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Stabbing Planes (also known as Branch and Cut) is a proof system introduced very recently which, informally speaking, extends the DPLL method by branching on integer linear inequalities instead of single variables. The techniques known so far to prove size and depth lower bounds for Stabbing Planes are generalizations of those used for the Cutting Planes proof system. For size lower bounds these are established by monotone circuit arguments, while for depth these are found via communication complexity and protection. As such these bounds apply for lifted versions of combinatorial statements. Rank lower bounds for Cutting Planes are also obtained by geometric arguments called protection lemmas. In this work we introduce two new geometric approaches to prove size/depth lower bounds in Stabbing Planes working for any formula: (1) the antichain method, relying on Sperner's Theorem and (2) the covering method which uses results on essential coverings of the boolean cube by linear polynomials, which in turn relies on Alon's combinatorial Nullenstellensatz. We demonstrate their use on classes of combinatorial principles such as the Pigeonhole principle, the Tseitin contradictions and the Linear Ordering Principle. By the first method we prove almost linear size lower bounds and optimal logarithmic depth lower bounds for the Pigeonhole principle and analogous lower bounds for the Tseitin contradictions over the complete graph and for the Linear Ordering Principle. By the covering method we obtain a superlinear size lower bound and a logarithmic depth lower bound for Stabbing Planes proof of Tseitin contradictions over a grid graph.

Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the present work, we consider unitary rational approximations to the exponential function on the imaginary axis, which map the imaginary axis to the unit circle. In the class of unitary rational functions, best approximations are shown to exist, to be uniquely characterized by equioscillation of a phase error, and to possess a super-linear convergence rate. Furthermore, the best approximations have full degree (i.e., non-degenerate), achieve their maximum approximation error at points of equioscillation, and interpolate at intermediate points. Asymptotic properties of poles, interpolation nodes, and equioscillation points of these approximants are studied. Three algorithms, which are found very effective to compute unitary rational approximations including candidates for best approximations, are sketched briefly. Some consequences to numerical time-integration are discussed. In particular, time propagators based on unitary best approximants are unitary, symmetric and A-stable.

Objective: To improve survival analysis using EHR data, we aim to develop a supervised topic model called MixEHR-SurG to simultaneously integrate heterogeneous EHR data and model survival hazard. Materials and Methods: Our technical contributions are three-folds: (1) integrating EHR topic inference with Cox proportional hazards likelihood; (2) inferring patient-specific topic hyperparameters using the PheCode concepts such that each topic can be identified with exactly one PheCode-associated phenotype; (3) multi-modal survival topic inference. This leads to a highly interpretable survival and guided topic model that can infer PheCode-specific phenotype topics associated with patient mortality. We evaluated MixEHR-G using a simulated dataset and two real-world EHR datasets: the Quebec Congenital Heart Disease (CHD) data consisting of 8,211 subjects with 75,187 outpatient claim data of 1,767 unique ICD codes; the MIMIC-III consisting of 1,458 subjects with multi-modal EHR records. Results: Compared to the baselines, MixEHR-G achieved a superior dynamic AUROC for mortality prediction, with a mean AUROC score of 0.89 in the simulation dataset and a mean AUROC of 0.645 on the CHD dataset. Qualitatively, MixEHR-G associates severe cardiac conditions with high mortality risk among the CHD patients after the first heart failure hospitalization and critical brain injuries with increased mortality among the MIMIC-III patients after their ICU discharge. Conclusion: The integration of the Cox proportional hazards model and EHR topic inference in MixEHR-SurG led to not only competitive mortality prediction but also meaningful phenotype topics for systematic survival analysis. The software is available at GitHub: //github.com/li-lab-mcgill/MixEHR-SurG.

