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#chain-rule

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01 ·Calculus & Optimization·★ MEMBER·11 min read Matrix Calculus from Scratch — Derive the Backward Pass Yourself Where does the transpose in ∂L/∂W = XᵀG actually come from? Matrix calculus is not a formula sheet to memorize — it is one move: rotate dX to the right inside a trace. From denominator layout and shape-checking to the gradients of a linear layer and softmax + cross-entropy, ending with a double-precision gradient check. 02 ·Calculus & Optimization·FREE·7 min read Calculus for AI — The Gradient Is an Arrow Saying Which Way Is Better No epsilon-delta limits, no integration by parts. Training is measuring a slope and stepping the other way. A derivative is a multiplier, a gradient is a list of slopes, the chain rule is multiplication — and Jacobians and Hessians only need to be recognised, not computed.