Backpropagation

Or: the same architecture + the same data + different learning algorithms = radically different internal structure A gap in the Platonic Representation Hypothesis The Platonic Representation Hypothesis (Huh et al., ICML 2024) claims that different neural networks converge toward the same internal representation of reality. They tested this across dozens of architectures — CNNs, ViTs, language models — and found increasing alignment as models get bigger. It's a compelling result. But every single model they tested was trained with backpropagation. ...

This post starts from the ordinary derivative and builds to gradient descent for neural networks. If you already know multivariable calculus, you can skip to Why the Gradient is Steepest. If you're here for the ML connection, skip to Applied to Machine Learning. But I'd encourage reading the whole thing — several of the "obvious" steps are where my own misconceptions lived. Starting from One Dimension The Derivative as a Rate You have a function $f(x)$. The derivative $f'(x)$ tells you: if you nudge $x$ by a tiny amount $\Delta x$, how much does $f$ change? ...