Pith Number

pith:L7NYTNST

pith:2026:L7NYTNSTZJXPIILKGOVVKEXZ54

not attested not anchored not stored refs pending

Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes

Jianjun Cao, Liu Hanqing, Yuanze Li, Zijian Zhou

Floating-point precision limits trigger slingshot loss spikes by creating numerical feature inflation in neural network training.

arxiv:2605.06152 v3 · 2026-05-07 · cs.LG · cs.CL · math.OC · stat.ML

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\usepackage{pith}
\pithnumber{L7NYTNSTZJXPIILKGOVVKEXZ54}

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Record completeness

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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

This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. ... We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially.

C2weakest assumption

The assumption that, once the logit difference exceeds the absorption-error threshold, the gradient of the correct class is rounded exactly to zero during backpropagation while incorrect-class gradients remain nonzero, and that this imbalance necessarily creates an exponential positive feedback loop with the features.

C3one line summary

Slingshot loss spikes arise from floating-point precision limits that round correct-class gradients to zero, breaking zero-sum constraints and driving exponential parameter growth through numerical feature inflation.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:05:56.307519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fdb89b653ca6ef4216a33ab5512f9ef29b3b23ece549439da00d82227a108e7

Aliases

arxiv: 2605.06152 · arxiv_version: 2605.06152v3 · doi: 10.48550/arxiv.2605.06152 · pith_short_12: L7NYTNSTZJXP · pith_short_16: L7NYTNSTZJXPIILK · pith_short_8: L7NYTNST

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L7NYTNSTZJXPIILKGOVVKEXZ54 \
  | 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: 5fdb89b653ca6ef4216a33ab5512f9ef29b3b23ece549439da00d82227a108e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30d360ecf2d6eab91e508e8d66faefea61f8ca43dab8def0f9c1ed9e16f7486a",
    "cross_cats_sorted": [
      "cs.CL",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T12:45:21Z",
    "title_canon_sha256": "b286a045e76c4eba4a7313944c8d26b736e3eb958e213f3b7b49d9e25c003486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06152",
    "kind": "arxiv",
    "version": 3
  }
}