Darby’s Paper Lab

Interactive essays, visualizations, and deep-dive tutorials on the papers behind modern sequence modeling.

Interactive demo State space models July 2026

HiPPO: Optimal Polynomial Memory for Sequence Models

The memory theory underneath S4 and Mamba. A state space model watches a signal stream by and keeps only N numbers — yet it can reconstruct the whole history on demand. Draw your own signal, choose how the past is weighted, and watch optimal polynomial memory work in real time.

Open the interactive guide →

In the pipeline

  • The S4 convolution kernel, visualized — how a recurrence becomes one long filter
  • Mamba-2 and state space duality — the SSM–attention equivalence, made precise