arXiv subjects

Chen Cai

Publications and source records attributed to Chen Cai.

At least 37 records · Page 2Linked to original sources

arXiv2024

Balancing Performance and Cost for Two-Hop Cooperative Communications: Stackelberg Game and Distributed Multi-Agent Reinforcement Learning

This paper aims to balance performance and cost in a two-hop wireless cooperative communication network where the source and relays have contradictory optimization goals and make decisions in a distributed manner. This differs from most existing works that have typically assumed that source and relay nodes follow a schedule created implicitly by a central controller. We propose that the relays form an alliance in an attempt to maximize the benefit of relaying while the source aims to increase the channel capacity cost-effectively. To this end, we establish the trade problem as a Stackelberg game, and prove the existence of its equilibrium. Another important aspect is that we use multi-agent reinforcement learning (MARL) to approach the equilibrium in a situation where the instantaneous channel state information (CSI) is unavailable, and the source and relays do not have knowledge of each other's goal. A multi-agent deep deterministic policy gradient-based framework is designed, where the relay alliance and the source act as agents. Experiments demonstrate that the proposed method can obtain an acceptable performance that is close to the game-theoretic equilibrium for all players under time-invariant environments, which considerably outperforms its potential alternatives and is only about 2.9% away from the optimal solution.

eess.SY↗

arXiv2024

Top-Down Framework for Weakly-supervised Grounded Image Captioning

Weakly-supervised grounded image captioning (WSGIC) aims to generate the caption and ground (localize) predicted object words in the input image without using bounding box supervision. Recent two-stage solutions mostly apply a bottom-up pipeline: (1) encode the input image into multiple region features using an object detector; (2) leverage region features for captioning and grounding. However, utilizing independent proposals produced by object detectors tends to make the subsequent grounded captioner overfitted in finding the correct object words, overlooking the relation between objects, and selecting incompatible proposal regions for grounding. To address these issues, we propose a one-stage weakly-supervised grounded captioner that directly takes the RGB image as input to perform captioning and grounding at the top-down image level. Specifically, we encode the image into visual token representations and propose a Recurrent Grounding Module (RGM) in the decoder to obtain precise Visual Language Attention Maps (VLAMs), which recognize the spatial locations of the objects. In addition, we explicitly inject a relation module into our one-stage framework to encourage relation understanding through multi-label classification. This relation semantics served as contextual information facilitating the prediction of relation and object words in the caption. We observe that the relation semantic not only assists the grounded captioner in generating a more accurate caption but also improves the grounding performance. We validate the effectiveness of our proposed method on two challenging datasets (Flick30k Entities captioning and MSCOCO captioning). The experimental results demonstrate that our method achieves state-of-the-art grounding performance.

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arXiv2023

On the Connection Between MPNN and Graph Transformer

Graph Transformer (GT) recently has emerged as a new paradigm of graph learning algorithms, outperforming the previously popular Message Passing Neural Network (MPNN) on multiple benchmarks. Previous work (Kim et al., 2022) shows that with proper position embedding, GT can approximate MPNN arbitrarily well, implying that GT is at least as powerful as MPNN. In this paper, we study the inverse connection and show that MPNN with virtual node (VN), a commonly used heuristic with little theoretical understanding, is powerful enough to arbitrarily approximate the self-attention layer of GT. In particular, we first show that if we consider one type of linear transformer, the so-called Performer/Linear Transformer (Choromanski et al., 2020; Katharopoulos et al., 2020), then MPNN + VN with only O(1) depth and O(1) width can approximate a self-attention layer in Performer/Linear Transformer. Next, via a connection between MPNN + VN and DeepSets, we prove the MPNN + VN with O(n^d) width and O(1) depth can approximate the self-attention layer arbitrarily well, where d is the input feature dimension. Lastly, under some assumptions, we provide an explicit construction of MPNN + VN with O(1) width and O(n) depth approximating the self-attention layer in GT arbitrarily well. On the empirical side, we demonstrate that 1) MPNN + VN is a surprisingly strong baseline, outperforming GT on the recently proposed Long Range Graph Benchmark (LRGB) dataset, 2) our MPNN + VN improves over early implementation on a wide range of OGB datasets and 3) MPNN + VN outperforms Linear Transformer and MPNN on the climate modeling task.

