series · 4 parts · in progress
The Kernel as an Instrument
A trained network carries its own kernel, and a kernel can be measured. Decompose it, cut modes out of it, count the concepts it will admit to having, and find out which parts of the design were doing the work all along.
Start reading → The Trained Network, Under Mercer's Microscope- 01 The Trained Network, Under Mercer's Microscope Every hidden representation induces an empirical kernel. Decompose it into ranked modes, audit their stability and semantic evidence, then repeat the measurement on grayscale CIFAR-100 where one hundred classes leave room for a genuine concept-count test.
- 02 The Concept That Would Not Die An empirical feature covariance gives a trained kernel network ranked orthogonal axes. Deleting one axis is an exact algebraic intervention; the experiment asks whether it is also a semantic one. It is not: the damage spreads broadly and a small probe recovers the targeted distinction.
- 03 How to Interrogate a Kernel Network A network whose hidden units are kernel prototypes is supposed to be legible. Legible claims are cheap unless someone can check them, so this post builds the checking: five instruments that put a trained Yat network under oath, each one asking a question that only this kernel makes askable. The first instrument finds that the softening constant in the formula sits ten thousand times below the distances it is supposed to soften, so the trained network never uses it at all: a term can be load-bearing in the theory and idle in the artifact, and only an audit tells you which.
- 04 A Network Made of Parts Cut the image into patches, run one shared kernel bank over every patch, average the results, and classify. Linearity makes the output exactly decomposable into per-patch score contributions. The architecture was also supposed to fix three failures of the whole-image network. It fixed none: softening falls with distance, and concepts remain distributed across most of the bank at every tested granularity.
This series is still being written. New parts land in the archive and the RSS feed as they publish.