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In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-arm Bandit (RMAB) problem with a continuous state space. We prove that the arms are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation. This result has two degenerated cases of interest: (i) In the single-source case, the Whittle index policy reproduces earlier threshold-based sampling policies for the remote estimation of Wiener and Ornstein-Uhlenbeck processes. When the instantaneous estimation error of the Gauss-Markov process crosses the optimal threshold, the Whittle index is precisely equal to 0. In addition, a new optimal sampling policy for the remote estimation of the unstable Ornstein-Uhlenbeck process is obtained. (ii) In the signal-agnostic case, we find an exact expression of the Whittle index for Age of Information (AoI)-based remote estimation, which complements earlier results by allowing for random transmission times. Our numerical results show that the proposed policy performs better than the signal-agnostic AoI-based Whittle index policy and the Maximum-Age-First, Zero-Wait (MAF-ZW) policy. The performance gain of the proposed policy is high when some of the Gauss-Markov processes are highly unstable or when the sample transmission times follow a heavy-tail distribution.

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In this paper, we present a comprehensive survey on online test-time adaptation (OTTA), a paradigm focused on adapting machine learning models to novel data distributions upon batch arrival. Despite the proliferation of OTTA methods recently, the field is mired in issues like ambiguous settings, antiquated backbones, and inconsistent hyperparameter tuning, obfuscating the real challenges and making reproducibility elusive. For clarity and a rigorous comparison, we classify OTTA techniques into three primary categories and subject them to benchmarks using the potent Vision Transformer (ViT) backbone to discover genuinely effective strategies. Our benchmarks span not only conventional corrupted datasets such as CIFAR-10/100-C and ImageNet-C but also real-world shifts embodied in CIFAR-10.1 and CIFAR-10-Warehouse, encapsulating variations across search engines and synthesized data by diffusion models. To gauge efficiency in online scenarios, we introduce novel evaluation metrics, inclusive of FLOPs, shedding light on the trade-offs between adaptation accuracy and computational overhead. Our findings diverge from existing literature, indicating: (1) transformers exhibit heightened resilience to diverse domain shifts, (2) the efficacy of many OTTA methods hinges on ample batch sizes, and (3) stability in optimization and resistance to perturbations are critical during adaptation, especially when the batch size is 1. Motivated by these insights, we pointed out promising directions for future research. The source code will be made available.

In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error estimate. Following the same principles, we also develop a novel numerical scheme for the heat equation that yields a better error estimate compared to the classical implicit finite differences scheme.

In this study, we propose a novel adversarial reprogramming (AR) approach for low-resource spoken command recognition (SCR), and build an AR-SCR system. The AR procedure aims to modify the acoustic signals (from the target domain) to repurpose a pretrained SCR model (from the source domain). To solve the label mismatches between source and target domains, and further improve the stability of AR, we propose a novel similarity-based label mapping technique to align classes. In addition, the transfer learning (TL) technique is combined with the original AR process to improve the model adaptation capability. We evaluate the proposed AR-SCR system on three low-resource SCR datasets, including Arabic, Lithuanian, and dysarthric Mandarin speech. Experimental results show that with a pretrained AM trained on a large-scale English dataset, the proposed AR-SCR system outperforms the current state-of-the-art results on Arabic and Lithuanian speech commands datasets, with only a limited amount of training data.

In this work, we aim to characterize the statistical complexity of realizable regression both in the PAC learning setting and the online learning setting. Previous work had established the sufficiency of finiteness of the fat shattering dimension for PAC learnability and the necessity of finiteness of the scaled Natarajan dimension, but little progress had been made towards a more complete characterization since the work of Simon (SICOMP '97). To this end, we first introduce a minimax instance optimal learner for realizable regression and propose a novel dimension that both qualitatively and quantitatively characterizes which classes of real-valued predictors are learnable. We then identify a combinatorial dimension related to the Graph dimension that characterizes ERM learnability in the realizable setting. Finally, we establish a necessary condition for learnability based on a combinatorial dimension related to the DS dimension, and conjecture that it may also be sufficient in this context. Additionally, in the context of online learning we provide a dimension that characterizes the minimax instance optimal cumulative loss up to a constant factor and design an optimal online learner for realizable regression, thus resolving an open question raised by Daskalakis and Golowich in STOC '22.

In this work, our goal is to develop a theoretical framework that can eventually be used for analyzing the effectiveness of visual stories such as feature films to comic books. To develop this theoretical framework, we introduce a new story element called moments. Our conjecture is that any linear story such as the story of a feature film can be decomposed into a set of moments that follow each other. Moments are defined as the perception of the actions, interactions, and expressions of all characters or a single character during a given time period. We categorize the moments into two major types: story moments and discourse moments. Each type of moment can further be classified into three types, which we call universal storytelling moments. We believe these universal moments foster or deteriorate the emotional attachment of the audience to a particular character or the story. We present a methodology to catalog the occurrences of these universal moments as they are found in the story. The cataloged moments can be represented using curves or color strips. Therefore, we can visualize a character's journey through the story as either a 3D curve or a color strip. We also demonstrated that both story and discourse moments can be transformed into one lump-sum attraction parameter. The attraction parameter in time provides a function that can be plotted graphically onto a timeline illustrating changes in the emotional attachment of audience to a character or the story. By inspecting these functions the story analyst can analytically decipher the moments in the story where the attachment is being established, maintained, strengthened, or conversely where it is languishing.

In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.

In this paper, we propose a deep reinforcement learning framework called GCOMB to learn algorithms that can solve combinatorial problems over large graphs. GCOMB mimics the greedy algorithm in the original problem and incrementally constructs a solution. The proposed framework utilizes Graph Convolutional Network (GCN) to generate node embeddings that predicts the potential nodes in the solution set from the entire node set. These embeddings enable an efficient training process to learn the greedy policy via Q-learning. Through extensive evaluation on several real and synthetic datasets containing up to a million nodes, we establish that GCOMB is up to 41% better than the state of the art, up to seven times faster than the greedy algorithm, robust and scalable to large dynamic networks.

In this paper, we propose a novel multi-task learning architecture, which incorporates recent advances in attention mechanisms. Our approach, the Multi-Task Attention Network (MTAN), consists of a single shared network containing a global feature pool, together with task-specific soft-attention modules, which are trainable in an end-to-end manner. These attention modules allow for learning of task-specific features from the global pool, whilst simultaneously allowing for features to be shared across different tasks. The architecture can be built upon any feed-forward neural network, is simple to implement, and is parameter efficient. Experiments on the CityScapes dataset show that our method outperforms several baselines in both single-task and multi-task learning, and is also more robust to the various weighting schemes in the multi-task loss function. We further explore the effectiveness of our method through experiments over a range of task complexities, and show how our method scales well with task complexity compared to baselines.

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