{"paper":{"title":"Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A hybrid principal-vector pruning framework refines Koopman subspace invariance with error bounds and rank-one update efficiency for lifted linear prediction.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Dhruv Shah, Jorge Cort\\'es","submitted_at":"2026-05-13T08:04:38Z","abstract_excerpt":"The accuracy of Koopman operator approximations over\n  finite-dimensional spaces relies critically on their invariance\n  properties. These can be rigorously quantified via the principal\n  angles between a candidate subspace and its image under the Koopman\n  operator. This paper proposes a unified algebraic framework for\n  subspace pruning designed to systematically refine the invariance\n  error. We establish the geometric equivalence between\n  consistency-based methods and principal-vector pruning, and build on\n  this insight to introduce a hybrid strategy that balances between\n  multiple and "},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We establish the geometric equivalence between consistency-based methods and principal-vector pruning, and build on this insight to introduce a hybrid strategy that balances between multiple and single principal vector pruning for improved numerical stability and scalability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the principal angles between a candidate subspace and its image under the Koopman operator provide a sufficient and refinable measure of invariance error that can be systematically reduced by pruning without losing essential dynamical information.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hybrid principal-vector pruning framework refines Koopman subspace invariance with error bounds and rank-one update efficiency for lifted linear prediction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"f8770d56de386337c2899322b120ef4bce64ba71a7fb5ccb7e1fda40c4b1e086"},"source":{"id":"2605.13135","kind":"arxiv","version":1},"verdict":{"id":"b7090252-19bc-4972-bfe8-d1895ea025c3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:52:06.109846Z","strongest_claim":"We establish the geometric equivalence between consistency-based methods and principal-vector pruning, and build on this insight to introduce a hybrid strategy that balances between multiple and single principal vector pruning for improved numerical stability and scalability.","one_line_summary":"A hybrid principal-vector pruning framework refines Koopman subspace invariance with error bounds and rank-one update efficiency for lifted linear prediction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the principal angles between a candidate subspace and its image under the Koopman operator provide a sufficient and refinable measure of invariance error that can be systematically reduced by pruning without losing essential dynamical information.","pith_extraction_headline":""},"references":{"count":50,"sample":[{"doi":"","year":null,"title":"We construct a transformation matrixT∈R s×(s−k) by padding Ewith zeros to align with the originals-dimensional space: T= E 0k×(s−k) .(25)","work_id":"f385af87-08a1-473d-bc87-5108b21a864c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"We then perform a QR decomposition ofCas C=Q CRC,(26) whereQ C ∈R s×(s−k) is orthogonal andR new =R C ∈ R(s−k)×(s−k) is the new upper triangular factor","work_id":"88c34ff8-fa4f-478a-a493-2f540a2741c2","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The matricesW new andR new are a valid QR decomposition ofKU new, i.e., KU new =W newRC","work_id":"9cdd8e5f-c1df-4a95-8e95-36f8b8f2e78c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"We employ these eigenfunctions as the ground truth for evaluating the accuracy of the pruning algorithms","work_id":"42294a03-60f6-4382-86e9-df03707b35b2","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Note that kernel EDMD performs the orthogonal projection using the kernel inner product, which is different from the standard L2(µX)inner product used in our other examples","work_id":"71ebac14-bb5a-4883-bd80-4d88c923743c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":50,"snapshot_sha256":"25b46c0bb9775c2c856a75dff6cb45e9190a38882688ed61651029e1a16d439b","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d0080ea76305fcad04d7f969d5ff0be8776983fe28495ff294ad2ee0dec9e3c4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}