Numerous psychological studies have been carried out and several, often conflicting, models of mentat imagery have been proposed. This paper does not present another computational model, but instead treats imagery as a problem solving paradigm in artificial intelligence. We describe a concept of computational imagery [Papadias & Glasgow, 1991], which has potential applications to problems whose solutions by humans involve the use of mental imagery. As a basis for computational imagery, we define a knowledge representation scheme that brings to the foreground the most important visual and spatial properties of an image. Although psychological theories are used as a guide to these properties, we do not adhere to a strict cognitive model; whenever possible we attempt to overcome the limitations of the human information processing system.

Fuentetaja, Raquel (Universidad Carlos III de Madrid) | Barley, Michael (University of Auckland) | Borrajo, Daniel (Universidad Carlos III de Madrid) | Douglas, Jordan (University of Auckland) | Franco, Santiago (University of Huddersfield) | Riddle, Patricia (University of Auckland)

Two key aspects of problem solving are representation and search heuristics. Both theoretical and experimental studies have shown that there is no one best problem representation nor one best search heuristic. Therefore, some recent methods, e.g., portfolios, learn a good combination of problem solvers to be used in a given domain or set of domains. There are even dynamic portfolios that select a particular combination of problem solvers specific to a problem. These approaches: (1) need to perform a learning step; (2) do not usually focus on changing the representation of the input domain/problem; and (3) frequently do not adapt the portfolio to the specific problem. This paper describes a meta-reasoning system that searches through the space of combinations of representations and heuristics to find one suitable for optimally solving the specific problem. We show that this approach can be better than selecting a combination to use for all problems within a domain and is competitive with state of the art optimal planners.

Abstract: Replacing static word embeddings with contextualized word representations has yielded significant improvements on many NLP tasks. However, just how contextual are the contextualized representations produced by models such as ELMo and BERT? Are there infinitely many context-specific representations for each word, or are words essentially assigned one of a finite number of word-sense representations? For one, we find that the contextualized representations of all words are not isotropic in any layer of the contextualizing model. While representations of the same word in different contexts still have a greater cosine similarity than those of two different words, this self-similarity is much lower in upper layers.

Here we are dealing with the oldest data set, created billions of years ago -- the set of integers -- and mostly the set consisting of two numbers: 0 and 1. All of us have learned how to write numbers even before attending primary school. Yet, it is attached to the most challenging unsolved mathematical problems of all times, such as the distribution of the digits of Pi in the decimal system. The table below reflects this contrast, being a blend of rudimentary and deep results. It is a reference for statisticians, number theorists, data scientists, and computer scientists, with a focus on probabilistic results. You will not find it in any textbook. Some of the systems described here (logistic map of exponent p 1/2, nested square roots, auto-correlations in continued fractions) are research results published here for the first time.