{"paper":{"title":"Tensor Programs III: Neural Matrix Laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.NE","authors_text":"Greg Yang","submitted_at":"2020-09-22T16:59:24Z","abstract_excerpt":"In a neural network (NN), *weight matrices* linearly transform inputs into *preactivations* that are then transformed nonlinearly into *activations*. A typical NN interleaves multitudes of such linear and nonlinear transforms to express complex functions. Thus, the (pre-)activations depend on the weights in an intricate manner. We show that, surprisingly, (pre-)activations of a randomly initialized NN become *independent* from the weights as the NN's widths tend to infinity, in the sense of asymptotic freeness in random matrix theory. We call this the Free Independence Principle (FIP), which h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10685","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.10685/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}