How we learn things we don’t know already: A theory of learning structured representations from experience

Abstract

How a system represents information tightly constrains the kinds of problems it can solve.Humans routinely solve problems that appear to require structured representations of stimulus properties and relations. Answering the question of how we acquire these representations has central importance in an account of human cognition. We propose a theory of how a system can learn invariant responses to instances of similarity and relative magnitude, and how structured relational representations can be learned from initially unstructured inputs. We instantiate that theory in the DORA (Discovery of Relations by Analogy) computational framework. The result is a system that learns structured representations of relations from unstructured flat feature vector representations of objects with absolute properties. The resulting representations meet the requirements of human structured relational representations, and the model captures several specific phenomena from the literature on cognitive development. In doing so, we address a major limitation of current accounts of cognition, and provide an existence proof for how structured representations might be learned from experience. KEYWORDS: relation learning, predicate learning, neural networks, similarity, relative magnitude, invariance, learning structured representations . CC-BY-NC-ND 4.0 International license not peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was . http://dx.doi.org/10.1101/198804 doi: bioRxiv preprint first posted online Oct. 18, 2017; Learning structured representations 3 To reason relationally is to reason about objects based on the relations that those objects play, rather than based on the literal features of those objects (see, e.g., Holyoak, 2012;Holyoak & Thagard, 1995). For example, when we make an analogy between the nucleus of an atom and the sun, we do so based on a common relation-e.g., that both nuclei and suns are larger than their orbiting bodies (planets and electrons respectively)-despite the fact that nuclei and suns are otherwise not particularly similar. Humans routinely draw inferences based on relations, from the mundane ("my kid won't eat a portion that big"), to the sublime ("the cardinal number of the reals between 0-1 is larger than the cardinal number of the positive integers"), and relational reasoning has been shown to importantly contribute to abilities such as analogy (e.g., Holyoak & Thagard, 1995), categorisation (e.g., Medin, Goldstone, & Gentner, 1993), concept learning (e.g., Doumas & Hummel, 2004, 2013, and visual cognition (e.g., Biederman, 1987, Hummel, 2013. In fact, the capacity to represent and reason about relations has been posited as the key difference in human and non-human animal cognition (Penn, Holyoak, & Povinelli, 2008).Perhaps the most plausible explanation of how humans are able to reason relationally is that we can represent relations as abstract structures that take arguments-i.e., as predicates (see, e.g., Holyoak, 2012;Holyoak ...

A compositional neural architecture for language

“…Note that embedding probabilistic activation functions within an analysis-bysynthesis model does not mean that abstract symbolic representations of language are no longer necessary -in fact, such an account claims that symbols are the perceptual targets to be inferred during comprehension, and are what is 'counted' or induced during statistical learning and during language acquisition (cf. Doumas, Puebla, & Martin, 2017;Doumas & Martin, 2018;Holland, Holyoak, Nisbett, & Thagard, 1986;Martin, 2016;, 2019a, 2019b. Perceptual inference asserts that sensory cues activate latent representations in the neural system that have been learned through experience 4 .…”

“…of inputs that are composed together during processing as needed during multiplexing, and in principle, to produce a theoretically limitless set of combinations of states. As such, in sequences, implicit ordinal and time sensitive relationships matter and carry information, and in fact, can be used to signal the hierarchical relationships that have been compressed into that sequence and which can be reconstructed from that sequence (Doumas et al, 2008;Doumas, Puebla, & Martin, 2017;Doumas & Martin, 2018;, 2019a, 2019b.…”

“…Representations that must be sequenced from a hierarchy, and vice versa, can be composed and decomposed only if activation across layers is desynchronized at some point in time. This fact gives rise to rhythmic computation in the network, where time is used to carry information about the relationships between representations that are present in the input (see Doumas et al, 2008;Doumas & Martin, 2018;Doumas, Puebla, & Martin, 2017;, 2019a. The mechanism of rhythmic computation is based on a principle of cortical organization, that "neurons that fire together, wire together" (Hebb, 1949).…”

“…In contrast, Discovery of Relations by Analogy (DORA; a symbolic-connectionist model of relational reasoning; the full computational specifics can be found in Doumas, Puebla, &Sandhofer, 2008) exploits the synchrony principle, but it does so by using 'both sides' of the distinction (see Figure 2 for a cartoon illustration). In order to keep representations separable while binding them together for processing, the model is sensitive to asynchrony of firing.…”

“…As a result, the model oscillates, with pulses of activation related to activating distributed word codes and a slower pulse of activation that codes the phrase (see . Inhibition and yoked integrative inhibitors are used to turn the word units off as they pass activation to phrase nodes; for a detailed description of the DORA model, including pseudocode, see Doumas et al 2008Doumas et al , 2017Doumas & Martin, 2018;, 2019a In the terminology from Section I, forming a phrase from words (see Phrase-Specified Pseudocode examples in Table 2) draws on an iterative process whereby a path is formed through the neural trajectory manifold; each dimension is claimed to correspond with levels of linguistic representation. Gain modulation controls the progression of transforms through the path, and each timestep brings sensory representations towards latent structure in comprehension, while in production each timestep moves progressively towards articulatory gestures.…”