Pith Number

pith:Y4U6JS2S

pith:2020:Y4U6JS2SCK7JI5UFDPZPUQJZBV

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Hopfield Networks is All You Need

Bernhard Sch\"afl, David Kreil, Geir Kjetil Sandve, G\"unter Klambauer, Hubert Ramsauer, Johannes Brandstetter, Johannes Lehner, Lukas Gruber, Markus Holzleitner, Michael Kopp, Michael Widrich, Milena Pavlovi\'c, Philipp Seidl, Sepp Hochreiter, Thomas Adler, Victor Greiff

A modern Hopfield network with continuous states has an update rule identical to the attention mechanism in transformers.

arxiv:2008.02217 v3 · 2020-07-16 · cs.NE · cs.CL · cs.LG · stat.ML

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Claims

C1strongest claim

The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models.

C2weakest assumption

That the continuous-state Hopfield dynamics remain stable and useful when inserted as layers inside large-scale gradient-trained networks without introducing new optimization difficulties or losing the claimed exponential capacity.

C3one line summary

Modern Hopfield networks store exponentially many patterns, retrieve them in one update, and have an update rule equivalent to transformer attention, enabling new Hopfield layers that improve results on multiple instance learning and drug design tasks.

References

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[1] Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , series =

[2] van den Oord and Y

[3] A Simple Framework for Contrastive Learning of Visual Representations , author=. CoRR , volume=

[4] Advances in Neural Information Processing Systems , pages=

[5] Layer normalization , author=. ArXiv , eprint=

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Cited by

23 papers in Pith

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Self-Organization and Spectral Mechanism of Attractor Landscapes in High-Capacity Kernel Hopfield Networks

TTT3R: 3D Reconstruction as Test-Time Training

Receipt and verification

First computed	2026-05-17T23:38:14.915710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c729e4cb5212be9476851bf2fa41390d6396ba71a78601f5e49c5282ead7108e

Aliases

arxiv: 2008.02217 · arxiv_version: 2008.02217v3 · doi: 10.48550/arxiv.2008.02217 · pith_short_12: Y4U6JS2SCK7J · pith_short_16: Y4U6JS2SCK7JI5UF · pith_short_8: Y4U6JS2S

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Y4U6JS2SCK7JI5UFDPZPUQJZBV \
  | 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: c729e4cb5212be9476851bf2fa41390d6396ba71a78601f5e49c5282ead7108e

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.NE",
    "submitted_at": "2020-07-16T17:52:37Z",
    "title_canon_sha256": "aa4c7031940ca65cfd28ae9a8ea533d9d267004f60a6c8e30a5d154df26fd115"
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