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We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a "price of adaptivity" (PoA) that, roughly speaking, measures the multiplicative increase in suboptimality due to uncertainty in these parameters. When the initial distance to the optimum is unknown but a gradient norm bound is known, we show that the PoA is at least logarithmic for expected suboptimality, and double-logarithmic for median suboptimality. When there is uncertainty in both distance and gradient norm, we show that the PoA must be polynomial in the level of uncertainty. Our lower bounds nearly match existing upper bounds, and establish that there is no parameter-free lunch.

The value of text classification's future research has encountered challenges and uncertainties, due to the extraordinary efficacy demonstrated by large language models (LLMs) across numerous downstream NLP tasks. In this era of open-ended language modeling, where task boundaries are gradually fading, an urgent question emerges: have we made significant advances in text classification under the full benefit of LLMs? To answer this question, we propose RGPT, an adaptive boosting framework tailored to produce a specialized text classification LLM by recurrently ensembling a pool of strong base learners. The base learners are constructed by adaptively adjusting the distribution of training samples and iteratively fine-tuning LLMs with them. Such base learners are then ensembled to be a specialized text classification LLM, by recurrently incorporating the historical predictions from the previous learners. Through a comprehensive empirical comparison, we show that RGPT significantly outperforms 8 SOTA PLMs and 7 SOTA LLMs on four benchmarks by 1.36% on average. Further evaluation experiments show a clear surpassing of RGPT over human classification.

The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications.

Spatial statistical modeling and prediction involve generating and manipulating an n*n symmetric positive definite covariance matrix, where n denotes the number of spatial locations. However, when n is large, processing this covariance matrix using traditional methods becomes prohibitive. Thus, coupling parallel processing with approximation can be an elegant solution to this challenge by relying on parallel solvers that deal with the matrix as a set of small tiles instead of the full structure. Each processing unit can process a single tile, allowing better performance. The approximation can also be performed at the tile level for better compression and faster execution. The Tile Low-Rank (TLR) approximation, a tile-based approximation algorithm, has recently been used in spatial statistics applications. However, the quality of TLR algorithms mainly relies on ordering the matrix elements. This order can impact the compression quality and, therefore, the efficiency of the underlying linear solvers, which highly depends on the individual ranks of each tile. Thus, herein, we aim to investigate the accuracy and performance of some existing ordering algorithms that are used to order the geospatial locations before generating the spatial covariance matrix. Furthermore, we highlight the pros and cons of each ordering algorithm in the context of spatial statistics applications and give hints to practitioners on how to choose the ordering algorithm carefully. We assess the quality of the compression and the accuracy of the statistical parameter estimates of the Mat\'ern covariance function using TLR approximation under various ordering algorithms and settings of correlations.

6G promises a paradigm shift in which positioning and sensing are inherently integrated, enhancing not only the communication performance but also enabling location- and context-aware services. Historically, positioning and sensing have been viewed through the lens of cost and performance trade-offs, implying an escalated demand for resources, such as radio, physical, and computational resources, for improved performance. However, 6G goes beyond this traditional perspective to encompass a set of broader values, namely sustainability, inclusiveness, and trustworthiness. From a joint industrial/academic perspective, this paper aims to shed light on these important value indicators and their relationship with the conventional key performance indicators in the context of positioning and sensing.

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads, and these insights also provide natural suggestions for alternative architectures.

In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. From a computational standpoint, the LMC is a substantially easier model to work with than other multidimensional alternatives. Up to now, this fact has been largely overlooked in the literature. Starting from an analogy with matrix normal models, we propose a reformulation of the LMC likelihood that highlights the linear, rather than cubic, computational complexity as a function of the dimension of the response vector. Further, we describe in detail how those simplifications can be included in a Gaussian hierarchical model. In addition, we demonstrate in two examples how the disentangled version of the likelihood we derive can be exploited to improve Markov chain Monte Carlo (MCMC) based computations when conducting Bayesian inference. The first is an interwoven approach that combines samples from centered and whitened parametrizations of the latent LMC distributed random fields. The second is a sparsity-inducing method that introduces structural zeros in the coregionalization matrix in an attempt to reduce the number of parameters in a principled way. It also provides a new way to investigate the strength of the correlation among the components of the outcome vector. Both approaches come at virtually no additional cost and are shown to significantly improve MCMC performance and predictive performance respectively. We apply our methodology to a dataset comprised of air pollutant measurements in the state of California.

Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most promising solution is distributed training which distributes the workload of training across multiple computing nodes. However, the workflows, computational patterns, communication patterns, and optimization techniques of distributed GNN training remain preliminarily understood. In this paper, we provide a comprehensive survey of distributed GNN training by investigating various optimization techniques used in distributed GNN training. First, distributed GNN training is classified into several categories according to their workflows. In addition, their computational patterns and communication patterns, as well as the optimization techniques proposed by recent work are introduced. Second, the software frameworks and hardware platforms of distributed GNN training are also introduced for a deeper understanding. Third, distributed GNN training is compared with distributed training of deep neural networks, emphasizing the uniqueness of distributed GNN training. Finally, interesting issues and opportunities in this field are discussed.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.