Pith Number

pith:WWKRFPTL

pith:2026:WWKRFPTL57FUW6SVYDP5XPI4TV

not attested not anchored not stored refs resolved

Silent Collapse in Recursive Learning Systems

Zhipeng Zhang

Recursive models lose internal diversity even as standard metrics remain stable or improve.

arxiv:2605.14588 v1 · 2026-05-14 · cs.LG

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4 Citations open

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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

under broad recursive conditions, model internal distributions -- predictive entropy, representational diversity, and tail coverage -- progressively contract even as conventional metrics appear stable or improving.

C2weakest assumption

The three trajectory-level precursors reliably appear multiple generations before any degradation in standard validation metrics, and the MTR loop can estimate trust and modulate learning intensity effectively without access to pristine real data.

C3one line summary

Recursive learning systems undergo silent collapse of internal distributions, preceded by entropy contraction, representation freezing, and tail erosion, which the MTR framework can monitor and avert.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Language models are unsupervised multitask learners.OpenAI Blog, 1(8):9, 2019 2019

[2] Brown, Benjamin Mann, Nick Ryder, et al 1901

[3] Christiano, Jan Leike, Tom B 2017

[4] Concrete problems in ai safety 2016

[5] Ai models collapse when trained on recursively generated data.Nature, 632:755–760,

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.278956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b59512be6befcb4b7a55c0dfdbbd1c9d71d6dbd398dad06432d45caab14b4327

Aliases

arxiv: 2605.14588 · arxiv_version: 2605.14588v1 · doi: 10.48550/arxiv.2605.14588 · pith_short_12: WWKRFPTL57FU · pith_short_16: WWKRFPTL57FUW6SV · pith_short_8: WWKRFPTL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WWKRFPTL57FUW6SVYDP5XPI4TV \
  | 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: b59512be6befcb4b7a55c0dfdbbd1c9d71d6dbd398dad06432d45caab14b4327

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5db07391d10b542455d1e754ac6ac323d33a0a3b89f5ed536b2612e8e6d786a9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T08:59:26Z",
    "title_canon_sha256": "191797cb5e6fe65f4862420a0ef09e0742dddc66f6caac4888e6aff0ff04fa78"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}