---
OA_place: publisher
OA_type: gold
_id: '20817'
abstract:
- lang: eng
  text: We present Mechanistic PDE Networks -- a model for discovery of governing
    partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal
    data as space-time dependent linear partial differential equations in neural network
    hidden representations. The represented PDEs are then solved and decoded for specific
    tasks. The learned PDE representations naturally express the spatiotemporal dynamics
    in data in neural network hidden space, enabling increased modeling power. Solving
    the PDE representations in a compute and memory-efficient way, however, is a significant
    challenge. We develop a native, GPU-capable, parallel, sparse and differentiable
    multigrid solver specialized for linear partial differential equations that acts
    as a module in Mechanistic PDE Networks. Leveraging the PDE solver we propose
    a discovery architecture that can discovers nonlinear PDEs in complex settings,
    while being robust to noise. We validate PDE discovery on a number of PDEs including
    reaction-diffusion and Navier-Stokes equations.
acknowledgement: "AP. This project has received funding from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 101034413.\r\nFL. This research was funded in whole or in part
  by the Austrian Science Fund (FWF) 10.55776/COE12. For open access purposes, the
  author has applied a CC BY public\r\ncopyright license to any author accepted manuscript
  version arising from this submission."
alternative_title:
- PMLR
article_processing_charge: No
arxiv: 1
author:
- first_name: Adeel A
  full_name: Pervez, Adeel A
  id: fca6d90c-d47f-11ee-bc87-93ff51604981
  last_name: Pervez
- first_name: Efstratios
  full_name: Gavves, Efstratios
  last_name: Gavves
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Pervez AA, Gavves E, Locatello F. Mechanistic PDE networks for discovery of
    governing equations. In: <i>42nd International Conference on Machine Learning</i>.
    Vol 267. ML Research Press; 2025:48962-48973.'
  apa: 'Pervez, A. A., Gavves, E., &#38; Locatello, F. (2025). Mechanistic PDE networks
    for discovery of governing equations. In <i>42nd International Conference on Machine
    Learning</i> (Vol. 267, pp. 48962–48973). Vancouver, Canada: ML Research Press.'
  chicago: Pervez, Adeel A, Efstratios Gavves, and Francesco Locatello. “Mechanistic
    PDE Networks for Discovery of Governing Equations.” In <i>42nd International Conference
    on Machine Learning</i>, 267:48962–73. ML Research Press, 2025.
  ieee: A. A. Pervez, E. Gavves, and F. Locatello, “Mechanistic PDE networks for discovery
    of governing equations,” in <i>42nd International Conference on Machine Learning</i>,
    Vancouver, Canada, 2025, vol. 267, pp. 48962–48973.
  ista: 'Pervez AA, Gavves E, Locatello F. 2025. Mechanistic PDE networks for discovery
    of governing equations. 42nd International Conference on Machine Learning. ICML:
    International Conference on Machine Learning, PMLR, vol. 267, 48962–48973.'
  mla: Pervez, Adeel A., et al. “Mechanistic PDE Networks for Discovery of Governing
    Equations.” <i>42nd International Conference on Machine Learning</i>, vol. 267,
    ML Research Press, 2025, pp. 48962–73.
  short: A.A. Pervez, E. Gavves, F. Locatello, in:, 42nd International Conference
    on Machine Learning, ML Research Press, 2025, pp. 48962–48973.
