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Expressive power of tensor-network factorizations for probabilistic modeling

Neural Information Processing Systems

Many problems in diverse areas of computer science and physics involve constructing efficient representations of high-dimensional functions. Neural networks are a particular example of such representations that have enjoyed great empirical success, and much effort has been dedicated to understanding their expressive power - i.e. the set of functions that they can efficiently represent. Analogously, tensor networks are a class of powerful representations of high-dimensional arrays (tensors), for which a variety of algorithms and methods have been developed.



Decoding Communications with Partial Information

arXiv.org Artificial Intelligence

Machine language acquisition is often presented as a problem of imitation learning: there exists a community of language users from which a learner observes speech acts and attempts to decode the mappings between utterances and situations. However, an interesting consideration that is typically unaddressed is partial observability, i.e. the learner is assumed to see all relevant information. This paper explores relaxing this assumption, thereby posing a more challenging setting where such information needs to be inferred from knowledge of the environment, the actions taken, and messages sent. We see several motivating examples of this problem, demonstrate how they can be solved in a toy setting, and formally explore challenges that arise in more general settings. A learning-based algorithm is then presented to perform the decoding of private information to facilitate language acquisition.