我们研究归一化对馈送前馈类型深神经网络层的影响。给定的图层$ i $，带有$ n_ {i} $隐藏单位，可以通过$ 1/n_ {i}^{\ gamma_ {i}} $带有$ \ gamma_ {i} 1] $，我们研究了$ \ gamma_ {i} $选择对神经网络输出（例如方差）的统计行为的影响，以及MNIST数据集的测试准确性。我们发现，就神经网络的输出和测试准确性的差异而言，最佳选择是选择$ \ gamma_ {i} $等于一个，即平均场比例。我们还发现，对于外层，尤其如此，因为神经网络的行为在外层的缩放层中更敏感，而不是内层的缩放。数学分析的机制是神经网络输出的渐近扩展。该分析的一个重要实际结果是，它提供了一种系统性和数学知情的方式来选择学习率超级标准。这样的选择可以保证，随着$ n_i $的增长，神经网络的行为在统计上具有稳健的方式。

我们介绍了一种新颖的几何形状不可逆的扰动，该扰动加速了langevin算法的贝叶斯计算的收敛性。有充分的文献证明，兰格文动力学存在扰动，该动力学在加速其收敛的同时保留其不变度的度量。不可逆的扰动和可逆扰动（例如Riemannian歧管Langevin Dynamics（RMLD））已被单独显示以改善Langevin Samplers的性能。我们同时考虑了这两种扰动，通过呈现一种新型的RMLD不可逆扰动形式，该形式由基础几何形状告知。通过数值示例，我们表明，这种新的不可逆扰动可以改善估计性性能，而不是不可逆的扰动，而这些扰动不会考虑到几何。此外，我们证明，不可逆转的扰动通常可以与Langevin算法的随机梯度版本结合使用。最后，尽管连续的不可逆扰动不能损害兰格文估计器的性能，但考虑离散化时，情况有时会更加复杂。为此，我们描述了一个离散的示例，其中不可逆性增加了所得估计量的偏差和差异。

High-dimensional PDEs have been a longstanding computational challenge. We propose to solve highdimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since meshes become infeasible in higher dimensions. Instead of forming a mesh, the neural network is trained on batches of randomly sampled time and space points. The algorithm is tested on a class of high-dimensional free boundary PDEs, which we are able to accurately solve in up to 200 dimensions. The algorithm is also tested on a high-dimensional Hamilton-Jacobi-Bellman PDE and Burgers' equation. The deep learning algorithm approximates the general solution to the Burgers' equation for a continuum of different boundary conditions and physical conditions (which can be viewed as a high-dimensional space). We call the algorithm a "Deep Galerkin Method (DGM)" since it is similar in spirit to Galerkin methods, with the solution approximated by a neural network instead of a linear combination of basis functions. In addition, we prove a theorem regarding the approximation power of neural networks for a class of quasilinear parabolic PDEs.

Differentiable Architecture Search (DARTS) has attracted considerable attention as a gradient-based Neural Architecture Search (NAS) method. Since the introduction of DARTS, there has been little work done on adapting the action space based on state-of-art architecture design principles for CNNs. In this work, we aim to address this gap by incrementally augmenting the DARTS search space with micro-design changes inspired by ConvNeXt and studying the trade-off between accuracy, evaluation layer count, and computational cost. To this end, we introduce the Pseudo-Inverted Bottleneck conv block intending to reduce the computational footprint of the inverted bottleneck block proposed in ConvNeXt. Our proposed architecture is much less sensitive to evaluation layer count and outperforms a DARTS network with similar size significantly, at layer counts as small as 2. Furthermore, with less layers, not only does it achieve higher accuracy with lower GMACs and parameter count, GradCAM comparisons show that our network is able to better detect distinctive features of target objects compared to DARTS.

This paper deals with the problem of statistical and system heterogeneity in a cross-silo Federated Learning (FL) framework where there exist a limited number of Consumer Internet of Things (CIoT) devices in a smart building. We propose a novel Graph Signal Processing (GSP)-inspired aggregation rule based on graph filtering dubbed ``G-Fedfilt''. The proposed aggregator enables a structured flow of information based on the graph's topology. This behavior allows capturing the interconnection of CIoT devices and training domain-specific models. The embedded graph filter is equipped with a tunable parameter which enables a continuous trade-off between domain-agnostic and domain-specific FL. In the case of domain-agnostic, it forces G-Fedfilt to act similar to the conventional Federated Averaging (FedAvg) aggregation rule. The proposed G-Fedfilt also enables an intrinsic smooth clustering based on the graph connectivity without explicitly specified which further boosts the personalization of the models in the framework. In addition, the proposed scheme enjoys a communication-efficient time-scheduling to alleviate the system heterogeneity. This is accomplished by adaptively adjusting the amount of training data samples and sparsity of the models' gradients to reduce communication desynchronization and latency. Simulation results show that the proposed G-Fedfilt achieves up to $3.99\% $ better classification accuracy than the conventional FedAvg when concerning model personalization on the statistically heterogeneous local datasets, while it is capable of yielding up to $2.41\%$ higher accuracy than FedAvg in the case of testing the generalization of the models.

