Pith Number

pith:OPXDY4I7

pith:2016:OPXDY4I77QZCOJIAYK7MZBA62N

not attested not anchored not stored refs resolved

Training Deep Nets with Sublinear Memory Cost

Bing Xu, Carlos Guestrin, Chiyuan Zhang, Tianqi Chen

An algorithm trains an n-layer deep network using O(sqrt(n)) memory at the cost of one extra forward pass.

arxiv:1604.06174 v2 · 2016-04-21 · cs.LG

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

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

we design an algorithm that costs O(sqrt(n)) memory to train a n layer network, with only the computational cost of an extra forward pass per mini-batch.

C2weakest assumption

The computation graph can be cleanly segmented into sqrt(n) intervals where recomputing forward passes inside each interval is both correct and cheaper than storing all intermediate activations.

C3one line summary

An algorithm trains n-layer networks with O(sqrt(n)) memory via selective recomputation of activations, at the cost of one extra forward pass.

References

19 extracted · 19 resolved · 2 Pith anchors

[1] Mart ´ın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Good- fellow, Andrew Harp, Geoffr 2015

[2] Seltzer, Malcolm Slaney, Andreas Stolcke, Yongqiang Wang, Huaming Wang, Kaisheng Yao, Dong Yu, Yu Zhang, and Geoffrey Zweig 2014

[3] Aho, Ravi Sethi, and Jeffrey D 1986

[4] Goodfellow, Arnaud Bergeron, Nicolas Bouchard, and Yoshua Bengio 2012

[5] Theano: a CPU and GPU math expression compiler 2010

Formal links

2 machine-checked theorem links

Cited by

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Weave of Formal Thought

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Receipt and verification

First computed	2026-07-04T20:58:46.587642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73ee3c711ffc32272500c2becc841ed34b1fd3e6c2e152b19cec9bc8ffd27284

Aliases

arxiv: 1604.06174 · arxiv_version: 1604.06174v2 · doi: 10.48550/arxiv.1604.06174 · pith_short_12: OPXDY4I77QZC · pith_short_16: OPXDY4I77QZCOJIA · pith_short_8: OPXDY4I7

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/OPXDY4I77QZCOJIAYK7MZBA62N \
  | 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: 73ee3c711ffc32272500c2becc841ed34b1fd3e6c2e152b19cec9bc8ffd27284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c787b38ba02754d98018eff0fb4fc2ae10b4a8b51e8bf91a93b9912c20a48fb4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2016-04-21T04:15:27Z",
    "title_canon_sha256": "09e011e37ca446694c16a9daae35de00bbd8cefc18f9a0e6f527cd1274393225"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.06174",
    "kind": "arxiv",
    "version": 2
  }
}