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Most existing approaches concentrate on adjusting the overall data distribution but neglect the underlying interactions between samples during training. However, we argue that such interactions cannot be overlooked, as real-world data samples frequently exhibit directional influences on each other, making the training order crucial. Intuitively, we can prioritize train-units with greater influence to improves learning efficiency. In this work, we propose $D^3$, a Dynamic Directional graph-constrained Data scheduling framework. $D^3$ formulates the complex interactions among train-units as a dynamic influence graph, where edges represent loss-based dependencies. It then solves a constrained optimization problem over this graph to derive the training order, which ensures that the data sequence resp","title":"D$^3$: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training","url":"https://arxiv.org/abs/2605.31164","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.31164v1 Announce Type: cross \nAbstract: Training data plays a central role in large language models (LLMs) optimization, motivating extensive research on data scheduling strategies. Most existing approaches concentrate on adjusting the overall data distribution but neglect the underlying interactions between samples during training. However, we argue that such interactions cannot be overlooked, as real-world data samples frequently exhibit directional influences on each other, making the training order crucial. Intuitively, we can prioritize train-units with greater influence to improves learning efficiency. In this work, we propose $D^3$, a Dynamic Directional graph-constrained Data scheduling framework. $D^3$ formulates the complex interactions among train-units as a dynamic influence graph, where edges represent loss-based dependencies. It then solves a constrained optimization problem over this graph to derive the training order, which ensures that the data sequence resp","title":"D$^3$: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-01T04:43:13Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.31164"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:dc39f8989bfc57e6df79fecbc6e425cb79ebb5d7a6d6b9889ad30bd664cdfca210b17d4e87fbd08ae3cef13ddbce54ba42d9768107fdd587f87d1e0fcbaffb00","signer":"crovia.substrate","subject":{"observed_at":"2026-06-01T04:43:13Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.31164"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"924b57e89ab006f320b0c152f62c4c1f0b40242c9a4e94e9c9d1dacd5e07d4bb","leaf_index":163931,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"5e6ed5bf916b1af264973053f4a5873bd39393d819c8ade8deff780f60fe8c80","side":"left"},{"sibling":"302c38bc585a1b38e74b068f32c9051dc51888e5d044fdd081c034909c46ee58","side":"left"},{"sibling":"22b45820afc9e02696f7b3df5df48264f77a1db7cdf9e05c24590eebaebeea1f","side":"right"},{"sibling":"a4eaea9cde7c5db77e343069421933b8be4e5e74266995970ca609cd71bd0bf8","side":"left"},{"sibling":"783e488a5c3788f190112785ced2a9e5c54d1476b9c8502b54b1a37bfface4af","side":"left"},{"sibling":"dfc75d876c3c72c4618885129dffa5c4358f9b0a7a9f107a153d3e90a549c5bc","side":"right"},{"sibling":"a1ff84cd2c69f189b478824886ec6dfb932db86d85674c90e121b3e31e941af7","side":"left"},{"sibling":"c80f3e378be31136ba3005ae1d4e6fb73ee42b46d44ded3d5ec7b012545b00f5","side":"right"},{"sibling":"86fede29e507d01bfe35484a1579149e8e99b3527ff48559423f6056d11af46a","side":"right"},{"sibling":"fc601f0745c37fc5f7c249300e654db05d61bb9059885eeb0b0a5047b5d28408","side":"right"},{"sibling":"6ed9290cdae063f13bfeb71c4c5440595cabb61fd4b39225b9cc913ffb336dd7","side":"right"},{"sibling":"a0446b923d1ce90021e78edff07f6bfc7cc2a1326a565c5f0786b82a24dd0a2a","side":"right"},{"sibling":"e598fd53912c30e58ca8e58d7d8a338fe0f2ecb63fdd99225bc703c499c948ec","side":"right"},{"sibling":"fc4873333221ec8167697f75b6f6a8a08491a8cf18952defb65fb6d4958fa5e7","side":"right"},{"sibling":"05c8a827da2a05549ee3250310777009120c687885816bf6c7c74801bfaa346d","side":"right"},{"sibling":"5ea2f2dc9f046df723b6bd9932d61a9a3d80a76e79ce1b939b3d93ff79b5a91c","side":"left"},{"sibling":"ce41d9b82f34b16efd653dfb3552acc4e2512939e47903e5fc979fbed00c5764","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":164217,"merkle_root":"a1098816aea1b60b8fe37b62410469bc5024a2c335bbec4f6ef2add7875dbdf2","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260601T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-01T05:37:41Z","sig_algorithm":"ed25519","signature":"d7f91db1d54b9495c499440c2828f4bd53360555391ce6e25adea5183bc1fa0f697d80708a099d0b0429e6f8cb6c71e7fccf82acb3c84481149974fb26074708","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_14146656acfd7498d2e04509e638e1bda4572d8b657163ace1b6762e96850f10"}}