Abstract
Normative models of neural computation offer simplified yet lucid mathematical descriptions of murky biological phenomena. Previously, online Principal Component Analysis (PCA) was used to model a network of single-compartment neurons accounting for weighted summation of upstream neural activity in the soma and Hebbian/anti-Hebbian synaptic learning rules. However, synaptic plasticity in biological neurons often depends on the integration of synaptic currents over a dendritic compartment rather than total current in the soma. Motivated by this observation, we model a pyramidal neuronal network using online Canonical Correlation Analysis (CCA). Given two related datasets represented by distal and proximal dendritic inputs, CCA projects them onto the subspace which maximizes the correlation between their projections. First, adopting a normative approach and starting from a single-channel CCA objective function, we derive an online gradient-based optimization algorithm whose steps can be interpreted as the operation of a pyramidal neuron. To model networks of pyramidal neurons, we introduce a novel multi-channel CCA objective function, and derive from it an online gradient-based optimization algorithm whose steps can be interpreted as the operation of a pyramidal neuron network including its architecture, dynamics, and synaptic learning rules. Next, we model a neuron with more than two dendritic compartments by deriving its operation from a known objective function for multi-view CCA. Finally, we confirm the functionality of our networks via numerical simulations. Overall, our work presents a simplified but informative abstraction of learning in a pyramidal neuron network, and demonstrates how such networks can integrate multiple sources of inputs.
Highlights
As neural networks evolved for competitive behaviorally-relevant tasks, it is natural to model them using a normative approach, where one starts from a principled objective function and derives an online optimization algorithm that models an operation of a neural system
To model networks of pyramidal neurons, we introduce a novel multi-channel Canonical Correlation Analysis (CCA) objective function, and derive from it an online gradient-based optimization algorithm whose steps can be interpreted as the operation of a pyramidal neuron network including its architecture, dynamics, and synaptic learning rules
In addition to the phenomena explained by the Oja model, the extension (Pehlevan et al, 2015) accounted for the anti-Hebbian learning rules of the lateral synaptic connections
Summary
As neural networks evolved for competitive behaviorally-relevant tasks, it is natural to model them using a normative approach, where one starts from a principled objective function and derives an online optimization algorithm that models an operation of a neural system. In addition to the phenomena explained by the Oja model, the extension (Pehlevan et al, 2015) accounted for the anti-Hebbian learning rules of the lateral synaptic connections (synaptic weight is proportional to the negative of the correlation between pre- and post-synaptic activity) Because of their analytical tractability, the output of such network models can be predicted for any input. We propose to model information processing in pyramidal neurons as online CCA algorithms (Hotelling, 1992; Yang et al, 2019) Because we derive these models from principled objective functions, we can predict the output of the network for any input analytically.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
