{"paper":{"title":"Predictability, complexity and learning","license":"","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.other","cs.LG","nlin.AO","q-bio.OT"],"primary_cat":"physics.data-an","authors_text":"Ilya Nemenman, Naftali Tishby, William Bialek","submitted_at":"2000-07-20T00:45:11Z","abstract_excerpt":"We define {\\em predictive information} $I_{\\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\\rm pred} (T)$ can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then $I_{\\rm pred} (T)$ grows logarithmically with a coefficient that counts the dimensionality of the model space. In contrast, power--law growth is associated, for example, with the learning o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0007070","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":""},"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"}