Leaky magnitude-of-sum activity accumulator

Read the equation

The state retains 99% of its previous energy value and takes 1% of the absolute sum of the current components. Opposite-sign components can cancel before the absolute value, so this is not the Euclidean norm or sum of absolute activities. With nonnegative initialization it stays nonnegative and smooths its scalar target over time.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

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Original context

y[i] = tanh(Σ_j W[i][j] × x[j] + b[i])   // Forward pass

state[i] = 0.95 × state[i] + 0.05 × (y[i] + core[i])

energy = 0.99 × energy + 0.01 × |Σ state|

Step 3: Integration Metrics

φ_local = tanh(energy)                    // Per-strand coherence

φ_global = tanh(Σ(all states) / 256)     // Global coherence

energy = 0.99 × energy + 0.01 × |Σ state|