Mapping the seafloor with underwater imaging cameras is of significant importance for various applications including marine engineering, geology, geomorphology, archaeology and biology. For shallow waters, among the underwater imaging challenges, caustics i.e., the complex physical phenomena resulting from the projection of light rays being refracted by the wavy surface, is likely the most crucial one. Caustics is the main factor during underwater imaging campaigns that massively degrade image quality and affect severely any 2D mosaicking or 3D reconstruction of the seabed. In this work, we propose a novel method for correcting the radiometric effects of caustics on shallow underwater imagery. Contrary to the state-of-the-art, the developed method can handle seabed and riverbed of any anaglyph, correcting the images using real pixel information, thus, improving image matching and 3D reconstruction processes. In particular, the developed method employs deep learning architectures in order to classify image pixels to "non-caustics" and "caustics". Then, exploits the 3D geometry of the scene to achieve a pixel-wise correction, by transferring appropriate color values between the overlapping underwater images. Moreover, to fill the current gap, we have collected, annotated and structured a real-world caustic dataset, namely R-CAUSTIC, which is openly available. Overall, based on the experimental results and validation the developed methodology is quite promising in both detecting caustics and reconstructing their intensity.

360-degree panoramic videos have gained considerable attention in recent years due to the rapid development of head-mounted displays (HMDs) and panoramic cameras. One major problem in streaming panoramic videos is that panoramic videos are much larger in size compared to traditional ones. Moreover, the user devices are often in a wireless environment, with limited battery, computation power, and bandwidth. To reduce resource consumption, researchers have proposed ways to predict the users' viewports so that only part of the entire video needs to be transmitted from the server. However, the robustness of such prediction approaches has been overlooked in the literature: it is usually assumed that only a few models, pre-trained on past users' experiences, are applied for prediction to all users. We observe that those pre-trained models can perform poorly for some users because they might have drastically different behaviors from the majority, and the pre-trained models cannot capture the features in unseen videos. In this work, we propose a novel meta learning based viewport prediction paradigm to alleviate the worst prediction performance and ensure the robustness of viewport prediction. This paradigm uses two machine learning models, where the first model predicts the viewing direction, and the second model predicts the minimum video prefetch size that can include the actual viewport. We first train two meta models so that they are sensitive to new training data, and then quickly adapt them to users while they are watching the videos. Evaluation results reveal that the meta models can adapt quickly to each user, and can significantly increase the prediction accuracy, especially for the worst-performing predictions.

Background samples provide key contextual information for segmenting regions of interest (ROIs). However, they always cover a diverse set of structures, causing difficulties for the segmentation model to learn good decision boundaries with high sensitivity and precision. The issue concerns the highly heterogeneous nature of the background class, resulting in multi-modal distributions. Empirically, we find that neural networks trained with heterogeneous background struggle to map the corresponding contextual samples to compact clusters in feature space. As a result, the distribution over background logit activations may shift across the decision boundary, leading to systematic over-segmentation across different datasets and tasks. In this study, we propose context label learning (CoLab) to improve the context representations by decomposing the background class into several subclasses. Specifically, we train an auxiliary network as a task generator, along with the primary segmentation model, to automatically generate context labels that positively affect the ROI segmentation accuracy. Extensive experiments are conducted on several challenging segmentation tasks and datasets. The results demonstrate that CoLab can guide the segmentation model to map the logits of background samples away from the decision boundary, resulting in significantly improved segmentation accuracy. Code is available.

Reinforcement learning (RL) gained considerable attention by creating decision-making agents that maximize rewards received from fully observable environments. However, many real-world problems are partially or noisily observable by nature, where agents do not receive the true and complete state of the environment. Such problems are formulated as partially observable Markov decision processes (POMDPs). Some studies applied RL to POMDPs by recalling previous decisions and observations or inferring the true state of the environment from received observations. Nevertheless, aggregating observations and decisions over time is impractical for environments with high-dimensional continuous state and action spaces. Moreover, so-called inference-based RL approaches require large number of samples to perform well since agents eschew uncertainty in the inferred state for the decision-making. Active inference is a framework that is naturally formulated in POMDPs and directs agents to select decisions by minimising expected free energy (EFE). This supplies reward-maximising (exploitative) behaviour in RL, with an information-seeking (exploratory) behaviour. Despite this exploratory behaviour of active inference, its usage is limited to discrete state and action spaces due to the computational difficulty of the EFE. We propose a unified principle for joint information-seeking and reward maximization that clarifies a theoretical connection between active inference and RL, unifies active inference and RL, and overcomes their aforementioned limitations. Our findings are supported by strong theoretical analysis. The proposed framework's superior exploration property is also validated by experimental results on partial observable tasks with high-dimensional continuous state and action spaces. Moreover, the results show that our model solves reward-free problems, making task reward design optional.

Structural Health Monitoring (SHM) describes a process for inferring quantifiable metrics of structural condition, which can serve as input to support decisions on the operation and maintenance of infrastructure assets. Given the long lifespan of critical structures, this problem can be cast as a sequential decision making problem over prescribed horizons. Partially Observable Markov Decision Processes (POMDPs) offer a formal framework to solve the underlying optimal planning task. However, two issues can undermine the POMDP solutions. Firstly, the need for a model that can adequately describe the evolution of the structural condition under deterioration or corrective actions and, secondly, the non-trivial task of recovery of the observation process parameters from available monitoring data. Despite these potential challenges, the adopted POMDP models do not typically account for uncertainty on model parameters, leading to solutions which can be unrealistically confident. In this work, we address both key issues. We present a framework to estimate POMDP transition and observation model parameters directly from available data, via Markov Chain Monte Carlo (MCMC) sampling of a Hidden Markov Model (HMM) conditioned on actions. The MCMC inference estimates distributions of the involved model parameters. We then form and solve the POMDP problem by exploiting the inferred distributions, to derive solutions that are robust to model uncertainty. We successfully apply our approach on maintenance planning for railway track assets on the basis of a "fractal value" indicator, which is computed from actual railway monitoring data.