We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of symmetries which, when satisfied by the target function $f^*$ and the input distribution, are preserved by the dynamics. We then study more specific cases. When $f^*$ is odd, we show that the dynamics of the predictor reduces to that of a (non-linearly parameterized) linear predictor, and its exponential convergence can be guaranteed. When $f^*$ has a low-dimensional structure, we prove that the gradient flow PDE reduces to a lower-dimensional PDE. Furthermore, we present informal and numerical arguments that suggest that the input neurons align with the lower-dimensional structure of the problem.

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。

Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high sensitivity to change in input parameters. The heavy-tail characteristics of financial time series are in fact the cause for these erratic fluctuations of weights that consequently create substantial transaction costs. In robustifying the weights we present a toolbox for stabilizing costs and weights for global minimum Markowitz portfolios. Utilizing a projected gradient descent (PGD) technique, we avoid the estimation and inversion of the covariance operator as a whole and concentrate on robust estimation of the gradient descent increment. Using modern tools of robust statistics we construct a computationally efficient estimator with almost Gaussian properties based on median-of-means uniformly over weights. This robustified Markowitz approach is confirmed by empirical studies on equity markets. We demonstrate that robustified portfolios reach the lowest turnover compared to shrinkage-based and constrained portfolios while preserving or slightly improving out-of-sample performance.

Recommendation Systems (RSs) are ubiquitous in modern society and are one of the largest points of interaction between humans and AI. Modern RSs are often implemented using deep learning models, which are infamously difficult to interpret. This problem is particularly exasperated in the context of recommendation scenarios, as it erodes the user's trust in the RS. In contrast, the newly introduced Tsetlin Machines (TM) possess some valuable properties due to their inherent interpretability. TMs are still fairly young as a technology. As no RS has been developed for TMs before, it has become necessary to perform some preliminary research regarding the practicality of such a system. In this paper, we develop the first RS based on TMs to evaluate its practicality in this application domain. This paper compares the viability of TMs with other machine learning models prevalent in the field of RS. We train and investigate the performance of the TM compared with a vanilla feed-forward deep learning model. These comparisons are based on model performance, interpretability/explainability, and scalability. Further, we provide some benchmark performance comparisons to similar machine learning solutions relevant to RSs.

We propose an approach for semantic imitation, which uses demonstrations from a source domain, e.g. human videos, to accelerate reinforcement learning (RL) in a different target domain, e.g. a robotic manipulator in a simulated kitchen. Instead of imitating low-level actions like joint velocities, our approach imitates the sequence of demonstrated semantic skills like "opening the microwave" or "turning on the stove". This allows us to transfer demonstrations across environments (e.g. real-world to simulated kitchen) and agent embodiments (e.g. bimanual human demonstration to robotic arm). We evaluate on three challenging cross-domain learning problems and match the performance of demonstration-accelerated RL approaches that require in-domain demonstrations. In a simulated kitchen environment, our approach learns long-horizon robot manipulation tasks, using less than 3 minutes of human video demonstrations from a real-world kitchen. This enables scaling robot learning via the reuse of demonstrations, e.g. collected as human videos, for learning in any number of target domains.

By transferring knowledge from large, diverse, task-agnostic datasets, modern machine learning models can solve specific downstream tasks either zero-shot or with small task-specific datasets to a high level of performance. While this capability has been demonstrated in other fields such as computer vision, natural language processing or speech recognition, it remains to be shown in robotics, where the generalization capabilities of the models are particularly critical due to the difficulty of collecting real-world robotic data. We argue that one of the keys to the success of such general robotic models lies with open-ended task-agnostic training, combined with high-capacity architectures that can absorb all of the diverse, robotic data. In this paper, we present a model class, dubbed Robotics Transformer, that exhibits promising scalable model properties. We verify our conclusions in a study of different model classes and their ability to generalize as a function of the data size, model size, and data diversity based on a large-scale data collection on real robots performing real-world tasks. The project's website and videos can be found at robotics-transformer.github.io

