Multivariate calculus from first principles
Automatic differentiation can compute millions of derivatives in one backward pass, but a single bug in a custom operation can quietly send the wrong gradient through your whole model. A gradient check catches that bug with a finite difference: step a small distance h to each side of the point you care about, read off how much the function changed, and treat the slope of that short secant line as an independent estimate of the true tangent slope.
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▶ Finite Differences & Gradient Checking