{"paper":{"title":"Weight space structure and analysis using a finite replica number in the Ising perceptron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Tomoyuki Obuchi, Yoshiyuki Kabashima","submitted_at":"2009-10-13T12:50:43Z","abstract_excerpt":"The weight space of the Ising perceptron in which a set of random patterns is stored is examined using the generating function of the partition function $\\phi(n)=(1/N)\\log [Z^n]$ as the dimension of the weight vector $N$ tends to infinity, where $Z$ is the partition function and $[ ... ]$ represents the configurational average. We utilize $\\phi(n)$ for two purposes, depending on the value of the ratio $\\alpha=M/N$, where $M$ is the number of random patterns. For $\\alpha < \\alpha_{\\rm s}=0.833 ...$, we employ $\\phi(n)$, in conjunction with Parisi's one-step replica symmetry breaking scheme in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2281","kind":"arxiv","version":2},"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"}