我们提出了二极管网络的定向渗透反问题：给定的信息，有关哪种节点允许电流从一个到另一个到另一个节点，是否可以找到与观察到的电流一致的二极管的配置？我们实施了一种分裂和相连的迭代投影方法来解决该问题，并证明了我们方法的至高无上的问题，而不是针对问题的非平凡实例的详尽方法。我们发现，当某些但并非所有渗透数据都隐藏时，问题最困难，而重建最困难的网络通常是电流对添加或去除单个二极管最敏感的网络。

我们对无上下文的语法推断实施了分裂和相连的迭代投影方法。与大多数最新的自然语言处理模型不同，我们的方法需要相对较少的离散参数，从而使推断的语法直接可解释 - 可以从解决方案中读取如何构建语法有效的句子。我们方法的另一个优点是，与许多其他模型所采用的数百GB培训数据相比，仅几句句子从几句句子中推断出有意义的语法规则。我们演示了应用我们的方法的几种方法：对单词进行分类并从头开始推断语法，采用现有语法并完善其类别和规则，并采用现有的语法并扩大其词典，因为它在新数据中遇到新单词。

当约束组是非凸块时，迭代投影方法可能被捕获在非解决方案。有两种参数可用于避免这种行为，这项研究提供了两者的例子。第一种称为HyperParameter的参数包括出现在迭代规则本身的定义中的任何类型的参数。第二种包括在约束集的定义中的度量参数，当要解决的问题时出现的特征具有两个或更多种变量。通过示例，我们展示了适当调整两种参数的重要性，并提供观察到的行为的启发式解释。

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.

We consider the problem of constructing minimax rate-optimal estimators for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. Minimax rate-optimal estimators for such functionals are typically constructed through higher-order bias corrections of plug-in and one-step type estimators and, in turn, depend on estimators of nuisance functions. In this paper, we consider a parallel question of interest regarding the optimality and/or sub-optimality of plug-in and one-step bias-corrected estimators for the specific doubly robust functional of interest. Specifically, we verify that by using undersmoothing and sample splitting techniques when constructing nuisance function estimators, one can achieve minimax rates of convergence in all H\"older smoothness classes of the nuisance functions (i.e. the propensity score and outcome regression) provided that the marginal density of the covariates is sufficiently regular. Additionally, by demonstrating suitable lower bounds on these classes of estimators, we demonstrate the necessity to undersmooth the nuisance function estimators to obtain minimax optimal rates of convergence.

Generative AI has matured to a point where large-scale models can generate text that seems indistinguishable from human-written text and remarkably photorealistic images. Automatically measuring how close the distribution of generated data is to the target real data distribution is a key step in diagnosing existing models and developing better models. We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. These scores are statistical summaries of divergence frontiers capturing two types of errors in generative modeling. We explore four approaches to statistically estimate these scores: vector quantization, non-parametric estimation, classifier-based estimation, and parametric Gaussian approximations. We provide statistical bounds for the vector quantization approach. Empirically, we find that the proposed scores paired with a range of $f$-divergences and statistical estimation methods can quantify the gaps between the distributions of human-written text and those of modern neural language models by correlating with human judgments and identifying known properties of the generated texts. We conclude the paper by demonstrating its applications to other AI domains and discussing practical recommendations.

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While powerful, existing tensor RPCA algorithms can be difficult to use in practice, as their performance can be sensitive to the choice of additional hyperparameters, which are not straightforward to tune. In this paper, we describe a fast and simple self-supervised model for tensor RPCA using deep unfolding by only learning four hyperparameters. Despite its simplicity, our model expunges the need for ground truth labels while maintaining competitive or even greater performance compared to supervised deep unfolding. Furthermore, our model is capable of operating in extreme data-starved scenarios. We demonstrate these claims on a mix of synthetic data and real-world tasks, comparing performance against previously studied supervised deep unfolding methods and Bayesian optimization baselines.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

When designing a new API for a large project, developers need to make smart design choices so that their code base can grow sustainably. To ensure that new API components are well designed, developers can learn from existing API components. However, the lack of standardized method for comparing API designs makes this learning process time-consuming and difficult. To address this gap we developed the API-Spector, to the best of our knowledge one of the first API-to-API specification recommendation engines. API-Spector retrieves relevant specification components written in OpenAPI (a widely adopted language used to describe web APIs). API-Spector presents several significant contributions, including: (1) novel methods of processing and extracting key information from OpenAPI specifications, (2) innovative feature extraction techniques that are optimized for the highly technical API specification domain, and (3) a novel log-linear probabilistic model that combines multiple signals to retrieve relevant and high quality OpenAPI specification components given a query specification. We evaluate API-Spector in both quantitative and qualitative tasks and achieve an overall of 91.7% recall@1 and 56.2% F1, which surpasses baseline performance by 15.4% in recall@1 and 3.2% in F1. Overall, API-Spector will allow developers to retrieve relevant OpenAPI specification components from a public or internal database in the early stages of the API development cycle, so that they can learn from existing established examples and potentially identify redundancies in their work. It provides the guidance developers need to accelerate development process and contribute thoughtfully designed APIs that promote code maintainability and quality.

Vehicle routing problems and other combinatorial optimization problems have been approximately solved by reinforcement learning agents with policies based on encoder-decoder models with attention mechanisms. These techniques are of substantial interest but still cannot solve the complex routing problems that arise in a realistic setting which can have many trucks and complex requirements. With the aim of making reinforcement learning a viable technique for supply chain optimization, we develop new extensions to encoder-decoder models for vehicle routing that allow for complex supply chains using classical computing today and quantum computing in the future. We make two major generalizations. First, our model allows for routing problems with multiple trucks. Second, we move away from the simple requirement of having a truck deliver items from nodes to one special depot node, and instead allow for a complex tensor demand structure. We show how our model, even if trained only for a small number of trucks, can be embedded into a large supply chain to yield viable solutions.