Neurotransmitter Ion Receptor Glial Endocannabinoid Network A biophysically grounded, discrete-ion framework for neural computation — breaking 80 years of voltage abstraction.
Picture trying to understand a symphony orchestra from the lobby, with one low-quality microphone taped to the back wall. You can hear volume rising and falling — but not the oboe, not the second violins entering a half-beat late, not that eighty different instruments are involved. A theory built only from that microphone would be a theory of loudness over time and nothing else. This is almost exactly what happened in 1943.
In 1943, the only signal recoverable from outside a neuron was a voltage trace. McCulloch and Pitts built a model from it. Nine years later, Hodgkin and Huxley proved that voltage is the derived epiphenomenon — the microphone reading — of discrete ions moving through specific molecular gates in integer steps, subject to conservation laws and finite molecular inventories.
Artificial intelligence kept the voltage. The biology went a different direction without us.
The standard neuron formula — $y = \sigma(Wx + b)$ — is an unconstrained, continuous, unbounded operation. Real nervous systems compute through:
Ions that are chemically non-interchangeable (Na⁺, K⁺, Cl⁻, Ca²⁺ are not the same variable)
Receptors that count a fixed integer number of ligands before a fixed ionic quantum translocates
A glial layer that continuously renegotiates the capacity ceiling within which synaptic computation occurs
Retrograde endocannabinoid signaling — discovered 30 years later than it should have been, in part due to cannabis prohibition under the Marihuana Tax Act of 1937 — by which the postsynaptic neuron instructs its own upstream neighbor locally, without any global error signal
An audit of 23 model classes from McCulloch–Pitts through GPT-3, evaluated against five of these properties, finds that none represent all five, and most represent none.
NIRGEN goes backstage.
🧠 What NIRGEN Is
NIRGEN (Neurotransmitter Ion Receptor Glial Endocannabinoid Network) is a discrete, biophysically grounded Ionic Neural Network (INN) framework derived from six threads of post-1943 neuroscience literature.
Computation proceeds through:
Conservation laws — total ionic mass $D$ is invariant across all timesteps $\tau$
Geometric capacity limits — intracellular and extracellular compartments have hard physical ceilings set by cell diameter and cleft thickness
Stoichiometric gating — receptors require an integer headcount before an integer quantum translocates; vesicles require an extrusion threshold before releasing ions back into the cleft
Local retrograde feedback — output modulates upstream receptor inventories without a global loss signal
The nirgen Python package lets you construct, fit, and test INN models built on this framework.
✨ Key Results
XOR without a hidden layer. A single NIRGEN unit solves the XOR parity problem through compartment saturation — not geometric transformation. This is physically impossible within the standard voltage abstraction.
Monotonicity broken by physics. Compartment capacity limits naturally produce non-monotonic input–output relationships that emerge from mass conservation, not from activation function engineering.
Exact conservation. Mass invariance error is held at exactly $0$ across all forward passes. Physical matter laws are not approximated.
Biophysically grounded parameters. Trainable weights are physical receptor inventories ($r_{l_i}$) and readily releasable vesicle pools ($V_{l_o}$) — not abstract scalars.
The paper's experimental section walks through three full worked experiments using the nirgen package. The snippet below shows the general workflow:
python
1import nirgen
23# Define a single NIRGEN unit (INN neuron) with biophysical defaults4# d_endo=20µm soma diameter, cleft_thickness=20nm, single ion species5model = nirgen.NIRGENUnit(6 d_endo=20,# soma diameter (µm)7 cleft_nm=20,# perisynaptic cleft thickness (nm)8 n_input_patches=2,# number of input receptor patches (l_i)9 n_output_patches=1,# number of output vesicle patches (l_o)10)1112# XOR dataset — full 2-bit permutation grid13X =[[0,0],[0,1],[1,0],[1,1]]14y =[0,1,1,0]1516# Fit using relaxation backpropagation with Straight-Through Estimator (STE)17model.fit(X, y, epochs=500, lr=0.05)1819# Evaluate — single unit solves XOR via compartment saturation20preds = model.predict(X)21print(preds)
See the preprint (Section: Experiments) for full runnable examples of all six experimental configurations.
