[Paper Review] A probabilistic model for learning in cortical microcircuit motifs with data-based divisive inhibition

Robert Legenstein, Zeno Jonke+2 more|arXiv (Cornell University)|Jul 17, 2017

Neural dynamics and brain function28 references20 citations

TL;DR

This paper proposes a probabilistic generative model for cortical microcircuit motifs in layer 2/3 that replaces the traditional Winner-Take-All (WTA) framework with a noisy-OR-like model under data-based divisive inhibition. It demonstrates that spike-timing dependent plasticity (STDP) approximates online expectation maximization (EM), enabling the network to perform blind source separation by learning modular representations of superimposed inputs.

ABSTRACT

Previous theoretical studies on the interaction of excitatory and inhibitory neurons proposed to model this cortical microcircuit motif as a so-called Winner-Take-All (WTA) circuit. A recent modeling study however found that the WTA model is not adequate for data-based softer forms of divisive inhibition as found in a microcircuit motif in cortical layer 2/3. We investigate here through theoretical analysis the role of such softer divisive inhibition for the emergence of computational operations and neural codes under spike-timing dependent plasticity (STDP). We show that in contrast to WTA models - where the network activity has been interpreted as probabilistic inference in a generative mixture distribution - this network dynamics approximates inference in a noisy-OR-like generative model that explains the network input based on multiple hidden causes. Furthermore, we show that STDP optimizes the parameters of this model by approximating online the expectation maximization (EM) algorithm. This theoretical analysis corroborates a preceding modelling study which suggested that the learning dynamics of this layer 2/3 microcircuit motif extracts a specific modular representation of the input and thus performs blind source separation on the input statistics.

Motivation & Objective

• To address the limitations of Winner-Take-All (WTA) models in explaining cortical microcircuit dynamics with softer, data-based divisive inhibition.
• To develop a probabilistic generative model that better captures the computational function of layer 2/3 microcircuits with PV+ interneuron-mediated inhibition.
• To show that STDP in this model approximates online expectation maximization (EM) for learning generative model parameters.
• To establish a theoretical foundation for how such microcircuits extract modular representations of input statistics through STDP.

Proposed method

• Formulates a generative model with a Gaussian prior over active excitatory neurons and a noisy-OR-like likelihood term to explain input patterns.
• Applies neural sampling theory to show that the microcircuit motif approximates probabilistic inference in the proposed generative model.
• Derives a plasticity rule that optimizes model parameters by approximating online expectation maximization (EM) for generative model learning.
• Demonstrates that this plasticity rule can be approximated by a biologically plausible STDP-like learning rule.
• Uses simulations with 64-dimensional bar patterns to validate the model’s ability to reconstruct superimposed inputs.
• Employs KL divergence metrics to compare true and approximate posteriors, assessing inference accuracy during learning.

Experimental results

Research questions

• RQ1 How does softer, data-based divisive inhibition in cortical layer 2/3 microcircuits affect the emergence of computational operations compared to traditional WTA models?
• RQ2 Can a probabilistic generative model explain the observed blind source separation in this microcircuit motif?
• RQ3 Does STDP in this network approximate online expectation maximization (EM) for learning the generative model parameters?
• RQ4 What is the role of normalization or homeostatic mechanisms in enabling effective source separation in this model?
• RQ5 How well does the network approximate posterior inference in the generative model during learning?

Key findings

• The network dynamics with divisive inhibition approximate probabilistic inference in a noisy-OR-like generative model, rather than a mixture model as in WTA circuits.
• STDP effectively approximates online expectation maximization (EM), enabling the network to learn the parameters of the generative model in an unsupervised manner.
• The model successfully performs blind source separation, disentangling superimposed input patterns into their independent components.
• The KL divergence between the true and approximate posterior decreases over time, indicating improved inference accuracy during learning.
• The model remains robust when prior parameters are adjusted, suggesting stability in learning under varying assumptions.
• Reconstruction of input patterns using the maximum a posteriori hidden state shows high fidelity, confirming effective representation learning.