[ to2d · lab notebook ]
Working out AI from first principles
Control theory and signals as the native language of model-powered systems — recovering the functions inside models, composing them as graphs, and keeping the behavior reliable. Built from the math up, in the open.
Now working on
All maths →[ 00 ]
newConvolution & systems with memory
Weighted history of input, leaky integrators, impulse response, and the step to transfer functions — the first of the mathematical foundations the rest of the stack builds on.
A model is a black box only until you can write down the function inside it. I'm working that out from the ground up — starting with the mathematics of systems that have memory, and building toward interpretability, autoresearch, and reliable deployed systems.
The lens is control theory and system identification, and it is the same at every scale. A convolution kernel is a weighted history of its input; a trained layer has a transfer function; its memory has poles and timescales. The math at the bottom and the production system at the top are one project seen at different altitudes — and earlier work on reliability boundaries and operator systems sits at the top of that stack.
The stack
foundation → top[ 00 ]
Maths
Systems with memory from first principles: convolution, leaky integrators, transfer functions. The ground the rest of the stack stands on.
[ 01 ]
Model Graph
The smallest primitives: a model-powered system as a graph of transforms.
[ 02 ]
Interpretability
Recover the function inside a trained model: transfer functions, poles, timescales, causal graphs.
[ 03 ]
Autoresearch
The loop: identify, adversarially validate, and store as a causal graph.
[ 04 ]
Reliable Systems
Hold the behavior steady at the boundaries that matter, in a changing environment.