Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Finally, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty for solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a coupled multiwavelets neural operator (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a 2ˆ 4ˆ improvement relative L2 error compared to the best results from the state-of-the-art models. Human perception relies on detecting and processing waves. While our eyes detect waves of electromagnetic radiation, our ears detect waves of compression in the surrounding air.

Near-term quantum systems tend to be noisy. Crosstalk noise has been recognized as one of several major types of noises in superconducting Noisy Intermediate-Scale Quantum (NISQ) devices. Crosstalk arises from the concurrent execution of two-qubit gates on nearby qubits, such as \texttt{CX}. It might significantly raise the error rate of gates in comparison to running them individually. Crosstalk can be mitigated through scheduling or hardware machine tuning. Prior scientific studies, however, manage crosstalk at a really late phase in the compilation process, usually after hardware mapping is done. It may miss great opportunities of optimizing algorithm logic, routing, and crosstalk at the same time. In this paper, we push the envelope by considering all these factors simultaneously at the very early compilation stage. We propose a crosstalk-aware quantum program compilation framework called CQC that can enhance crosstalk mitigation while achieving satisfactory circuit depth. Moreover, we identify opportunities for translation from intermediate representation to the circuit for application-specific crosstalk mitigation, for instance, the \texttt{CX} ladder construction in variational quantum eigensolvers (VQE). Evaluations through simulation and on real IBM-Q devices show that our framework can significantly reduce the error rate by up to 6$\times$, with only $\sim$60\% circuit depth compared to state-of-the-art gate scheduling approaches. In particular, for VQE, we demonstrate 49\% circuit depth reduction with 9.6\% fidelity improvement over prior art on the H4 molecule using IBMQ Guadalupe. Our CQC framework will be released on GitHub.

Estimating the prevalence of a medical condition, or the proportion of the population in which it occurs, is a fundamental problem in healthcare and public health. Accurate estimates of the relative prevalence across groups -- capturing, for example, that a condition affects women more frequently than men -- facilitate effective and equitable health policy which prioritizes groups who are disproportionately affected by a condition. However, it is difficult to estimate relative prevalence when a medical condition is underreported. In this work, we provide a method for accurately estimating the relative prevalence of underreported medical conditions, building upon the positive unlabeled learning framework. We show that under the commonly made covariate shift assumption -- i.e., that the probability of having a disease conditional on symptoms remains constant across groups -- we can recover the relative prevalence, even without restrictive assumptions commonly made in positive unlabeled learning and even if it is impossible to recover the absolute prevalence. We conduct experiments on synthetic and real health data which demonstrate our method's ability to recover the relative prevalence more accurately than do baselines, and demonstrate the method's robustness to plausible violations of the covariate shift assumption. We conclude by illustrating the applicability of our method to case studies of intimate partner violence and hate speech.

The notion of causality assumes a paramount position within the realm of human cognition. Over the past few decades, there has been significant advancement in the domain of causal effect estimation across various disciplines, including but not limited to computer science, medicine, economics, and industrial applications. Given the continued advancements in deep learning methodologies, there has been a notable surge in its utilization for the estimation of causal effects using counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective functions to estimate counterfactual data unbiasedly. Different from the existing surveys on causal models in machine learning, this review mainly focuses on the overview of the deep causal models, and its core contributions are as follows: 1) we cast insight on a comprehensive overview of deep causal models from both timeline of development and method classification perspectives; 2) we outline some typical applications of causal effect estimation to industry; 3) we also endeavor to present a detailed categorization and analysis on relevant datasets, source codes and experiments.

European Union talks on world-leading comprehensive artificial intelligence regulations were paused Thursday after 22 straight hours, with officials yet to hammer out a deal on a rulebook for the rapidly advancing technology behind popular services like ChatGPT. European Commissioner Thierry Breton tweeted that talks, which began Wednesday afternoon in Brussels and ran through the night, would resume on Friday morning. "Lots of progress made over past 22 hours" on the EU's Artificial Intelligence Act, he wrote. Representatives of the bloc's 27 member states, lawmakers and executive commissioners are under the gun to secure a political agreement for the flagship AI Act. They spent hours wrangling over controversial points such as generative AI and AI-powered police facial recognition.

Google officially introduced its most capable large language model to date, Gemini. CEO Sundar Pichai said it's the first of "a new generation of AI models, inspired by the way people understand and interact with the world." Of course, it's all very complex, but Google's multimillion-dollar investment in AI has created a model more flexible than anything before it. The system has been developed from the ground up as an integrated multimodal AI. As Engadget's Andrew Tarantola puts it, "think of many foundational AI models as groups of smaller models all stacked together." Gemini is trained to seamlessly understand and reason on all kinds of inputs, and this should make it pretty capable in the face of complex coding requests and even physics problems.

In the winter of 2020, on one of my aimless, frigid quarantine walks around my silent neighborhood, I remember being struck by a thought: did a medieval European peasant know that he was living through what is now widely known as the Dark Ages? Was there some moment when he leaned against his hoe in the fields, gazed up at the uncaring sky, and dimly perceived that he was unlucky enough to have been born into a bad century, perhaps even a bad millennium, too late for classical antiquity and too early for the Renaissance? I was sympathetic toward that notional peasant, because I was feeling the same way. The tide of history was overwhelming; I was minuscule, my life brought to a terrifying standstill by an airborne virus. I thought that if the humans who survived into the year 2500 looked back on my era, they would see it as cursed or benighted, the beginning of a downward slide.

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations, non-intrusive PCE allows the construction of these surrogates using a set of simulation response evaluations. In this context, the PCE coefficients can be obtained using linear regression, which is also known as point collocation or stochastic response surfaces. Regression exhibits better scalability and can handle noisy function evaluations in contrast to other non-intrusive approaches, such as projection. However, since over-sampling is generally advisable for the linear regression approach, the simulation requirements become prohibitive for expensive forward models. We propose to leverage transfer learning whereby knowledge gained through similar PCE surrogate construction tasks (source domains) is transferred to a new surrogate-construction task (target domain) which has a limited number of forward model simulations (training data). The proposed transfer learning strategy determines how much, if any, information to transfer using new techniques inspired by Bayesian modeling and data assimilation. The strategy is scrutinized using numerical investigations and applied to an engineering problem from the oil and gas industry.

This paper presents CyberSecEval, a comprehensive benchmark developed to help bolster the cybersecurity of Large Language Models (LLMs) employed as coding assistants. As what we believe to be the most extensive unified cybersecurity safety benchmark to date, CyberSecEval provides a thorough evaluation of LLMs in two crucial security domains: their propensity to generate insecure code and their level of compliance when asked to assist in cyberattacks. Through a case study involving seven models from the Llama 2, Code Llama, and OpenAI GPT large language model families, CyberSecEval effectively pinpointed key cybersecurity risks. More importantly, it offered practical insights for refining these models. A significant observation from the study was the tendency of more advanced models to suggest insecure code, highlighting the critical need for integrating security considerations in the development of sophisticated LLMs. CyberSecEval, with its automated test case generation and evaluation pipeline covers a broad scope and equips LLM designers and researchers with a tool to broadly measure and enhance the cybersecurity safety properties of LLMs, contributing to the development of more secure AI systems.