. At each time period, this reduced graph expands by combining with a new graph and aligning shared nodes, and then it undergoes a "zoom out" process by reduction to maintain a stable size. We design a graph coarsening algorithm based on node representation proximities to efficiently reduce a graph and preserve topological information. We empirically demonstrate the learning process on the reduced graph can approximate that of the original graph. Our experiments validate the effectiveness of the proposed framework on three real-world datasets using different backbone GNN models.

SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements

This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. We prove that given $O(\log N)$ pairs of voltage and current measurements, it is possible to recover sparse $N$-node resistor networks that can well preserve the effective resistance distances on the original graph. In addition, the learned graphs also preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. To achieve more scalable performance, we also introduce a solver-free method (SF-SGL) that exploits multilevel spectral approximation of the graphs and allows for a scalable and flexible decomposition of the entire graph spectrum (to be learned) into multiple different eigenvalue clusters (frequency bands). Such a solver-free approach allows us to more efficiently identify the most spectrally-critical edges for reducing various ranges of spectral embedding distortions. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning sparse resistor networks without sacrificing solution quality. We also introduce a data-driven EDA algorithm for vectorless power/thermal integrity verifications to allow estimating worst-case voltage/temperature (gradient) distributions across the entire chip by leveraging a few voltage/temperature measurements.

HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering

This paper introduces a scalable algorithmic framework (HyperEF) for spectral coarsening (decomposition) of large-scale hypergraphs by exploiting hyperedge effective resistances. Motivated by the latest theoretical framework for low-resistance-diameter decomposition of simple graphs, HyperEF aims at decomposing large hypergraphs into multiple node clusters with only a few inter-cluster hyperedges. The key component in HyperEF is a nearly-linear time algorithm for estimating hyperedge effective resistances, which allows incorporating the latest diffusion-based non-linear quadratic operators defined on hypergraphs. To achieve good runtime scalability, HyperEF searches within the Krylov subspace (or approximate eigensubspace) for identifying the nearly-optimal vectors for approximating the hyperedge effective resistances. In addition, a node weight propagation scheme for multilevel spectral hypergraph decomposition has been introduced for achieving even greater node coarsening ratios. When compared with state-of-the-art hypergraph partitioning (clustering) methods, extensive experiment results on real-world VLSI designs show that HyperEF can more effectively coarsen (decompose) hypergraphs without losing key structural (spectral) properties of the original hypergraphs, while achieving over $70\times$ runtime speedups over hMetis and $20\times$ speedups over HyperSF.

GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networks

Graph neural networks (GNNs) have been increasingly deployed in various applications that involve learning on non-Euclidean data. However, recent studies show that GNNs are vulnerable to graph adversarial attacks. Although there are several defense methods to improve GNN robustness by eliminating adversarial components, they may also impair the underlying clean graph structure that contributes to GNN training. In addition, few of those defense models can scale to large graphs due to their high computational complexity and memory usage. In this paper, we propose GARNET, a scalable spectral method to boost the adversarial robustness of GNN models. GARNET first leverages weighted spectral embedding to construct a base graph, which is not only resistant to adversarial attacks but also contains critical (clean) graph structure for GNN training. Next, GARNET further refines the base graph by pruning additional uncritical edges based on probabilistic graphical model. GARNET has been evaluated on various datasets, including a large graph with millions of nodes. Our extensive experiment results show that GARNET achieves adversarial accuracy improvement and runtime speedup over state-of-the-art GNN (defense) models by up to 13.27% and 14.7x, respectively.

HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering

Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the ever-increasing computational challenges, graph coarsening can be potentially applied for preprocessing a given hypergraph by aggressively aggregating its vertices (nodes). However, state-of-the-art hypergraph partitioning (clustering) methods that incorporate heuristic graph coarsening techniques are not optimized for preserving the structural (global) properties of hypergraphs. In this work, we propose an efficient spectral hypergraph coarsening scheme (HyperSF) for well preserving the original spectral (structural) properties of hypergraphs. Our approach leverages a recent strongly-local max-flow-based clustering algorithm for detecting the sets of hypergraph vertices that minimize ratio cut. To further improve the algorithm efficiency, we propose a divide-and-conquer scheme by leveraging spectral clustering of the bipartite graphs corresponding to the original hypergraphs. Our experimental results for a variety of hypergraphs extracted from real-world VLSI design benchmarks show that the proposed hypergraph coarsening algorithm can significantly improve the multi-way conductance of hypergraph clustering as well as runtime efficiency when compared with existing state-of-the-art algorithms.

SGL: Spectral Graph Learning from Measurements

This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current measurements, it is possible to recover ultra-sparse $N$-node resistor networks which can well preserve the effective resistance distances on the graph. Also, the learned graphs preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning ultra-sparse resistor networks without sacrificing solution quality.