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pith:JCCRHYMM

pith:2026:JCCRHYMMAG4N6OHO4IFYTMLVTE

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An Amortized Efficiency Threshold for Comparing Neural and Heuristic Solvers in Combinatorial Optimization

Sohaib Afifi

Neural solvers become net energy-efficient after a fixed number of deployments once training cost is amortized against lower per-instance use.

arxiv:2605.14624 v1 · 2026-05-14 · cs.LG · cs.AI · cs.NE

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

26 extracted · 26 resolved · 2 Pith anchors

[1] Product environmental reports.https://www.apple.com/environment/, 2023 2023

[2] Le, Mohammad Norouzi, and Samy Bengio 2017

[3] RL4CO: An extensive reinforcement learning for combinatorial optimization benchmark 2024

[4] Lee, Gu-Yeon Wei, David Brooks, and Carole-Jean Wu 2021

[5] An extension of the Lin-Kernighan-Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems.Roskilde University Technical Report, 2017 2017

Receipt and verification

First computed	2026-05-17T23:39:04.034391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

488513e18c01b8df38eee20b89b175991793db6e15c2bd3efcbe76bf8cb255af

Aliases

arxiv: 2605.14624 · arxiv_version: 2605.14624v1 · doi: 10.48550/arxiv.2605.14624 · pith_short_12: JCCRHYMMAG4N · pith_short_16: JCCRHYMMAG4N6OHO · pith_short_8: JCCRHYMM

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/JCCRHYMMAG4N6OHO4IFYTMLVTE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 488513e18c01b8df38eee20b89b175991793db6e15c2bd3efcbe76bf8cb255af

Canonical record JSON

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    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T09:39:15Z",
    "title_canon_sha256": "6bf6d7e5356b46f7fab78fc28f445600a8f5aeb37bbae8120bb9f4f0a8fdd5e8"
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