The Influence of Initial Connectivity on Biologically Plausible Learning

TL;DR

The paper shows that the magnitude of initial recurrent connectivity critically shapes learning dynamics under biologically plausible rules in RNNs. By analyzing the maximum Lyapunov exponent before and after training, it reveals why smaller initial gains can hinder learning and demonstrates that gradient flossing, when adapted to bio-plausible learning, improves performance for suboptimal initializations. The work extends theoretical parallels with backpropagation through time to bio-plausible settings and provides a practical remedy with potential implications for neuroscience experiments and neuromorphic hardware design. Overall, initial connectivity and Lyapunov stability emerge as key factors guiding the efficiency and reliability of brain-like learning rules.

Abstract

Understanding how the brain learns can be advanced by investigating biologically plausible learning rules -- those that obey known biological constraints, such as locality, to serve as valid brain learning models. Yet, many studies overlook the role of architecture and initial synaptic connectivity in such models. Building on insights from deep learning, where initialization profoundly affects learning dynamics, we ask a key but underexplored neuroscience question: how does initial synaptic connectivity shape learning in neural circuits? To investigate this, we train recurrent neural networks (RNNs), which are widely used for brain modeling, with biologically plausible learning rules. Our findings reveal that initial weight magnitude significantly influences the learning performance of such rules, mirroring effects previously observed in training with backpropagation through time (BPTT). By examining the maximum Lyapunov exponent before and after training, we uncovered the greater demands that certain initialization schemes place on training to achieve desired information propagation properties. Consequently, we extended the recently proposed gradient flossing method, which regularizes the Lyapunov exponents, to biologically plausible learning and observed an improvement in learning performance. To our knowledge, we are the first to examine the impact of initialization on biologically plausible learning rules for RNNs and to subsequently propose a biologically plausible remedy. Such an investigation can lead to neuroscientific predictions about the influence of initial connectivity on learning dynamics and performance, as well as guide neuromorphic design.

Figures (5)

• Figure 1: Influence of weight initialization on biologically plausible learning. A) RNN Setup for Brain Learning Models. B) Loss curves throughout training for different initial gains using the standard backpropagation through time (BPTT) algorithm. Here, gain reflects the initial weight magnitude: recurrent weights are initialized as $W^{(0)}_{h,ij} \sim \mathcal{N}(0, gain^2/N)$. C) Loss curve throughout training for different initial gains using e-prop, a biologically plausible learning rule for RNNs. Note: the plots in B) and C) begin after 200 training iterations to provide a more focused view of the results. This figure illustrates the Romo task but similar trends are observed for the 2AF and DMS tasks (Figure \ref{['fig:more_tasks']}). Learning curves for more intermediate gain values are examined in Appendix Figure \ref{['fig:more_gains']}. Solid lines/shaded regions: mean/standard deviation of loss curves across independent runs with different seeds.
• Figure 2: Similar trends as Figure \ref{['fig:main_learning_curve']} observed for the 2AF and DMS tasks. A) Learning curve for the 2AF task across different initial gains using backpropagation through time (BPTT). B) Similar to A) but for e-prop. C) Similar to A) but for the DMS task. D) Similar to B) but for the DMS task. Plotting convention follows that of Figure \ref{['fig:main_learning_curve']}.
• Figure 3: The maximum Lyapunov exponent (Max LE) computed before and after training across various weight initialization gains for training via A) BPTT and B) e-prop. Gain is defined similarly as in Figure \ref{['fig:main_learning_curve']}. Certain initial weight magnitudes result in more significant changes in the Max LE. Solid lines/shaded regions: mean/standard deviation of Max LE across independent runs with different seeds.
• Figure 4: Initialization via pretraining with gradient flossing improves e-prop learning performance, particularly for suboptimal initialization gains. Note: The plot begins after 2000 iterations to provide a more focused view of the results.
• Figure 5: Figure \ref{['fig:main_learning_curve']} repeated for more intermediate gain values for A) BPTT and B) e-prop. Noticeable gap in the learning curve is observed between $gain=0.2$ with the others before convergence, even with hyperparameter tuning. Plotting convention follows that of Figure \ref{['fig:main_learning_curve']}.