There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_) is a program with index n in some exhaustive enumeration of all possible programs. This has implications for solving the liar paradox and for generalization of G\"odel incompleteness theorem to formal systems other than PA.
We consider large-scale nonlinear least squares problems with sparse residuals, each one of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of independent problems of smaller sizes is proposed and analysed. The smaller size problems are modified in a way that offsets the error made by disregarding dependencies that allow us to split the original problem. The resulting method is a modification of the Levenberg-Marquardt method with smaller computational costs. Global convergence is proved as well as local linear convergence under suitable assumptions on sparsity. The method is tested on the network localization simulated problems with up to one million variables and its efficiency is demonstrated.
Present-day federated learning (FL) systems deployed over edge networks consists of a large number of workers with high degrees of heterogeneity in data and/or computing capabilities, which call for flexible worker participation in terms of timing, effort, data heterogeneity, etc. To satisfy the need for flexible worker participation, we consider a new FL paradigm called "Anarchic Federated Learning" (AFL) in this paper. In stark contrast to conventional FL models, each worker in AFL has the freedom to choose i) when to participate in FL, and ii) the number of local steps to perform in each round based on its current situation (e.g., battery level, communication channels, privacy concerns). However, such chaotic worker behaviors in AFL impose many new open questions in algorithm design. In particular, it remains unclear whether one could develop convergent AFL training algorithms, and if yes, under what conditions and how fast the achievable convergence speed is. Toward this end, we propose two Anarchic Federated Averaging (AFA) algorithms with two-sided learning rates for both cross-device and cross-silo settings, which are named AFA-CD and AFA-CS, respectively. Somewhat surprisingly, we show that, under mild anarchic assumptions, both AFL algorithms achieve the best known convergence rate as the state-of-the-art algorithms for conventional FL. Moreover, they retain the highly desirable {\em linear speedup effect} with respect of both the number of workers and local steps in the new AFL paradigm. We validate the proposed algorithms with extensive experiments on real-world datasets.
The Data Science for Pavement Challenge (DSPC) seeks to accelerate the research and development of automated vision systems for pavement condition monitoring and evaluation by providing a platform with benchmarked datasets and codes for teams to innovate and develop machine learning algorithms that are practice-ready for use by industry. The first edition of the competition attracted 22 teams from 8 countries. Participants were required to automatically detect and classify different types of pavement distresses present in images captured from multiple sources, and under different conditions. The competition was data-centric: teams were tasked to increase the accuracy of a predefined model architecture by utilizing various data modification methods such as cleaning, labeling and augmentation. A real-time, online evaluation system was developed to rank teams based on the F1 score. Leaderboard results showed the promise and challenges of machine for advancing automation in pavement monitoring and evaluation. This paper summarizes the solutions from the top 5 teams. These teams proposed innovations in the areas of data cleaning, annotation, augmentation, and detection parameter tuning. The F1 score for the top-ranked team was approximately 0.9. The paper concludes with a review of different experiments that worked well for the current challenge and those that did not yield any significant improvement in model accuracy.
Programming languages like P4 enable specifying the behavior of network data planes in software. However, with increasingly powerful and complex applications running in the network, the risk of faults also increases. Hence, there is growing recognition of the need for methods and tools to statically verify the correctness of P4 code, especially as the language lacks basic safety guarantees. Type systems are a lightweight and compositional way to establish program properties, but there is a significant gap between the kinds of properties that can be proved using simple type systems (e.g., SafeP4) and those that can be obtained using full-blown verification tools (e.g., p4v). In this paper, we close this gap by developing $\Pi$4, a dependently-typed version of P4 based on decidable refinements. We motivate the design of $\Pi$4, prove the soundness of its type system, develop an SMT-based implementation, and present case studies that illustrate its applicability to a variety of data plane programs.
