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

AO_SCPLOWBSTRACTC_SCPLOWOne of the most compelling ideas for bridging neuroscience and artificial neural networks is the establishment of a framework based on three main components: network architecture, optimization mechanism, and loss (or objective) function to be minimized. While the first two components have been extensively explored, the definition of a loss or objective function in neuroscience has been addressed less thoroughly, often from perspectives such as predictive coding. In this work, we propose an elementary loss function grounded in the comparison of neuronal responses to two signals: an external one, used for learning, and an internal one, reflecting the acquired knowledge. The loss function is thus simply the basic difference between the two, which, in terms of logical signals, corresponds to a well-known non-linearly separable function: the XOR function. We illustrate with a computational example how a binarized image recognition algorithm can be straightforwardly implemented in an autoencoder, and we show how a neuronal motif organized around an inhibitory neuron could implement such XOR operation and provide a feedback signal that makes optimization possible.