物理知识的神经网络（PINN）将问题领域的物理知识作为对损失函数的软限制，但最近的工作表明这可能导致优化困难。在这里，我们研究了搭配点的位置对这些模型训练性的影响。我们发现，随着训练的进行，可以通过适应搭配点的位置来显着提高香草·皮恩的性能。具体而言，我们提出了一种新型的自适应搭配方案，该方案逐渐将更多的搭配点（不增加数量）分配给模型正在造成更高误差的区域（基于域中损失函数的梯度）。加上在任何优化失速过程中对训练的明智重新启动（通过简单地重新采样搭配点以调整损失景观）会导致预测错误的更好估计。我们提出了一些问题的结果，包括具有不同强迫函数的2D泊松和扩散 - 辅助系统。我们发现，针对这些问题的训练香草PINN可以导致解决方案中的预测误差高达70％，尤其是在低搭配点的状态下。相比之下，我们的自适应方案可以达到较小误差的顺序，其计算复杂性与基线相似。此外，我们发现自适应方法始终如一地执行PAR或比香草Pinn方法稍好，即使对于大型搭配点方案也是如此。所有实验的代码都是开源的。

最近在科学机器学习的工作已经开发出所谓的物理信息的神经网络（Pinn）模型。典型方法是将物理域知识纳入经验丢失功能的软限制，并使用现有的机器学习方法来培训模型。我们展示了，虽然现有的Pinn方法可以学习良好的模型，但它们可以轻松地未能学习相关的物理现象，甚至更复杂的问题。特别是，我们分析了众多不同的普遍物理兴趣的情况，包括使用对流，反应和扩散运营商学习微分方程。我们提供了证据表明Pinns中的软正规化，涉及基于PDE的差分运营商，可以引入许多微妙的问题，包括使问题更加不良。重要的是，我们表明，这些可能的失败模式不是由于NN架构中缺乏富有效力，但Pinn的设置使得损失景观很难优化。然后，我们描述了两个有希望的解决方案来解决这些故障模式。第一种方法是使用课程正则化，其中Pinn的丢失项从简单的PDE正则化开始，并且随着NN训练而变得逐渐变得更加复杂。第二种方法是将问题构成为序列到序列的学习任务，而不是学习一次性地预测整个时空。广泛的测试表明，与常规Pinn训练相比，我们可以通过这些方法实现最多1-2个数量级。

With the advent of Neural Style Transfer (NST), stylizing an image has become quite popular. A convenient way for extending stylization techniques to videos is by applying them on a per-frame basis. However, such per-frame application usually lacks temporal-consistency expressed by undesirable flickering artifacts. Most of the existing approaches for enforcing temporal-consistency suffers from one or more of the following drawbacks. They (1) are only suitable for a limited range of stylization techniques, (2) can only be applied in an offline fashion requiring the complete video as input, (3) cannot provide consistency for the task of stylization, or (4) do not provide interactive consistency-control. Note that existing consistent video-filtering approaches aim to completely remove flickering artifacts and thus do not respect any specific consistency-control aspect. For stylization tasks, however, consistency-control is an essential requirement where a certain amount of flickering can add to the artistic look and feel. Moreover, making this control interactive is paramount from a usability perspective. To achieve the above requirements, we propose an approach that can stylize video streams while providing interactive consistency-control. Apart from stylization, our approach also supports various other image processing filters. For achieving interactive performance, we develop a lite optical-flow network that operates at 80 Frames per second (FPS) on desktop systems with sufficient accuracy. We show that the final consistent video-output using our flow network is comparable to that being obtained using state-of-the-art optical-flow network. Further, we employ an adaptive combination of local and global consistent features and enable interactive selection between the two. By objective and subjective evaluation, we show that our method is superior to state-of-the-art approaches.

Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, for a computer to learn from data accurately and efficiently, some auxiliary information about the data distribution and target function should be provided to it through the learning model. This notion of auxiliary information relates to the concept of regularization in statistical learning theory. A common feature among real-world datasets is that data domains are multiscale and target functions are well-behaved and smooth. In this paper, we propose a learning model that exploits this multiscale data structure and discuss its statistical and computational benefits. The hierarchical learning model is inspired by the logical and progressive easy-to-hard learning mechanism of human beings and has interpretable levels. The model apportions computational resources according to the complexity of data instances and target functions. This property can have multiple benefits, including higher inference speed and computational savings in training a model for many users or when training is interrupted. We provide a statistical analysis of the learning mechanism using multiscale entropies and show that it can yield significantly stronger guarantees than uniform convergence bounds.

