为了理论上了解训练有素的深神经网络的行为，有必要研究来自随机初始化的梯度方法引起的动态。然而，这些模型的非线性和组成结构使得这些动态难以分析。为了克服这些挑战，最近出现了大宽度的渐近学作为富有成效的观点，并导致了对真实世界的深网络的实用洞察。对于双层神经网络，已经通过这些渐近学理解，训练模型的性质根据初始随机权重的规模而变化，从内核制度（大初始方差）到特征学习制度（对于小初始方差）。对于更深的网络，更多的制度是可能的，并且在本文中，我们详细研究了与神经网络的“卑鄙字段”限制相对应的“小”初始化的特定选择，我们称之为可分配的参数化（IP）。首先，我们展示了标准I.I.D.零平均初始化，具有多于四个层的神经网络的可集参数，从无限宽度限制的静止点开始，并且不会发生学习。然后，我们提出了各种方法来避免这种琐碎的行为并详细分析所得到的动态。特别是，这些方法中的一种包括使用大的初始学习速率，并且我们表明它相当于最近提出的最大更新参数化$ \ mu $ p的修改。我们将结果与图像分类任务的数值实验确认，其另外显示出在尚未捕获的激活功能的各种选择之间的行为中的强烈差异。

我们提供了与随机敏感和非敏感背景公平在线学习的环境和一般方法。该设置是播放器和性质之间的重复游戏，在每个阶段都在每个阶段都根据上下文选择动作。灵感来自不知意的概念，我们假设玩家只能在做出决定之前访问非敏感上下文，而我们讨论两种自然案例访问敏感上下文和性质不知道敏感的背景。适应Blackwell的可平衡性理论来处理未知背景分配的情况，我们为学习目标提供了一般的必要和充分条件，以与一些公平的限制兼容。将这种条件实例化（Group-Wise）无遗憾和（Group-Wise）校准目标，以及作为额外约束的人口统计奇偶校验。当目标与约束不兼容时，所提供的框架允许在两者之间表征最佳权衡。

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has resulted in opening doors to solving a variety of real-world problems ranging from mathematical finance to stochastic control for industrial applications. Although feasible, these deep learning methods are still constrained by training time and memory. Tackling these shortcomings, Tensor Neural Networks (TNN) demonstrate that they can provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. Besides TNN, we also introduce Tensor Network Initializer (TNN Init), a weight initialization scheme that leads to faster convergence with smaller variance for an equivalent parameter count as compared to a DNN. We benchmark TNN and TNN Init by applying them to solve the parabolic PDE associated with the Heston model, which is widely used in financial pricing theory.

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. PINNs integrate the physical constraints by minimizing the partial differential equations (PDEs) residuals on a set of collocation points. The distribution of these collocation points appears to have a huge impact on the performance of PINNs and the assessment of the sampling methods for these points is still an active topic. In this paper, we propose a Fixed-Budget Online Adaptive Mesh Learning (FBOAML) method, which decomposes the domain into sub-domains, for training collocation points based on local maxima and local minima of the PDEs residuals. The stopping criterion is based on a data set of reference, which leads to an adaptive number of iterations for each specific problem. The effectiveness of FBOAML is demonstrated in the context of non-parameterized and parameterized problems. The impact of the hyper-parameters in FBOAML is investigated in this work. The comparison with other adaptive sampling methods is also illustrated. The numerical results demonstrate important gains in terms of accuracy of PINNs with FBOAML over the classical PINNs with non-adaptive collocation points. We also apply FBOAML in a complex industrial application involving coupling between mechanical and thermal fields. We show that FBOAML is able to identify the high-gradient location and even give better prediction for some physical fields than the classical PINNs with collocation points taken on a pre-adapted finite element mesh.