conference:
  end_date: 2025-07-19
  location: Vancouver, Canada
  name: 'ICML: International Conference on Machine Learning'
  start_date: 2025-07-13
corr_author: '1'
date_created: 2025-12-14T23:02:04Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2026-09-16T07:17:18Z
day: '01'
ddc:
- '000'
department:
- _id: FrLo
ec_funded: 1
external_id:
  arxiv:
  - '2502.18377'
file:
- access_level: open_access
  checksum: 933cb673fb41416f537278fb990df6c3
  content_type: application/pdf
  creator: dernst
  date_created: 2025-12-16T12:21:49Z
  date_updated: 2025-12-16T12:21:49Z
  file_id: '20827'
  file_name: 2025_ICML_Pervez.pdf
  file_size: 993381
  relation: main_file
  success: 1
file_date_updated: 2025-12-16T12:21:49Z
has_accepted_license: '1'
intvolume: '       267'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 48962-48973
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 42nd International Conference on Machine Learning
publication_identifier:
  eissn:
  - 2640-3498
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/ alpz/mech-nn-discovery-pde
scopus_import: '1'
status: public
title: Mechanistic PDE networks for discovery of governing equations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22832'
abstract:
- lang: eng
  text: "In many scientific experiments, the data annotating cost constraints the
    pace\r\nfor testing novel hypotheses. Yet, modern machine learning pipelines offer
    a\r\npromising solution—provided their predictions yield correct conclusions.
    We\r\nfocus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the\r\ntreatment
    effect in an unlabeled target experiment, relying on training data with\r\nthe
    same outcome annotated but potentially different treatment or effect modifiers.\r\nWe
    first show that conditional calibration guarantees valid PPCI at population\r\nlevel.
    Then, we introduce a sufficient representation constraint transferring validity\r\nacross
    experiments, which we propose to enforce in practice in Deconfounded\r\nEmpirical
    Risk Minimization, our new model-agnostic training objective. We\r\nvalidate our
    method on synthetic and real-world scientific data, solving impossible\r\nproblem
    instances for Empirical Risk Minimization even with standard invariance\r\nconstraints.
    In particular, for the first time, we achieve valid causal inference\r\non a scientific
    experiment with complex recording and no human annotations,\r\nfine-tuning a foundational
    model on our similar annotated experiment."
acknowledgement: "We thank the Causal Learning and Artificial Intelligence group at
  ISTA for the continuous feedback\r\non the project and valuable discussions. We
  thank the Social Immunity group at ISTA, particularly\r\nJinook Oh, for the annotation
  program and Michaela Hoenigsberger for supporting our ecological\r\nexperiment.
  Riccardo Cadei is supported by a Google Research Scholar Award and a Google Initiated\r\nGift
  to Francesco Locatello. This research was funded in part by the Austrian Science
  Fund (FWF)\r\n10.55776/COE12). It was further partially supported by the ISTA Interdisciplinary
  Project Committee\r\nfor the collaborative project “ALED” between Francesco Locatello
  and Sylvia Cremer. For open\r\naccess purposes, the author has applied a CC BY public
  copyright license to any author accepted\r\nmanuscript version arising from this
  submission.\r\n"
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Riccardo
  full_name: Cadei, Riccardo
  id: 0fa8b76f-72f0-11ef-b75a-a5da96e5ad6b
  last_name: Cadei
- first_name: Ilker
  full_name: Demirel, Ilker
  last_name: Demirel
- first_name: Piersilvio
  full_name: De Bartolomeis, Piersilvio
  last_name: De Bartolomeis
- first_name: Lukas
  full_name: Lindorfer, Lukas
  id: 85f0e6d3-06b3-11ec-8982-8c5049fa4455
  last_name: Lindorfer
- first_name: Sylvia
  full_name: Cremer, Sylvia
  id: 2F64EC8C-F248-11E8-B48F-1D18A9856A87
  last_name: Cremer
  orcid: 0000-0002-2193-3868
- first_name: Cordelia
  full_name: Schmid, Cordelia
  last_name: Schmid
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Cadei R, Demirel I, De Bartolomeis P, et al. Prediction-Powered Causal Inferences.
    In: <i>39th Conference on Neural Information Processing Systems</i>. Vol 38. Neural
    Information Processing Systems Foundation; 2025:82200-82229. doi:<a href="https://doi.org/10.52202/085713-2479">10.52202/085713-2479</a>'
  apa: 'Cadei, R., Demirel, I., De Bartolomeis, P., Lindorfer, L., Cremer, S., Schmid,
    C., &#38; Locatello, F. (2025). Prediction-Powered Causal Inferences. In <i>39th
    Conference on Neural Information Processing Systems</i> (Vol. 38, pp. 82200–82229).
