{"id":"openai-math/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder","pdf":"https://github.com/openai/math/blob/main/preprints/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-spherical-perceptron-with-bi-orthogonally-invariant-disorder-September-24-2026","tags":["statistical-physics","machine-learning","random-matrices"],"score":0,"title":"The spherical perceptron with bi-orthogonally invariant disorder","domain":"Probability and statistical mechanics","family":"222","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We determine the limiting free energy of a spherical perceptron with a bounded continuous activation and a bi-orthogonally invariant disorder matrix. The singular values may have any compact limiting distribution, provided there are no outliers. We give an explicit variational formula for this limit.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Perceptron free energies and microscopic jamming exponents"}