Pith Number

pith:4GZLISFO

pith:2023:4GZLISFORWYFPHMHLGN4SDP2P6

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Progress measures for grokking via mechanistic interpretability

Jacob Steinhardt, Jess Smith, Lawrence Chan, Neel Nanda, Tom Lieberum

Transformers on modular addition learn a Fourier rotation algorithm that gradually replaces memorization during training.

arxiv:2301.05217 v3 · 2023-01-12 · cs.LG · cs.AI

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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

We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space.

C2weakest assumption

That the identified Fourier circuit is the dominant mechanism and that ablations in Fourier space fully isolate it without missing other co-occurring computations that could also produce the observed behavior.

C3one line summary

Grokking arises from gradual amplification of a Fourier-based circuit in the weights followed by removal of memorizing components.

References

43 extracted · 43 resolved · 8 Pith anchors

[1] More is different for AI , url=

[3] OpenAI blog , volume=

[4] Advances in neural information processing systems , volume=

[9] 2022 ACM Conference on Fairness, Accountability, and Transparency , pages= 2022

[10] Beren's Blog - Thoughts on AI, Neuroscience, and other things that interest me

Formal links

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Cited by

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Receipt and verification

First computed	2026-05-17T23:39:21.566368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1b2b448ae8db0579d87599bc90dfa7f8b70549e054c6ffc140d0ac4dadecf36

Aliases

arxiv: 2301.05217 · arxiv_version: 2301.05217v3 · doi: 10.48550/arxiv.2301.05217 · pith_short_12: 4GZLISFORWYF · pith_short_16: 4GZLISFORWYFPHMH · pith_short_8: 4GZLISFO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4GZLISFORWYFPHMHLGN4SDP2P6 \
  | 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: e1b2b448ae8db0579d87599bc90dfa7f8b70549e054c6ffc140d0ac4dadecf36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21d2e0a1f4ee7261ee53ba1f358b8ab53995d1926f8e62a563a00647a1530f9c",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-01-12T18:56:49Z",
    "title_canon_sha256": "2b8da6a68b450756d12923b1c2f434a107b1e93fe063bab567c85bdd1c56c5f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.05217",
    "kind": "arxiv",
    "version": 3
  }
}