Long-form
Essays
Technical arguments you can manipulate: intuition, equations, implementation and the places where each model breaks.
06
Nonlinearities create frequencies—and aliases
Follow newly created harmonics across the sampling boundary.
07RoPE: relative position as phase difference
Rotate content vectors and inspect relative attention scores.
08Why fewer operations can still run slower
Follow FFT stages into memory traffic and hardware utilisation.
09Memory as a dynamical system
Connect decaying, rotating states to filters and sequence models.
01The Fourier transform, made visible
Compose a signal, then inspect the magnitude and phase that describe it.
02Aliasing is everywhere
See why different continuous signals can become identical after sampling.
03Convolution: FIR filters → CNNs → fast computation
Follow one operation across filtering, learned kernels and frequency space.
04Sinusoidal positional encodings, from first principles
Build a vector representation of position from paired periodic coordinates.
05Building a GPU STFT pipeline
Map a time–frequency transform from equations to buffers and execution.