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arXiv2023

Local-to-global Perspectives on Graph Neural Networks

This thesis presents a local-to-global perspective on graph neural networks (GNN), the leading architecture to process graph-structured data. After categorizing GNN into local Message Passing Neural Networks (MPNN) and global Graph transformers, we present three pieces of work: 1) study the convergence property of a type of global GNN, Invariant Graph Networks, 2) connect the local MPNN and global Graph Transformer, and 3) use local MPNN for graph coarsening, a standard subroutine used in global modeling.

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arXiv2022

Convergence of Invariant Graph Networks

Although theoretical properties such as expressive power and over-smoothing of graph neural networks (GNN) have been extensively studied recently, its convergence property is a relatively new direction. In this paper, we investigate the convergence of one powerful GNN, Invariant Graph Network (IGN) over graphs sampled from graphons. We first prove the stability of linear layers for general $k$-IGN (of order $k$) based on a novel interpretation of linear equivariant layers. Building upon this result, we prove the convergence of $k$-IGN under the model of \citet{ruiz2020graphon}, where we access the edge weight but the convergence error is measured for graphon inputs. Under the more natural (and more challenging) setting of \citet{keriven2020convergence} where one can only access 0-1 adjacency matrix sampled according to edge probability, we first show a negative result that the convergence of any IGN is not possible. We then obtain the convergence of a subset of IGNs, denoted as IGN-small, after the edge probability estimation. We show that IGN-small still contains function class rich enough that can approximate spectral GNNs arbitrarily well. Lastly, we perform experiments on various graphon models to verify our statements.

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arXiv2022

Generative Coarse-Graining of Molecular Conformations

Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes accurate backmapping, i.e., restoring fine-grained (FG) coordinates from CG coordinates, a long-standing challenge. Inspired by the recent progress in generative models and equivariant networks, we propose a novel model that rigorously embeds the vital probabilistic nature and geometric consistency requirements of the backmapping transformation. Our model encodes the FG uncertainties into an invariant latent space and decodes them back to FG geometries via equivariant convolutions. To standardize the evaluation of this domain, we provide three comprehensive benchmarks based on molecular dynamics trajectories. Experiments show that our approach always recovers more realistic structures and outperforms existing data-driven methods with a significant margin.

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arXiv2022

A simple yet effective baseline for non-attributed graph classification

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation learning on graphs in general. As the developed methodologies become more sophisticated, it is important to understand which components of the increasingly complex methods are necessary or most effective. As a first step, we develop a simple yet meaningful graph representation, and explore its effectiveness in graph classification. We test our baseline representation for the graph classification task on a range of graph datasets. Interestingly, this simple representation achieves similar performance as the state-of-the-art graph kernels and graph neural networks for non-attributed graph classification. Its performance on classifying attributed graphs is slightly weaker as it does not incorporate attributes. However, given its simplicity and efficiency, we believe that it still serves as an effective baseline for attributed graph classification. Our graph representation is efficient (linear-time) to compute. We also provide a simple connection with the graph neural networks. Note that these observations are only for the task of graph classification while existing methods are often designed for a broader scope including node embedding and link prediction. The results are also likely biased due to the limited amount of benchmark datasets available. Nevertheless, the good performance of our simple baseline calls for the development of new, more comprehensive benchmark datasets so as to better evaluate and analyze different graph learning methods. Furthermore, given the computational efficiency of our graph summary, we believe that it is a good candidate as a baseline method for future graph classification (or even other graph learning) studies.

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arXiv2022

Traffic4cast at NeurIPS 2021 -- Temporal and Spatial Few-Shot Transfer Learning in Gridded Geo-Spatial Processes

The IARAI Traffic4cast competitions at NeurIPS 2019 and 2020 showed that neural networks can successfully predict future traffic conditions 1 hour into the future on simply aggregated GPS probe data in time and space bins. We thus reinterpreted the challenge of forecasting traffic conditions as a movie completion task. U-Nets proved to be the winning architecture, demonstrating an ability to extract relevant features in this complex real-world geo-spatial process. Building on the previous competitions, Traffic4cast 2021 now focuses on the question of model robustness and generalizability across time and space. Moving from one city to an entirely different city, or moving from pre-COVID times to times after COVID hit the world thus introduces a clear domain shift. We thus, for the first time, release data featuring such domain shifts. The competition now covers ten cities over 2 years, providing data compiled from over 10^12 GPS probe data. Winning solutions captured traffic dynamics sufficiently well to even cope with these complex domain shifts. Surprisingly, this seemed to require only the previous 1h traffic dynamic history and static road graph as input.