🏗️ Architecture
Single Receptor Species / Single Vesicle Species / Single Ion Species / Single Neuron Model
A NIRGEN unit models a single ion species ($\text{ion}_1$) partitioned across bounded topological sub-domains:
Problem Input (x) ──► [Input Patches l_i] ──► Receptor Gating (r_e) ──► Ion Translocation
│
Diffusion Bridge
│
Problem Output (y) ◄── [Output Patches l_o] ◄── Vesicle Fusion (V_e) ◄── Intracellular Pool
Geometric Capacities
Compartment ceilings are derived from measured biological values, not set as hyperparameters:
Compartment
Dimension
Ion density
Intracellular soma
$d_{\text{endo}} = 20,\mu\text{m}$
$\rho \approx 2.92,\text{ions/nm}^2$
Extracellular cleft
thickness $= 20,\text{nm}$
$\rho \approx 2.92,\text{ions/nm}^2$
Conservation Invariant
$$S_{B_{\text{ecto}}}^{(\tau)} + S_{B_{\text{endo}}}^{(\tau)} = D \leq C_{B_{\text{endo}}} + C_{B_{\text{ecto}}}$$
This holds exactly at every discrete timestep $\tau$.
Trainable Parameters
Optimization updates only physically meaningful quantities:
Receptor inventories $r_{l_i}$ — the headcount threshold at each input patch before ion translocation occurs
Vesicle pools $V_{l_o}$ — the extrusion threshold at each output patch before ions are released back into the cleft
🔬 Biological Audit: 23 Model Classes
The accompanying preprint reviews six threads of post-1943 neuroscience literature and audits 23 model classes — from McCulloch–Pitts (1943) through GPT-3 — against five biophysical properties:
Property
Description
Ion specificity
Na⁺, K⁺, Cl⁻, Ca²⁺ are chemically distinct and non-interchangeable
Astrocytes continuously modify the capacity environment
Retrograde signaling
Postsynaptic endocannabinoid feedback without a global error signal
Result: No model class satisfies all five. Most satisfy none.
NIRGEN is the first framework designed to satisfy all five simultaneously.
🧪 Experimental Design
Group A — Structural Integrity & Geometry
Experiment
Description
1 — Geometric Scaling Grid
Sweeps soma scales ($d_{\text{endo}} \in {10, 15, 20, 25},\mu\text{m}$) and cleft profiles ($10$–$40,\text{nm}$) to locate optimal physical volumes for structural stability
2 — Local Budget Allocation
Evaluates varying concentration gradients by shifting the ectosphere budget split ($\gamma \in {0.1, 0.25, 0.5, 0.75, 0.9}$) under a frozen total ionic pool
3 — Free-Floating Control
Removes the localized budget coefficient ($\delta$) to assess performance when dynamics draw unconstrained from the macro ambient pool $P$
Group B — Ablations & Relaxations
Experiment
Description
4 — Gating Hardness Sweep
Anneals the soft-minimum sharpness parameter ($\kappa_{\text{start}} \to \kappa_{\text{end}}$) from smooth approximations down to hard discrete boundaries
5 — Sub-pool Ratios ($\alpha$, $\beta$)
Ablates the stoichiometric allocation weights dividing ions into flux-eligible and ligand-binding pools
6 — The Continuous Impostor
Replaces discrete floor boundaries with an unconstrained continuous projection of equal parameter width — measuring the exact performance decay when physical limits are abandoned
📊 Benchmarks
Calibration and task performance are verified every 50 epochs across three paradigms:
1. $n$-Bit XOR Parity
Evaluated via full permutation grids. Tests the network's ability to exploit localized compartment saturation to collapse output headroom when co-active inputs collide. Standard connectionist networks require at least one hidden layer for this task. NIRGEN solves it in a single unit.
2. Stoichiometric Convergence Rate
Tracks parameter trajectory smoothness using Straight-Through Estimators (STE) and Fourier-series smooth floor surrogates against traditional Adam optimization. The floor surrogate uses $J = 10$ Fourier terms.
3. Mass Invariance Error
A strict conservation audit tracking numerical drift across prolonged forward passes. Acceptable variance is fixed at exactly $0$ — physical matter conservation is not a soft regularizer.
Single ion species. This iteration tracks a single generic monovalent ion pool ($R = {\text{ion}_1}$). Real tissue relies on overlapping, chemically specific competitive interactions between Na⁺, K⁺, Cl⁻, and Ca²⁺.
Discrete step horizon. The forward pass resolves across tight discrete intervals. Fine-grained volume transmission and asynchronous wave propagation are omitted from this version.
Instrument Concept Bias. Standard ML evaluation suites measure vector transformations, not resource allocation dynamics. Benchmarking an INN against tasks designed for dot-product networks risks the exact conceptual category error this paradigm argues against.
📜 Preprint & Citation
The formal derivation, biological literature review, 23-model audit, and full experimental results are available in the preprint:
Garvey, M. (2026).Shadows of Consciousness: An Investigation into Ionic Neural Networks Using the Neurotransmitter Ion Receptor Glial Endocannabinoid Network (NIRGEN) Paradigm. Zenodo. https://doi.org/10.5281/zenodo.22379848
