Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces . The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

Large language models (LLMs) have demonstrated remarkable capabilities in understanding and generating natural language data.

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces . The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

We comment on Cai and Wang (2020, arXiv:2006.13318), who analyze over-smoothing in GNNs via Dirichlet energy. We show that under mild spectral conditions (including with Leaky-ReLU), the Dirichlet energy of node embeddings decreases exponentially with depth; we further extend the result to spectral polynomial filters and provide a short proof for the Leaky-ReLU case. Experiments on edge deletion and weight amplification illustrate when Dirichlet energy increases, hinting at practical ways to relieve over-smoothing.

Labor shortage due to the declining birth rate has become a serious problem in the construction industry, and automation of construction work is attracting attention as a solution to this problem. This paper proposes a method to realize state estimation of dump truck position, orientation and articulation angle using multiple GNSS for automatic operation of dump trucks. RTK-GNSS is commonly used for automation of construction equipment, but in mountainous areas, mobile networks often unstable, and RTK-GNSS using GNSS reference stations cannot be used. Therefore, this paper develops a state estimation method for dump trucks that does not require a GNSS reference station by using the Centimeter Level Augmentation Service (CLAS) of the Japanese Quasi-Zenith Satellite System (QZSS). Although CLAS is capable of centimeter-level position estimation, its positioning accuracy and ambiguity fix rate are lower than those of RTK-GNSS. To solve this problem, we construct a state estimation method by factor graph optimization that combines CLAS positioning and moving-base RTK-GNSS between multiple GNSS antennas. Evaluation tests under real-world environments have shown that the proposed method can estimate the state of dump trucks with the same accuracy as conventional RTK-GNSS, but does not require a GNSS reference station.

Synthetic data generation is a promising technique to facilitate the use of sensitive data while mitigating the risk of privacy breaches. However, for synthetic data to be useful in downstream analysis tasks, it needs to be of sufficient quality. Various methods have been proposed to measure the utility of synthetic data, but their results are often incomplete or even misleading. In this paper, we propose using density ratio estimation to improve quality evaluation for synthetic data, and thereby the quality of synthesized datasets. We show how this framework relates to and builds on existing measures, yielding global and local utility measures that are informative and easy to interpret. We develop an estimator which requires little to no manual tuning due to automatic selection of a nonparametric density ratio model. Through simulations, we find that density ratio estimation yields more accurate estimates of global utility than established procedures. A real-world data application demonstrates how the density ratio can guide refinements of synthesis models and can be used to improve downstream analyses. We conclude that density ratio estimation is a valuable tool in synthetic data generation workflows and provide these methods in the accessible open source R-package densityratio.

In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we study the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps. Furthermore, we establish information-theoretic lower bounds for meta-learners w.r.t. both the number of tasks and in-context examples. These findings shed light on the roles of task diversity and representation learning for ICL.

Tomiji Suzuki, 89, started coding in retirement and is now making apps for Japan's fast-growing elderly demographic, using ChatGPT to fine-tune his skills. So far, Suzuki has developed 11 free iPhone apps to help Japan's aging population, including his latest: a slideshow of items to remember when leaving the house, from a wallet and hearing aids to patient registration cards. He was inspired to create the app, which features his granddaughter's voice, after he realized he had forgotten his dentures as he was about to board a bullet train.

Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework, seeking to integrate deep learning with Bayesian methodologies seamlessly. However, there exists a gap in the theoretical understanding of Bayesian approaches in deep learning for classification. This study presents an attempt to bridge that gap. By leveraging PAC-Bayes bounds techniques, we present theoretical results on the prediction or misclassification error of a probabilistic approach utilizing Spike-and-Slab priors for sparse deep learning in classification. We establish non-asymptotic results for the prediction error. Additionally, we demonstrate that, by considering different architectures, our results can achieve minimax optimal rates in both low and high-dimensional settings, up to a logarithmic factor. Moreover, our additional logarithmic term yields slight improvements over previous works. Additionally, we propose and analyze an automated model selection approach aimed at optimally choosing a network architecture with guaranteed optimality.