    San Diego, CA, United States: Neural Information Processing Systems Foundation.
    <a href="https://doi.org/10.52202/085713-2479">https://doi.org/10.52202/085713-2479</a>'
  chicago: Cadei, Riccardo, Ilker Demirel, Piersilvio De Bartolomeis, Lukas Lindorfer,
    Sylvia Cremer, Cordelia Schmid, and Francesco Locatello. “Prediction-Powered Causal
    Inferences.” In <i>39th Conference on Neural Information Processing Systems</i>,
    38:82200–229. Neural Information Processing Systems Foundation, 2025. <a href="https://doi.org/10.52202/085713-2479">https://doi.org/10.52202/085713-2479</a>.
  ieee: R. Cadei <i>et al.</i>, “Prediction-Powered Causal Inferences,” in <i>39th
    Conference on Neural Information Processing Systems</i>, San Diego, CA, United
    States, 2025, vol. 38, pp. 82200–82229.
  ista: 'Cadei R, Demirel I, De Bartolomeis P, Lindorfer L, Cremer S, Schmid C, Locatello
    F. 2025. Prediction-Powered Causal Inferences. 39th Conference on Neural Information
    Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in
    Neural Information Processing Systems, vol. 38, 82200–82229.'
  mla: Cadei, Riccardo, et al. “Prediction-Powered Causal Inferences.” <i>39th Conference
    on Neural Information Processing Systems</i>, vol. 38, Neural Information Processing
    Systems Foundation, 2025, pp. 82200–29, doi:<a href="https://doi.org/10.52202/085713-2479">10.52202/085713-2479</a>.
  short: R. Cadei, I. Demirel, P. De Bartolomeis, L. Lindorfer, S. Cremer, C. Schmid,
    F. Locatello, in:, 39th Conference on Neural Information Processing Systems, Neural
    Information Processing Systems Foundation, 2025, pp. 82200–82229.
conference:
  end_date: 2025-12-07
  location: San Diego, CA, United States
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2025-12-02
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: "We share all the code implementation in the supplementary
  material.\r\nOur new experimental ecology dataset preview is anonymously shared
  on Figshare at\r\nhttps://figshare.com/s/9a490b6f6eeebd73350b. We further rely on
  ISTAnt dataset publicly\r\navailable at https://doi.org/10.6084/m9.figshare.26484934.v2.
  The synthetic experiments\r\non CausalMNIST relies on MNIST dataset LeCun [1998],
  publicly available. Additional\r\nexperimental details are reported in Section 5
  and Appendices B-C."
date_created: 2026-09-06T22:02:01Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-09-17T06:56:40Z
day: '01'
department:
- _id: FrLo
- _id: GradSch
- _id: SyCr
doi: 10.52202/085713-2479
external_id:
  arxiv:
  - '2502.06343'
fulldoi: https://doi.org/10.52202/085713-2479
intvolume: '        38'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2502.06343
month: '12'
oa: 1
oa_version: Preprint
page: 82200-82229
project:
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 39th Conference on Neural Information Processing Systems
publication_identifier:
  isbn:
  - '9798331338275'
  issn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Prediction-Powered Causal Inferences
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...
---
OA_place: publisher
OA_type: free access
_id: '21076'
abstract:
- lang: eng
  text: In many scientific experiments, the data annotating cost constraints the pace
    for testing novel hypotheses. Yet, modern machine learning pipelines offer a promising
    solution—provided their predictions yield correct conclusions. We focus on Prediction-Powered
    Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled
    target experiment, relying on training data with the same outcome annotated but
    potentially different treatment or effect modifiers. We first show that conditional
    calibration guarantees valid PPCI at population level. Then, we introduce a sufficient
    representation constraint transferring validity across experiments, which we propose
    to enforce in practice in Deconfounded Empirical Risk Minimization, our new model-agnostic
    training objective. We validate our method on synthetic and real-world scientific
    data, solving impossible problem instances for Empirical Risk Minimization even
    with standard invariance constraints. In particular, for the first time, we achieve
    valid causal inference on a scientific experiment with complex recording and no
    human annotations, fine-tuning a foundational model on our similar annotated experiment.
acknowledgement: We thank the Causal Learning and Artificial Intelligence group at
  ISTA for the continuous feedback on the project and valuable discussions. We thank
  the Social Immunity group at ISTA, particularly Jinook Oh, for the annotation program
  and Michaela Hoenigsberger for supporting our ecological experiment. Riccardo Cadei
  is supported by a Google Research Scholar Award and a Google Initiated Gift to Francesco
  Locatello. This research was funded in part by the Austrian Science Fund (FWF) 10.55776/COE12).
