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Tensors and compositionality in neural systems.

ABSTRACT: Neither neurobiological nor process models of meaning composition specify the operator through which constituent parts are bound together into compositional structures. In this paper, we argue that a neurophysiological computation system cannot achieve the compositionality exhibited in human thought and language if it were to rely on a multiplicative operator to perform binding, as the tensor product (TP)-based systems that have been widely adopted in cognitive science, neuroscience and artificial intelligence do. We show via simulation and two behavioural experiments that TPs violate variable-value independence, but human behaviour does not. Specifically, TPs fail to capture that in the statements fuzzy cactus and fuzzy penguin, both cactus and penguin are predicated by fuzzy(x) and belong to the set of fuzzy things, rendering these arguments similar to each other. Consistent with that thesis, people judged arguments that shared the same role to be similar, even when those arguments themselves (e.g., cacti and penguins) were judged to be dissimilar when in isolation. By contrast, the similarity of the TPs representing fuzzy(cactus) and fuzzy(penguin) was determined by the similarity of the arguments, which in this case approaches zero. Based on these results, we argue that neural systems that use TPs for binding cannot approximate how the human mind and brain represent compositional information during processing. We describe a contrasting binding mechanism that any physiological or artificial neural system could use to maintain independence between a role and its argument, a prerequisite for compositionality and, thus, for instantiating the expressive power of human thought and language in a neural system. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.

SUBMITTER: Martin AE

PROVIDER: S-EPMC6939350 | biostudies-literature | 2020 Feb

REPOSITORIES: biostudies-literature

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Tensors and compositionality in neural systems.

Martin Andrea E AE Doumas Leonidas A A LAA

Philosophical transactions of the Royal Society of London. Series B, Biological sciences 20191216 1791

Neither neurobiological nor process models of meaning composition specify the operator through which constituent parts are bound together into compositional structures. In this paper, we argue that a neurophysiological computation system cannot achieve the compositionality exhibited in human thought and language if it were to rely on a multiplicative operator to perform binding, as the tensor product (TP)-based systems that have been widely adopted in cognitive science, neuroscience and artifici ...[more]

PMID: 31840579

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Project description:Emotions are signaled by complex arrays of face and body actions. The main point of contention in contemporary treatments is whether these arrays are discrete, holistic constellations reflecting emotion categories, or whether they are compositional-comprised of smaller components, each of which contributes some aspect of emotion to the complex whole. We address this question by investigating spontaneous face and body displays of athletes and place it in the wider context of human communicative signals and, in particular, of language. A defining property of human language is compositionality-the ability to combine and recombine a relatively small number of elements to create a vast number of complex meaningful expressions, and to interpret them. We ask whether this property of language can be discerned in a more ancient communicative system: intense emotional displays. In an experiment, participants interpreted a range of emotions and their strengths in pictures of athletes who had just won or lost a competition. By matching participants' judgements with minutely coded features of face and body, we find evidence for compositionality. The distribution of participants' responses indicates that most of the athletes' face and body features contribute to displays of dominance or submission. More particular emotional components related, for example, to positive valence (e.g. happy) or goal obstruction (e.g. frustrated), were also found to significantly correlate with certain face and body features. We propose that the combination of features linked to broader components (i.e, dominant or submissive) and to more particular emotions (e.g, happy or frustrated) reflects more complex emotional states. In sum, we find that the corporeal expression of intense, unfiltered emotion has compositional properties, potentially providing an ancient scaffolding upon which, millions of years later, the abstract and constrained compositional system of human language could build.

Project description:Compositionality refers to a structural property of human language, according to which the meaning of a complex expression is a function of the meaning of its parts and the way they are combined. Compositionality is a defining characteristic of all human language, spoken and signed. Comparative research into the emergence of human language aims at identifying precursors to such key features of human language in the communication of other primates. While it is known that chimpanzees, our closest relatives, produce a variety of gestures, facial expressions and vocalizations in interactions with their group members, little is known about how these signals combine simultaneously. Therefore, the aim of the current study is to investigate whether there is evidence for compositional structures in the communication of chimpanzees. We investigated two semi-wild groups of chimpanzees, with focus on their manual gestures and their combinations with facial expressions across different social contexts. If there are compositional structures in chimpanzee communication, adding a facial expression to a gesture should convey a different message than the gesture alone, a difference that we expect to be measurable by the recipient's response. Furthermore, we expect context-dependent usage of these combinations. Based on a form-based coding procedure of the collected video footage, we identified two frequently used manual gestures (stretched arm gesture and bent arm gesture) and two facial expression (bared teeth face and funneled lip face). We analyzed whether the recipients' response varied depending on the signaler's usage of a given gesture + face combination and the context in which these were used. Overall, our results suggest that, in positive contexts, such as play or grooming, specific combinations had an impact on the likelihood of the occurrence of particular responses. Specifically, adding a bared teeth face to a gesture either increased the likelihood of affiliative behavior (for stretched arm gesture) or eliminated the bias toward an affiliative response (for bent arm gesture). We show for the first time that the components under study are recombinable, and that different combinations elicit different responses, a property that we refer to as componentiality. Yet our data do not suggest that the components have consistent meanings in each combination-a defining property of compositionality. We propose that the componentiality exhibited in this study represents a necessary stepping stone toward a fully evolved compositional system.

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Tensors and compositionality in neural systems.

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Tensors and compositionality in neural systems.

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