Symbolic pattern emergence in LAWS expert classes

Let $\mathcal{M}$ be a sufficiently capable base model trained on a corpus containing code, mathematics, and structured data, and let $n^*$ be a PLT trie node with probability $P_{\mathcal{M}}(n^*)\geq\varepsilon$. Symbolic pattern emergence. With probability approaching $1$ as $\varepsilon\to0$, every such node has an expert belonging to one of the finite primitive function classes linear, lookup, arithmetic, template, or small MLP.

The proposed mechanism is that repeated high-probability patterns drive gradient descent toward minimum-description-length functions, with transformer implicit regularization selecting primitive functions. Characterizing the MDL functions representable by transformers is left open.