There has been a recent surge of interest in the question of whether and how deep learning algorithms might be capable of abstract reasoning, much of which has centered around datasets based on Raven’s Progressive Matrices (RPM), a visual analogy problem set commonly employed to assess fluid intelligence. This has led to the development of algorithms that are capable of solving RPM-like problems directly from pixel-level inputs. However, these algorithms require extensive direct training on analogy problems, and typically generalize poorly to novel problem types. This is in stark contrast to human reasoners, who are capable of solving RPM and other analogy problems zero-shot — that is, with no direct training on those problems. Indeed, it’s this capacity for zero-shot reasoning about novel problem types, i.e. fluid intelligence, that RPM was originally designed to measure. I will present some results from our recent efforts to model this capacity for zero-shot reasoning, based on an extension of a recently proposed approach to analogical mapping we refer to as Probabilistic Analogical Mapping (PAM). Our RPM model uses deep learning to extract attributed graph representations from pixel-level inputs, and then performs alignment of objects between source and target analogs using gradient descent to optimize a graph-matching objective. This extended version of PAM features a number of new capabilities that underscore the flexibility of the overall approach, including 1) the capacity to discover solutions that emphasize either object similarity or relation similarity, based on the demands of a given problem, 2) the ability to extract a schema representing the overall abstract pattern that characterizes a problem, and 3) the ability to directly infer the answer to a problem, rather than relying on a set of possible answer choices. This work suggests that PAM is a promising framework for modeling human zero-shot reasoning.

Hongjing Lu will present a new computational model of Probabilistic Analogical Mapping (PAM, in collaboration with Nick Ichien and Keith Holyoak) that finds systematic correspondences between inputs generated by machine learning. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts (word embeddings created by Word2vec) and of relations between concepts (created by our BART model). We have used PAM to simulate a broad range of phenomena involving analogical mapping by both adults and children. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations. More details can be found https://arxiv.org/ftp/arxiv/papers/2103/2103.16704.pdf