Lloret Iglesias, L. | Search bioRxiv

bioRxiv2026

Signed-XOR Error and Sparse Coding in a Dale-Complaint Substrate for Sequence Memorization

How much machinery does a network need to memorize and recall discrete sequences when constrained to a biologically plausible substrate? We address this question using 50 short monophonic melodies in 4/4, used only as a controlled sequence-memory benchmark. Each beat is encoded with two clean one-hot populations - a 12-way pitch code and a separate 2-way {onset, sustain} code - and the decoder emits the same 14-dimensional code, so the autoregressive loop closes in a single neural format. The model obeys Dales law: latent units are excitatory or inhibitory, synaptic weights are non-negative, the decoder is implemented as explicit multi-contact bundles, and the encoder is a frozen sparse random projection wired at cortical ([~]10%) density. On this substrate, a local ENGRAMMER signed-XOR read-out rule combined with a sparse k-winner-take-all code stores the training corpus exactly. With a modest latent expansion (L = 512), the model reaches 100% teacher-forced and autoregressive pitch accuracy, recognizes all training melodies, and separates all held-out melodies as novel with zero overlap. Ablations show that the signed error, sparse code, explicit E/I routing, and multi-contact synapses are the main load-bearing ingredients, whereas learning the encoder is strongly detrimental and dense input wiring does not help. Capacity sweeps show that Dales law mainly increases the capacity required for stable autoregressive recall: teacher-forced storage saturates between L = 128 and L = 256, while free-running recall becomes perfect by L = 512. A matched random corpus reaches the same final fidelity and is recalled at least as well at every capacity, indicating that musical structure does not improve recall on this benchmark and that final fidelity is set by capacity rather than by structure. The result is a Dale-compliant, gradient-free sparse associative memory rather than a general sequence learner.

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bioRxiv2026

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

AO_SCPLOWBSTRACTC_SCPLOWBiological 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 Dales 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 852 x) 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. Author SummaryHow does a brain decide which of its connections to adjust when it makes a mistake? Unlike an artificial network, it has no global error signal supplied from outside: each connection can react only to the neurons it directly touches. We ask whether a small, repeating wiring pattern could provide such a local correction signal. The pattern we study, the signed-XOR motif, compares an incoming signal with the brains own prediction of it. When the two agree, the circuit stays quiet, so already-expected activity is not relayed onward. When they disagree, it does more than flag an error: it also indicates the direction of the fix, routing it through two separate channels, one meaning "strengthen", the other "weaken", consistent with the biological rule that each neuron acts with a single sign. We provide open software to search for this pattern in three nervous systems, a worm, a fly, and a detailed model of mouse visual cortex, and find it more often than chance wiring predicts, with a striking layer-specific distribution in cortex. We also simulated the eight-cell circuit with realistic spiking neurons and confirmed that it can perform the computation, but only when its inhibitory cell is a fast-spiking type like those concentrated in the enriched layers. We do not claim that any brain uses this circuit to learn or memorize. What we provide is a specific motif that could deliver a local, directional error signal that may be useful for a neuromorphic implementation.

neuroscience↗

bioRxiv2026

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.

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