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Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this paper, we provide bounds on the reach of a smooth algebraic variety in terms of several invariants of interest: the condition number, Smale's $\gamma$ and the bit-size. We also provide probabilistic bounds for random algebraic varieties under some general assumptions.

Deep learning research has uncovered the phenomenon of benign overfitting for overparameterized statistical models, which has drawn significant theoretical interest in recent years. Given its simplicity and practicality, the ordinary least squares (OLS) interpolator has become essential to gain foundational insights into this phenomenon. While properties of OLS are well established in classical, underparameterized settings, its behavior in high-dimensional, overparameterized regimes is less explored (unlike for ridge or lasso regression) though significant progress has been made of late. We contribute to this growing literature by providing fundamental algebraic and statistical results for the minimum $\ell_2$-norm OLS interpolator. In particular, we provide algebraic equivalents of (i) the leave-$k$-out residual formula, (ii) Cochran's formula, and (iii) the Frisch-Waugh-Lovell theorem in the overparameterized regime. These results aid in understanding the OLS interpolator's ability to generalize and have substantive implications for causal inference. Under the Gauss-Markov model, we present statistical results such as an extension of the Gauss-Markov theorem and an analysis of variance estimation under homoskedastic errors for the overparameterized regime. To substantiate our theoretical contributions, we conduct simulations that further explore the stochastic properties of the OLS interpolator.

Risk assessment of a robot in controlled environments, such as laboratories and proving grounds, is a common means to assess, certify, validate, verify, and characterize the robots' safety performance before, during, and even after their commercialization in the real-world. A standard testing program that acquires the risk estimate is expected to be (i) repeatable, such that it obtains similar risk assessments of the same testing subject among multiple trials or attempts with the similar testing effort by different stakeholders, and (ii) reliable against a variety of testing subjects produced by different vendors and manufacturers. Both repeatability and reliability are fundamental and crucial for a testing algorithm's validity, fairness, and practical feasibility, especially for standardization. However, these properties are rarely satisfied or ensured, especially as the subject robots become more complex, uncertain, and varied. This issue was present in traditional risk assessments through Monte-Carlo sampling, and remains a bottleneck for the recent accelerated risk assessment methods, primarily those using importance sampling. This study aims to enhance existing accelerated testing frameworks by proposing a new algorithm that provably integrates repeatability and reliability with the already established formality and efficiency. It also features demonstrations assessing the risk of instability from frontal impacts, initiated by push-over disturbances on a controlled inverted pendulum and a 7-DoF planar bipedal robot Rabbit managed by various control algorithms.

Embodied intelligence empowers agents with a profound sense of perception, enabling them to respond in a manner closely aligned with real-world situations. Large Language Models (LLMs) delve into language instructions with depth, serving a crucial role in generating plans for intricate tasks. Thus, LLM-based embodied models further enhance the agent's capacity to comprehend and process information. However, this amalgamation also ushers in new challenges in the pursuit of heightened intelligence. Specifically, attackers can manipulate LLMs to produce irrelevant or even malicious outputs by altering their prompts. Confronted with this challenge, we observe a notable absence of multi-modal datasets essential for comprehensively evaluating the robustness of LLM-based embodied models. Consequently, we construct the Embodied Intelligent Robot Attack Dataset (EIRAD), tailored specifically for robustness evaluation. Additionally, two attack strategies are devised, including untargeted attacks and targeted attacks, to effectively simulate a range of diverse attack scenarios. At the same time, during the attack process, to more accurately ascertain whether our method is successful in attacking the LLM-based embodied model, we devise a new attack success evaluation method utilizing the BLIP2 model. Recognizing the time and cost-intensive nature of the GCG algorithm in attacks, we devise a scheme for prompt suffix initialization based on various target tasks, thus expediting the convergence process. Experimental results demonstrate that our method exhibits a superior attack success rate when targeting LLM-based embodied models, indicating a lower level of decision-level robustness in these models.

Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict trust assumption. In the context of computation and storage, it is required that honest nodes outnumber adversarial ones by a certain margin. However, in several emerging real-world cases, particularly, in decentralized blockchain-oriented applications, such assumptions are often unrealistic. Consequently, despite the important role of coding in addressing significant challenges within decentralized systems, its applications become constrained. Still, in decentralized platforms, a distinctive characteristic emerges, offering new avenues for secure coding beyond the constraints of conventional methods. In these scenarios, the adversary benefits when the legitimate decoder recovers the data, and preferably with a high estimation error. This incentive motivates them to act rationally, trying to maximize their gains. In this paper, we propose a game theoretic formulation for coding, called the game of coding, that captures this unique dynamic where each of the adversary and the data collector (decoder) have a utility function to optimize. The utility functions reflect the fact that both the data collector and the adversary are interested in increasing the chance of data being recoverable by the data collector. Moreover, the utility functions express the interest of the data collector to estimate the input with lower estimation error, but the opposite interest of the adversary. As a first, still highly non-trivial step, we characterize the equilibrium of the game for the repetition code with a repetition factor of 2, for a wide class of utility functions with minimal assumptions.

Technologies adopted by the public sector have transformed the work practices of employees in public agencies by creating different means of communication and decision-making. Although much of the recent research in the future of work domain has concentrated on the effects of technological advancements on public sector employees, the influence on work practices of external stakeholders engaging with this sector remains under-explored. In this paper, we focus on a digital platform called OneStop which is deployed by several building departments across the U.S. and aims to integrate various steps and services into a single point of online contact between public sector employees and the public. Drawing on semi-structured interviews with 22 stakeholders, including local business owners, experts involved in the construction process, community representatives, and building department employees, we investigate how this technology transition has impacted the work of these different stakeholders. We observe a multifaceted perspective and experience caused by the adoption of OneStop. OneStop exacerbated inequitable practices for local business owners due to a lack of face-to-face interactions with the department employees. For the public sector employees, OneStop standardized the work practices, representing the building department's priorities and values. Based on our findings, we discuss tensions around standardization, equality, and equity in technology transition, as well as design implications for equitable practices in the public sector.

The Causal Roadmap outlines a systematic approach to asking and answering questions of cause-and-effect: define the quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. To protect research integrity, it is essential that the algorithm for statistical estimation and inference be pre-specified prior to conducting any effectiveness analyses. However, it is often unclear which algorithm will perform optimally for the real-data application. Instead, there is a temptation to simply implement one's favorite algorithm -- recycling prior code or relying on the default settings of a computing package. Here, we call for the use of simulations that realistically reflect the application, including key characteristics such as strong confounding and dependent or missing outcomes, to objectively compare candidate estimators and facilitate full specification of the Statistical Analysis Plan. Such simulations are informed by the Causal Roadmap and conducted after data collection but prior to effect estimation. We illustrate with two worked examples. First, in an observational longitudinal study, outcome-blind simulations are used to inform nuisance parameter estimation and variance estimation for longitudinal targeted minimum loss-based estimation (TMLE). Second, in a cluster randomized trial with missing outcomes, treatment-blind simulations are used to examine Type-I error control in Two-Stage TMLE. In both examples, realistic simulations empower us to pre-specify an estimation approach that is expected to have strong finite sample performance and also yield quality-controlled computing code for the actual analysis. Together, this process helps to improve the rigor and reproducibility of our research.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.

Transformers have achieved great success in many artificial intelligence fields, such as natural language processing, computer vision, and audio processing. Therefore, it is natural to attract lots of interest from academic and industry researchers. Up to the present, a great variety of Transformer variants (a.k.a. X-formers) have been proposed, however, a systematic and comprehensive literature review on these Transformer variants is still missing. In this survey, we provide a comprehensive review of various X-formers. We first briefly introduce the vanilla Transformer and then propose a new taxonomy of X-formers. Next, we introduce the various X-formers from three perspectives: architectural modification, pre-training, and applications. Finally, we outline some potential directions for future research.