HEBBIAN LEARNING · BCM rule: ΔW

Read the equation

This relation defines BCM rule: ΔW in the source section “HEBBIAN LEARNING · BCM rule: ΔW”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read BCM rule: ΔW as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

                W[i][j] *= (1.0f - decay);
                // Clamp
                W[i][j] = std::max(-1.0f, std::min(1.0f, W[i][j]));
            }
        }
    }

    // BCM rule: ΔW = η·y·(y - θ)·x where θ is sliding threshold
    void update_bcm(const float* pre, const float* post, float* theta) {
        for (size_t i = 0; i < DIM; ++i) {
            // Update threshold (exponential moving average of y²)
            theta[i] = 0.99f * theta[i] + 0.01f * post[i] * post[i];

            for (size_t j = 0; j < DIM; ++j) {
                float delta = lr * post[i] * (post[i] - theta[i]) * pre[j];
                W[i][j] += delta;
                W[i][j] *= (1.0f - decay);
                W[i][j] = std::max(-1.0f, std::min(1.0f, W[i][j]));

BCM rule: ΔW = η·y·(y - θ)·x where θ is sliding threshold

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