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Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representation of Stone relation algebras and for Stone relation algebras to be relation algebras.

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Selinger gave a superoperator model of a first-order quantum programming language and proved that it is fully definable and hence fully abstract. This paper proposes an extension of the superoperator model to higher-order programs based on modules over superoperators or, equivalently, enriched presheaves over the category of superoperators. The enriched presheaf category can be easily proved to be a model of intuitionistic linear logic with cofree exponential, from which one can cave out a model of classical linear logic by a kind of bi-orthogonality construction. Although the structures of an enriched presheaf category are usually rather complex, a morphism in the classical model can be expressed simply as a matrix of completely positive maps. The model inherits many desirable properties from the superoperator model. A conceptually interesting property is that our model has only a state whose "total probability" is bounded by 1, i.e. does not have a state where true and false each occur with probability 2/3. Another convenient property inherited from the superoperator model is a $\omega$CPO-enrichment. Remarkably, our model has a sufficient structure to interpret arbitrary recursive types by the standard domain theoretic technique. We introduce Quantum FPC, a quantum $\lambda$-calculus with recursive types, and prove that our model is a fully abstract model of Quantum FPC.

We show, using three empirical applications, that linear regression estimates which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that don't impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. The tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust results at little efficiency cost.

We proposed an extension of Akaike's relative power contribution that could be applied to data with correlations between noises. This method decomposes the power spectrum into a contribution of the terms caused by correlation between two noises, in addition to the contributions of the independent noises. Numerical examples confirm that some of the correlated noise has the effect of reducing the power spectrum.

The vision of AI collaborators has long been a staple of stories and science fiction, where artificial agents understand nuances of collaboration and human communication. They assist their human partners and teams and have special talents. Government advisory groups and leaders in AI have advocated for years that AIs should be human compatible and effective collaborators. Nonetheless, robust AIs that collaborate like talented people remain out of reach. The simpler dream of effective information tools that augment human intelligence (IA) has its roots in the 1960s and helped to drive an information technology revolution. With the vast increase in hybrid and remote work since the COVID pandemic, the benefits and requirements for better coordination, collaboration, and communication are in focus for the workplace. Many factors (such as the costs of homes near work) are impeding a mass return to in-person work at the office. Are human-like AI teammates part of a solution? If we just need better tools for collaboration, how artificially intelligent (AI) could and should these tools be? This position paper reviews the arc of technology and calls by others for human-machine teaming. It draws on earlier research in psychology and the social sciences about what human-like collaboration actually requires. This paper argues that current mainstream AI cannot produce robust, intelligent, and human-compatible collaborators. It sets a context for a second paper that proposes exploring a radical shift in technology and methodology for creating resilient, intelligent, and human-compatible AIs (Stefik & Price, 2023). The aspirational goal is that such AIs would learn, share what they learn, and collaborate to achieve high standards.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality; however, little is known concretely about the expected behavior or convergence of Bayesian local optimization routines. We first study the behavior of the local approach, and find that the statistics of individual local solutions of Gaussian process sample paths are surprisingly good compared to what we would expect to recover from global methods. We then present the first rigorous analysis of such a Bayesian local optimization algorithm recently proposed by M\"uller et al. (2021), and derive convergence rates in both the noisy and noiseless settings.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.

