Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because their probability of error grows exponentially as the argument expands. Here we show that under a cognitively-plausible belief formation mechanism that combines deductive and abductive reasoning, mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with four hand-constructed cases from Euclid, Apollonius, Spinoza, and Andrew Wiles. Our results bear both on recent work in the history and philosophy of mathematics, and on a question, basic to cognitive science, of how we form beliefs, and justify them to others.

Researchers have long been interested in the role that norms can play in governing agent actions in multi-agent systems. Much work has been done on formalising normative concepts from human society and adapting them for the government of open software systems, and on the simulation of normative processes in human and artificial societies. However, there has been comparatively little work on applying normative MAS mechanisms to understanding the norms in human society. This work investigates this issue in the context of international politics. Using the GDELT dataset, containing machine-encoded records of international events extracted from news reports, we extracted bilateral sequences of inter-country events and applied a Bayesian norm mining mechanism to identify norms that best explained the observed behaviour. A statistical evaluation showed that the normative model fitted the data significantly better than a probabilistic discrete event model.

Given a graph rewrite system, a graph G is a quine graph if it has a non-void maximal collection of non-conflicting matches of left patterns of graphs rewrites, such that after the parallel application of the rewrites we obtain a graph isomorphic with G. Such graphs exhibit a metabolism, they can multiply or they can die, when reduced by a random rewriting algorithm. These are introductory notes to the pages of artificial chemistry experiments with chemlambda, lambda calculus or interaction combinators, available from the entry page https://chemlambda.github.io/index.html . The experiments are bundled into pages, all of them based on a library of programs, on a database which contains hundreds of graphs and on a database of about 150 pages of text comments and a collection of more than 200 animations, most of them which can be re-done live, via the programs. There are links to public repositories of other contributors to these experiments, with versions of these programs in python, haskell, awk or javascript.

Roman Urdu is an informal form of the Urdu language written in Roman script, which is widely used in South Asia for online textual content. It lacks standard spelling and hence poses several normalization challenges during automatic language processing. In this article, we present a feature-based clustering framework for the lexical normalization of Roman Urdu corpora, which includes a phonetic algorithm UrduPhone, a string matching component, a feature-based similarity function, and a clustering algorithm Lex-Var. UrduPhone encodes Roman Urdu strings to their pronunciation-based representations. The string matching component handles character-level variations that occur when writing Urdu using Roman script.

Care.Coach, a Silicon Valley healthcare startup, disclosed today details of a rapid expansion of its virtual avatar program for health plans to combat COVID-19's exacerbation of the loneliness epidemic in the United States. The company, founded in 2012 by Massachusetts Institute of Technology (MIT) graduate Victor Wang, develops virtual avatars that provide companionship to individuals who live with complex health conditions and chronic loneliness. A large body of published research demonstrates that the feeling of loneliness increases morbidity and mortality; in a time of social distancing, self-isolation, and quarantine, loneliness has become a clear public health crisis. Care.Coach is rising to the challenge by providing its customers with as many avatars as are needed to support these at-risk populations. For the past 8 years, Care.Coach has been working with care providers to help those populations which possess "outsized risk", focusing on older adults with psychosocial risks such as loneliness, depression, and anxiety, alongside medical risks such as diabetes, hypertension, COPD, heart failure, and medication non-adherence.

One of the long-standing questions in search systems is the role of diversity in results. From a product perspective, showing diverse results provides the user with more choice and should lead to an improved experience. However, this intuition is at odds with common machine learning approaches to ranking which directly optimize the relevance of each individual item without a holistic view of the result set. In this paper, we describe our journey in tackling the problem of diversity for Airbnb search, starting from heuristic based approaches and concluding with a novel deep learning solution that produces an embedding of the entire query context by leveraging Recurrent Neural Networks (RNNs). We hope our lessons learned will prove useful to others and motivate further research in this area.

In this paper we propose a deep recurrent model based on the order flow for the stationary modelling of the high-frequency directional prices movements. The order flow is the microsecond stream of orders arriving at the exchange, driving the formation of prices seen on the price chart of a stock or currency. To test the stationarity of our proposed model we train our model on data before the 2017 Bitcoin bubble period and test our model during and after the bubble. We show that without any retraining, the proposed model is temporally stable even as Bitcoin trading shifts into an extremely volatile "bubble trouble" period. The significance of the result is shown by benchmarking against existing state-of-the-art models in the literature for modelling price formation using deep learning.

Ant Credit Pay is a consumer credit service in Ant Financial Service Group. Similar to credit card, loan default is one of the major risks of this credit product. Hence, effective algorithm for default prediction is the key to losses reduction and profits increment for the company. However, the challenges facing in our scenario are different from those in conventional credit card service. The first one is scalability. The huge volume of users and their behaviors in Ant Financial requires the ability to process industrial-scale data and perform model training efficiently. The second challenges is the cold-start problem. Different from the manual review for credit card application in conventional banks, the credit limit of Ant Credit Pay is automatically offered to users based on the knowledge learned from big data. However, default prediction for new users is suffered from lack of enough credit behaviors. It requires that the proposal should leverage other new data source to alleviate the cold-start problem. Considering the above challenges and the special scenario in Ant Financial, we try to incorporate default prediction with network information to alleviate the cold-start problem. In this paper, we propose an industrial-scale distributed network representation framework, termed NetDP, for default prediction in Ant Credit Pay. The proposal explores network information generated by various interaction between users, and blends unsupervised and supervised network representation in a unified framework for default prediction problem. Moreover, we present a parameter-server-based distributed implement of our proposal to handle the scalability challenge. Experimental results demonstrate the effectiveness of our proposal, especially in cold-start problem, as well as the efficiency for industrial-scale dataset.

Deep generative models reproduce complex empirical data but cannot extrapolate to novel environments. An intuitive idea to promote extrapolation capabilities is to enforce the architecture to have the modular structure of a causal graphical model, where one can intervene on each module independently of the others in the graph. We develop a framework to formalize this intuition, using the principle of Independent Causal Mechanisms, and show how over-parameterization of generative neural networks can hinder extrapolation capabilities. Our experiments on the generation of human faces shows successive layers of a generator architecture implement independent mechanisms to some extent, allowing meaningful extrapolations. Finally, we illustrate that independence of mechanisms may be enforced during training to improve extrapolation.

Boosting is a well-known method for improving the accuracy of weak learners in machine learning. However, its theoretical generalization guarantee is missing in literature. In this paper, we propose an efficient boosting method with theoretical generalization guarantees for binary classification. Three key ingredients of the proposed boosting method are: a) the \textit{fully-corrective greedy} (FCG) update in the boosting procedure, b) a differentiable \textit{squared hinge} (also called \textit{truncated quadratic}) function as the loss function, and c) an efficient alternating direction method of multipliers (ADMM) algorithm for the associated FCG optimization. The used squared hinge loss not only inherits the robustness of the well-known hinge loss for classification with outliers, but also brings some benefits for computational implementation and theoretical justification. Under some sparseness assumption, we derive a fast learning rate of the order ${\cal O}((m/\log m)^{-1/4})$ for the proposed boosting method, which can be further improved to ${\cal O}((m/\log m)^{-1/2})$ if certain additional noise assumption is imposed, where $m$ is the size of sample set. Both derived learning rates are the best ones among the existing generalization results of boosting-type methods for classification. Moreover, an efficient early stopping scheme is provided for the proposed method. A series of toy simulations and real data experiments are conducted to verify the developed theories and demonstrate the effectiveness of the proposed method.