Traffic accidents, being a significant contributor to both human casualties and property damage, have long been a focal point of research for many scholars in the field of traffic safety. However, previous studies, whether focusing on static environmental assessments or dynamic driving analyses, as well as pre-accident predictions or post-accident rule analyses, have typically been conducted in isolation. There has been a lack of an effective framework for developing a comprehensive understanding and application of traffic safety. To address this gap, this paper introduces AccidentGPT, a comprehensive accident analysis and prevention multi-modal large model. AccidentGPT establishes a multi-modal information interaction framework grounded in multi-sensor perception, thereby enabling a holistic approach to accident analysis and prevention in the field of traffic safety. Specifically, our capabilities can be categorized as follows: for autonomous driving vehicles, we provide comprehensive environmental perception and understanding to control the vehicle and avoid collisions. For human-driven vehicles, we offer proactive long-range safety warnings and blind-spot alerts while also providing safety driving recommendations and behavioral norms through human-machine dialogue and interaction. Additionally, for traffic police and management agencies, our framework supports intelligent and real-time analysis of traffic safety, encompassing pedestrian, vehicles, roads, and the environment through collaborative perception from multiple vehicles and road testing devices. The system is also capable of providing a thorough analysis of accident causes and liability after vehicle collisions. Our framework stands as the first large model to integrate comprehensive scene understanding into traffic safety studies.

In this work, we study the problem of stability of Graph Convolutional Neural Networks (GCNs) under random small perturbations in the underlying graph topology, i.e. under a limited number of insertions or deletions of edges. We derive a novel bound on the expected difference between the outputs of unperturbed and perturbed GCNs. The proposed bound explicitly depends on the magnitude of the perturbation of the eigenpairs of the Laplacian matrix, and the perturbation explicitly depends on which edges are inserted or deleted. Then, we provide a quantitative characterization of the effect of perturbing specific edges on the stability of the network. We leverage tools from small perturbation analysis to express the bounds in closed, albeit approximate, form, in order to enhance interpretability of the results, without the need to compute any perturbed shift operator. Finally, we numerically evaluate the effectiveness of the proposed bound.

There exists a growing discourse around the domination of Big Tech on the landscape of artificial intelligence (AI) research, yet our comprehension of this phenomenon remains cursory. This paper aims to broaden and deepen our understanding of Big Tech's reach and power within AI research. It highlights the dominance not merely in terms of sheer publication volume but rather in the propagation of new ideas or \textit{memes}. Current studies often oversimplify the concept of influence to the share of affiliations in academic papers, typically sourced from limited databases such as arXiv or specific academic conferences. The main goal of this paper is to unravel the specific nuances of such influence, determining which AI ideas are predominantly driven by Big Tech entities. By employing network and memetic analysis on AI-oriented paper abstracts and their citation network, we are able to grasp a deeper insight into this phenomenon. By utilizing two databases: OpenAlex and S2ORC, we are able to perform such analysis on a much bigger scale than previous attempts. Our findings suggest, that while Big Tech-affiliated papers are disproportionately more cited in some areas, the most cited papers are those affiliated with both Big Tech and Academia. Focusing on the most contagious memes, their attribution to specific affiliation groups (Big Tech, Academia, mixed affiliation) seems to be equally distributed between those three groups. This suggests that the notion of Big Tech domination over AI research is oversimplified in the discourse. Ultimately, this more nuanced understanding of Big Tech's and Academia's influence could inform a more symbiotic alliance between these stakeholders which would better serve the dual goals of societal welfare and the scientific integrity of AI research.

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning. An exponential family can either be normalized subtractively by its cumulant function or equivalently normalized divisively by its partition function. Both subtractive and divisive normalizers are strictly convex and smooth functions inducing pairs of Bregman and Jensen divergences. It is well-known that skewed Bhattacharryya distances between probability densities of an exponential family amounts to skewed Jensen divergences induced by the cumulant function between their corresponding natural parameters, and in limit cases that the sided Kullback-Leibler divergences amount to reverse-sided Bregman divergences. In this note, we first show that the $\alpha$-divergences between unnormalized densities of an exponential family amounts scaled $\alpha$-skewed Jensen divergences induced by the partition function. We then show how comparative convexity with respect to a pair of quasi-arithmetic means allows to deform convex functions and define dually flat spaces with corresponding divergences when ordinary convexity is preserved.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language

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.