许多用于反问题和数据同化的现代算法都依赖于集成Kalman更新，以将先前的预测与观察到的数据融为一体。合奏Kalman方法通常具有小的合奏尺寸，这在生成每个粒子成本高昂的应用中至关重要。本文对合奏Kalman更新进行了非反应分析，该分析严格地解释了为什么由于快速衰减或近似稀疏性而导致先前的协方差具有适度的有效尺寸，那么小合奏的大小就足够了。我们在统一的框架中介绍了我们的理论，比较了使用扰动观测值，平方根滤波和本地化的集合卡尔曼更新的几个实现。作为我们分析的一部分，我们为可能具有独立感兴趣的大约稀疏矩阵开发了新的无维度协方差估计界限。

我们考虑了使用显微镜或X射线散射技术产生的图像数据自组装的模型的贝叶斯校准。为了说明BCP平衡结构中的随机远程疾病，我们引入了辅助变量以表示这种不确定性。然而，这些变量导致了高维图像数据的综合可能性，通常可以评估。我们使用基于测量运输的可能性方法以及图像数据的摘要统计数据来解决这一具有挑战性的贝叶斯推理问题。我们还表明，可以计算出有关模型参数的数据中的预期信息收益（EIG），而无需额外的成本。最后，我们介绍了基于二嵌段共聚物薄膜自组装和自上而下显微镜表征的ohta-kawasaki模型的数值案例研究。为了进行校准，我们介绍了一些基于域的能量和傅立叶的摘要统计数据，并使用EIG量化了它们的信息性。我们证明了拟议方法研究数据损坏和实验设计对校准结果的影响的力量。

由于神经操作员能够在功能空间之间近似高维参数图，因此最近引起了重大关注。目前，在神经操作员文献中仅解决了参数函数近似。在这项工作中，我们调查将参数导数信息纳入神经操作员培训中；该信息可以改善功能近似值，此外，它可用于改善衍生物相对于参数的近似值，这通常是高维外环问题的可扩展解决方案的关键（例如，贝叶斯逆问题）。参数雅各布信息由于其高维度而正式棘手，可以正式地合并，以解决我们基于减少的SVD，随机草图和减少基础替代物的使用提出的这种关注。所有这些策略仅需要$ O（r）$ jacobian动作来构建样本雅各布数据，并允许我们减少与雅各布培训相关的线性代数和内存成本，从输入和输出维度的产品中降低到$ o。 （r^2）$，其中$ r $是与缩小技术相关的维度。参数PDE问题的数值结果表明，在训练问题中添加导数信息可以显着改善参数图近似值，尤其是在几乎没有数据的情况下。与参数图相比，当雅各布动作相比便宜时，可以在经济上代替参数地图数据。此外，我们表明，随着Jacobian培训数据的引入，Jacobian误差近似显着改善。该结果为在外环算法中使用衍生知识的神经操作员（恐龙）打开了大门，他们可以通过重复评估来摊销额外的培训数据成本。

我们提出了一种从有限的训练数据学习高维参数映射的解析替代框架。在许多需要重复查询复杂计算模型的许多应用中出现了对参数代理的需求。这些应用包括贝叶斯逆问题，最佳实验设计和不确定度的最佳设计和控制等“外环”问题，以及实时推理和控制问题。许多高维参数映射承认低维结构，这可以通过映射信息的输入和输出的绘图信息的减少基础来利用。利用此属性，我们通过自适应地构造其输入和输出的缩小基础之间的Reset近似来制定用于学习这些地图的低维度近似的框架。最近的近似近似理论作为控制流的离散化，我们证明了我们所提出的自适应投影Reset框架的普遍近似性，这激励了Resnet构造的相关迭代算法。该策略代表了近似理论和算法的汇合，因为两者都使用顺序最小化流量。在数值例子中，我们表明，在训练数据少量的培训数据中，能够实现显着高精度，使其能够实现培训数据生成的最小计算投资的理想代理策略。

Retrieval-augmented in-context learning has emerged as a powerful approach for addressing knowledge-intensive tasks using frozen language models (LM) and retrieval models (RM). Existing work has combined these in simple "retrieve-then-read" pipelines in which the RM retrieves passages that are inserted into the LM prompt. To begin to fully realize the potential of frozen LMs and RMs, we propose Demonstrate-Search-Predict (DSP), a framework that relies on passing natural language texts in sophisticated pipelines between an LM and an RM. DSP can express high-level programs that bootstrap pipeline-aware demonstrations, search for relevant passages, and generate grounded predictions, systematically breaking down problems into small transformations that the LM and RM can handle more reliably. We have written novel DSP programs for answering questions in open-domain, multi-hop, and conversational settings, establishing in early evaluations new state-of-the-art in-context learning results and delivering 37-200%, 8-40%, and 80-290% relative gains against vanilla LMs, a standard retrieve-then-read pipeline, and a contemporaneous self-ask pipeline, respectively.

