{"paper":{"title":"An Amortized Efficiency Threshold for Comparing Neural and Heuristic Solvers in Combinatorial Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Neural solvers become net energy-efficient after a fixed number of deployments once training cost is amortized against lower per-instance use.","cross_cats":["cs.AI","cs.NE"],"primary_cat":"cs.LG","authors_text":"Sohaib Afifi","submitted_at":"2026-05-14T09:39:15Z","abstract_excerpt":"A common critique of neural combinatorial-optimization solvers is that they are less energy-efficient than CPU metaheuristics, given the operational energy cost of training them on GPUs. This paper examines the inferential step from \"training is expensive\" to \"neural solvers are net-inefficient\", which is where the critique actually goes wrong. Training the network costs a large fixed amount of GPU energy; running the metaheuristic costs a small amount of CPU energy on every instance, repeated as long as the solver is deployed. The two are not commensurable until a deployment volume is fixed. "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We define the Amortized Efficiency Threshold (AET) as the deployment volume above which a neural solver breaks even with a heuristic baseline in total energy or carbon, under an explicit constraint on solution quality. We show that the cumulative-energy ratio between the two solvers tends to a constant strictly below one whenever the network wins per-instance.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The per-instance energy consumption of the neural solver is lower than the heuristic and remains constant across deployments, allowing the cumulative ratio to converge to a value below one independent of training cost measurement.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper introduces the Amortized Efficiency Threshold (AET) to identify the deployment volume at which neural combinatorial optimization solvers become more energy-efficient overall than heuristic baselines after amortizing training costs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Neural solvers become net energy-efficient after a fixed number of deployments once training cost is amortized against lower per-instance use.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bbb371b799f51a08f68f586748ea7b4176874ccf179edddce6b4f5e0ee05d288"},"source":{"id":"2605.14624","kind":"arxiv","version":1},"verdict":{"id":"4ae45ebc-2368-4559-876f-16a64c4de455","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T04:44:29.917885Z","strongest_claim":"We define the Amortized Efficiency Threshold (AET) as the deployment volume above which a neural solver breaks even with a heuristic baseline in total energy or carbon, under an explicit constraint on solution quality. We show that the cumulative-energy ratio between the two solvers tends to a constant strictly below one whenever the network wins per-instance.","one_line_summary":"The paper introduces the Amortized Efficiency Threshold (AET) to identify the deployment volume at which neural combinatorial optimization solvers become more energy-efficient overall than heuristic baselines after amortizing training costs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The per-instance energy consumption of the neural solver is lower than the heuristic and remains constant across deployments, allowing the cumulative ratio to converge to a value below one independent of training cost measurement.","pith_extraction_headline":"Neural solvers become net energy-efficient after a fixed number of deployments once training cost is amortized against lower per-instance use."},"references":{"count":26,"sample":[{"doi":"","year":2023,"title":"Product environmental reports.https://www.apple.com/environment/, 2023","work_id":"5f9f781b-5368-4751-bc49-0585ce805838","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Le, Mohammad Norouzi, and Samy Bengio","work_id":"1b791fa7-1cef-43c0-956c-d5e913bc8422","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"RL4CO: An extensive reinforcement learning for combinatorial optimization benchmark","work_id":"84e58379-ff41-4527-8df1-59b211f2038d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Lee, Gu-Yeon Wei, David Brooks, and Carole-Jean Wu","work_id":"6e9b3f1d-73e2-4d27-9b3f-bf147ec06aa8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"An extension of the Lin-Kernighan-Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems.Roskilde University Technical Report, 2017","work_id":"0899700f-2edc-4739-ad10-c96825279761","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":26,"snapshot_sha256":"b3ab6478e0fe7ba6eba4bbb6db7e5d63aa11d0bc4195a99ac88de517e6439704","internal_anchors":2},"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"}