What Neural Network Field Theory Can and Cannot Realise on a Computer
Read the original on arXiv Machine Learning →The paper investigates the limits of implementing neural network field theory on a computer, focusing on function classes that are regular enough for computation. It presents a no‑go theorem showing that finite‑width network ensembles cannot consistently realize either a quantum or effective field theory due to violations of reflection positivity and lack of scale separation. The study distinguishes between finite‑width and infinite‑width interpretations, concluding that only smeared correlators of the infinite‑width limit are computable with controlled error, and identifies two possible ways to evade the theorem—by relaxing finite variance or exact rotation invariance.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.