To face the dependency on fossil fuels and limit carbon emissions, fuel cells are a very promising technology and appear to be a key candidate to tackle the increase of the energy demand and promote the energy transition. To meet future needs for both transport and stationary applications, the time to market of fuel cell stacks must be drastically reduced. Here, a new concept to shorten their development time by introducing a disruptive and highefficiency data augmentation approach based on artificial intelligence is presented. Our results allow reducing the testing time before introducing a product on the market from a thousand to a few hours. The innovative concept proposed here can support engineering and research tasks during the fuel cell development process to achieve decreased development costs alongside a reduced time to market.

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug-in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of cnvergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.

We introduce the XPER (eXplainable PERformance) methodology to measure the specific contribution of the input features to the predictive or economic performance of a model. Our methodology offers several advantages. First, it is both model-agnostic and performance metric-agnostic. Second, XPER is theoretically founded as it is based on Shapley values. Third, the interpretation of the benchmark, which is inherent in any Shapley value decomposition, is meaningful in our context. Fourth, XPER is not plagued by model specification error, as it does not require re-estimating the model. Fifth, it can be implemented either at the model level or at the individual level. In an application based on auto loans, we find that performance can be explained by a surprisingly small number of features. XPER decompositions are rather stable across metrics, yet some feature contributions switch sign across metrics. Our analysis also shows that explaining model forecasts and model performance are two distinct tasks.

We propose a novel method for high-quality facial texture reconstruction from RGB images using a novel capturing routine based on a single smartphone which we equip with an inexpensive polarization foil. Specifically, we turn the flashlight into a polarized light source and add a polarization filter on top of the camera. Leveraging this setup, we capture the face of a subject with cross-polarized and parallel-polarized light. For each subject, we record two short sequences in a dark environment under flash illumination with different light polarization using the modified smartphone. Based on these observations, we reconstruct an explicit surface mesh of the face using structure from motion. We then exploit the camera and light co-location within a differentiable renderer to optimize the facial textures using an analysis-by-synthesis approach. Our method optimizes for high-resolution normal textures, diffuse albedo, and specular albedo using a coarse-to-fine optimization scheme. We show that the optimized textures can be used in a standard rendering pipeline to synthesize high-quality photo-realistic 3D digital humans in novel environments.

Turning the weights to zero when training a neural network helps in reducing the computational complexity at inference. To progressively increase the sparsity ratio in the network without causing sharp weight discontinuities during training, our work combines soft-thresholding and straight-through gradient estimation to update the raw, i.e. non-thresholded, version of zeroed weights. Our method, named ST-3 for straight-through/soft-thresholding/sparse-training, obtains SoA results, both in terms of accuracy/sparsity and accuracy/FLOPS trade-offs, when progressively increasing the sparsity ratio in a single training cycle. In particular, despite its simplicity, ST-3 favorably compares to the most recent methods, adopting differentiable formulations or bio-inspired neuroregeneration principles. This suggests that the key ingredients for effective sparsification primarily lie in the ability to give the weights the freedom to evolve smoothly across the zero state while progressively increasing the sparsity ratio. Source code and weights available at https://github.com/vanderschuea/stthree

The 1$^{\text{st}}$ Workshop on Maritime Computer Vision (MaCVi) 2023 focused on maritime computer vision for Unmanned Aerial Vehicles (UAV) and Unmanned Surface Vehicle (USV), and organized several subchallenges in this domain: (i) UAV-based Maritime Object Detection, (ii) UAV-based Maritime Object Tracking, (iii) USV-based Maritime Obstacle Segmentation and (iv) USV-based Maritime Obstacle Detection. The subchallenges were based on the SeaDronesSee and MODS benchmarks. This report summarizes the main findings of the individual subchallenges and introduces a new benchmark, called SeaDronesSee Object Detection v2, which extends the previous benchmark by including more classes and footage. We provide statistical and qualitative analyses, and assess trends in the best-performing methodologies of over 130 submissions. The methods are summarized in the appendix. The datasets, evaluation code and the leaderboard are publicly available at https://seadronessee.cs.uni-tuebingen.de/macvi.