Pith Number

pith:75CWPNKQ

pith:2026:75CWPNKQXMP5DM6EA6CIGINBNY

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Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training

Anna Rumshisky, Namrata Shivagunde, Sherin Muckatira, Vijeta Deshpande

Low-rank pre-training methods reach geometrically distinct loss basins than full-rank training even at matched perplexity.

arxiv:2605.13652 v1 · 2026-05-13 · cs.LG · cs.AI · cs.CL

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Claims

C1strongest claim

We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. Full-rank training settles into a sharper basin than low-rank methods along random directions, while the reverse holds for the top-1 PCA direction.

C2weakest assumption

That the 16 metrics across 1-D loss landscape, interpolation, spectral structure, and activation similarity sufficiently characterize meaningful differences in solution quality, generalization, and downstream performance.

C3one line summary

Low-rank pre-training methods converge to geometrically and spectrally distinct basins from full-rank training and from each other, even at similar validation perplexity.

References

30 extracted · 30 resolved · 1 Pith anchors

[1] A modern look at the relationship between sharpness and generaliza- tion 2023

[2] Understanding pre-training and fine-tuning from loss landscape perspectives 2025

[3] Fira: Can we achieve full-rank training of llms under low-rank constraint?ArXiv, abs/2410.01623, 2024 2024

[4] Linear mode connectivity and the lottery ticket hypothesis 2020

[5] The language model evaluation harness, 07 2024 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:17.448889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff4567b550bb1fd1b3c407848321a16e22e6c4cd7a2bbee5cd426b5aa1bdb53a

Aliases

arxiv: 2605.13652 · arxiv_version: 2605.13652v1 · doi: 10.48550/arxiv.2605.13652 · pith_short_12: 75CWPNKQXMP5 · pith_short_16: 75CWPNKQXMP5DM6E · pith_short_8: 75CWPNKQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/75CWPNKQXMP5DM6EA6CIGINBNY \
  | 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: ff4567b550bb1fd1b3c407848321a16e22e6c4cd7a2bbee5cd426b5aa1bdb53a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbe06d6966ca0f1da8317ca4cb7edc912392e2916f0a5f55be6b1dc8db123c29",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T15:11:37Z",
    "title_canon_sha256": "b761ae48dffb740662929dc60450dcc022e1b609a0c695cc77bb0181259b9197"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}