Neural bases of variable binding in symbolic representations : experimental and modelling exploration

Abstract : The aim of this thesis is to understand how the brain computes and represents symbolic structures, such like those encountered in language or mathematics. The existence of parts in structures like morphemes, words and phrases has been established through decades of linguistic analysis and psycholinguistic experiments. Nonetheless the neural implementation of the operations that support the extreme combinatorial nature of language remains unsettled. Some basic composition operations that allow the stable internal representation of sensory objects in the sensory cortex, like hierarchical pattern recognition, receptive fields, pooling and normalization, have started to be understood[5]. But models of the binding operations required for construction of complex, possibly hierarchical, symbolic structures on which precise manipulation of its components is a requisite, lack empirical testing and are still unable to predict neuroimaging signals. In this sense, bridging the gap between experimental neuroimaging evidence and the available modelling solutions to the binding problem is a crucial step for the advancement of our understanding of the brain computation and representation of symbolic structures. From the recognition of this problem, the goal of this PhD became the identification and experimental test of the theories, based on neural networks, capable of dealing with symbolic structures, for which we could establish testable predictions against existing fMRI and ECoG neuroimaging measurements derived from language processing tasks. We identified two powerful but very different modelling approaches to the problem. The first is in the context of the tradition of Vectorial Symbolic Architectures (VSA) that bring precise mathematical modelling to the operations required to represent structures in the neural units of artificial neural networks and manipulate them. This is Smolensky’s formalism with tensor product representations (TPR)[10], which he demonstrates can encompass most of the previous work in VSA, like Synchronous Firing[9], Holographic Reduced Representations[8] and Recursive Auto-Associative Memories[1]. The second, is the Neural Blackboard Architecture (NBA) developed by Marc De Kamps and Van der Velde[11], that importantly differentiates itself by proposing an implementation of binding by process in circuits formed by neural assemblies of spiking neural networks. Instead of solving binding by assuming precise and particular algebraic operations on vectors, the NBA proposes the establishment of transient connectivity changes in a circuit structure of neural assemblies, such that the potential _ow of neural activity allowed by working memory mechanisms after a binding process takes place, implicitly represents symbolic structures. The first part of the thesis develops in more detail the theory behind each of these models and their relationship from the common perspective of solving the binding problem. Both models are capable of addressing most of the theoretical challenges posed currently for the neural modelling of symbolic structures, including those presented by Jackendo_[3]. Nonetheless they are very different, Smolenky’s TPR relies mostly on spatial static considerations of artificial neural units with explicit completely distributed and spatially stable representations implemented through vectors, while the NBA relies on temporal dynamic considerations of biologically based spiking neural units with implicit semi-local and spatially unstable representations implemented through neural assemblies. For the second part of the thesis, we identified the superposition principle, which consists on the addition of the neural activations of each of the sub-parts of a symbolic structure, as one of the most crucial assumptions of Smolensky’s TPR. (...)
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Martín Pérez-Guevara. Neural bases of variable binding in symbolic representations : experimental and modelling exploration. Neurons and Cognition [q-bio.NC]. Université Sorbonne Paris Cité, 2017. English. ⟨NNT : 2017USPCB082⟩. ⟨tel-02134664⟩

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