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arXiv2022

Equivariant Subgraph Aggregation Networks

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in their expressive power. This paper proposes a novel framework called Equivariant Subgraph Aggregation Networks (ESAN) to address this issue. Our main observation is that while two graphs may not be distinguishable by an MPNN, they often contain distinguishable subgraphs. Thus, we propose to represent each graph as a set of subgraphs derived by some predefined policy, and to process it using a suitable equivariant architecture. We develop novel variants of the 1-dimensional Weisfeiler-Leman (1-WL) test for graph isomorphism, and prove lower bounds on the expressiveness of ESAN in terms of these new WL variants. We further prove that our approach increases the expressive power of both MPNNs and more expressive architectures. Moreover, we provide theoretical results that describe how design choices such as the subgraph selection policy and equivariant neural architecture affect our architecture's expressive power. To deal with the increased computational cost, we propose a subgraph sampling scheme, which can be viewed as a stochastic version of our framework. A comprehensive set of experiments on real and synthetic datasets demonstrates that our framework improves the expressive power and overall performance of popular GNN architectures.

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arXiv2021

Traffic4cast -- Large-scale Traffic Prediction using 3DResNet and Sparse-UNet

The IARAI competition Traffic4cast 2021 aims to predict short-term city-wide high-resolution traffic states given the static and dynamic traffic information obtained previously. The aim is to build a machine learning model for predicting the normalized average traffic speed and flow of the subregions of multiple large-scale cities using historical data points. The model is supposed to be generic, in a way that it can be applied to new cities. By considering spatiotemporal feature learning and modeling efficiency, we explore 3DResNet and Sparse-UNet approaches for the tasks in this competition. The 3DResNet based models use 3D convolution to learn the spatiotemporal features and apply sequential convolutional layers to enhance the temporal relationship of the outputs. The Sparse-UNet model uses sparse convolutions as the backbone for spatiotemporal feature learning. Since the latter algorithm mainly focuses on non-zero data points of the inputs, it dramatically reduces the computation time, while maintaining a competitive accuracy. Our results show that both of the proposed models achieve much better performance than the baseline algorithms. The codes and pretrained models are available at https://github.com/resuly/Traffic4Cast-2021.

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arXiv2021

Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective permeability, while the topology and geometry of the pore space are represented by a persistence-based Morse graph. Together, they constitute the database for training, validating, and testing the neural networks. While the graph and Euclidean convolutional approaches both employ neural networks to generate low-dimensional latent space to represent the features of the micro-structures for forward predictions, the SE(3) equivariant neural network is found to generate more accurate predictions, especially when the training data is limited. Numerical experiments have also shown that the new SE(3) approach leads to predictions that fulfill the material frame indifference whereas the predictions from classical convolutional neural networks (CNN) may suffer from spurious dependence on the coordinate system of the training data. Comparisons among predictions inferred from training the CNN and those from graph convolutional neural networks (GNN) with and without the equivariant constraint indicate that the equivariant graph neural network seems to perform better than the CNN and GNN without enforcing equivariant constraints.

physics.geo-ph↗

arXiv2021

Graph Coarsening with Neural Networks

As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data. Graph coarsening is one popular technique to reduce the size of a graph while maintaining essential properties. Despite rich graph coarsening literature, there is only limited exploration of data-driven methods in the field. In this work, we leverage the recent progress of deep learning on graphs for graph coarsening. We first propose a framework for measuring the quality of coarsening algorithm and show that depending on the goal, we need to carefully choose the Laplace operator on the coarse graph and associated projection/lift operators. Motivated by the observation that the current choice of edge weight for the coarse graph may be sub-optimal, we parametrize the weight assignment map with graph neural networks and train it to improve the coarsening quality in an unsupervised way. Through extensive experiments on both synthetic and real networks, we demonstrate that our method significantly improves common graph coarsening methods under various metrics, reduction ratios, graph sizes, and graph types. It generalizes to graphs of larger size ($25\times$ of training graphs), is adaptive to different losses (differentiable and non-differentiable), and scales to much larger graphs than previous work.

