The Elbàlor Neuron: A Metabolic Complex Activation for Lifelong Learning with Phase-Space Conservation, Orthogonal Weight Freezing, Complex-STDP Memory, Larmor Phase Driver, and Pearl Rungs 1–3 Causality

I present the Elbàlor Neuron, a complex-valued activation that replaces magnitude suppression with phase rotation driven by a thermal state. Where earlier metabolic neurons reduce output magnitude as thermal state rises, the NecroComplex neuron keeps signal energy intact and redirects it into the phase dimension. Different tasks occupy distinct angular subspaces. Interference is structurally reduced without sacrificing capacity. Four architectures are presented: Architecture A (Phase Reserve, local), Architecture B (Phase Memory Matrix, global), Architecture C (Per-Neuron Timing-Based STDP), and Architecture D (Anti-Rupture + Amplified Phase Memory with graduated defensive response). Architecture D combines complete freezing of hot neurons (p_min = 0), amplified blocked gradient signal, circular phase wrapping, and a smooth graduated defensive boost. Headline results. The Graduated Defense variant of Architecture D, running with per-task optimizers, thermal snapshot/restore, and orthogonal gradient projection, achieves 0.0000 forgetting on the two-task MNIST→FashionMNIST benchmark against a Dense ReLU baseline at 0.1918, 0.0002 forgetting with 0.5183 final accuracy on the five-task cross-dataset MLP benchmark, and 0.0128 forgetting with 0.5868 final accuracy on CNN. Beats Dense, EWC, SI, and SiLU CNN in both metrics on both splits. Complex-STDP. A cross-neuron causal memory matrix C, written by the phase of the difference between fast and slow complex activity traces. The outer product dz ⊗ conj(dz) produces LTP for consistent temporal orderings and LTD for reversed orderings automatically, without a hand-coded rule. Phase interference is proven both at the outer-product level and at the accumulation level. Larmor phase driver. Each feature gets its own frequency from a linear spectrum omega = linspace(ω_low, ω_high, d). Each token position gets its own phase. The resulting complex activity trace carries real temporal-ordering signal: delta_C[i,j] picks up angle (omega[i] − omega[j]) · Δt so the phase axis of the C matrix does real work instead of collapsing to real. At transformer scale, LarmorArchD trains stably for 2000 steps on language with Qwen tokenizer, loss dropping from 16.30 to 0.33 with coherent generation. Thermal state caps at 0.90, phase traces stay alive (z_imag ≈ 9.0). Pearl rungs 1–3 causality. The neuron performs its own interventions. C_obs accumulates observational statistics P(j | i). C_do accumulates interventional statistics P(j | do(i)). C_struct captures cross-domain invariants via Welford variance accumulation. A counterfactual query runs Pearl's three-step abduction → action → prediction procedure. A control test proves the interventional memory collapses to zero when interventions are disabled. Inference-time continual learning. With inference_learning=True, base weights stay frozen during model.eval() while C_obs, C_do, phase_mem, and thermal_mag continue to update, self-regulated by autonomy gates (Boring-Shit Filter, Brain-Rot Shield). Task partitioning is available without labels via task_bias_mode="emergent". The full architecture is verified by 99 tests across eight files. Three plumbing mechanisms are documented as structurally necessary, not optional: per-task optimizer, thermal snapshot/restore, and orthogonal gradient projection. Remove any one and the mechanism fails. The Law of Balor: Heat does not kill the signal. It redirects it. Every number is from an actual run. Every bug is documented with root cause and fix.

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Publication Details

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Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-14
DOI
https://doi.org/10.5281/zenodo.23370896
Primary Topic
Neural Networks and Applications
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article
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article

The Elbàlor Neuron: A Metabolic Complex Activation for Lifelong Learning with Phase-Space Conservation, Orthogonal Weight Freezing, Complex-STDP Memory, Larmor Phase Driver, and Pearl Rungs 1–3 Causality

Heylel Yaka
Zenodo (CERN European Organization for Nuclear Research)
Neural Networks and Applications
article

The Elbàlor Neuron: A Metabolic Complex Activation for Lifelong Learning with Phase-Space Conservation, Orthogonal Weight Freezing, Complex-STDP Memory, Larmor Phase Driver, and Pearl Rungs 1–3 Causality

Heylel Yaka
article en

Abstract

I present the Elbàlor Neuron, a complex-valued activation that replaces magnitude suppression with phase rotation driven by a thermal state. Where earlier metabolic neurons reduce output magnitude as thermal state rises, the NecroComplex neuron keeps signal energy intact and redirects it into the phase dimension. Different tasks occupy distinct angular subspaces. Interference is structurally reduced without sacrificing capacity. Four architectures are presented: Architecture A (Phase Reserve, local), Architecture B (Phase Memory Matrix, global), Architecture C (Per-Neuron Timing-Based STDP), and Architecture D (Anti-Rupture + Amplified Phase Memory with graduated defensive response). Architecture D combines complete freezing of hot neurons (p_min = 0), amplified blocked gradient signal, circular phase wrapping, and a smooth graduated defensive boost. Headline results. The Graduated Defense variant of Architecture D, running with per-task optimizers, thermal snapshot/restore, and orthogonal gradient projection, achieves 0.0000 forgetting on the two-task MNIST→FashionMNIST benchmark against a Dense ReLU baseline at 0.1918, 0.0002 forgetting with 0.5183 final accuracy on the five-task cross-dataset MLP benchmark, and 0.0128 forgetting with 0.5868 final accuracy on CNN. Beats Dense, EWC, SI, and SiLU CNN in both metrics on both splits. Complex-STDP. A cross-neuron causal memory matrix C, written by the phase of the difference between fast and slow complex activity traces. The outer product dz ⊗ conj(dz) produces LTP for consistent temporal orderings and LTD for reversed orderings automatically, without a hand-coded rule. Phase interference is proven both at the outer-product level and at the accumulation level. Larmor phase driver. Each feature gets its own frequency from a linear spectrum omega = linspace(ω_low, ω_high, d). Each token position gets its own phase. The resulting complex activity trace carries real temporal-ordering signal: delta_C[i,j] picks up angle (omega[i] − omega[j]) · Δt so the phase axis of the C matrix does real work instead of collapsing to real. At transformer scale, LarmorArchD trains stably for 2000 steps on language with Qwen tokenizer, loss dropping from 16.30 to 0.33 with coherent generation. Thermal state caps at 0.90, phase traces stay alive (z_imag ≈ 9.0). Pearl rungs 1–3 causality. The neuron performs its own interventions. C_obs accumulates observational statistics P(j | i). C_do accumulates interventional statistics P(j | do(i)). C_struct captures cross-domain invariants via Welford variance accumulation. A counterfactual query runs Pearl's three-step abduction → action → prediction procedure. A control test proves the interventional memory collapses to zero when interventions are disabled. Inference-time continual learning. With inference_learning=True, base weights stay frozen during model.eval() while C_obs, C_do, phase_mem, and thermal_mag continue to update, self-regulated by autonomy gates (Boring-Shit Filter, Brain-Rot Shield). Task partitioning is available without labels via task_bias_mode="emergent". The full architecture is verified by 99 tests across eight files. Three plumbing mechanisms are documented as structurally necessary, not optional: per-task optimizer, thermal snapshot/restore, and orthogonal gradient projection. Remove any one and the mechanism fails. The Law of Balor: Heat does not kill the signal. It redirects it. Every number is from an actual run. Every bug is documented with root cause and fix.

Zenodo (CERN European Organization for Nuclear Research)
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Neural Networks and Applications
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