Pith Number

pith:Y5YZUJBB

pith:2026:Y5YZUJBBGHKAOTAPD4EGO5AM43

not attested not anchored not stored refs pending

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior

Laura Gomezjurado Gonzalez

In encoder-decoder arithmetic models the grokking delay stems from decoder inability to use structure the encoder has already learned.

arxiv:2604.13082 v2 · 2026-03-30 · cs.LG · cs.AI

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5YZUJBBGHKAOTAPD4EGO5AM43}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

In encoder-decoder arithmetic models the long delay reflects limited access to already learned structure rather than failure to acquire that structure; transplanting a trained encoder accelerates grokking by 2.75 times while freezing a converged encoder and retraining only the decoder eliminates the plateau and yields 97.6% accuracy.

C2weakest assumption

That the causal effects observed in one-step Collatz prediction and the 15-base comparison isolate decoder access as the general cause of grokking delays without confounding factors from architecture, optimization, or task-specific arithmetic.

C3one line summary

The grokking delay in encoder-decoder models on one-step Collatz prediction stems from decoder inability to use early-learned encoder representations of parity and residue structure, with numeral base acting as a strong inductive bias that can raise accuracy from failure to 99.8%.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics

Receipt and verification

First computed	2026-06-19T16:11:23.038086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7719a242131d4074c0f1f0867740ce6e61045eca6182b035e1c00390b24b887

Aliases

arxiv: 2604.13082 · arxiv_version: 2604.13082v2 · doi: 10.48550/arxiv.2604.13082 · pith_short_12: Y5YZUJBBGHKA · pith_short_16: Y5YZUJBBGHKAOTAP · pith_short_8: Y5YZUJBB

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/Y5YZUJBBGHKAOTAPD4EGO5AM43 \
  | 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: c7719a242131d4074c0f1f0867740ce6e61045eca6182b035e1c00390b24b887

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5e2c056b38027a2fab43f01d9c02969ae242a2034d6e847b793b3b7ffd5aed9",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-30T22:20:38Z",
    "title_canon_sha256": "cfa70a576d760eebe73bf7f49145cf8130d0aba48f6ecd0d92be10be183c2b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13082",
    "kind": "arxiv",
    "version": 2
  }
}