Foveated imaging provides a better tradeoff between situational awareness (field of view) and resolution and is critical in long-wavelength infrared regimes because of the size, weight, power, and cost of thermal sensors. We demonstrate computational foveated imaging by exploiting the ability of a meta-optical frontend to discriminate between different polarization states and a computational backend to reconstruct the captured image/video. The frontend is a three-element optic: the first element which we call the "foveal" element is a metalens that focuses s-polarized light at a distance of $f_1$ without affecting the p-polarized light; the second element which we call the "perifoveal" element is another metalens that focuses p-polarized light at a distance of $f_2$ without affecting the s-polarized light. The third element is a freely rotating polarizer that dynamically changes the mixing ratios between the two polarization states. Both the foveal element (focal length = 150mm; diameter = 75mm), and the perifoveal element (focal length = 25mm; diameter = 25mm) were fabricated as polarization-sensitive, all-silicon, meta surfaces resulting in a large-aperture, 1:6 foveal expansion, thermal imaging capability. A computational backend then utilizes a deep image prior to separate the resultant multiplexed image or video into a foveated image consisting of a high-resolution center and a lower-resolution large field of view context. We build a first-of-its-kind prototype system and demonstrate 12 frames per second real-time, thermal, foveated image, and video capture in the wild.

Large-scale data is an essential component of machine learning as demonstrated in recent advances in natural language processing and computer vision research. However, collecting large-scale robotic data is much more expensive and slower as each operator can control only a single robot at a time. To make this costly data collection process efficient and scalable, we propose Policy Assisted TeleOperation (PATO), a system which automates part of the demonstration collection process using a learned assistive policy. PATO autonomously executes repetitive behaviors in data collection and asks for human input only when it is uncertain about which subtask or behavior to execute. We conduct teleoperation user studies both with a real robot and a simulated robot fleet and demonstrate that our assisted teleoperation system reduces human operators' mental load while improving data collection efficiency. Further, it enables a single operator to control multiple robots in parallel, which is a first step towards scalable robotic data collection. For code and video results, see https://clvrai.com/pato

Clustering analysis of sequence data continues to address many applications in engineering design, aided with the rapid growth of machine learning in applied science. This paper presents an unsupervised machine learning algorithm to extract defining characteristics of earthquake ground-motion records, also called latent features, to aid in ground-motion clustering and selection. In this context, a latent feature is a low dimensional machine-discovered spectral characteristic learned through nonlinear relationships of a neural network autoencoder. Clustering can be performed on the latent features and used to select a representative archetypal subgroup from a large ground-motion suite. The objective of efficient ground-motion selection is to choose records representative of what the structure will probabilistically experience in its lifetime. Three examples are presented to validate this approach, including a synthetic spectral dataset and spectra from field recorded ground-motion records. Deep embedding clustering of ground motion spectra improves on the results of static feature extraction, utilizing characteristics that represent the sparse spectral content of ground motions.

Class-Incremental Learning is a challenging problem in machine learning that aims to extend previously trained neural networks with new classes. This is especially useful if the system is able to classify new objects despite the original training data being unavailable. While the semantic segmentation problem has received less attention than classification, it poses distinct problems and challenges since previous and future target classes can be unlabeled in the images of a single increment. In this case, the background, past and future classes are correlated and there exist a background-shift. In this paper, we address the problem of how to model unlabeled classes while avoiding spurious feature clustering of future uncorrelated classes. We propose to use Evidential Deep Learning to model the evidence of the classes as a Dirichlet distribution. Our method factorizes the problem into a separate foreground class probability, calculated by the expected value of the Dirichlet distribution, and an unknown class (background) probability corresponding to the uncertainty of the estimate. In our novel formulation, the background probability is implicitly modeled, avoiding the feature space clustering that comes from forcing the model to output a high background score for pixels that are not labeled as objects. Experiments on the incremental Pascal VOC, and ADE20k benchmarks show that our method is superior to state-of-the-art, especially when repeatedly learning new classes with increasing number of increments.