CONTRASTIVE LEARNING · L

Read the equation

This relation defines L in the source section “CONTRASTIVE LEARNING · L”. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase. Uses logarithmic scaling; its base and the positivity of its argument matter. 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 L as the quantity being defined or updated by this relation.

2. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase.

3. Uses logarithmic scaling; its base and the positivity of its argument matter.

4. 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

        norm = std::sqrt(norm) + 1e-8f;
        for (size_t i = 0; i < DIM; ++i) {
            output[i] /= norm;
        }
    }

    // InfoNCE loss
    // L = -log(exp(sim(z_i, z_j)/τ) / Σ_k exp(sim(z_i, z_k)/τ))
    float infonce_loss(const float* anchor, const float* positive,
                       const float negatives[][DIM], size_t num_negatives) const {
        float z_anchor[DIM], z_positive[DIM];
        project(anchor, z_anchor);
        project(positive, z_positive);

        // Similarity with positive
        float sim_pos = 0.0f;
        for (size_t i = 0; i < DIM; ++i) {
            sim_pos += z_anchor[i] * z_positive[i];

L = -log(exp(sim(z_i, z_j)/τ) / Σ_k exp(sim(z_i, z_k)/τ))

Related builds