Pith Number

pith:KQGQ3HUF

pith:2026:KQGQ3HUFVD5QJXTDZURY2OGC6I

not attested not anchored not stored refs resolved

SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization

Hyun-Tae Kim, Wooin Lee

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.

arxiv:2604.07663 v2 · 2026-04-09 · cs.LG

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\pithnumber{KQGQ3HUFVD5QJXTDZURY2OGC6I}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

3 extracted · 3 resolved · 1 Pith anchors

[1] Layer Normalization 2016 · arXiv:1607.06450

[2] DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L = 2024

[3] Opt." refers to optimizer state memory, while 2048

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-26T01:15:51.382011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

540d0d9e85a8fb04de63cd238d38c2f2182086c8d712ff6ee20cb40ffaa9e74d

Aliases

arxiv: 2604.07663 · arxiv_version: 2604.07663v2 · doi: 10.48550/arxiv.2604.07663 · pith_short_12: KQGQ3HUFVD5Q · pith_short_16: KQGQ3HUFVD5QJXTD · pith_short_8: KQGQ3HUF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KQGQ3HUFVD5QJXTDZURY2OGC6I \
  | 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: 540d0d9e85a8fb04de63cd238d38c2f2182086c8d712ff6ee20cb40ffaa9e74d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a8f77f162041ef977b19efbf3b0e41f621029f50f0f7f23836c3f9a532a3e23",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-09T00:07:38Z",
    "title_canon_sha256": "aa16abe577c9cc3b4f2638308385ac68083532f098b0c3f4f4a2f80d4b295b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07663",
    "kind": "arxiv",
    "version": 2
  }
}