Rishi Bommasani,Drew A. Hudson,Ehsan Adeli,Russ Altman,Simran Arora,Sydney von Arx,Michael S. Bernstein,Jeannette Bohg,Antoine Bosselut,Emma Brunskill,Erik Brynjolfsson,Shyamal Buch,Dallas Card,Rodrigo Castellon,Niladri Chatterji,Annie Chen,Kathleen Creel,Jared Quincy Davis,Dora Demszky,Chris Donahue,Moussa Doumbouya,Esin Durmus,Stefano Ermon,John Etchemendy,Kawin Ethayarajh,Li Fei-Fei,Chelsea Finn,Trevor Gale,Lauren Gillespie,Karan Goel,Noah Goodman,Shelby Grossman,Neel Guha,Tatsunori Hashimoto,Peter Henderson,John Hewitt,Daniel E. Ho,Jenny Hong,Kyle Hsu,Jing Huang,Thomas Icard,Saahil Jain,Dan Jurafsky,Pratyusha Kalluri,Siddharth Karamcheti,Geoff Keeling,Fereshte Khani,Omar Khattab,Pang Wei Kohd,Mark Krass,Ranjay Krishna,Rohith Kuditipudi,Ananya Kumar,Faisal Ladhak,Mina Lee,Tony Lee,Jure Leskovec,Isabelle Levent,Xiang Lisa Li,Xuechen Li,Tengyu Ma,Ali Malik,Christopher D. Manning,Suvir Mirchandani,Eric Mitchell,Zanele Munyikwa,Suraj Nair,Avanika Narayan,Deepak Narayanan,Ben Newman,Allen Nie,Juan Carlos Niebles,Hamed Nilforoshan,Julian Nyarko,Giray Ogut,Laurel Orr,Isabel Papadimitriou,Joon Sung Park,Chris Piech,Eva Portelance,Christopher Potts,Aditi Raghunathan,Rob Reich,Hongyu Ren,Frieda Rong,Yusuf Roohani,Camilo Ruiz,Jack Ryan,Christopher Ré,Dorsa Sadigh,Shiori Sagawa,Keshav Santhanam,Andy Shih,Krishnan Srinivasan,Alex Tamkin,Rohan Taori,Armin W. Thomas,Florian Tramèr,Rose E. Wang,William Wang,Bohan Wu,Jiajun Wu,Yuhuai Wu,Sang Michael Xie,Michihiro Yasunaga,Jiaxuan You,Matei Zaharia,Michael Zhang,Tianyi Zhang,Xikun Zhang,Yuhui Zhang,Lucia Zheng,Kaitlyn Zhou,Percy Liang
Rishi Bommasani,Drew A. Hudson,Ehsan Adeli,Russ Altman,Simran Arora,Sydney von Arx,Michael S. Bernstein,Jeannette Bohg,Antoine Bosselut,Emma Brunskill,Erik Brynjolfsson,Shyamal Buch,Dallas Card,Rodrigo Castellon,Niladri Chatterji,Annie Chen,Kathleen Creel,Jared Quincy Davis,Dora Demszky,Chris Donahue,Moussa Doumbouya,Esin Durmus,Stefano Ermon,John Etchemendy,Kawin Ethayarajh,Li Fei-Fei,Chelsea Finn,Trevor Gale,Lauren Gillespie,Karan Goel,Noah Goodman,Shelby Grossman,Neel Guha,Tatsunori Hashimoto,Peter Henderson,John Hewitt,Daniel E. Ho,Jenny Hong,Kyle Hsu,Jing Huang,Thomas Icard,Saahil Jain,Dan Jurafsky,Pratyusha Kalluri,Siddharth Karamcheti,Geoff Keeling,Fereshte Khani,Omar Khattab,Pang Wei Kohd,Mark Krass,Ranjay Krishna,Rohith Kuditipudi,Ananya Kumar,Faisal Ladhak,Mina Lee,Tony Lee,Jure Leskovec,Isabelle Levent,Xiang Lisa Li,Xuechen Li,Tengyu Ma,Ali Malik,Christopher D. Manning,Suvir Mirchandani,Eric Mitchell,Zanele Munyikwa,Suraj Nair,Avanika Narayan,Deepak Narayanan,Ben Newman,Allen Nie,Juan Carlos Niebles,Hamed Nilforoshan,Julian Nyarko,Giray Ogut,Laurel Orr,Isabel Papadimitriou,Joon Sung Park,Chris Piech,Eva Portelance,Christopher Potts,Aditi Raghunathan,Rob Reich,Hongyu Ren,Frieda Rong,Yusuf Roohani,Camilo Ruiz,Jack Ryan,Christopher Ré,Dorsa Sadigh,Shiori Sagawa,Keshav Santhanam,Andy Shih,Krishnan Srinivasan,Alex Tamkin,Rohan Taori,Armin W. Thomas,Florian Tramèr,Rose E. Wang,William Wang,Bohan Wu,Jiajun Wu,Yuhuai Wu,Sang Michael Xie,Michihiro Yasunaga,Jiaxuan You,Matei Zaharia,Michael Zhang,Tianyi Zhang,Xikun Zhang,Yuhui Zhang,Lucia Zheng,Kaitlyn Zhou,Percy Liang

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

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