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Backpropagation From Scratch: Deriving the Four Equations, Verified Against PyTorch (Ep:03.04)
Backpropagation is four equations, applied layer by layer. Module 3 of From Zero to Agents derives all four from the chain rule, implements them in raw NumPy with no autograd,…
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Why Your Training Loss Exploded to NaN: The Math of Learning Rate, Not Guesswork
A loss curve that spikes to NaN mid-training isn’t random instability — it’s a provable consequence of crossing an exact convergence threshold. Here’s the derivation, and what it means for…
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The Math Behind Every LLM, in Five Steps: Vectors to Cross-Entropy Loss
One continuous derivation connects vectors, matrices, gradients, and probability into the exact training objective behind every modern language model. Here’s the full arc, with the reasoning that forces each step.
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Why Learning Rate Matters: Gradient Descent Convergence, Proven With a Closed-Form Equation (Ep:02.03)
A learning rate that’s too large doesn’t just train slower — it can make loss diverge to infinity, provably. Module 2 of From Zero to Agents derives the exact convergence…
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Derivatives and Gradients — The Mechanism Behind “Learning” (Ep:02.02)
Every neural network “learns” by following a gradient downhill. Module 2 of From Zero to Agents builds derivatives, partial derivatives, and the chain rule from first principles, verifies them against…