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arXiv2020

Energy consumption forecasting using a stacked nonparametric Bayesian approach

In this paper, the process of forecasting household energy consumption is studied within the framework of the nonparametric Gaussian Process (GP), using multiple short time series data. As we begin to use smart meter data to paint a clearer picture of residential electricity use, it becomes increasingly apparent that we must also construct a detailed picture and understanding of consumer's complex relationship with gas consumption. Both electricity and gas consumption patterns are highly dependent on various factors, and the intricate interplay of these factors is sophisticated. Moreover, since typical gas consumption data is low granularity with very few time points, naive application of conventional time-series forecasting techniques can lead to severe over-fitting. Given these considerations, we construct a stacked GP method where the predictive posteriors of each GP applied to each task are used in the prior and likelihood of the next level GP. We apply our model to a real-world dataset to forecast energy consumption in Australian households across several states. We compare intuitively appealing results against other commonly used machine learning techniques. Overall, the results indicate that the proposed stacked GP model outperforms other forecasting techniques that we tested, especially when we have a multiple short time-series instances.

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arXiv2020

Elder-Rule-Staircodes for Augmented Metric Spaces

An augmented metric space is a metric space $(X, d_X)$ equipped with a function $f_X: X \to \mathbb{R}$. This type of data arises commonly in practice, e.g, a point cloud $X$ in $\mathbb{R}^d$ where each point $x\in X$ has a density function value $f_X(x)$ associated to it. An augmented metric space $(X, d_X, f_X)$ naturally gives rise to a 2-parameter filtration $\mathcal{K}$. However, the resulting 2-parameter persistent homology $\mathrm{H}_{\bullet}(\mathcal{K})$ could still be of wild representation type, and may not have simple indecomposables. In this paper, motivated by the elder-rule for the zeroth homology of 1-parameter filtration, we propose a barcode-like summary, called the elder-rule-staircode, as a way to encode $\mathrm{H}_0(\mathcal{K})$. Specifically, if $n = |X|$, the elder-rule-staircode consists of $n$ number of staircase-like blocks in the plane. We show that if $\mathrm{H}_0(\mathcal{K})$ is interval decomposable, then the barcode of $\mathrm{H}_0(\mathcal{K})$ is equal to the elder-rule-staircode. Furthermore, regardless of the interval decomposability, the fibered barcode, the dimension function (a.k.a. the Hilbert function), and the graded Betti numbers of $\mathrm{H}_0(\mathcal{K})$ can all be efficiently computed once the elder-rule-staircode is given. Finally, we develop and implement an efficient algorithm to compute the elder-rule-staircode in $O(n^2\log n)$ time, which can be improved to $O(n^2α(n))$ if $X$ is from a fixed dimensional Euclidean space $\mathbb{R}^d$, where $α(n)$ is the inverse Ackermann function.

math.AT↗

arXiv2020

A Note on Over-Smoothing for Graph Neural Networks

Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results \cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure "expressiveness" of embedding is conceptually clean; it leads to simpler proofs than \cite{oono2019graph} and can handle more non-linearities.

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arXiv2020

Understanding the Power of Persistence Pairing via Permutation Test

Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we also propose the so-called \emph{permutation test} for persistence diagrams to delineate critical values and pairings of critical values. For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests. Our results help provide insights on when persistence diagram based summaries could be more suitable.

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arXiv2019

Group Representation Theory for Knowledge Graph Embedding

Knowledge graph embedding has recently become a popular way to model relations and infer missing links. In this paper, we present a group theoretical perspective of knowledge graph embedding, connecting previous methods with different group actions. Furthermore, by utilizing Schur's lemma from group representation theory, we show that the state of the art embedding method RotatE can model relations from any finite Abelian group.

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arXiv2019

Network Representation Learning: Consolidation and Renewed Bearing

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for non-linear dimensionality reduction in a manner akin to previous efforts based on manifold learning with uses for downstream database processing, machine learning and visualization. In this systematic yet comprehensive experimental survey, we benchmark several popular network representation learning methods operating on two key tasks: link prediction and node classification. We examine the performance of 12 unsupervised embedding methods on 15 datasets. To the best of our knowledge, the scale of our study -- both in terms of the number of methods and number of datasets -- is the largest to date. Our results reveal several key insights about work-to-date in this space. First, we find that certain baseline methods (task-specific heuristics, as well as classic manifold methods) that have often been dismissed or are not considered by previous efforts can compete on certain types of datasets if they are tuned appropriately. Second, we find that recent methods based on matrix factorization offer a small but relatively consistent advantage over alternative methods (e.g., random-walk based methods) from a qualitative standpoint. Specifically, we find that MNMF, a community preserving embedding method, is the most competitive method for the link prediction task. While NetMF is the most competitive baseline for node classification. Third, no single method completely outperforms other embedding methods on both node classification and link prediction tasks. We also present several drill-down analysis that reveals settings under which certain algorithms perform well (e.g., the role of neighborhood context on performance) -- guiding the end-user.

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