Toward defining loss functions in neuroscience: an XOR-based neuronal mechanism for local learning

Abstract

Of the three components often used to map deep learning onto neuroscience (architecture, learning rule and loss function), the biological counterpart of the loss is the least understood. For binary signals, the mismatch between an externally evoked response and its internally generated reconstruction is the XOR function, and its two asymmetric components, undershoot and overshoot, form a signed error that also indicates the direction of the required change. In a companion study, an eight-neuron, Dale-compliant signed-XOR motif, a six-neuron XOR comparator with two feedback neurons of opposite identity, was found in several connectomes and shown in spiking simulations to compute this signed error. Here we ask whether this signed error can serve as an effective learning signal. We use the logical function of one comparator per output unit as the only error signal of a binary autoencoder, with fixed random sign feedback to the hidden layer. Without backpropagation, a fully connected autoencoder trained for five epochs on binarized MNIST reaches 97.7% bit-wise and 94.8% balanced reconstruction accuracy (five seeds), and a convolutional variant with 533 parameters reaches 96.3% and 89.2%; without the sign of the error, learning collapses. Controls show that performance is carried by the comparator-driven decoder: a suitably initialised fixed random encoder reconstructs digits about as well or better, encoder learning improves digit readout mainly in narrow hidden layers, and a gradient-trained reference reaches 99.3% and 97.3% balanced accuracy. The signed error thus suffices for the synapses it reaches directly; credit assignment to earlier layers remains open.