Pith Number

pith:HWR2B3TF

pith:2025:HWR2B3TF4DD2CAN2KQSAKH373P

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A projection-based framework for gradient-free and parallel learning

Andreas Bergmeister, Manish Krishan Lal, Stefanie Jegelka, Suvrit Sra

Neural network training can be recast as projecting parameters onto local constraints from each operation instead of using gradients.

arxiv:2506.05878 v3 · 2025-06-06 · cs.LG

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\pithnumber{HWR2B3TF4DD2CAN2KQSAKH373P}

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Record completeness

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3 Author claim open · sign in to claim

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 reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network.

C2weakest assumption

That iterative projection algorithms applied to the composed local constraints will converge to useful network parameters that achieve competitive performance on standard benchmarks, as claimed in the demonstration of PJAX on MLPs, CNNs, and RNNs.

C3one line summary

Neural network training is recast as a large-scale feasibility problem solved by composing and iterating projection operators, implemented in a new JAX framework called PJAX.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:20.868308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3da3a0ee65e0c7a101ba5424051f7fdbe904b1b0d42a35b917f47fac16b0f9a5

Aliases

arxiv: 2506.05878 · arxiv_version: 2506.05878v3 · doi: 10.48550/arxiv.2506.05878 · pith_short_12: HWR2B3TF4DD2 · pith_short_16: HWR2B3TF4DD2CAN2 · pith_short_8: HWR2B3TF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HWR2B3TF4DD2CAN2KQSAKH373P \
  | 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: 3da3a0ee65e0c7a101ba5424051f7fdbe904b1b0d42a35b917f47fac16b0f9a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cc6083d4c3c2155d7181744a6353df264095aab098c64ca274e5cf630e9006a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-06-06T08:44:56Z",
    "title_canon_sha256": "5c3f8bbbf5f04f514e074c4999dcf318e101aaed9961118f1f93979e4f86a626"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05878",
    "kind": "arxiv",
    "version": 3
  }
}