19 · CP or Tucker in Practice

Deep dive 19 of Tensors for Machine Learning. Sections 10 and 11 fitted Tucker and CP to one small taxi tensor. This deep dive takes them to three tensors people factorize for a living, and asks which one to choose:

CP and Tucker differ in one object, the core tensor, and the right core depends on whether the factorization has to predict entries nobody observed or store a known tensor in fewer numbers.

On the FB15k-237 knowledge graph the job is prediction: what can a core express? On a trained ResNet-18 convolution kernel the job is storage: what does a core cost, and what do CP’s savings hide? Then the question both leave open — which rank to fit — and a photograph that can be asked either job, and ranks the two models in opposite orders.

A take-home of about two hours, with no minutes on the six-hour workshop clock. It works through the ML blog post CP or Tucker in practice.

Study here, then run the real thing: notebook 19 on Colab · all the notebooks

Built from the workshop’s own material by Ravi Kalia and Sebastian Laverde Chunza, CC BY 4.0.