We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a high-confidence lower bound on the optimal k-means value. This lower bound is data-driven; it does not make any assumption on the data nor how it is generated. We provide code and an extensive set of numerical experiments where we use this approach to certify approximate optimality of clustering solutions obtained by k-means++.
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人工智能的最新趋势是将验证的模型用于语言和视觉任务，这些模型已经实现了非凡的表现，但也令人困惑。因此，以各种方式探索这些模型的能力对该领域至关重要。在本文中，我们探讨了模型的可靠性，在其中我们将可靠的模型定义为一个不仅可以实现强大的预测性能，而且在许多涉及不确定性（例如选择性预测，开放式设置识别）的决策任务上，在许多决策任务上表现出色，而且表现良好。强大的概括（例如，准确性和适当的评分规则，例如在分布数据集中和分发数据集上的对数可能性）和适应性（例如，主动学习，几乎没有射击不确定性）。我们设计了40个数据集的10种任务类型，以评估视觉和语言域上可靠性的不同方面。为了提高可靠性，我们分别开发了VIT-PLEX和T5-PLEX，分别针对视觉和语言方式扩展了大型模型。 PLEX极大地改善了跨可靠性任务的最先进，并简化了传统协议，因为它可以改善开箱即用的性能，并且不需要设计分数或为每个任务调整模型。我们演示了高达1B参数的模型尺寸的缩放效果，并预处理数据集大小最多4B示例。我们还展示了PLEX在具有挑战性的任务上的功能，包括零射门的开放式识别，主动学习和对话语言理解中的不确定性。
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对不确定度和鲁棒性的高质量估计对于众多现实世界的应用来说至关重要，特别是对于深入学习，这是利用许多部署的ML系统。因此，比较改善这些估计的技术的能力对于研究和实践相似非常重要。然而，由于一系列原因，通常缺乏方法的竞争比较，包括：计算广泛调整的可用性，加入足够多的基线，以及用于再现性的具体文件。在本文中，我们介绍了不确定性的基线：在各种任务中的标准和最先进的深度学习方法的高质量实现。从本撰写中，集合跨越9项方法，每个方法都有至少5个度量。每个基线都是一个独立的实验管道，易于可重复使用和可伸缩的部件。我们的目标是提供具有新方法或应用的实验的即时出发点。此外，我们还提供模型检查点，实验输出为Python笔记本，以及用于比较结果的排行榜。代码在https://github.com/google/uncertainty-baselines。
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While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.
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Attention mechanisms form a core component of several successful deep learning architectures, and are based on one key idea: ''The output depends only on a small (but unknown) segment of the input.'' In several practical applications like image captioning and language translation, this is mostly true. In trained models with an attention mechanism, the outputs of an intermediate module that encodes the segment of input responsible for the output is often used as a way to peek into the `reasoning` of the network. We make such a notion more precise for a variant of the classification problem that we term selective dependence classification (SDC) when used with attention model architectures. Under such a setting, we demonstrate various error modes where an attention model can be accurate but fail to be interpretable, and show that such models do occur as a result of training. We illustrate various situations that can accentuate and mitigate this behaviour. Finally, we use our objective definition of interpretability for SDC tasks to evaluate a few attention model learning algorithms designed to encourage sparsity and demonstrate that these algorithms help improve interpretability.
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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.
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Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.
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KL-regularized reinforcement learning from expert demonstrations has proved successful in improving the sample efficiency of deep reinforcement learning algorithms, allowing them to be applied to challenging physical real-world tasks. However, we show that KL-regularized reinforcement learning with behavioral reference policies derived from expert demonstrations can suffer from pathological training dynamics that can lead to slow, unstable, and suboptimal online learning. We show empirically that the pathology occurs for commonly chosen behavioral policy classes and demonstrate its impact on sample efficiency and online policy performance. Finally, we show that the pathology can be remedied by non-parametric behavioral reference policies and that this allows KL-regularized reinforcement learning to significantly outperform state-of-the-art approaches on a variety of challenging locomotion and dexterous hand manipulation tasks.
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Three main points: 1. Data Science (DS) will be increasingly important to heliophysics; 2. Methods of heliophysics science discovery will continually evolve, requiring the use of learning technologies [e.g., machine learning (ML)] that are applied rigorously and that are capable of supporting discovery; and 3. To grow with the pace of data, technology, and workforce changes, heliophysics requires a new approach to the representation of knowledge.
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In the Earth's magnetosphere, there are fewer than a dozen dedicated probes beyond low-Earth orbit making in-situ observations at any given time. As a result, we poorly understand its global structure and evolution, the mechanisms of its main activity processes, magnetic storms, and substorms. New Artificial Intelligence (AI) methods, including machine learning, data mining, and data assimilation, as well as new AI-enabled missions will need to be developed to meet this Sparse Data challenge.
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