{"paper":{"title":"A projection-based framework for gradient-free and parallel learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Neural network training can be recast as projecting parameters onto local constraints from each operation instead of using gradients.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andreas Bergmeister, Manish Krishan Lal, Stefanie Jegelka, Suvrit Sra","submitted_at":"2025-06-06T08:44:56Z","abstract_excerpt":"We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That iterative projection algorithms applied to the composed local constraints will converge to useful network parameters that achieve competitive performance on standard benchmarks, as claimed in the demonstration of PJAX on MLPs, CNNs, and RNNs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Neural network training is recast as a large-scale feasibility problem solved by composing and iterating projection operators, implemented in a new JAX framework called PJAX.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Neural network training can be recast as projecting parameters onto local constraints from each operation instead of using gradients.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5d41efa5fb69a748cf79a7db80027657a0fe622683e5496494f609616bba8e20"},"source":{"id":"2506.05878","kind":"arxiv","version":3},"verdict":{"id":"eaa96aa3-0a98-487d-9e97-3e22eed94e4d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T10:35:39.746245Z","strongest_claim":"We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network.","one_line_summary":"Neural network training is recast as a large-scale feasibility problem solved by composing and iterating projection operators, implemented in a new JAX framework called PJAX.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That iterative projection algorithms applied to the composed local constraints will converge to useful network parameters that achieve competitive performance on standard benchmarks, as claimed in the demonstration of PJAX on MLPs, CNNs, and RNNs.","pith_extraction_headline":"Neural network training can be recast as projecting parameters onto local constraints from each operation instead of using gradients."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05878/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8f90ada4906c79fd22c508f64884e66fb247dae67c4a0059605ebfb505788138"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}