United States

Many fundamental low-rank optimization problems, such as matrix completion, phase retrieval, and robust PCA, can be formulated as the matrix sensing problem. Two main approaches for solving matrix sensing are based on semidefinite programming (SDP) and Burer-Monteiro (B-M) factorization. The former suffers from high computational and space complexities, whereas the latter may return a spurious solution due to the non-convexity of the problem. The existing theoretical guarantees for the success of these methods have led to similar conservative conditions, which may wrongly imply that these methods have comparable performances. In this paper, we shed light on some major differences between these two methods. First, we present a class of structured matrix completion problems for which the B-M methods fail with an overwhelming probability, while the SDP method works correctly. Second, we identify a class of highly sparse matrix completion problems for which the B-M method works and the SDP method fails. Third, we prove that although the B-M method exhibits the same performance independent of the rank of the unknown solution, the success of the SDP method is correlated to the rank of the solution and improves as the rank increases. Unlike the existing literature that has mainly focused on those instances of matrix sensing for which both SDP and B-M work, this paper offers the first result on the unique merit of each method over the alternative approach. 


AAAI 2023

Semidefinite Programming Versus Burer-Monteiro Factorization for Matrix Sensing

matrix & tensor methods

optimization

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

poster

Predicting the trajectories of pedestrians in crowded conditions is an important task for applications like autonomous navigation systems. Previous studies have tackled this problem using two strategies. They (1) infer all future steps recursively, or (2) predict the potential destinations of pedestrians at once and interpolate the intermediate steps to arrive there. However, these strategies often suffer from the accumulated errors of the recursive inference, or restrictive assumptions about social relations in the intermediate path. In this paper, we present a graph convolutional network-based trajectory prediction. Firstly, we propose a control point prediction that divides the future path into three sections and infers the intermediate destinations of pedestrians to reduce the accumulated error. To do this, we construct multi-relational weighted graphs to account for their physical and complex social relations. We then introduce a trajectory refinement step based on a spatio-temporal and multi-relational graph. By considering the social interactions between neighbors, better prediction results are achievable. In experiments, the proposed network achieves state-of-the-art performance on various real-world trajectory prediction benchmarks.

A Set of Control Points Conditioned Pedestrian Trajectory Prediction

High-resolution (HR) images are usually downscaled to lowresolution (LR) ones for better display and afterward upscaled back to the original size to recover details. Recent work in image rescaling formulates downscaling and upscaling as a unified task and learns a bijective mapping between HR and LR via invertible networks. However, in real-world applications (e.g., social media), most images are compressed for transmission. Lossy compression will lead to irreversible information loss on LR images, hence damaging the inverse upscaling procedure and degrading the reconstruction accuracy. In this paper, we propose the Self-Asymmetric Invertible Network (SAIN) for compression-aware image rescaling. To tackle the distribution shift, we first develop an end-toend asymmetric framework with two separate bijective mappings for high-quality and compressed LR images, respectively. Then, based on empirical analysis of this framework, we model the distribution of the lost information (including downscaling and compression) using isotropic Gaussian mixtures and propose the Enhanced Invertible Block to derive high-quality/compressed LR images in one forward pass. Besides, we design a set of losses to regularize the learned LR images and enhance the invertibility. Extensive experiments demonstrate the consistent improvements of SAIN across various image rescaling datasets in terms of both quantitative and qualitative evaluation under standard image compression formats (i.e., JPEG and WebP).

Self-Asymmetric Invertible Network for Compression-Aware Image Rescaling

The ability to combine learned knowledge and skills to solve novel tasks is a key aspect of generalization in humans that allows us to understand and perform tasks described by novel language utterances. While progress has been made in supervised learning settings, no work has yet studied compositional generalization of a reinforcement learning agent following natural language instructions in an embodied environment. We develop a set of tasks in a photo-realistic simulated kitchen environment that allow us to study the degree to which a behavioral policy captures the systematicity in language by studying its zero-shot generalization performance on held out natural language instructions. We show that our agent which leverages a novel additive action-value decomposition in tandem with attention based subgoal prediction is able to exploit composition in text instructions to generalize to unseen tasks.

