In particular the generative adversarial networks (GANs) [3] provide an impressively powerful waytorepresent classes ofsignals.

Classification is a fundamental task in science and engineering on which machine learning methods have shown outstanding performances. However, it is challenging to determine whether such methods have achieved the Bayes error rate, that is, the lowest error rate attained by any classifier. This is mainly due to the fact that the Bayes error rate is not known in general and hence, effectively estimating it is paramount. Inspired by the work by Ishida et al. (2023), we propose an estimator for the Bayes error rate of supervised multi-class classification problems. We analyze several theoretical aspects of such estimator, including its consistency, unbiasedness, convergence rate, variance, and robustness. We also propose a denoising method that reduces the noise that potentially corrupts the data labels, and we improve the robustness of the proposed estimator to outliers by incorporating the median-of-means estimator. Our analysis demonstrates the consistency, asymptotic unbiasedness, convergence rate, and robustness of the proposed estimators.

The Adam optimizer is a cornerstone of modern deep learning, yet the empirical necessity of each of its individual components is often taken for granted. This paper presents a focused investigation into the role of bias-correction, a feature whose contribution remains poorly understood. Through a series of systematic ablations on vision and language modelling tasks, we demonstrate that the conventional wisdom surrounding bias correction is misleading. In particular, we demonstrate that in the optimal hyper-parameter configuration, the inclusion of bias correction leads to no improvement in final test performance. Moreover, unless appropriate learning rate scheduling is implemented, the inclusion of bias correction can sometimes be detrimental to performance. We further reinterpret bias correction as a form of implicit learning rate scheduling whose behaviour is strongly dependent on the choice of smoothing hyper-parameters $β_1, β_2 \in [0,1)$. Our findings challenge the universal inclusion of this component.

General-purpose foundation models for neural time series can help accelerate neuroscientific discoveries and enable applications such as brain computer interfaces (BCIs). A key component in scaling these models is population-level representation learning, which leverages information across channels to capture spatial as well as temporal structure. Population-level approaches have recently shown that such representations can be both efficient to learn on top of pretrained temporal encoders and produce useful representations for decoding a variety of downstream tasks. However, these models remain sensitive to mismatches in preprocessing, particularly on time-scales, between pretraining and downstream settings. We systematically examine how time-scale mismatches affects generalization and find that existing representations lack invariance. To address this, we introduce Time-scale Augmented Pretraining (TSAP), which consistently improves robustness to different time-scales across decoding tasks and builds invariance in the representation space. These results highlight handling preprocessing diversity as a key step toward building generalizable neural foundation models.

We would like to thank the reviewers for their positive and constructive comments. Below we respond to each of your comments. Response: Thanks, we will expand our discussion of related work, in particular including references [2]-[4] below. Comment: It would be interesting to know if the approach of [1] works here and gives similar results. The notion of regret in the "Prediction with specialist experts' advice" section of [1] (this is the relevant Why do we need to specify the "first" alive expert, rather than the alive expert with the optimal performance?

Feedback control of fluid-based systems poses significant challenges due to their high-dimensional, nonlinear, and multiscale dynamics, which demand real-time, three-dimensional, multi-component measurements for sensing. While such measurements are feasible in digital simulations, they are often only partially accessible in the real world. In this paper, we propose a method to adapt feedback control policies obtained from full-state measurements to setups with only partial measurements. Our approach is demonstrated in a simulated environment by minimising the aerodynamic drag of a simplified road vehicle. Reinforcement learning algorithms can optimally solve this control task when trained on full-state measurements by placing sensors in the wake. However, in real-world applications, sensors are limited and typically only on the vehicle, providing only partial measurements. To address this, we propose to train a Domain Specific Feature Transfer (DSFT) map reconstructing the full measurements from the history of the partial measurements. By applying this map, we derive optimal policies based solely on partial data. Additionally, our method enables determination of the optimal history length and offers insights into the architecture of optimal control policies, facilitating their implementation in real-world environments with limited sensor information.

This paper proposes a novel approach based on deep reinforcement learning (DRL) for the 2D+1 packing problem with spatial constraints. This problem is an extension of the traditional 2D packing problem, incorporating an additional constraint on the height dimension. Therefore, a simulator using the OpenAI Gym framework has been developed to efficiently simulate the packing of rectangular pieces onto two boards with height constraints. Furthermore, the simulator supports multidiscrete actions, enabling the selection of a position on either board and the type of piece to place. Finally, two DRL-based methods (Proximal Policy Optimization -- PPO and the Advantage Actor-Critic -- A2C) have been employed to learn a packing strategy and demonstrate its performance compared to a well-known heuristic baseline (MaxRect-BL). In the experiments carried out, the PPO-based approach proved to be a good solution for solving complex packaging problems and highlighted its potential to optimize resource utilization in various industrial applications, such as the manufacturing of aerospace composites.

Classification is a fundamental task in science and engineering on which machine learning methods have shown outstanding performances. However, it is challenging to determine whether such methods have achieved the Bayes error rate, that is, the lowest error rate attained by any classifier. This is mainly due to the fact that the Bayes error rate is not known in general and hence, effectively estimating it is paramount. Inspired by the work by Ishida et al. (2023), we propose an estimator for the Bayes error rate of supervised multi-class classification problems. We analyze several theoretical aspects of such estimator, including its consistency, unbiasedness, convergence rate, variance, and robustness.

This survey paper provides a comprehensive analysis of big data algorithms in recommendation systems, addressing the lack of depth and precision in existing literature. It proposes a two-pronged approach: a thorough analysis of current algorithms and a novel, hierarchical taxonomy for precise categorization. The taxonomy is based on a tri-level hierarchy, starting with the methodology category and narrowing down to specific techniques. Such a framework allows for a structured and comprehensive classification of algorithms, assisting researchers in understanding the interrelationships among diverse algorithms and techniques. Covering a wide range of algorithms, this taxonomy first categorizes algorithms into four main analysis types: User and Item Similarity-Based Methods, Hybrid and Combined Approaches, Deep Learning and Algorithmic Methods, and Mathematical Modeling Methods, with further subdivisions into sub-categories and techniques. The paper incorporates both empirical and experimental evaluations to differentiate between the techniques. The empirical evaluation ranks the techniques based on four criteria. The experimental assessments rank the algorithms that belong to the same category, sub-category, technique, and sub-technique. Also, the paper illuminates the future prospects of big data techniques in recommendation systems, underscoring potential advancements and opportunities for further research in this field

This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic environment. The proposed algorithm is reference-free and utilizes historical data from previous iterations to enhance the performance of the autonomous system. Unlike existing algorithms, the i2LQR computes the optimal solution in an iterative manner at each timestamp, rendering it well-suited for iterative tasks with changing constraints at different iterations. To evaluate the performance of the proposed algorithm, we conduct numerical simulations for an iterative task aimed at minimizing completion time. The results show that i2LQR achieves an optimized performance with respect to learning-based MPC (LMPC) as the benchmark in static environments, and outperforms LMPC in dynamic environments with both static and dynamics obstacles.