过度参数化神经网络（NNS）的小概括误差可以通过频率偏见现象来部分解释，在频率偏置现象中，基于梯度的算法将低频失误最小化，然后再减少高频残差。使用神经切线内核（NTK），可以为训练提供理论上严格的分析，其中数据是从恒定或分段构剂概率密度绘制的数据。由于大多数训练数据集不是从此类分布中汲取的，因此我们使用NTK模型和数据依赖性的正交规则来理论上量化NN训练的频率偏差，给定完全不均匀的数据。通过用精心选择的Sobolev规范替换损失函数，我们可以进一步扩大，抑制，平衡或逆转NN训练中的内在频率偏差。

神经操作员是科学机器学习中一种流行的技术，可以从数据中学习未知物理系统行为的数学模型。当数值求解器不可用或对基础物理学的理解不佳时，神经运算符对于学习与局部微分方程（PDE）相关的解决方案运算符特别有用。在这项工作中，我们试图提供理论基础，以了解学习时间依赖性PDE所需的培训数据量。从任何空间尺寸$ n \ geq 1 $中的抛物线PDE中给定输入输出对，我们得出了学习相关解决方案运算符的第一个理论上严格的方案，该方案采取了带有绿色功能$ g $的卷积的形式。到目前为止，严格学习与时间相关PDE相关的Green的功能一直是科学机器学习领域的主要挑战。通过将$ g $的层次低级结构与随机数字线性代数结合在一起，我们构建了$ g $的近似值，该$ g $实现了$ \ smash {\ smash {\ smashcal {\ mathcal {o}（\ gamma_ \ epsilon^epsilon^{ - 1/2} \ epsilon）}} $在$ l^1 $ -NORM中具有高概率，最多可以使用$ \ smash {\ MathCal {\ Mathcal {o}（\ Epsilon^{ - \ frac {n+2} {2} {2} {2} {2} {2} {2} } \ log（1/\ epsilon））}} $输入输出培训对，其中$ \ gamma_ \ epsilon $是衡量学习$ g $的培训数据集质量的量度，而$ \ epsilon> 0 $就足够了小的。

Koopman运算符是无限维的运算符，可全球线性化非线性动态系统，使其光谱信息可用于理解动态。然而，Koopman运算符可以具有连续的光谱和无限维度的子空间，使得它们的光谱信息提供相当大的挑战。本文介绍了具有严格融合的数据驱动算法，用于从轨迹数据计算Koopman运算符的频谱信息。我们引入了残余动态模式分解（ResDMD），它提供了第一种用于计算普通Koopman运算符的Spectra和PseudtoStra的第一种方案，无需光谱污染。使用解析器操作员和RESDMD，我们还计算与测量保存动态系统相关的光谱度量的平滑近似。我们证明了我们的算法的显式收敛定理，即使计算连续频谱和离散频谱的密度，也可以实现高阶收敛即使是混沌系统。我们展示了在帐篷地图，高斯迭代地图，非线性摆，双摆，洛伦茨系统和11美元延长洛伦兹系统的算法。最后，我们为具有高维状态空间的动态系统提供了我们的算法的核化变体。这使我们能够计算与具有20,046维状态空间的蛋白质分子的动态相关的光谱度量，并计算出湍流流过空气的误差界限的非线性Koopman模式，其具有雷诺数为$> 10 ^ 5 $。一个295,122维的状态空间。

We derive a set of causal deep neural networks whose architectures are a consequence of tensor (multilinear) factor analysis. Forward causal questions are addressed with a neural network architecture composed of causal capsules and a tensor transformer. The former estimate a set of latent variables that represent the causal factors, and the latter governs their interaction. Causal capsules and tensor transformers may be implemented using shallow autoencoders, but for a scalable architecture we employ block algebra and derive a deep neural network composed of a hierarchy of autoencoders. An interleaved kernel hierarchy preprocesses the data resulting in a hierarchy of kernel tensor factor models. Inverse causal questions are addressed with a neural network that implements multilinear projection and estimates the causes of effects. As an alternative to aggressive bottleneck dimension reduction or regularized regression that may camouflage an inherently underdetermined inverse problem, we prescribe modeling different aspects of the mechanism of data formation with piecewise tensor models whose multilinear projections are well-defined and produce multiple candidate solutions. Our forward and inverse neural network architectures are suitable for asynchronous parallel computation.

The existing methods for video anomaly detection mostly utilize videos containing identifiable facial and appearance-based features. The use of videos with identifiable faces raises privacy concerns, especially when used in a hospital or community-based setting. Appearance-based features can also be sensitive to pixel-based noise, straining the anomaly detection methods to model the changes in the background and making it difficult to focus on the actions of humans in the foreground. Structural information in the form of skeletons describing the human motion in the videos is privacy-protecting and can overcome some of the problems posed by appearance-based features. In this paper, we present a survey of privacy-protecting deep learning anomaly detection methods using skeletons extracted from videos. We present a novel taxonomy of algorithms based on the various learning approaches. We conclude that skeleton-based approaches for anomaly detection can be a plausible privacy-protecting alternative for video anomaly detection. Lastly, we identify major open research questions and provide guidelines to address them.

