From homeostasis to credit assignment: a signed-XOR connectomic motif for local directional error signalling

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From homeostasis to credit assignment: a signed-XOR connectomic motif for local directional error signalling

Authors

Pena Fernandez, M.; Gonzalez Rios, A.; Lloret Iglesias, L.; Marco de Lucas, J.

Abstract

Biological neural circuits are widely thought to require local error signals that tell synapses not only that a prediction is wrong, but also in which direction to change. We previously proposed that a six-neuron XOR motif acts as a homeostatic comparator: matched sensory and predictive signals cancel locally, whereas mismatches propagate an error signal. We also showed that a shallow autoencoder can learn MNIST using a signed-XOR learning rule with local decoder errors and random feedback alignment, without gradient backpropagation. Here we introduce the signed-XOR motif, an eight-neuron, twelve-edge directed signed circuit that extends the XOR comparator with two feedback channels of opposite neurotransmitter identity. By construction, the motif can convert a binary mismatch into directional error signalling, with one pathway encoding potentiation and the other depression, while respecting Dale's principle. We provide open-source tools to enumerate the motif at connectome scale and test its enrichment against degree- and sign-preserving null models. The motif is enriched 24.3x in C. Elegans (Z=52.2), significantly enriched in 59/80 FlyWire Drosophila neuropils including AVLP\_L (13.9x, Z=94.4), and strongly enriched in layers 2/3--5 of a biophysically detailed mouse primary visual cortex model (global 315x; per-pivot medians up to 852x) while absent from layer~6. The same layer-specific pattern is found in the axon-proofread subset of the EM-reconstructed MICrONS connectome. A Brian2 leaky integrate-and-fire implementation reproduces the signed-XOR truth table, remains robust to Poisson drive, produces a graded signed error, and requires a fast-spiking parvalbumin-like pivot. These results identify signed-XOR as a recurrent connectomic pattern compatible with local homeostatic error cancellation and directional credit-assignment signals.

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