Over the last decade, an approach that has gained a lot of popularity to tackle non-parametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of probability distributions. The main goal of our work is to understand the optimality of two-sample tests constructed based on this approach. First, we show that the popular MMD (maximum mean discrepancy) two-sample test is not optimal in terms of the separation boundary measured in Hellinger distance. Second, we propose a modification to the MMD test based on spectral regularization by taking into account the covariance information (which is not captured by the MMD test) and prove the proposed test to be minimax optimal with a smaller separation boundary than that achieved by the MMD test. Third, we propose an adaptive version of the above test which involves a data-driven strategy to choose the regularization parameter and show the adaptive test to be almost minimax optimal up to a logarithmic factor. Moreover, our results hold for the permutation variant of the test where the test threshold is chosen elegantly through the permutation of the samples. Through numerical experiments on synthetic and real-world data, we demonstrate the superior performance of the proposed test in comparison to the MMD test.

When annotators label data, a key metric for quality assurance is inter-annotator agreement (IAA): the extent to which annotators agree on their labels. Though many IAA measures exist for simple categorical and ordinal labeling tasks, relatively little work has considered more complex labeling tasks, such as structured, multi-object, and free-text annotations. Krippendorff's alpha, best known for use with simpler labeling tasks, does have a distance-based formulation with broader applicability, but little work has studied its efficacy and consistency across complex annotation tasks. We investigate the design and evaluation of IAA measures for complex annotation tasks, with evaluation spanning seven diverse tasks: image bounding boxes, image keypoints, text sequence tagging, ranked lists, free text translations, numeric vectors, and syntax trees. We identify the difficulty of interpretability and the complexity of choosing a distance function as key obstacles in applying Krippendorff's alpha generally across these tasks. We propose two novel, more interpretable measures, showing they yield more consistent IAA measures across tasks and annotation distance functions.

Generating a chain of thought (CoT) can increase large language model (LLM) performance on a wide range of tasks. Zero-shot CoT evaluations, however, have been conducted primarily on logical tasks (e.g. arithmetic, commonsense QA). In this paper, we perform a controlled evaluation of zero-shot CoT across two sensitive domains: harmful questions and stereotype benchmarks. We find that using zero-shot CoT reasoning in a prompt can significantly increase a model's likelihood to produce undesirable output. Without future advances in alignment or explicit mitigation instructions, zero-shot CoT should be avoided on tasks where models can make inferences about marginalized groups or harmful topics.

Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be inferred from observations. Particle filtering can perform such inference given approximate transition and observation models. However, these models are often unknown a priori, yielding a difficult parameter estimation problem since observations jointly carry transition and observation noise. In this work, we consider learning maximum-likelihood parameters using particle methods. Recent methods addressing this problem typically differentiate through time in a particle filter, which requires workarounds to the non-differentiable resampling step, that yield biased or high variance gradient estimates. By contrast, we exploit Fisher's identity to obtain a particle-based approximation of the score function (the gradient of the log likelihood) that yields a low variance estimate while only requiring stepwise differentiation through the transition and observation models. We apply our method to real data collected from autonomous vehicles (AVs) and show that it learns better models than existing techniques and is more stable in training, yielding an effective smoother for tracking the trajectories of vehicles around an AV.

Neural information retrieval (IR) systems have progressed rapidly in recent years, in large part due to the release of publicly available benchmarking tasks. Unfortunately, some dimensions of this progress are illusory: the majority of the popular IR benchmarks today focus exclusively on downstream task accuracy and thus conceal the costs incurred by systems that trade away efficiency for quality. Latency, hardware cost, and other efficiency considerations are paramount to the deployment of IR systems in user-facing settings. We propose that IR benchmarks structure their evaluation methodology to include not only metrics of accuracy, but also efficiency considerations such as a query latency and the corresponding cost budget for a reproducible hardware setting. For the popular IR benchmarks MS MARCO and XOR-TyDi, we show how the best choice of IR system varies according to how these efficiency considerations are chosen and weighed. We hope that future benchmarks will adopt these guidelines toward more holistic IR evaluation.