Pith Number

pith:4INHS5MX

pith:2018:4INHS5MXU4CTF2NA44M3Q76XZI

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Neural Ordinary Differential Equations

David Duvenaud, Jesse Bettencourt, Ricky T. Q. Chen, Yulia Rubanova

Deep neural networks can replace discrete layers with continuous dynamics defined by ordinary differential equations.

arxiv:1806.07366 v5 · 2018-06-19 · cs.LG · cs.AI · stat.ML

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Claims

C1strongest claim

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver.

C2weakest assumption

That a neural network can be trained to produce a vector field whose integral yields useful representations, and that standard ODE solvers remain numerically stable and differentiable enough for end-to-end gradient descent across the range of problems considered.

C3one line summary

Neural networks are redefined as continuous dynamical systems by learning the derivative of the hidden state with a neural network and integrating it with an ODE solver.

References

60 extracted · 60 resolved · 16 Pith anchors

[1] Computationally efficient convolved multiple output G aussian processes 2011

[2] OptNet : Differentiable optimization as a layer in neural networks 2017

[3] A general-purpose software framework for dynamic optimization 2013

[4] CasADi -- A software framework for nonlinear optimization and optimal control 2018

[5] Automatic differentiation in machine learning: a survey 2018

Formal links

3 machine-checked theorem links

Cited by

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Receipt and verification

First computed	2026-05-17T23:38:52.504180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e21a797597a70532e9a0e719b87fd7ca2036c66123e7de14314c9cf8640ccbdf

Aliases

arxiv: 1806.07366 · arxiv_version: 1806.07366v5 · doi: 10.48550/arxiv.1806.07366 · pith_short_12: 4INHS5MXU4CT · pith_short_16: 4INHS5MXU4CTF2NA · pith_short_8: 4INHS5MX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4INHS5MXU4CTF2NA44M3Q76XZI \
  | 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: e21a797597a70532e9a0e719b87fd7ca2036c66123e7de14314c9cf8640ccbdf

Canonical record JSON

{
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    "cross_cats_sorted": [
      "cs.AI",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2018-06-19T17:50:12Z",
    "title_canon_sha256": "cae7d85b5a1ddff55631b70fa27eb07d01a0ad8011cd62c9a6516cbfeae065f8"
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