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Numerical stability: why log-sum-exp exists and how float32 silently lies
A machine learning model produces three logits: 1,000, 1,001, and 999. You apply softmax, expecting three probabilities that sum to one.
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Gradient descent variants on one loss surface: momentum, RMSProp, Adam visualized
Imagine four hikers trying to reach the bottom of the same mountain valley. Each can measure the slope beneath their feet, but none has a complete map of the terrain.
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Entropy and cross-entropy: why your loss function is an information measure
Every time a language model predicts the next token, it makes a bet about the future. If it assigns a high probability to the token that actually appears, the bet was good. If it assigns a tiny probab
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Distributions you’ll actually meet: Gaussian, Bernoulli, and the long tail
Most people meet the Gaussian distribution in school, draw a bell curve, and quietly assume that real-world data behaves something like it.
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Probability for ML: Bayes’ rule, likelihood, and why models output logits
Machine learning models often appear mysterious at the point where they produce an answer. A classifier receives an input, performs millions or billions of calculations, and returns something like “sp
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The chain rule at scale: from calc-101 to backprop through a million parameters
A neural network with a million trainable parameters sounds as though it should require a million separate calculus problems.
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Derivatives and gradients: the one calculus lesson ML actually uses
Machine learning can look like a huge collection of algorithms, architectures, and optimization tricks. Underneath most of them, however, sits one compact idea:
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Eigenvalues and SVD without tears: compress an image to see them work
An RGB image looks visual to us, but to NumPy it is three matrices: one each for red, green, and blue. Real images contain repeated structure—smooth gradients, correlated colors, recurring edges, and
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Matrix multiplication is all you need: shapes, batching, and why GPUs love it
If you learn one operation in modern machine learning, make it matrix multiplication (often shortened to matmul ).