Since the work of Minsky and Papert ( 1969 ), it has been understood that single-layer neural networks cannot solve nonlinearly separable classifications (i.e., XOR). We describe and test a novel divergent autoassociative architecture capable of solving nonlinearly separable classifications with a single layer of weights. The proposed network consists of class-specific linear autoassociators. The power of the model comes from treating classification problems as within-class feature prediction rather than directly optimizing a discriminant function. We show unprecedented learning capabilities for a simple, single-layer network (i.e., solving XOR) and demonstrate that the famous limitation in acquiring nonlinearly separable problems is not just about the need for a hidden layer; it is about the choice between directly predicting classes or learning to classify indirectly by predicting features.

Leading accounts of analogy based on structure mapping theory (Gentner 1983 Gentner, D. 1983. Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7: 155–170. [Crossref], [Web of Science ®] , [Google Scholar], 1989 Gentner, D. 1989. “The mechanisms of analogical learning”. In Similarity and Analogical Reasoning, Edited by: Vosniadou, S and Ortony, A. 199–241. London: Cambridge University Press. [Crossref] , [Google Scholar]) give an important explanatory role to re-representation. Structural alignment is insufficiently flexible to account for human analogical processing if semantically compatible, but non-identically coded, representational elements are not permitted to match. A process of re-representation can selectively allow non-identical representational elements to be considered matches and placed in structural correspondence during comparison. However, re-representation is only a posited theoretical construct with minimal supporting evidence. An experimental paradigm called inference probing is introduced which offers a new level of empirical support for the psychological reality of re-representation. Behavioural results are presented that bear on accounts of analogy, similarity, knowledge representation and reasoning.

It is well known that the human visual system can reconstruct depth from simple random-dot displays given binocular disparity or motion information. This fact has lent support to the notion that stereo and structure from motion systems rely on low-level primitives derived from image intensities. In contrast, the judgment of surface transparency is often considered to be a higher-level visual process that, in addition to pictorial cues, utilizes stereo and motion information to separate the transparent from the opaque parts. We describe a new illusion and present psychophysical results that question this sequential view by showing that depth from transparency and opacity can override the bias to see rigid motion. The brain's computation of transparency may involve a two-way interaction with the computation of structure from motion.