{"paper":{"title":"SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"SAGE replaces AdamW in hybrid LLM optimizers by adding a bounded per-dimension scale that tames embedding-layer gradients, cutting memory while raising perplexity performance.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Hyun-Tae Kim, Wooin Lee","submitted_at":"2026-04-09T00:07:38Z","abstract_excerpt":"The AdamW optimizer, while standard for LLM pretraining, is a critical memory bottleneck, consuming optimizer states equivalent to twice the model's size. Although light-state optimizers like SinkGD attempt to address this issue, we identify the embedding layer dilemma: these methods fail to handle the sparse, high-variance gradients inherent to embeddings, forcing a hybrid design that reverts to AdamW and partially negates the memory gains. We propose SAGE (Sign Adaptive GradiEnt), a novel optimizer that resolves this dilemma by replacing AdamW in this hybrid structure. SAGE combines a Lion-s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On Llama models up to 1.3B parameters, our SAGE-based hybrid achieves new state-of-the-art perplexity, outperforming all baselines, including SinkGD hybrid, while significantly reducing optimizer state memory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the high-variance, sparse gradients in the embedding layer can be sufficiently controlled by a single per-dimension scale provably bounded by 1.0 without reintroducing the instability that forced prior methods back to AdamW.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SAGE replaces AdamW in memory-efficient LLM hybrids with a Lion-style sign update plus a provably bounded O(d) adaptive scale, delivering SOTA perplexity on Llama-1.3B while cutting optimizer-state memory.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"SAGE replaces AdamW in hybrid LLM optimizers by adding a bounded per-dimension scale that tames embedding-layer gradients, cutting memory while raising perplexity performance.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9959ef4638bbf38b963afe1a2259eda47df1e90fb591bc7e06d3b07a3a633033"},"source":{"id":"2604.07663","kind":"arxiv","version":2},"verdict":{"id":"b0946ce6-2077-4e74-877c-38f3fb057507","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:33:19.243230Z","strongest_claim":"On Llama models up to 1.3B parameters, our SAGE-based hybrid achieves new state-of-the-art perplexity, outperforming all baselines, including SinkGD hybrid, while significantly reducing optimizer state memory.","one_line_summary":"SAGE replaces AdamW in memory-efficient LLM hybrids with a Lion-style sign update plus a provably bounded O(d) adaptive scale, delivering SOTA perplexity on Llama-1.3B while cutting optimizer-state memory.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the high-variance, sparse gradients in the embedding layer can be sufficiently controlled by a single per-dimension scale provably bounded by 1.0 without reintroducing the instability that forced prior methods back to AdamW.","pith_extraction_headline":"SAGE replaces AdamW in hybrid LLM optimizers by adding a bounded per-dimension scale that tames embedding-layer gradients, cutting memory while raising perplexity performance."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.07663/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":3,"sample":[{"doi":"","year":2016,"title":"Layer Normalization","work_id":"20a2d720-0046-4c7c-bcd6-327ec8143f69","ref_index":1,"cited_arxiv_id":"1607.06450","is_internal_anchor":true},{"doi":"","year":2024,"title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2048,"title":"Opt.\" refers to optimizer state memory, while","work_id":"68f80759-6f11-4808-8e11-3247f4a03dd9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"2577a907f5d50e501c1dd2a2c777f4dce9b45a3f6abf1b802efbb7184d046c09","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"d2e5cd0875624164da59059db0f1aca195c89aacecf5a84d78bc5af301a8de37"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}