October 2022

60 ideas from “Compositional Inductive Biases in Function Learning” (2017) by Eric Schulz et al.

Positive semi-definite kernels are closed under addition and multiplication, and every positive definite kernel defines a reproducing kernel Hilbert space. At the time, this paper & its citations seemed like a bridge between my thoughts related to mnemonics and my year's worth of independent studies with Prof. John Holmes (now at Ohio State) in functional analysis & distribution theory. This paper models human function learning using a compositional grammar described in Duvenaud et al.'s 2013 paper.

- "structural regularities free up memory capacity because they are compressible"

- "compositionality helps memorizing structure by providing naturally occurring chunks"

- "if structure exists that a grammar can express, then one can save an unbounded # of bits by detecting that structure."