Shifted logarithm in the implemented primitive

Read the equation

The comment gives log(x) and derivative 1/x, but the body evaluates log(x+EPSILON) and derivative 1/(x+EPSILON). This positive shift changes both the value and the domain to x+EPSILON>0. It mitigates a zero input but does not make every negative input valid.

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

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

    z->inputs = {x};
    z->backward_fn = [x, z, e]() {
        x->grad += z->grad * e;
    };
    return tape.record(z);
}

// Log: z = log(x), dz/dx = 1/x
inline GradNodePtr log_op(GradNodePtr x, TapeRecorder& tape) {
    auto z = std::make_shared<GradNode>(std::log(x->value + EPSILON));
    z->inputs = {x};
    z->backward_fn = [x, z]() {
        x->grad += z->grad / (x->value + EPSILON);
    };
    return tape.record(z);
}

// Power: z = x^p, dz/dx = p * x^(p-1)

Log: z = log(x), dz/dx = 1/x

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