Pith Number

pith:IJ3L5UAQ

pith:2026:IJ3L5UAQ2NP5GQFZE7CMPQAAGB

not attested not anchored not stored refs resolved

Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs

Jingzhou Jiang, Kar Yan Tam, Yi Yang

Layer-wise dynamics in language models reveal performance signals beyond final representations.

arxiv:2605.12714 v1 · 2026-05-12 · cs.LG · cs.CL

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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

Applying LRD to 31 models on 30 MTEB tasks reveals architectural and task-level differences that are not apparent from final-layer representations alone... These results show that layer-wise structure provides signal for both interpretation and deployment decisions.

C2weakest assumption

That the three proposed measurements (Frenet, NRS, GFMI) capture dynamics that are causally relevant to downstream performance rather than merely correlated on the tested set of models and tasks.

C3one line summary

LRD framework with Frenet, NRS, and GFMI metrics shows layer-wise structure in 31 models provides usable signal for model selection and pruning on MTEB tasks.

References

78 extracted · 78 resolved · 10 Pith anchors

[1] Princeton University Press 2008

[2] The Falcon Series of Open Language Models 2023 · arXiv:2311.16867

[3] Laplacian eigenmaps for dimensionality reduction and data representation.Neural computation, 15(6):1373–1396 2003

[4] Manifold regularization: A geometric framework for learning from labeled and unlabeled examples.Journal of machine learning research, 7(11), 2006 2006

[5] A full-text learning to rank dataset for medical information retrieval 2016

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.499594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4276bed010d35fd340b927c4c7c0003053a3ef69893ab3379a7d7cb1090a88f2

Aliases

arxiv: 2605.12714 · arxiv_version: 2605.12714v1 · doi: 10.48550/arxiv.2605.12714 · pith_short_12: IJ3L5UAQ2NP5 · pith_short_16: IJ3L5UAQ2NP5GQFZ · pith_short_8: IJ3L5UAQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IJ3L5UAQ2NP5GQFZE7CMPQAAGB \
  | 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: 4276bed010d35fd340b927c4c7c0003053a3ef69893ab3379a7d7cb1090a88f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dbab8f8ccbd0cebd9692cdd441dd1ad8c9dec3c8a50c89e89dd8e3558a65434",
    "cross_cats_sorted": [
      "cs.CL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T20:22:45Z",
    "title_canon_sha256": "97bad1d980c31a6c0d7217e1c85058ab6b563cfd7aab6b18cbb3b4e82b24fa8c"
  },
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  "source": {
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    "kind": "arxiv",
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}