[Paper Review] A simple normative network approximates local non-Hebbian learning in the cortex

Siavash Golkar, David Lipshutz+3 more|arXiv (Cornell University)|Oct 23, 2020

Neural dynamics and brain function65 references4 citations

TL;DR

This paper proposes Bio-RRR, a biologically plausible online learning algorithm that approximates Reduced-Rank Regression (RRR) objectives like RRMSE and CCA using local synaptic plasticity rules. It models cortical processing by linking calcium plateau potentials to a backpropagating error signal, enabling efficient, real-time feature extraction with no global weight transport, and achieves performance competitive with state-of-the-art methods on real-world data.

ABSTRACT

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.

Motivation & Objective

• To develop a normative model of cortical processing that explains how instructive signals guide sensory feature extraction using biologically plausible learning rules.
• To address the weight transport problem in backpropagation by replacing global error signals with local, calcium plateau-dependent plasticity.
• To derive online optimization algorithms for RRMSE and CCA that can be implemented in neural networks with local synaptic updates.
• To interpret the calcium plateau potential in pyramidal neurons as a backpropagating error signal in a normative framework.
• To demonstrate that the proposed algorithm performs competitively with existing state-of-the-art methods on real-world datasets.

Proposed method

• The authors derive offline and online optimization algorithms for a family of Reduced-Rank Regression (RRR) objectives, including RRMSE and CCA, by parametrizing the projection matrix via low-rank decomposition.
• They enforce a whitening constraint on the input projection matrix to ensure solution uniqueness and stability, leading to a constrained optimization problem over matrices Vx and Vy.
• The algorithm uses a normalizing matrix Σ⁻¹ = s·Cyy + (1−s)·In to interpolate between RRMSE (s=0) and CCA (s=1), enabling a unified framework for both objectives.
• The online algorithm updates synaptic weights using local pre- and post-synaptic activities, with plasticity rules derived from gradient descent on the RRR objective.
• The calcium plateau potential is modeled as a backpropagating error signal that modulates synaptic plasticity, enabling local learning without global error transmission.
• The neural network implementation uses a two-layer architecture resembling cortical microcircuits, with proximal synapses modified by feedforward input and distal dendrites integrating instructive signals.

Experimental results

Research questions

• RQ1 How can a normative learning framework be extended to cortical processing that relies on non-Hebbian, local plasticity rules?
• RQ2 Can a biologically plausible neural network implement RRMSE and CCA using only local synaptic updates and no global error backpropagation?
• RQ3 How can the calcium plateau potential in pyramidal neurons be interpreted as a backpropagating error signal in a learning context?
• RQ4 What is the relationship between the RRMSE and CCA objectives in the context of cortical feature extraction?
• RQ5 Does the proposed algorithm achieve performance comparable to state-of-the-art methods while remaining consistent with cortical physiology?

Key findings

• The proposed Bio-RRR algorithm achieves competitive performance on real-world datasets, matching or exceeding existing implementations of RRMSE and CCA in terms of prediction accuracy and correlation maximization.
• The algorithm successfully implements online learning without storing large data batches, making it suitable for real-time sensory processing.
• The calcium plateau potential is shown to encode a backpropagating error signal that enables local synaptic plasticity, resolving the weight transport problem in a biologically plausible way.
• The synaptic learning rules derived from the algorithm closely resemble experimentally observed non-Hebbian plasticity in cortical and hippocampal pyramidal neurons.
• The model demonstrates that a single framework can unify RRMSE and CCA through a continuous interpolation parameter s, with s=0 for RRMSE and s=1 for CCA.
• The solution is unique under the whitening constraint, ensuring stable and interpretable feature extraction from high-dimensional sensory inputs.