Search Abstracts | Symposia | Slide Sessions | Poster Sessions
A theory of magnitude and number learning
Poster Session D, Thursday, October 1, 4:30 - 6:30 pm, Wangari Maathai
Ryan M.C. Law1, Timothy T. Rogers2,3, Matthew A. Lambon Ralph1; 1MRC Cognition and Brain Sciences Unit, University of Cambridge, UK, 2Department of Psychology, University of Wisconsin-Madison, USA, 3Institute of Cognitive Neuroscience, University College London, UK
A theory of meaning in the brain must explain how content and structure are learned. Understanding “three sheep” requires not only object knowledge, but also numerical knowledge, which generalises across content (three can enumerate objects, events, sounds, etc.). The semantic system learns a semantic representation from experience, supporting inferences (Rogers et al., 2004; Lambon Ralph et al., 2017). But where do structural representations like number or magnitude come from? We propose that structural representations emerge as a latent property of any system under pressure to maintain sequential order, separate from the semantic system. The claim is not that serial memory directly produces numerical concepts. Rather, pressures to encode order may give rise to item-independent structural representations that form the computational precursor to magnitude and numerical representations. A system trained to maintain arbitrary sequences must learn structural regularities that generalise across content. Neuropsychological dissociations support this separation: Semantic dementia patients suffer conceptual knowledge degradation that preserves counting, sequencing, and numerical abilities, while acalculic patients show the reverse. Understanding the computational origins of this separation is an open question with consequences for theories of semantic cognition, number, and their breakdown. We built a dual-stream neural network model that assimilates these ideas formally. Inputs to the model were either sequences of features derived from a concept (e.g., SHEEP: has-wool, has-four-legs, is-herbivore) or random feature sequences. The ventral stream performs pattern completion over conceptual features—inputs are presented with missing components, and the model reconstructs the full representation—implementing the learning pressures associated with semantic memory and the anterior temporal lobe. The dorsal stream performs immediate serial recall, encoding inputs and reproducing them in their original order. This creates pressure to encode item-independent structural relations associated with posterior parietal systems. The model spontaneously develops a representational division of labour, recapitulating patient profiles. The ventral stream acquires rich conceptual structure organised by semantic similarity; the dorsal stream develops representations organised around sequential structure that generalise across items and encode magnitude-like information (sequence length). To test if the ventral-dorsal separation is necessary, we built a single-stream baseline model trained on the same tasks. It performed worse on both, confirming that architectural separation promotes efficient learning of both structure types. Thus, when sequential-ordering demands are architecturally segregated from semantic integration demands, abstract magnitude-like representations emerge. By integrating neuropsychology with formal modelling, this dual-stream framework provides an account of the origins of structural representations like number and magnitude and a principled explanation of clinical dissociations in the syndromes of semantic dementia and acquired acalculia.
Topic Areas: Meaning: Lexical Semantics, Disorders: Acquired