Transformer language models (TLMs) are critical for most NLP tasks, but they are difficult to create for low-resource languages because of how much pretraining data they require. In this work, we investigate two techniques for training monolingual TLMs in a low-resource setting: greatly reducing TLM size, and complementing the masked language modeling objective with two linguistically rich supervised tasks (part-of-speech tagging and dependency parsing). Results from 7 diverse languages indicate that our model, MicroBERT, is able to produce marked improvements in downstream task evaluations relative to a typical monolingual TLM pretraining approach. Specifically, we find that monolingual MicroBERT models achieve gains of up to 18% for parser LAS and 11% for NER F1 compared to a multilingual baseline, mBERT, while having less than 1% of its parameter count. We conclude reducing TLM parameter count and using labeled data for pretraining low-resource TLMs can yield large quality benefits and in some cases produce models that outperform multilingual approaches.

Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive manufacturing techniques often requires solving such inverse problems for specific sizes. One should, therefore, find multiple microarchitectural designs that exhibit the desired properties for a specimen with given dimensions. Moreover, the candidate microarchitectures should be resistant to fatigue and fracture, meaning that peak stresses should be minimized as well. Such a multi-objective inverse design problem is formidably difficult to solve but its solution is the key to real-world applications of mechanical metamaterials. Here, we propose a modular approach titled 'Deep-DRAM' that combines four decoupled models, including two deep learning models (DLM), a deep generative model (DGM) based on conditional variational autoencoders (CVAE), and direct finite element (FE) simulations. Deep-DRAM (deep learning for the design of random-network metamaterials) integrates these models into a unified framework capable of finding many solutions to the multi-objective inverse design problem posed here. The integrated framework first introduces the desired elastic properties to the DGM, which returns a set of candidate designs. The candidate designs, together with the target specimen dimensions are then passed to the DLM which predicts their actual elastic properties considering the specimen size. After a filtering step based on the closeness of the actual properties to the desired ones, the last step uses direct FE simulations to identify the designs with the minimum peak stresses.

Dual encoders are now the dominant architecture for dense retrieval. Yet, we have little understanding of how they represent text, and why this leads to good performance. In this work, we shed light on this question via distributions over the vocabulary. We propose to interpret the vector representations produced by dual encoders by projecting them into the model's vocabulary space. We show that the resulting distributions over vocabulary tokens are intuitive and contain rich semantic information. We find that this view can explain some of the failure cases of dense retrievers. For example, the inability of models to handle tail entities can be explained via a tendency of the token distributions to forget some of the tokens of those entities. We leverage this insight and propose a simple way to enrich query and passage representations with lexical information at inference time, and show that this significantly improves performance compared to the original model in out-of-domain settings.

Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and optimisation software tools. Despite the practicality of this technique, the performance of the differentiated programs, especially for functional languages and in the presence of vectors, is suboptimal. We present an AD system for a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source forward-mode AD and global optimisations such as loop transformations. In combination, gradient computation with forward-mode AD can be as efficient as reverse mode, and the Jacobian matrices required for numerical algorithms such as Gauss-Newton and Levenberg-Marquardt can be efficiently computed.

Graph Neural Networks (GNNs) are a family of graph networks inspired by mechanisms existing between nodes on a graph. In recent years there has been an increased interest in GNN and their derivatives, i.e., Graph Attention Networks (GAT), Graph Convolutional Networks (GCN), and Graph Recurrent Networks (GRN). An increase in their usability in computer vision is also observed. The number of GNN applications in this field continues to expand; it includes video analysis and understanding, action and behavior recognition, computational photography, image and video synthesis from zero or few shots, and many more. This contribution aims to collect papers published about GNN-based approaches towards computer vision. They are described and summarized from three perspectives. Firstly, we investigate the architectures of Graph Neural Networks and their derivatives used in this area to provide accurate and explainable recommendations for the ensuing investigations. As for the other aspect, we also present datasets used in these works. Finally, using graph analysis, we also examine relations between GNN-based studies in computer vision and potential sources of inspiration identified outside of this field.

Task transfer learning is a popular technique in image processing applications that uses pre-trained models to reduce the supervision cost of related tasks. An important question is to determine task transferability, i.e. given a common input domain, estimating to what extent representations learned from a source task can help in learning a target task. Typically, transferability is either measured experimentally or inferred through task relatedness, which is often defined without a clear operational meaning. In this paper, we present a novel metric, H-score, an easily-computable evaluation function that estimates the performance of transferred representations from one task to another in classification problems using statistical and information theoretic principles. Experiments on real image data show that our metric is not only consistent with the empirical transferability measurement, but also useful to practitioners in applications such as source model selection and task transfer curriculum learning.