Learning Compositional Tasks from Language Instructions

One-shot segmentation of brain tissues is typically a dual-model iterative learning: a registration model (reg-model) warps a carefully-labeled atlas onto unlabeled images to initialize their pseudo masks for training a segmentation model (seg-model); the seg-model revises the pseudo masks to enhance the reg-model for a better warping in the next iteration. However, there is a key weakness in such dual-model iteration that the spatial misalignment inevitably caused by the reg-model could misguide the seg-model, which makes it converge on an inferior segmentation performance eventually. In this paper, we propose a novel image-aligned style transformation to reinforce the dual-model iterative learning for robust one-shot segmentation of brain tissues. Specifically, we first utilize the reg-model to warp the atlas onto an unlabeled image, and then employ the Fourier-based amplitude exchange with perturbation to transplant the style of the unlabeled image into the aligned atlas. This allows the subsequent seg-model to learn on the aligned and style-transferred copies of the atlas instead of unlabeled images, which naturally guarantees the correct spatial correspondence of an image-mask training pair, without sacrificing the diversity of intensity patterns carried by the unlabeled images. Furthermore, we introduce a feature-aware content consistency in addition to the image-level similarity to constrain the reg-model for a promising initialization, which avoids the collapse of image-aligned style transformation in the first iteration. Experimental results on two public datasets demonstrate 1) a competitive segmentation performance of our method compared to the fully-supervised method, and 2) a superior performance over other state-of-the-art with an increase of average Dice by up to 4.67%. The source code is available at: https://github.com/JinxLv/One-shot-segmentation-via-IST.

Robust One-shot Segmentation of Brain Tissues via Image-aligned Style Transformation

In many applications we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called Game Implementation: Given a game in standard form and a set of desired strategies, can we design a set of payment promises such that, if the players take the payment promises into account, then all undominated strategies are desired? Furthermore, we aim to minimize the cost, that is, the worst-case amount of payments.

We study the tractability of computing such payment promises and determine more closely what obstructions we may have to overcome in doing so. We show that Game Implementation is NP-hard even for two players, solving in particular a long open question (Eidenbenz et al. 2011). This suggests more restrictions are necessary to obtain tractability. We thus study the regime in which players have only a small constant number of strategies and obtain the following. First, this case remains NP-hard even if each player's utility depends only on three others. Second, we repair a flawed efficient algorithm for the case of both small number of strategies and small number of players. Among further results, we characterize sets of desired strategies that can be implemented at zero cost as a kind of stable core of the game.

Game Implementation: What are the Obstructions?

Stochastic partial differential equations (SPDEs) are crucial for modelling dynamics with randomness in many areas including economics, physics, and atmospheric sciences. Recently, using deep learning approaches to learn the PDE solution for accelerating PDE simulation becomes increasingly popular. However, SPDEs have two unique properties that require new design on the models. First, the model to approximate the solution of SPDE should be generalizable over both initial conditions and the random sampled forcing term. Second, the random forcing terms usually have poor regularity whose statistics may diverge (e.g., the space-time white noise). To deal with the problems, in this work, we design a deep neural network called \emph{Deep Latent Regularity Net} (DLR-Net).  DLR-Net includes a regularity feature block as the main component, which maps the initial condition and the random forcing term to a set of regularity features. The processing of regularity features is inspired by regularity structure theory and the features provably compose a set of basis to represent the SPDE solution. The regularity features are then fed into a small backbone neural operator to get the output. We conduct experiments on various SPDEs including the dynamic $\Phi^4_1$ model and the stochastic 2D Navier-Stokes equation to predict their solutions, and the results demonstrate that the proposed DLR-Net can achieve SOTA accuracy compared with the baselines. Moreover, the inference time is over 20 times faster than the traditional numerical solver and is comparable with the baseline deep learning models.

