The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, namely, $\mathbb{F}_2$. In this paper, we study Cheeger-type inequalities for graphs endowed with a generalized coefficient group, called a sheaf; this is motivated by applications to locally testable codes. We prove that a graph is a good spectral expander if and only if it has good coboundary expansion relative to any (resp. some) constant sheaf, equivalently, relative to any `ordinary' coefficient group. We moreover show that sheaves that are close to being constant in a well-defined sense are also good coboundary expanders, provided that their underlying graph is an expander, thus giving the first example of good coboundary expansion in non-cosntant sheaves. By contrast, for general sheaves on graphs, it is impossible to relate the expansion of the graph and the coboundary expansion of the sheaf. In addition, we show that the normalized second eigenvalue of the (weighted) graph underlying a $q$-thick $d$-dimensional spherical building is $O(\frac{1}{\sqrt{q}-3d})$ if $q>9d^2$, and plug this into our results about coboundary expansion of sheaves to get explicit bounds on the coboundary expansion in terms of $q$ and $d$. It approaches a constant as $q$ grows. Along the way, we prove a new version of the Expander Mixing Lemma applying to $r$-partite weighted graphs.
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Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem, presenting an alternate perspective to the traditional optimization-based formulation. We model the planning problem as a probabilistic inference over a factor graph, with factor nodes capturing the joint distribution of motion objectives. By leveraging the duality between optimization and inference, a fast solution to the maximum a posteriori estimation of the factor graph is obtained via least-squares optimization. The localized design thinking inherent in this formulation ensures that motion objectives depend on a small subset of variables. We exploit the locality feature of the factor graph structure to integrate the minimum curvature path and local planning computations into a unified algorithm. This diverges from the conventional separation of global and local planning modules, where curvature minimization occurs at the global level. The proposed framework is evaluated through simulation, demonstrating superior cumulative curvature and average speed performance. Furthermore, the results highlight the computational efficiency of our approach. While acknowledging the structural design advantages and computational efficiency of the proposed approach, we also address its limitations and outline potential directions for future research.
We present Classy Ensemble, a novel ensemble-generation algorithm for classification tasks, which aggregates models through a weighted combination of per-class accuracy. Tested over 153 machine learning datasets we demonstrate that Classy Ensemble outperforms two other well-known aggregation algorithms -- order-based pruning and clustering-based pruning -- as well as the recently introduced lexigarden ensemble generator. We then present three enhancements: 1) Classy Cluster Ensemble, which combines Classy Ensemble and cluster-based pruning; 2) Deep Learning experiments, showing the merits of Classy Ensemble over four image datasets: Fashion MNIST, CIFAR10, CIFAR100, and ImageNet; and 3) Classy Evolutionary Ensemble, wherein an evolutionary algorithm is used to select the set of models which Classy Ensemble picks from. This latter, combining learning and evolution, resulted in improved performance on the hardest dataset.
We consider the performance of a least-squares regression model, as judged by out-of-sample $R^2$. Shapley values give a fair attribution of the performance of a model to its input features, taking into account interdependencies between features. Evaluating the Shapley values exactly requires solving a number of regression problems that is exponential in the number of features, so a Monte Carlo-type approximation is typically used. We focus on the special case of least-squares regression models, where several tricks can be used to compute and evaluate regression models efficiently. These tricks give a substantial speed up, allowing many more Monte Carlo samples to be evaluated, achieving better accuracy. We refer to our method as least-squares Shapley performance attribution (LS-SPA), and describe our open-source implementation.
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias and developed geometrically equivariant Graph Neural Networks (GNNs) to better characterize the geometry and topology of geometric graphs. Despite fruitful achievements, it still lacks a survey to depict how equivariant GNNs are progressed, which in turn hinders the further development of equivariant GNNs. To this end, based on the necessary but concise mathematical preliminaries, we analyze and classify existing methods into three groups regarding how the message passing and aggregation in GNNs are represented. We also summarize the benchmarks as well as the related datasets to facilitate later researches for methodology development and experimental evaluation. The prospect for future potential directions is also provided.
Images can convey rich semantics and induce various emotions in viewers. Recently, with the rapid advancement of emotional intelligence and the explosive growth of visual data, extensive research efforts have been dedicated to affective image content analysis (AICA). In this survey, we will comprehensively review the development of AICA in the recent two decades, especially focusing on the state-of-the-art methods with respect to three main challenges -- the affective gap, perception subjectivity, and label noise and absence. We begin with an introduction to the key emotion representation models that have been widely employed in AICA and description of available datasets for performing evaluation with quantitative comparison of label noise and dataset bias. We then summarize and compare the representative approaches on (1) emotion feature extraction, including both handcrafted and deep features, (2) learning methods on dominant emotion recognition, personalized emotion prediction, emotion distribution learning, and learning from noisy data or few labels, and (3) AICA based applications. Finally, we discuss some challenges and promising research directions in the future, such as image content and context understanding, group emotion clustering, and viewer-image interaction.
GAN inversion aims to invert a given image back into the latent space of a pretrained GAN model, for the image to be faithfully reconstructed from the inverted code by the generator. As an emerging technique to bridge the real and fake image domains, GAN inversion plays an essential role in enabling the pretrained GAN models such as StyleGAN and BigGAN to be used for real image editing applications. Meanwhile, GAN inversion also provides insights on the interpretation of GAN's latent space and how the realistic images can be generated. In this paper, we provide an overview of GAN inversion with a focus on its recent algorithms and applications. We cover important techniques of GAN inversion and their applications to image restoration and image manipulation. We further elaborate on some trends and challenges for future directions.
With the rise and development of deep learning, computer vision has been tremendously transformed and reshaped. As an important research area in computer vision, scene text detection and recognition has been inescapably influenced by this wave of revolution, consequentially entering the era of deep learning. In recent years, the community has witnessed substantial advancements in mindset, approach and performance. This survey is aimed at summarizing and analyzing the major changes and significant progresses of scene text detection and recognition in the deep learning era. Through this article, we devote to: (1) introduce new insights and ideas; (2) highlight recent techniques and benchmarks; (3) look ahead into future trends. Specifically, we will emphasize the dramatic differences brought by deep learning and the grand challenges still remained. We expect that this review paper would serve as a reference book for researchers in this field. Related resources are also collected and compiled in our Github repository: //github.com/Jyouhou/SceneTextPapers.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, XLNet outperforms BERT on 20 tasks, often by a large margin, and achieves state-of-the-art results on 18 tasks including question answering, natural language inference, sentiment analysis, and document ranking.
Generative Adversarial Networks (GANs) can produce images of surprising complexity and realism, but are generally modeled to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different objects in the world, including their relative scaling, spatial layout, occlusion, or viewpoint transformation is a challenging problem. In this work, we propose to model object composition in a GAN framework as a self-consistent composition-decomposition network. Our model is conditioned on the object images from their marginal distributions to generate a realistic image from their joint distribution by explicitly learning the possible interactions. We evaluate our model through qualitative experiments and user evaluations in both the scenarios when either paired or unpaired examples for the individual object images and the joint scenes are given during training. Our results reveal that the learned model captures potential interactions between the two object domains given as input to output new instances of composed scene at test time in a reasonable fashion.
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