We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered convex relaxations for the recovery of low-rank matrices and established that under a strict complementarity condition (SC), both the convergence rate and per-iteration runtime of standard gradient methods may improve dramatically. We develop the appropriate strict complementarity condition for the tensor nuclear norm ball and obtain the following main results under this condition: 1. When the objective to minimize is of the form $f(\mX)=g(\mA\mX)+\langle{\mC,\mX}\rangle$ , where $g$ is strongly convex and $\mA$ is a linear map (e.g., least squares), a quadratic growth bound holds, which implies linear convergence rates for standard projected gradient methods, despite the fact that $f$ need not be strongly convex. 2. For a smooth objective function, when initialized in certain proximity of an optimal solution which satisfies SC, standard projected gradient methods only require SVD computations (for projecting onto the tensor nuclear norm ball) of rank that matches the tubal rank of the optimal solution. In particular, when the tubal rank is constant, this implies nearly linear (in the size of the tensor) runtime per iteration, as opposed to super linear without further assumptions. 3. For a nonsmooth objective function which admits a popular smooth saddle-point formulation, we derive similar results to the latter for the well known extragradient method. An additional contribution which may be of independent interest, is the rigorous extension of many basic results regarding tensors of arbitrary order, which were previously obtained only for third-order tensors.
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Semantic facial attribute editing using pre-trained Generative Adversarial Networks (GANs) has attracted a great deal of attention and effort from researchers in recent years. Due to the high quality of face images generated by StyleGANs, much work has focused on the StyleGANs' latent space and the proposed methods for facial image editing. Although these methods have achieved satisfying results for manipulating user-intended attributes, they have not fulfilled the goal of preserving the identity, which is an important challenge. We present ID-Style, a new architecture capable of addressing the problem of identity loss during attribute manipulation. The key components of ID-Style include Learnable Global Direction (LGD), which finds a shared and semi-sparse direction for each attribute, and an Instance-Aware Intensity Predictor (IAIP) network, which finetunes the global direction according to the input instance. Furthermore, we introduce two losses during training to enforce the LGD to find semi-sparse semantic directions, which along with the IAIP, preserve the identity of the input instance. Despite reducing the size of the network by roughly 95% as compared to similar state-of-the-art works, it outperforms baselines by 10% and 7% in Identity preserving metric (FRS) and average accuracy of manipulation (mACC), respectively.
We prove upper and lower bounds for the threshold of the q-overlap-k-Exact cover problem. These results are motivated by the one-step replica symmetry breaking approach of Statistical Physics, and the hope of using an approach based on that of Mezard et al. (2005) to rigorously prove that for some values of the order parameter the overlap distribution of k-Exact Cover has discontinuous support.
Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (i.e., the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project's webpage in //hilamanor.github.io/GaussianDenoisingPosterior/
Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.
Action scene understanding in soccer is a challenging task due to the complex and dynamic nature of the game, as well as the interactions between players. This article provides a comprehensive overview of this task divided into action recognition, spotting, and spatio-temporal action localization, with a particular emphasis on the modalities used and multimodal methods. We explore the publicly available data sources and metrics used to evaluate models' performance. The article reviews recent state-of-the-art methods that leverage deep learning techniques and traditional methods. We focus on multimodal methods, which integrate information from multiple sources, such as video and audio data, and also those that represent one source in various ways. The advantages and limitations of methods are discussed, along with their potential for improving the accuracy and robustness of models. Finally, the article highlights some of the open research questions and future directions in the field of soccer action recognition, including the potential for multimodal methods to advance this field. Overall, this survey provides a valuable resource for researchers interested in the field of action scene understanding in soccer.
We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.
Wireless communications at high-frequency bands with large antenna arrays face challenges in beam management, which can potentially be improved by multimodality sensing information from cameras, LiDAR, radar, and GPS. In this paper, we present a multimodal transformer deep learning framework for sensing-assisted beam prediction. We employ a convolutional neural network to extract the features from a sequence of images, point clouds, and radar raw data sampled over time. At each convolutional layer, we use transformer encoders to learn the hidden relations between feature tokens from different modalities and time instances over abstraction space and produce encoded vectors for the next-level feature extraction. We train the model on a combination of different modalities with supervised learning. We try to enhance the model over imbalanced data by utilizing focal loss and exponential moving average. We also evaluate data processing and augmentation techniques such as image enhancement, segmentation, background filtering, multimodal data flipping, radar signal transformation, and GPS angle calibration. Experimental results show that our solution trained on image and GPS data produces the best distance-based accuracy of predicted beams at 78.44%, with effective generalization to unseen day scenarios near 73% and night scenarios over 84%. This outperforms using other modalities and arbitrary data processing techniques, which demonstrates the effectiveness of transformers with feature fusion in performing radio beam prediction from images and GPS. Furthermore, our solution could be pretrained from large sequences of multimodality wireless data, on fine-tuning for multiple downstream radio network tasks.
Extreme head postures pose a common challenge across a spectrum of facial analysis tasks, including face detection, facial landmark detection (FLD), and head pose estimation (HPE). These tasks are interdependent, where accurate FLD relies on robust face detection, and HPE is intricately associated with these key points. This paper focuses on the integration of these tasks, particularly when addressing the complexities posed by large-angle face poses. The primary contribution of this study is the proposal of a real-time multi-task detection system capable of simultaneously performing joint detection of faces, facial landmarks, and head poses. This system builds upon the widely adopted YOLOv8 detection framework. It extends the original object detection head by incorporating additional landmark regression head, enabling efficient localization of crucial facial landmarks. Furthermore, we conduct optimizations and enhancements on various modules within the original YOLOv8 framework. To validate the effectiveness and real-time performance of our proposed model, we conduct extensive experiments on 300W-LP and AFLW2000-3D datasets. The results obtained verify the capability of our model to tackle large-angle face pose challenges while delivering real-time performance across these interconnected tasks.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.
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