In machine learning, we traditionally evaluate the performance of a single model, averaged over a collection of test inputs. In this work, we propose a new approach: we measure the performance of a collection of models when evaluated on a $\textit{single input point}$. Specifically, we study a point's $\textit{profile}$: the relationship between models' average performance on the test distribution and their pointwise performance on this individual point. We find that profiles can yield new insights into the structure of both models and data -- in and out-of-distribution. For example, we empirically show that real data distributions consist of points with qualitatively different profiles. On one hand, there are "compatible" points with strong correlation between the pointwise and average performance. On the other hand, there are points with weak and even $\textit{negative}$ correlation: cases where improving overall model accuracy actually $\textit{hurts}$ performance on these inputs. We prove that these experimental observations are inconsistent with the predictions of several simplified models of learning proposed in prior work. As an application, we use profiles to construct a dataset we call CIFAR-10-NEG: a subset of CINIC-10 such that for standard models, accuracy on CIFAR-10-NEG is $\textit{negatively correlated}$ with accuracy on CIFAR-10 test. This illustrates, for the first time, an OOD dataset that completely inverts "accuracy-on-the-line" (Miller, Taori, Raghunathan, Sagawa, Koh, Shankar, Liang, Carmon, and Schmidt 2021)
We study the survival bandit problem, a variant of the multi-armed bandit problem introduced in an open problem by Perotto et al. (2019), with a constraint on the cumulative reward; at each time step, the agent receives a (possibly negative) reward and if the cumulative reward becomes lower than a prespecified threshold, the procedure stops, and this phenomenon is called ruin. This is the first paper studying a framework where the ruin might occur but not always. We first discuss that a sublinear regret is unachievable under a naive definition of the regret. Next, we provide tight lower bounds on the probability of ruin (as well as matching policies). Based on this lower bound, we define the survival regret as an objective to minimize and provide a policy achieving a sublinear survival regret (at least in the case of integral rewards) when the time horizon $T$ is known.
Background: Mental health problems are prevalent in college students. The COVID-19 pandemic exacerbated the problems, and created a surge in the popularity of telehealth and mobile health solutions. Despite that mobile health is a promising approach to help students with mental health needs, few studies exist in investigating key features students need in a mental health self-management tool. Objective: The objective of our study was to identified key requirements and features for the design of a student-centered mental health self-management tool. Methods: An interview study was first conducted to understand college students' needs and preferences on a mental health self-management tool. Functional information requirement analysis was then conducted to translate the needs into design implications. Results: A total of 153 university students were recruited for the semi-structured interview. The participants mentioned several features including coping techniques, artificial intelligence, time management, tracking, and communication with others. Participant's preferences on usability and privacy settings were also collected. The desired functions were analyzed and turned into design-agnostic information requirements. Conclusions: This study documents findings from interviews with university students to understand their needs and preferences for a tool to help with self-management of mental health.
Plagiarism in introductory programming courses is an enormous challenge for both students and institutions. For students, relying on the work of others too early in their academic development can make it impossible to acquire necessary skills for independent success in the future. For institutions, widespread student cheating can dilute the quality of the educational experience being offered. Currently available solutions consider only pairwise comparisons between student submissions and focus on punitive deterrence. Our approach instead relies on a class-wide statistical characterization that can be clearly and securely shared with students via an intuitive new p-value representing independence of student effort. A pairwise, compression-based similarity detection algorithm captures relationships between assignments more accurately. An automated deterrence system is used to warn students that their behavior is being closely monitored. High-confidence instances are made directly available for instructor review using our open-source toolkit. An unbiased scoring system aids students and the instructor in understanding true independence of effort. Preliminary results indicate that the system can provide meaningful measurements of independence from week one, improving the efficacy of technical education.
The COVID-19 pandemic has profoundly impacted the world, having taken the lives of over 6 million individuals. Accordingly, this pandemic has caused a shift in conversations surrounding the burden of diseases worldwide, welcoming insights from multidisciplinary fields including digital health and artificial intelligence. Africa faces a heavy disease burden that exacerbates the current COVID-19 pandemic and limits the scope of public health preparedness, response, containment, and case management. Herein, we examined the potential impact of transformative digital health technologies in mitigating the global health crisis with reference to African countries. Furthermore, we proposed recommendations for scaling up digital health technologies and artificial intelligence-based platforms to tackle the transmission of the SARS-CoV-2 and enable equitable vaccine access. Challenges related to the pandemic are numerous. Rapid response and management strategies - that is, contract tracing, case surveillance, diagnostic testing intensity, and most recently vaccine distribution mapping - can overwhelm the health care delivery system that is fragile. Although challenges are vast, digital health technologies can play an essential role in achieving sustainable resilient recovery and building back better. It is plausible that African nations are better equipped to rapidly identify, diagnose, and manage infected individuals for COVID-19, other diseases, future outbreaks, and pandemics.