Biologically plausible local synaptic learning rules robustly implement deep supervised learning

In deep neural networks, representational learning in the middle layer is essential for achieving efficient learning. However, the currently prevailing backpropagation learning rules (BP) are not necessarily biologically plausible and cannot be implemented in the brain in their current form. Therefore, to elucidate the learning rules used by the brain, it is critical to establish biologically plausible learning rules for practical memory tasks. For example, learning rules that result in a learning performance worse than that of animals observed in experimental studies may not be computations used in real brains and should be ruled out. Using numerical simulations, we developed biologically plausible learning rules to solve a task that replicates a laboratory experiment where mice learned to predict the correct reward amount. Although the extreme learning machine (ELM) and weight perturbation (WP) learning rules performed worse than the mice, the feedback alignment (FA) rule achieved a performance equal to that of BP. To obtain a more biologically plausible model, we developed a variant of FA, FA_Ex-100%, which implements direct dopamine inputs that provide error signals locally in the layer of focus, as found in the mouse entorhinal cortex. The performance of FA_Ex-100% was comparable to that of conventional BP. Finally, we tested whether FA_Ex-100% was robust against rule perturbations and biologically inevitable noise. FA_Ex-100% worked even when subjected to perturbations, presumably because it could calibrate the correct prediction error (e.g., dopaminergic signals) in the next step as a teaching signal if the perturbation created a deviation. These results suggest that simplified and biologically plausible learning rules, such as FA_Ex-100%, can robustly facilitate deep supervised learning when the error signal, possibly conveyed by dopaminergic neurons, is accurate. Schematic illustration of three learning rules: BP, backpropagation; FA, feedback alignment; and FA_Ex-100%, feedback alignment with 100% excitatory neurons in middle layer. BP requires the information in W2 to backprop. FA requires heterogeneity in the tentative impact of the middle layer neurons on the output. FA_Ex-100% is the most biologically plausible in the sense that it can be computed at a synaptic triad only with locally available information as explained below, but its performance is fairly good and comparable to that of BP. With the notations, y1i :=f( n-ary sumation jW1ijxj), y2 :=f( n-ary sumation iW2iy1i), and J:=e22=(y2-y )22, the gradient for BP is given by partial differential J partial differential W1ij=e W2i f '( n-ary sumation jW1ijxj)center dot xj, whose W2i is replaced by a random number Bi for FA and by 1 for FA_Ex100%. Therefore, for FA_Ex-100%, the synaptic weights in the middle layer are updated by the following rule: (Delta W)ij=-0.01 partial differential J partial differential W1ij=-0.01 xj theta(Ii) e, where theta is a step function and Ii is the current input to neuron i. This can be interpreted as (Delta W)ij proportional to prei x postj x dopamine. Interestingly, simplified and biologically plausible learning rules like FA_Ex-100% work robustly as far as the error signal, possibly conveyed by dopaminergic neurons, is accurate.

Automated summary

Representational learning in the middle layer is crucial for efficient learning in deep neural networks. However, the prevailing backpropagation learning rules are not biologically plausible and cannot be implemented in the brain. To address this, it is critical to establish biologically plausible learning rules for memory tasks. Using numerical simulations, biologically plausible learning rules were developed to replicate a laboratory experiment where mice learned to predict reward amounts.