{"paper":{"title":"Finite-size scaling of hetero-associative retrieval in continuous-signal-driven Ising spin systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A tri-layer Ising hetero-associative network maps continuous signals to spins and retrieves across modalities at an operational capacity near 0.5.","cross_cats":["stat.ML"],"primary_cat":"cond-mat.dis-nn","authors_text":"Andrea Ladiana","submitted_at":"2026-05-13T19:33:51Z","abstract_excerpt":"Real-world physical signals are continuous and high-dimensional, yet the statistical-mechanics machinery of associative memory operates on discrete Ising spins. We bridge this divide through a multilayer Ising framework that couples a geometry-preserving continuous-to-Ising encoder (PCA whitening composed with SimHash random-hyperplane projection) to Kanter-Sompolinsky pseudo-inverse memory couplings, embedded directly into the local-field equations of a tri-layer hetero-associative system. The pseudo-inverse correction renders the equal-weight mixture state thermodynamically unstable, so that"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The operational storage capacity obeys the Amit-Gutfreund-Sompolinsky finite-size correction alpha_c(N)=alpha_c(infinity)-c N^{-1/2}, extrapolating to an asymptotic operational limit alpha_c(infinity) approx 0.50 under macroscopic-basin retrieval, and the architecture reconstructs the macroscopic sleep state on parietal EEG and EOG axes from a single noisy frontal-EEG cue.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the PCA-whitening plus SimHash encoder preserves sufficient geometry for the pseudo-inverse couplings to produce a thermodynamically unstable equal-weight mixture whose selection by thermal fluctuations yields reliable cross-modal retrieval in the presence of quenched biological disorder.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A tri-layer Ising hetero-associative memory with PCA-SimHash encoding achieves finite-size capacity scaling to an asymptotic limit near 0.5 and demonstrates cross-modal reconstruction on sleep polysomnography data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A tri-layer Ising hetero-associative network maps continuous signals to spins and retrieves across modalities at an operational capacity near 0.5.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3f5d5b6b1bc3646a49b6353e6aa137c2abb6a8ee937c63358fb38351febb589b"},"source":{"id":"2605.14059","kind":"arxiv","version":1},"verdict":{"id":"f38ca5ca-0fac-474f-8f0a-1d366c4fa922","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:36:07.457285Z","strongest_claim":"The operational storage capacity obeys the Amit-Gutfreund-Sompolinsky finite-size correction alpha_c(N)=alpha_c(infinity)-c N^{-1/2}, extrapolating to an asymptotic operational limit alpha_c(infinity) approx 0.50 under macroscopic-basin retrieval, and the architecture reconstructs the macroscopic sleep state on parietal EEG and EOG axes from a single noisy frontal-EEG cue.","one_line_summary":"A tri-layer Ising hetero-associative memory with PCA-SimHash encoding achieves finite-size capacity scaling to an asymptotic limit near 0.5 and demonstrates cross-modal reconstruction on sleep polysomnography data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the PCA-whitening plus SimHash encoder preserves sufficient geometry for the pseudo-inverse couplings to produce a thermodynamically unstable equal-weight mixture whose selection by thermal fluctuations yields reliable cross-modal retrieval in the presence of quenched biological disorder.","pith_extraction_headline":"A tri-layer Ising hetero-associative network maps continuous signals to spins and retrieves across modalities at an operational capacity near 0.5."},"references":{"count":40,"sample":[{"doi":"","year":null,"title":"Layerσ is initialised with a (possibly noisy) copy of an archetypeµ; lay- ers τ and ϕ are initialised to random spin noise","work_id":"c8ed4c2c-039f-4727-a9f2-256a14ff4268","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"All layers are simultaneously initialised in a symmetric super- position of two archetypes,s(a) t=0 = sign(w1ξµ1,(a) + w2ξµ2,(a))","work_id":"cfcb7e4d-8294-4a75-9f9b-e88b37f4c197","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Easy mixture disentanglement.A baseline pro- tocol that isolates basin stability from symmetry breaking. 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