Deep Latent Regularity Network for Modeling Stochastic Partial Differential Equations

While large pre-trained language models (PLM) have shown their great skills at solving discriminative tasks, a significant gap remains when compared with humans for explanation-related tasks. Among them, explaining the reason why a statement is wrong (e.g., against commonsense) is incredibly challenging. The major difficulty is finding the conflict point, where the statement contradicts our real world. This paper proposes Neon, a two-phrase, unsupervised explanation generation framework. Neon first generates corrected instantiations of the statement (phase I), then uses them to prompt large PLMs to find the conflict point and complete the explanation (phase II). We conduct extensive experiments on two standard explanation benchmarks, i.e., ComVE and e-SNLI.  According to both automatic and human evaluations, Neon outperforms baselines, even for those with human-annotated instantiations. In addition to explaining a negative prediction, we further demonstrate that Neon remains effective when generalizing to different scenarios.

Unsupervised Explanation Generation via Correct Instantiations

As one of the most important research topics in the unsupervised learning field, Multi-View Clustering (MVC) has been widely studied in the past decade and numerous MVC methods have been developed. Among these methods, the recently emerged Graph Neural Networks (GNN) shine a light on modeling both topological structure and node attributes in the form of graphs, to guide unified embedding learning and clustering. However, the effectiveness of existing GNN-based MVC methods is still limited due to the insufficient consideration in utilizing the self-supervised information and graph information, which can be reflected from the following two aspects: 1) most of these models merely use the self-supervised information to guide the feature learning and fail to realize that such information can be also applied in graph learning and sample weighting; 2) the usage of graph information is generally limited to the feature aggregation in these models, yet it also provides valuable evidence in detecting noisy samples. To this end, in this paper we propose Self-Supervised Graph Attention Networks for Deep Weighted Multi-View Clustering (SGDMC), which promotes the performance of GNN-based deep MVC models by making full use of the self-supervised information and graph information. Specifically, a novel attention-allocating approach that considers both the similarity of node attributes and the self-supervised information is developed to comprehensively evaluate the relevance among different nodes. Meanwhile, to alleviate the negative impact caused by noisy samples and the discrepancy of cluster structures, we further design a sample-weighting strategy based on the attention graph as well as the discrepancy between the global pseudo-labels and the local cluster assignment. Experimental results on multiple real-world datasets demonstrate the effectiveness of our method over existing approaches.

Self-Supervised Graph Attention Networks for Deep Weighted Multi-View Clustering

Multilayer perceptron (MLP) has been widely used in two-view correspondence learning for only unordered correspondences provided, and it extracts deep features from individual correspondence effectively. However, the problem of lacking context information limits its performance and hence, many extra complex blocks are designed to capture such information in the follow-up studies. In this paper, from a novel perspective, we design a correspondence learning network called ConvMatch that for the first time can leverage convolutional neural network (CNN) as the backbone to capture better context, thus avoiding the complex design of extra blocks. Specifically, with the observation that sparse motion vectors and dense motion field can be converted into each other with interpolating and sampling, we regularize the putative motion vectors by estimating dense motion field implicitly, then rectify the errors caused by outliers in local areas with CNN, and finally obtain correct motion vectors from the rectified motion field. Extensive experiments reveal that ConvMatch with a simple CNN backbone consistently outperforms state-of-the-arts including MLP-based methods for relative pose estimation and homography estimation, and shows promising generalization ability to different datasets and descriptors. Our code is publicly available at https://github.com/SuhZhang/ConvMatch.

ConvMatch: Rethinking Network Design for Two-View Correspondence Learning

We propose an entity-agnostic representation learning method for handling the problem of inefficient parameter storage costs brought by embedding knowledge graphs. Conventional knowledge graph embedding methods map elements in a knowledge graph, including entities and relations, into continuous vector spaces by assigning them one or multiple specific embeddings  (i.e., vector representations). Thus the number of embedding parameters increases linearly as the growth of knowledge graphs. In our proposed model, Entity-Agnostic Representation Learning (EARL), we only learn the embeddings for a small set of entities and refer to them as reserved entities. To obtain the embeddings for the full set of entities, we encode their distinguishable information from their connected relations, k-nearest reserved entities, and multi-hop neighbors. We learn universal and entity-agnostic encoders for transforming distinguishable information into entity embeddings. This approach allows our proposed EARL to have a static, efficient, and lower parameter count than conventional knowledge graph embedding methods. Experimental results show that EARL uses fewer parameters and performs better on link prediction tasks than baselines, reflecting its parameter efficiency.

Semidefinite Programming Versus Burer-Monteiro Factorization for Matrix Sensing

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