The following results are from our simulation experiments on this platform, not from the published NEMO papers. They are predictions of the Assembly Calculus that we have validated computationally but not yet published.
The N400 is a negative deflection in the event-related potential (ERP) peaking around 400ms after stimulus onset, larger for semantically unexpected words. It is one of the most replicated findings in cognitive neuroscience — robust across languages, modalities, and experimental paradigms. The question has always been: what computation does it reflect? In the Assembly Calculus, we find a precise answer: the N400 maps to the total synaptic input summed across all neurons in a brain area before winner-take-all selection — what we call global pre-k-WTA energy.
The metric
In each simulation timestep, every neuron in a brain area receives synaptic input from two sources: the external stimulus (the word being processed) and recurrent connections from previously active neurons (the context). Before the top-k winner-take-all selection picks which neurons , the system computes the total input to each neuron:
all_inputs[j] = stimulus_input[j] + Σ recurrent_weights[i, j]
Global pre-k-WTA energy is the sum of all_inputs across all n neurons in the area. This aggregate quantity — analogous to the summed post-synaptic potentials that EEG electrodes record at the scalp — is our N400 analogue. We did not design it to match the N400; it is a natural property of the simulation dynamics that we measured and found to behave like one.
The mechanism: input redundancy
The key insight is that related primes and targets share neurons — their assemblies overlap. This overlap creates redundancy in the input:
Related prime (e.g., “nurse” before “doctor”): the prime's assembly has been co-activated with the target during training, creating Hebbian-strengthened connections. When the target arrives, the same neurons receive input from both the stimulus and the recurrent connections. But synaptic weights have a ceiling — they saturate. Overlapping inputs are capped rather than summing freely. The total energy across all neurons is lower.
Unrelated prime (e.g., “table” before “doctor”): the prime activates a disjoint set of neurons. Stimulus input goes to the target's neurons; recurrent input goes to the prime's neurons. No overlap, no saturation — the inputs add freely. The total energy is higher.
Mathematically, let S be the set of neurons driven by the target stimulus and P be the set receiving strong recurrent input from the prime. The total energy decomposes into three terms: neurons in S only (stimulus input), neurons in P only (recurrent input), and neurons in S ∩ P (capped input). When S ∩ P is large (related prime), the capping term dominates and total energy drops. When S ∩ P ≈ 0 (unrelated prime), all inputs are additive.
Results
| Metric pathway | Direction | Cohen's d | p-value |
|---|---|---|---|
| Global energy (sum of all_inputs) | Related < Unrelated | −25.2 | 0.001 |
| Settling dynamics (cumulative energy) | Related < Unrelated | −16.6 | 0.001 |
| Neuron-specific mean input | Reversed | −5.8 | 0.010 |
| Prediction error (cosine) | Null | −0.1 | 0.858 |
The global energy pathway produces the correct direction (related < unrelated) with a very large effect. The neuron-specific pathway is reversed — individual neurons that receive the target stimulus actually get more input when primed, because the Hebbian connections add to their input. But the global sum is lower because fewer total neurons are active (the activation is concentrated rather than ). The prediction-error pathway (cosine distance between expected and actual activation) shows no effect, ruling out a surprise-based interpretation.
Why the effect sizes are so large
Cohen's d = −25 is far outside the range of typical human ERP studies, where the N400 effect is usually d = −1 to −2. This does not mean the model exaggerates the effect — it means the model has almost no . In human EEG, the N400 signal is buried in trial-to-trial variability, muscle artifacts, volume conduction, and individual differences. In a deterministic simulation, the same input always produces the same output. The signal-to-noise ratio is effectively infinite, so the standardized effect size (which divides by the standard deviation of the noise) is enormous.
The parameter sweep confirms this interpretation: with the required parameters (k ≥ 100, connectivity p ≥ 0.05), the effect is consistent across 16 parameter combinations, with d ranging from −11 to −111. The effect vanishes entirely at k = 50 or p = 0.01, indicating that the mechanism requires both sufficient competition (large k) and sufficient connectivity (large p) to produce overlapping assemblies.
Connection to the N400 literature
The dominant interpretation of the N400, following Kutas & Federmeier (2011), is that it reflects the ease of semantic access — how readily a word's meaning is retrieved from long-term memory given the current context. Our finding gives this interpretation a specific mechanistic account: “ease of access” is the degree to which the target word's assembly is already partially activated by the context. Partial activation means input redundancy; redundancy means lower global energy; lower global energy means a smaller N400.
This account makes a testable prediction that goes beyond the existing literature: the N400 effect should scale with assembly overlap between prime and target, which is itself a function of the number of co-activation episodes during training. Words that have been encountered together more frequently should show a larger N400 reduction, with the relationship mediated by the specific overlap of their neural assemblies — not just by an abstract “semantic distance” in an embedding space. This prediction is testable in the simulation and, with appropriate experimental design, in human EEG.