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Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning

arXiv.org Machine Learning

We present a deep learning algorithm for the numerical solution of parametric families of high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is based on reformulating the numerical approximation of a whole family of Kolmogorov PDEs as a single statistical learning problem using the Feynman-Kac formula. Successful numerical experiments are presented, which empirically confirm the functionality and efficiency of our proposed algorithm in the case of heat equations and Black-Scholes option pricing models parametrized by affine-linear coefficient functions. We show that a single deep neural network trained on simulated data is capable of learning the solution functions of an entire family of PDEs on a full space-time region. Most notably, our numerical observations and theoretical results also demonstrate that the proposed method does not suffer from the curse of dimensionality, distinguishing it from almost all standard numerical methods for PDEs.


Lifelong Learning Without a Task Oracle

arXiv.org Artificial Intelligence

Supervised deep neural networks are known to undergo a sharp decline in the accuracy of older tasks when new tasks are learned, termed "catastrophic forgetting". Many state-of-the-art solutions to continual learning rely on biasing and/or partitioning a model to accommodate successive tasks incrementally. However, these methods largely depend on the availability of a task-oracle to confer task identities to each test sample, without which the models are entirely unable to perform. To address this shortcoming, we propose and compare several candidate task-assigning mappers which require very little memory overhead: (1) Incremental unsupervised prototype assignment using either nearest means, Gaussian Mixture Models or fuzzy ART backbones; (2) Supervised incremental prototype assignment with fast fuzzy ARTMAP; (3) Shallow perceptron trained via a dynamic coreset. Our proposed model variants are trained either from pre-trained feature extractors or task-dependent feature embeddings of the main classifier network. We apply these pipeline variants to continual learning benchmarks, comprised of either sequences of several datasets or within one single dataset. Overall, these methods, despite their simplicity and compactness, perform very close to a ground truth oracle, especially in experiments of inter-dataset task assignment. Moreover, best-performing variants only impose an average cost of 1.7% parameter memory increase.


An Analysis of Dataset Overlap on Winograd-Style Tasks

arXiv.org Artificial Intelligence

The Winograd Schema Challenge (WSC) and variants inspired by it have become important benchmarks for common-sense reasoning (CSR). Model performance on the WSC has quickly progressed from chance-level to near-human using neural language models trained on massive corpora. In this paper, we analyze the effects of varying degrees of overlap between these training corpora and the test instances in WSC-style tasks. We find that a large number of test instances overlap considerably with the corpora on which state-of-the-art models are (pre)trained, and that a significant drop in classification accuracy occurs when we evaluate models on instances with minimal overlap. Based on these results, we develop the KnowRef-60K dataset, which consists of over 60k pronoun disambiguation problems scraped from web data. KnowRef-60K is the largest corpus to date for WSC-style common-sense reasoning and exhibits a significantly lower proportion of overlaps with current pretraining corpora.


Project management overview - MODULE 2 - Scoping, Greenlighting, and Managing Machine Learning Initiatives

#artificialintelligence

Machine learning runs the world. It generates predictions for each individual customer, employee, voter, and suspect, and these predictions drive millions of business decisions more effectively, determining whom to call, mail, approve, test, diagnose, warn, investigate, incarcerate, set up on a date, or medicate. But, to make this work, you've got to bridge what is a prevalent gap between business leadership and technical know-how. Launching machine learning is as much a management endeavor as a technical one. Its success relies on a very particular business leadership practice.


Facebook's New AI System Can Pass Multiple-Choice Intelligence Tests

#artificialintelligence

Recently, a team of researchers from Facebook AI and Tel Aviv University proposed an AI system that solves the multiple-choice intelligence test, Raven's Progressive Matrices. The proposed AI system is a neural network model that combines multiple advances in generative models, including employing multiple pathways through the same network. Raven's Progressive Matrices, also known as Raven's Matrices, are multiple-choice intelligence tests. The test is used to measure abstract reasoning and is regarded as a non-verbal estimate of fluid intelligence. In this test, a person tries to finish the missing location in a 3X3 grid of abstract images.


Our children are not prepared for the AI era

#artificialintelligence

If our children are to thrive in the coming AI age, we need to overhaul everything from our primary and secondary schools to how we approach computer science and coding to lifelong learning. We need robust data literacy -- we won't understand the application of AI without understanding data -- and at the moment, very few of us do. Only once individuals can comprehend and parse data (and the issues surrounding it) can they then start applying that knowledge creatively, including in AI. This isn't the naive idea that people should just'learn to code' -- it's that children should be learning how to thrive in a data and technology-driven environment from day one.


Principal Data Analyst

#artificialintelligence

Our mission is to train the world's workforce in the careers of the future. Focused on self-empowerment through learning, Udacity is making innovative technologies such as self-driving cars available to a global community of aspiring technologists, while also enabling learners at all levels to skill up with essentials like programming, web and app development. Udacity is looking for people to join our Data team. If you love a challenge, and truly want to make a difference in the world, read on! At Udacity, the Data Team is deployed to inform and empower the business with insight, to drive growth and value.


BraveIT Session: The Business Applications of AI

#artificialintelligence

AI is useful in human resources, worker training, and professional development. One new AI-powered application, called Avenues, trains social workers through virtual reality scenarios using an Oculus VR headset, natural language processor, and a database of past child welfare cases. The social worker is confronted with various domestic situations and asked to decide on the best course of action, such as remove a child from the house or offer parents different support services. Created by Accenture, the Avenues application takes social workers through an immersive training experience that includes much of ambiguity and stress of real-life situations but allows them to practice making the tough decisions without real-life consequences.


Opinion

#artificialintelligence

Brianna Hill is a recent law school graduate. She knew it would be hard to contest a false report of cheating by proctoring software, the technology increasingly being used to monitor individuals taking tests remotely during the Covid-19 era. So she continued to complete her bar exam despite going into labor during the test this October. She sat still during contractions knowing she might be disqualified if the artificial intelligence couldn't watch her every move. Test-takers can't leave the view of the camera for any reason.


Bounded Risk-Sensitive Markov Game and Its Inverse Reward Learning Problem

arXiv.org Machine Learning

Classical game-theoretic approaches for multi-agent systems in both the forward policy design problem and the inverse reward learning problem often make strong rationality assumptions: agents perfectly maximize expected utilities under uncertainties. Such assumptions, however, substantially mismatch with observed humans' behaviors such as satisficing with sub-optimal, risk-seeking, and loss-aversion decisions. In this paper, we investigate the problem of bounded risk-sensitive Markov Game (BRSMG) and its inverse reward learning problem. {Drawing on iterative reasoning models and cumulative prospect theory, we embrace that humans have bounded intelligence and maximize risk-sensitive utilities in BRSMGs.} Convergence analysis for both the forward policy design and the inverse reward learning problems are established under the BRSMG framework. We also validate the proposed forward policy design and inverse reward learning algorithms in a navigation scenario. The results show that the behaviors of agents demonstrate both risk-averse and risk-seeking characteristics. Moreover, in the inverse reward learning task, the proposed bounded risk-sensitive inverse learning algorithm outperforms a baseline risk-neutral inverse learning algorithm by effectively recovering not only more accurate reward values but also the intelligence levels and the risk-measure parameters given demonstrations of agents' interactive behaviors.