Pith Number

pith:6ONAGNNX

pith:2026:6ONAGNNXV7PBJCVS34VTAMMXYU

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When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability

Jacob Meyer Cohen, Laurence Wroe, Logan Riggs Smith, Melwina Albuquerque, ML Nissen Gonzalez, Thomas Dooms

Tensor similarity is a weight-based metric that algebraically determines when two neural networks implement the same computation by ignoring irrelevant symmetries.

arxiv:2605.15183 v1 · 2026-05-14 · cs.LG

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4 Citations open

5 Replications 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

Tensor similarity captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.

C2weakest assumption

That the recursive algorithm correctly identifies functional equivalence for all tensor-based models without missing non-linear interactions or symmetries outside weight-space basis changes.

C3one line summary

Tensor similarity is a symmetry-invariant metric that measures functional equivalence between tensor-based networks using a recursive algorithm for cross-layer mechanisms.

References

30 extracted · 30 resolved · 11 Pith anchors

[1] David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba 2025

[2] Available: https://arxiv.org/abs/1704.05796 · arXiv:1704.05796

[3] Neural networks learn statistics of increasing complexity

[4] Convolutional Rectifier Networks as Generalized Tensor Decompositions · arXiv:1603.00162

[5] On the Expressive Power of Deep Learning: A Tensor Analysis · arXiv:1509.05009

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T21:40:25.131488Z
Last reissued	2026-05-17T21:57:18.510566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

f39a0335b7afde148ab2df2b303197c5020b979c1c18e65cd4daded5eddefac7

Aliases

arxiv: 2605.15183 · arxiv_version: 2605.15183v1 · pith_short_12: 6ONAGNNXV7PB · pith_short_16: 6ONAGNNXV7PBJCVS · pith_short_8: 6ONAGNNX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6ONAGNNXV7PBJCVS34VTAMMXYU \
  | 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: f39a0335b7afde148ab2df2b303197c5020b979c1c18e65cd4daded5eddefac7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcce65d5f71ac5fafe019f00c52eff421f7b4aecff078765275eb1bedcc95775",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T17:58:27Z",
    "title_canon_sha256": "7bde740558cb6b4bd2e9b8c8ef41968c551bd3f797b08f522c06d4d8b1fe8847"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15183",
    "kind": "arxiv",
    "version": 1
  }
}