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The distribution for the minimum of Brownian motion or the Cauchy process is well-known using the reflection principle. Here we consider the problem of finding the sample-by-sample minimum, which we call the online minimum search. We consider the possibility of the golden search method, but we show quantitatively that the bisection method is more efficient. In the bisection method there is a hierarchical parameter, which tunes the depth to which each sub-search is conducted, somewhat similarly to how a depth-first search works to generate a topological ordering on nodes. Finally, we consider the possibility of using harmonic measure, which is a novel idea that has so far been unexplored.

Automated Planning and Scheduling is among the growing areas in Artificial Intelligence (AI) where mention of LLMs has gained popularity. Based on a comprehensive review of 126 papers, this paper investigates eight categories based on the unique applications of LLMs in addressing various aspects of planning problems: language translation, plan generation, model construction, multi-agent planning, interactive planning, heuristics optimization, tool integration, and brain-inspired planning. For each category, we articulate the issues considered and existing gaps. A critical insight resulting from our review is that the true potential of LLMs unfolds when they are integrated with traditional symbolic planners, pointing towards a promising neuro-symbolic approach. This approach effectively combines the generative aspects of LLMs with the precision of classical planning methods. By synthesizing insights from existing literature, we underline the potential of this integration to address complex planning challenges. Our goal is to encourage the ICAPS community to recognize the complementary strengths of LLMs and symbolic planners, advocating for a direction in automated planning that leverages these synergistic capabilities to develop more advanced and intelligent planning systems.

The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini's indices. For the bivariate case we provide several results and we point out that they are "dependence-dispersion" indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini's indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered in order as well to apply multivariate Gini's indices to data.

Natural Language Processing (NLP) is now a cornerstone of requirements automation. One compelling factor behind the growing adoption of NLP in Requirements Engineering (RE) is the prevalent use of natural language (NL) for specifying requirements in industry. NLP techniques are commonly used for automatically classifying requirements, extracting important information, e.g., domain models and glossary terms, and performing quality assurance tasks, such as ambiguity handling and completeness checking. With so many different NLP solution strategies available and the possibility of applying machine learning alongside, it can be challenging to choose the right strategy for a specific RE task and to evaluate the resulting solution in an empirically rigorous manner. This book chapter presents guidelines for the selection of NLP techniques as well as for their evaluation in the context of RE. In particular, we discuss how to choose among different strategies such as traditional NLP, feature-based machine learning, and language-model-based methods. Our ultimate hope for this chapter is to serve as a stepping stone, assisting newcomers to NLP4RE in quickly initiating themselves into the NLP technologies most pertinent to the RE field.

Pearl's causal hierarchy establishes a clear separation between observational, interventional, and counterfactual questions. Researchers proposed sound and complete algorithms to compute identifiable causal queries at a given level of the hierarchy using the causal structure and data from the lower levels of the hierarchy. However, most of these algorithms assume that we can accurately estimate the probability distribution of the data, which is an impractical assumption for high-dimensional variables such as images. On the other hand, modern generative deep learning architectures can be trained to learn how to accurately sample from such high-dimensional distributions. Especially with the recent rise of foundation models for images, it is desirable to leverage pre-trained models to answer causal queries with such high-dimensional data. To address this, we propose a sequential training algorithm that, given the causal structure and a pre-trained conditional generative model, can train a deep causal generative model, which utilizes the pre-trained model and can provably sample from identifiable interventional and counterfactual distributions. Our algorithm, called Modular-DCM, uses adversarial training to learn the network weights, and to the best of our knowledge, is the first algorithm that can make use of pre-trained models and provably sample from any identifiable causal query in the presence of latent confounders with high-dimensional data. We demonstrate the utility of our algorithm using semi-synthetic and real-world datasets containing images as variables in the causal structure.

People living with Type 1 Diabetes (T1D) lose the ability to produce insulin naturally. To compensate, they inject synthetic insulin. One common way to inject insulin is through automated insulin delivery systems, which use sensors to monitor their metabolic state and an insulin pump device to adjust insulin to adapt. In this paper, we present the Metabolic Operating System, a new automated insulin delivery system that we designed from the ground up using security first principles. From an architecture perspective, we apply separation principles to simplify the core system and isolate non-critical functionality from the core closed-loop algorithm. From an algorithmic perspective, we evaluate trends in insulin technology and formulate a simple, but effective, algorithm given the state-of-the-art. From a safety perspective, we build in multiple layers of redundancy to ensure that the person using our system remains safe. Fundamentally, this paper is a paper on real-world experiences building and running an automated insulin delivery system. We report on the design iterations we make based on experiences working with one individual using our system. Our evaluation shows that an automated insulin delivery system built from the ground up using security first principles can still help manage T1D effectively. Our source code is open source and available on GitHub (link omitted).

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.

Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.