Despite the wild success of ChatGPT and other large language models, the artificial neural networks (ANNs) that underpin these systems might be on the wrong track. For one, ANNs are “super ...

Suppose we have a subspace \(\mathbb{S}\) of \(\mathbb{R}^n\) whose basis consists of \(k\) vectors \(\vec{v}_1,\vec{v}_2, \ldots , \vec{v}_k\). \[ \mathbb{S ...