In this work we design graph neural network architectures that can be used to obtain optimal approximation algorithms for a large class of combinatorial optimization problems using powerful algorithmic tools from semidefinite programming (SDP). Concretely, we prove that polynomial-sized message passing algorithms can represent the most powerful polynomial time algorithms for Max Constraint Satisfaction Problems assuming the Unique Games Conjecture. We leverage this result to construct efficient graph neural network architectures, OptGNN, that obtain high-quality approximate solutions on landmark combinatorial optimization problems such as Max Cut and maximum independent set. Our approach achieves strong empirical results across a wide range of real-world and synthetic datasets against both neural baselines and classical algorithms. Finally, we take advantage of OptGNN's ability to capture convex relaxations to design an algorithm for producing dual certificates of optimality (bounds on the optimal solution) from the learned embeddings of OptGNN.
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Reliance on the inherent knowledge of Large Language Models (LLMs) can cause issues such as hallucinations, lack of control, and difficulties in integrating variable knowledge. To mitigate this, LLMs can be probed to generate responses by grounding on external context, often given as input (knowledge-augmented models). Yet, previous research is often confined to a narrow view of the term "grounding", often only focusing on whether the response contains the correct answer or not, which does not ensure the reliability of the entire response. To address this limitation, we introduce a strict definition of grounding: a model is considered truly grounded when its responses (1) fully utilize necessary knowledge from the provided context, and (2) don't exceed the knowledge within the contexts. We introduce a new dataset and a grounding metric to assess this new definition and perform experiments across 13 LLMs of different sizes and training methods to provide insights into the factors that influence grounding performance. Our findings contribute to a better understanding of how to improve grounding capabilities and suggest an area of improvement toward more reliable and controllable LLM applications.
Are Large language models (LLMs) temporally grounded? Since LLMs cannot perceive and interact with the environment, it is impossible to answer this question directly. Instead, we provide LLMs with textual narratives and probe them with respect to their common-sense knowledge of the structure and duration of events, their ability to order events along a timeline, and self-consistency within their temporal model (e.g., temporal relations such as after and before are mutually exclusive for any pair of events). We evaluate state-of-the-art LLMs (such as LLaMA 2 and GPT-4) on three tasks reflecting these abilities. Generally, we find that LLMs lag significantly behind both human performance as well as small-scale, specialised LMs. In-context learning, instruction tuning, and chain-of-thought prompting reduce this gap only to a limited degree. Crucially, LLMs struggle the most with self-consistency, displaying incoherent behaviour in at least 27.23% of their predictions. Contrary to expectations, we also find that scaling the model size does not guarantee positive gains in performance. To explain these results, we study the sources from which LLMs may gather temporal information: we find that sentence ordering in unlabelled texts, available during pre-training, is only weakly correlated with event ordering. Moreover, public instruction tuning mixtures contain few temporal tasks. Hence, we conclude that current LLMs lack a consistent temporal model of textual narratives. Code, datasets, and LLM outputs are available at //github.com/yfqiu-nlp/temporal-llms.
The deep learning field is converging towards the use of general foundation models that can be easily adapted for diverse tasks. While this paradigm shift has become common practice within the field of natural language processing, progress has been slower in computer vision. In this paper we attempt to address this issue by investigating the transferability of various state-of-the-art foundation models to medical image classification tasks. Specifically, we evaluate the performance of five foundation models, namely SAM, SEEM, DINOv2, BLIP, and OpenCLIP across four well-established medical imaging datasets. We explore different training settings to fully harness the potential of these models. Our study shows mixed results. DINOv2 consistently outperforms the standard practice of ImageNet pretraining. However, other foundation models failed to consistently beat this established baseline indicating limitations in their transferability to medical image classification tasks.
Text embedding models have significantly contributed to advancements in natural language processing by adeptly capturing semantic properties of textual data. However, the ability of these models to generalize across a wide range of syntactic contexts remains under-explored. In this paper, we first develop an evaluation set, named \textbf{SR}, to scrutinize the capability for syntax understanding of text embedding models from two crucial syntactic aspects: Structural heuristics, and Relational understanding among concepts, as revealed by the performance gaps in previous studies. Our findings reveal that existing text embedding models have not sufficiently addressed these syntactic understanding challenges, and such ineffectiveness becomes even more apparent when evaluated against existing benchmark datasets. Furthermore, we conduct rigorous analysis to unearth factors that lead to such limitations and examine why previous evaluations fail to detect such ineffectiveness. Lastly, we propose strategies to augment the generalization ability of text embedding models in diverse syntactic scenarios. This study serves to highlight the hurdles associated with syntactic generalization and provides pragmatic guidance for boosting model performance across varied syntactic contexts.
In this paper, we propose a machine learning-based approach to address the lack of ability for designers to optimize urban land use planning from the perspective of vehicle travel demand. Research shows that our computational model can help designers quickly obtain feedback on the vehicle travel demand, which includes its total amount and temporal distribution based on the urban function distribution designed by the designers. It also assists in design optimization and evaluation of the urban function distribution from the perspective of vehicle travel. We obtain the city function distribution information and vehicle hours traveled (VHT) information by collecting the city point-of-interest (POI) data and online vehicle data. The artificial neural networks (ANNs) with the best performance in prediction are selected. By using data sets collected in different regions for mutual prediction and remapping the predictions onto a map for visualization, we evaluate the extent to which the computational model sees use across regions in an attempt to reduce the workload of future urban researchers. Finally, we demonstrate the application of the computational model to help designers obtain feedback on vehicle travel demand in the built environment and combine it with genetic algorithms to optimize the current state of the urban environment to provide recommendations to designers.
Feature attribution methods are popular in interpretable machine learning. These methods compute the attribution of each input feature to represent its importance, but there is no consensus on the definition of "attribution", leading to many competing methods with little systematic evaluation, complicated in particular by the lack of ground truth attribution. To address this, we propose a dataset modification procedure to induce such ground truth. Using this procedure, we evaluate three common methods: saliency maps, rationales, and attentions. We identify several deficiencies and add new perspectives to the growing body of evidence questioning the correctness and reliability of these methods applied on datasets in the wild. We further discuss possible avenues for remedy and recommend new attribution methods to be tested against ground truth before deployment. The code is available at \url{//github.com/YilunZhou/feature-attribution-evaluation}.
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the local geometry and update iteratively. Even though solving non-convex functions is NP-hard in the worst case, the optimization quality in practice is often not an issue -- optimizers are largely believed to find approximate global minima. Researchers hypothesize a unified explanation for this intriguing phenomenon: most of the local minima of the practically-used objectives are approximately global minima. We rigorously formalize it for concrete instances of machine learning problems.
In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
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