Department of Physics, Arizona State University, Tempe, Arizona 85287, USA (Dated: September 24, 2024) Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.

Query rewriting aims to generate a new query that can complement the original query to improve the information retrieval system. Recent studies on query rewriting, such as query2doc (Q2D), query2expand (Q2E) and querey2cot (Q2C), rely on the internal knowledge of Large Language Models (LLMs) to generate a relevant passage to add information to the query. Nevertheless, the efficacy of these methodologies may markedly decline in instances where the requisite knowledge is not encapsulated within the model's intrinsic parameters. In this paper, we propose a novel structured query rewriting method called Crafting the Path tailored for retrieval systems. Crafting the Path involves a three-step process that crafts query-related information necessary for finding the passages to be searched in each step. Specifically, the Crafting the Path begins with Query Concept Comprehension, proceeds to Query Type Identification, and finally conducts Expected Answer Extraction. Experimental results show that our method outperforms previous rewriting methods, especially in less familiar domains for LLMs. We demonstrate that our method is less dependent on the internal parameter knowledge of the model and generates queries with fewer factual inaccuracies. Furthermore, we observe that Crafting the Path has less latency compared to the baselines.

Embedding models are crucial for various natural language processing tasks but can be limited by factors such as limited vocabulary, lack of context, and grammatical errors. This paper proposes a novel approach to improve embedding performance by leveraging large language models (LLMs) to enrich and rewrite input text before the embedding process. By utilizing ChatGPT 3.5 to provide additional context, correct inaccuracies, and incorporate metadata, the proposed method aims to enhance the utility and accuracy of embedding models. The effectiveness of this approach is evaluated on three datasets: Banking77Classification, TwitterSemEval 2015, and Amazon Counter-factual Classification. Results demonstrate significant improvements over the baseline model on the TwitterSemEval 2015 dataset, with the best-performing prompt achieving a score of 85.34 compared to the previous best of 81.52 on the Massive Text Embedding Benchmark (MTEB) Leaderboard. However, performance on the other two datasets was less impressive, highlighting the importance of considering domain-specific characteristics. The findings suggest that LLM-based text enrichment has shown promising results to improve embedding performance, particularly in certain domains. Hence, numerous limitations in the process of embedding can be avoided.

Large language models (LLMs) have become the secret ingredient driving numerous industrial applications, showcasing their remarkable versatility across a diverse spectrum of tasks. From natural language processing and sentiment analysis to content generation and personalized recommendations, their unparalleled adaptability has facilitated widespread adoption across industries. This transformative shift driven by LLMs underscores the need to explore the underlying associated challenges and avenues for enhancement in their utilization. In this paper, our objective is to unravel and evaluate the obstacles and opportunities inherent in leveraging LLMs within an industrial context. To this end, we conduct a survey involving a group of industry practitioners, develop four research questions derived from the insights gathered, and examine 68 industry papers to address these questions and derive meaningful conclusions.

It was recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth's anomaly magnetic field immersed in overwhelming complex signals for magnetic navigation in a GPS-denied environment. The accuracy of the detected anomaly field corresponds to a positioning accuracy in the range of 10 to 40 meters. To increase the accuracy and reduce the uncertainty of weak signal detection as well as to directly obtain the position information, we exploit the machine-learning model of random forests that combines the output of multiple decision trees to give optimal values of the physical quantities of interest. In particular, from time-series data gathered from the cockpit of a flying airplane during various maneuvering stages, where strong background complex signals are caused by other elements of the Earth's magnetic field and the fields produced by the electronic systems in the cockpit, we demonstrate that the random-forest algorithm performs remarkably well in detecting the weak anomaly field and in filtering the position of the aircraft. With the aid of the conventional inertial navigation system, the positioning error can be reduced to less than 10 meters. We also find that, contrary to the conventional wisdom, the classic Tolles-Lawson model for calibrating and removing the magnetic field generated by the body of the aircraft is not necessary and may even be detrimental for the success of the random-forest method.

AI-Based Safety-Critical Systems (AI-SCS) are being increasingly deployed in the real world. These can pose a risk of harm to people and the environment. Reducing that risk is an overarching priority during development and operation. As more AI-SCS become autonomous, a layer of risk management via human intervention has been removed. Following an accident it will be important to identify causal contributions and the different responsible actors behind those to learn from mistakes and prevent similar future events. Many authors have commented on the "responsibility gap" where it is difficult for developers and manufacturers to be held responsible for harmful behaviour of an AI-SCS. This is due to the complex development cycle for AI, uncertainty in AI performance, and dynamic operating environment. A human operator can become a "liability sink" absorbing blame for the consequences of AI-SCS outputs they weren't responsible for creating, and may not have understanding of. This cross-disciplinary paper considers different senses of responsibility (role, moral, legal and causal), and how they apply in the context of AI-SCS safety. We use a core concept (Actor(A) is responsible for Occurrence(O)) to create role responsibility models, producing a practical method to capture responsibility relationships and provide clarity on the previously identified responsibility issues. Our paper demonstrates the approach with two examples: a retrospective analysis of the Tempe Arizona fatal collision involving an autonomous vehicle, and a safety focused predictive role-responsibility analysis for an AI-based diabetes co-morbidity predictor. In both examples our primary focus is on safety, aiming to reduce unfair or disproportionate blame being placed on operators or developers. We present a discussion and avenues for future research.

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.

To reason about where responsibility does and should lie in complex situations involving AI-enabled systems, we first need a sufficiently clear and detailed cross-disciplinary vocabulary for talking about responsibility. Responsibility is a triadic relation involving an actor, an occurrence, and a way of being responsible. As part of a conscious effort towards 'unravelling' the concept of responsibility to support practical reasoning about responsibility for AI, this paper takes the three-part formulation, 'Actor A is responsible for Occurrence O' and identifies valid combinations of subcategories of A, is responsible for, and O. These valid combinations - which we term "responsibility strings" - are grouped into four senses of responsibility: role-responsibility; causal responsibility; legal liability-responsibility; and moral responsibility. They are illustrated with two running examples, one involving a healthcare AI-based system and another the fatal collision of an AV with a pedestrian in Tempe, Arizona in 2018. The output of the paper is 81 responsibility strings. The aim is that these strings provide the vocabulary for people across disciplines to be clear and specific about the different ways that different actors are responsible for different occurrences within a complex event for which responsibility is sought, allowing for precise and targeted interdisciplinary normative deliberations.

The Uber safety driver at the wheel during the first known fatal self-driving car crash involving a pedestrian has pleaded guilty to and been sentenced for an endangerment charge. Rafaela Vasquez will serve three years of probation for her role in the 2018 Tempe, Arizona collision that killed Elaine Herzberg while she was jaywalking at night. The sentence honors the prosecutors' demands and is stiffer than the six months the defense team requested. The prosecution maintained that Vasquez was ultimately responsible. While an autonomous car was involved, Vasquez was supposed to concentrate on the road and take over if necessary.

Department of Physics, Arizona State University, Tempe, Arizona 85287, USA (Dated: November 21, 2022) Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both short-term prediction of the state variables and longterm prediction of the attractor of the system. A key to inducing the stochastic resonance is to include the amplitude of the noise in the set of hyperparameters for optimization. By so doing, the prediction accuracy, stability and horizon can be dramatically improved. The stochastic resonance phenomenon is demonstrated using two prototypical high-dimensional chaotic systems. The interplay between noise and nonlinear dynamics have revealed that, if the hyperparameters are often leads to surprising phenomena with potentially significant not optimized, noise in the training data can improve applications and thus has always been an active to certain extent the prediction performance.