Several self-supervised representation learning methods have been proposed for reinforcement learning (RL) with rich observations. For real-world applications of RL, recovering underlying latent states is crucial, particularly when sensory inputs contain irrelevant and exogenous information. In this work, we study how information bottlenecks can be used to construct latent states efficiently in the presence of task-irrelevant information. We propose architectures that utilize variational and discrete information bottlenecks, coined as RepDIB, to learn structured factorized representations. Exploiting the expressiveness bought by factorized representations, we introduce a simple, yet effective, bottleneck that can be integrated with any existing self-supervised objective for RL. We demonstrate this across several online and offline RL benchmarks, along with a real robot arm task, where we find that compressed representations with RepDIB can lead to strong performance improvements, as the learned bottlenecks help predict only the relevant state while ignoring irrelevant information.

We propose reconstruction probing, a new analysis method for contextualized representations based on reconstruction probabilities in masked language models (MLMs). This method relies on comparing the reconstruction probabilities of tokens in a given sequence when conditioned on the representation of a single token that has been fully contextualized and when conditioned on only the decontextualized lexical prior of the model. This comparison can be understood as quantifying the contribution of contextualization towards reconstruction -- the difference in the reconstruction probabilities can only be attributed to the representational change of the single token induced by contextualization. We apply this analysis to three MLMs and find that contextualization boosts reconstructability of tokens that are close to the token being reconstructed in terms of linear and syntactic distance. Furthermore, we extend our analysis to finer-grained decomposition of contextualized representations, and we find that these boosts are largely attributable to static and positional embeddings at the input layer.

Diffusion models have achieved justifiable popularity by attaining state-of-the-art performance in generating realistic objects from seemingly arbitrarily complex data distributions, including when conditioning generation on labels. Unfortunately, however, their iterative nature renders them very computationally inefficient during the sampling process. For the multi-class conditional generation problem, we propose a novel, structurally unique framework of diffusion models which are hierarchically branched according to the inherent relationships between classes. In this work, we demonstrate that branched diffusion models offer major improvements in efficiently generating samples from multiple classes. We also showcase several other advantages of branched diffusion models, including ease of extension to novel classes in a continual-learning setting, and a unique interpretability that offers insight into these generative models. Branched diffusion models represent an alternative paradigm to their traditional linear counterparts, and can have large impacts in how we use diffusion models for efficient generation, online learning, and scientific discovery.

The widely studied task of Natural Language Inference (NLI) requires a system to recognize whether one piece of text is textually entailed by another, i.e. whether the entirety of its meaning can be inferred from the other. In current NLI datasets and models, textual entailment relations are typically defined on the sentence- or paragraph-level. However, even a simple sentence often contains multiple propositions, i.e. distinct units of meaning conveyed by the sentence. As these propositions can carry different truth values in the context of a given premise, we argue for the need to recognize the textual entailment relation of each proposition in a sentence individually. We propose PropSegmEnt, a corpus of over 35K propositions annotated by expert human raters. Our dataset structure resembles the tasks of (1) segmenting sentences within a document to the set of propositions, and (2) classifying the entailment relation of each proposition with respect to a different yet topically-aligned document, i.e. documents describing the same event or entity. We establish strong baselines for the segmentation and entailment tasks. Through case studies on summary hallucination detection and document-level NLI, we demonstrate that our conceptual framework is potentially useful for understanding and explaining the compositionality of NLI labels.

People living with dementia often exhibit behavioural and psychological symptoms of dementia that can put their and others' safety at risk. Existing video surveillance systems in long-term care facilities can be used to monitor such behaviours of risk to alert the staff to prevent potential injuries or death in some cases. However, these behaviours of risk events are heterogeneous and infrequent in comparison to normal events. Moreover, analyzing raw videos can also raise privacy concerns. In this paper, we present two novel privacy-protecting video-based anomaly detection approaches to detect behaviours of risks in people with dementia. We either extracted body pose information as skeletons and use semantic segmentation masks to replace multiple humans in the scene with their semantic boundaries. Our work differs from most existing approaches for video anomaly detection that focus on appearance-based features, which can put the privacy of a person at risk and is also susceptible to pixel-based noise, including illumination and viewing direction. We used anonymized videos of normal activities to train customized spatio-temporal convolutional autoencoders and identify behaviours of risk as anomalies. We show our results on a real-world study conducted in a dementia care unit with patients with dementia, containing approximately 21 hours of normal activities data for training and 9 hours of data containing normal and behaviours of risk events for testing. We compared our approaches with the original RGB videos and obtained an equivalent area under the receiver operating characteristic curve performance of 0.807 for the skeleton-based approach and 0.823 for the segmentation mask-based approach. This is one of the first studies to incorporate privacy for the detection of behaviours of risks in people with dementia.