{"paper":{"title":"Graph Signal Separation with Learnable Spectral Filters","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"A learnable spectral filtering method separates multiple graph signals from their mixture by restricting each to the low-frequency subspace of its graph.","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Dorina Thanou, Keivan Faghih Niresi, Olga Fink","submitted_at":"2026-04-27T08:46:04Z","abstract_excerpt":"Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable spectral filtering framework. Our approach reconstructs latent components by passing a fixed random input through learnable spectral filters, operating within the low-frequency eigenspace of each source-specific graph Laplacian. The architecture implicitly biases the recovered signals toward smooth patterns by confining reconstruction to these low-frequency"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Numerical experiments confirm that this framework successfully isolates individual sources using solely the observed mixture and the underlying graph topology.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That restricting reconstruction to the low-frequency eigenspace of each source-specific graph Laplacian supplies a sufficiently strong and unique structural prior to separate the latent signals from their mixture, assuming the graphs are known, distinct, and that the signals are indeed smooth on those graphs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An unsupervised learnable spectral filtering method separates graph signals from a single mixture by reconstructing each source in its own low-frequency Laplacian subspace.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A learnable spectral filtering method separates multiple graph signals from their mixture by restricting each to the low-frequency subspace of its graph.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c30b1383b596d0ec044b134b28ede97a51b74899d5c5df9a4396f640d7213547"},"source":{"id":"2604.24185","kind":"arxiv","version":2},"verdict":{"id":"2ef59eb8-1609-4c7b-b5bc-a914ffaf5e23","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T02:08:00.030874Z","strongest_claim":"Numerical experiments confirm that this framework successfully isolates individual sources using solely the observed mixture and the underlying graph topology.","one_line_summary":"An unsupervised learnable spectral filtering method separates graph signals from a single mixture by reconstructing each source in its own low-frequency Laplacian subspace.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That restricting reconstruction to the low-frequency eigenspace of each source-specific graph Laplacian supplies a sufficiently strong and unique structural prior to separate the latent signals from their mixture, assuming the graphs are known, distinct, and that the signals are indeed smooth on those graphs.","pith_extraction_headline":"A learnable spectral filtering method separates multiple graph signals from their mixture by restricting each to the low-frequency subspace of its graph."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.24185/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T07:36:27.009257Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:23:14.977341Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"25c77d0006ba599ac981f270ff53865073ce9fcd51d03658b24ff58b6014f268"},"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"}