Pith Number

pith:T77PCZSF

pith:2014:T77PCZSFVOCERFD4WKSLSKUU3A

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NICE: Non-linear Independent Components Estimation

David Krueger, Laurent Dinh, Yoshua Bengio

A composition of coupling layers learns an invertible non-linear map that turns high-dimensional data into independent latent factors for exact likelihood training.

arxiv:1410.8516 v6 · 2014-10-30 · cs.LG

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Claims

C1strongest claim

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). ... The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy.

C2weakest assumption

That a composition of the proposed coupling layers (each based on a deep neural network) can represent sufficiently complex non-linear transformations while preserving trivial Jacobian determinant and inverse.

C3one line summary

NICE learns a composition of invertible neural-network layers that transform data into independent latent variables, enabling exact log-likelihood training and sampling for density estimation.

References

33 extracted · 33 resolved · 5 Pith anchors

[1] J., Bergeron, A., Bouchard, N., and Bengio, Y 2012

[2] Bengio, Y. (1991). Artificial Neural Networks and their Application to Sequence Recognition . PhD thesis, McGill University, (Computer Science), Montreal, Canada 1991

[3] Bengio, Y. (2009). Learning deep architectures for AI . Now Publishers 2009

[4] arXiv preprint arXiv:1407.7906 , year = 2014

[5] Bengio, Y. and Bengio, S. (2000). Modeling high-dimensional discrete data with multi-layer neural networks. In Solla, S., Leen, T., and M \"u ller, K.-R., editors, Advances in Neural Information Proce 2000

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Cited by

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Receipt and verification

First computed	2026-05-18T02:56:12.910105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ffef16645ab8448947cb2a4b92a94d8303c29ad2bebaa481a2a565929eaa26c

Aliases

arxiv: 1410.8516 · arxiv_version: 1410.8516v6 · doi: 10.48550/arxiv.1410.8516 · pith_short_12: T77PCZSFVOCE · pith_short_16: T77PCZSFVOCERFD4 · pith_short_8: T77PCZSF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T77PCZSFVOCERFD4WKSLSKUU3A \
  | 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: 9ffef16645ab8448947cb2a4b92a94d8303c29ad2bebaa481a2a565929eaa26c

Canonical record JSON

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    "abstract_canon_sha256": "588006fc4b87ba2e3f6fe1845c0d6a9d660db1a20677045c5394583d6e92a66d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2014-10-30T19:44:20Z",
    "title_canon_sha256": "3a84268e3097cae2e1731db974aa88b083ee7cfd3135bf182d0f9f939a8af702"
  },
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