  It was further partially supported by the ISTA Interdisciplinary Project Committee
  for the collaborative project “ALED” between Francesco Locatello and Sylvia Cremer.
  For open access purposes, the author has applied a CC BY public copyright license
  to any author accepted manuscript version arising from this submission.
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
author:
- first_name: Riccardo
  full_name: Cadei, Riccardo
  id: 0fa8b76f-72f0-11ef-b75a-a5da96e5ad6b
  last_name: Cadei
- first_name: Ilker
  full_name: Demirel, Ilker
  last_name: Demirel
- first_name: Piersilvio
  full_name: De Bartolomeis, Piersilvio
  last_name: De Bartolomeis
- first_name: Lukas
  full_name: Lindorfer, Lukas
  id: 85f0e6d3-06b3-11ec-8982-8c5049fa4455
  last_name: Lindorfer
- first_name: Sylvia
  full_name: Cremer, Sylvia
  id: 2F64EC8C-F248-11E8-B48F-1D18A9856A87
  last_name: Cremer
  orcid: 0000-0002-2193-3868
- first_name: Cordelia
  full_name: Schmid, Cordelia
  last_name: Schmid
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Cadei R, Demirel I, De Bartolomeis P, et al. Prediction-powered causal inferences.
    In: <i>39th Annual Conference on Neural Information Processing Systems</i>. Vol
    38. Neural Information Processing Systems Foundation; 2025. doi:<a href="https://doi.org/10.52202/085713-2479">10.52202/085713-2479</a>'
  apa: 'Cadei, R., Demirel, I., De Bartolomeis, P., Lindorfer, L., Cremer, S., Schmid,
    C., &#38; Locatello, F. (2025). Prediction-powered causal inferences. In <i>39th
    Annual Conference on Neural Information Processing Systems</i> (Vol. 38). San
    Diego, CA, United States: Neural Information Processing Systems Foundation. <a
    href="https://doi.org/10.52202/085713-2479">https://doi.org/10.52202/085713-2479</a>'
  chicago: Cadei, Riccardo, Ilker Demirel, Piersilvio De Bartolomeis, Lukas Lindorfer,
    Sylvia Cremer, Cordelia Schmid, and Francesco Locatello. “Prediction-Powered Causal
    Inferences.” In <i>39th Annual Conference on Neural Information Processing Systems</i>,
    Vol. 38. Neural Information Processing Systems Foundation, 2025. <a href="https://doi.org/10.52202/085713-2479">https://doi.org/10.52202/085713-2479</a>.
  ieee: R. Cadei <i>et al.</i>, “Prediction-powered causal inferences,” in <i>39th
    Annual Conference on Neural Information Processing Systems</i>, San Diego, CA,
    United States, 2025, vol. 38.
  ista: 'Cadei R, Demirel I, De Bartolomeis P, Lindorfer L, Cremer S, Schmid C, Locatello
    F. 2025. Prediction-powered causal inferences. 39th Annual Conference on Neural
    Information Processing Systems. NeurIPS: Neural Information Processing Systems,
    Advances in Neural Information Processing Systems, vol. 38.'
  mla: Cadei, Riccardo, et al. “Prediction-Powered Causal Inferences.” <i>39th Annual
    Conference on Neural Information Processing Systems</i>, vol. 38, Neural Information
    Processing Systems Foundation, 2025, doi:<a href="https://doi.org/10.52202/085713-2479">10.52202/085713-2479</a>.
  short: R. Cadei, I. Demirel, P. De Bartolomeis, L. Lindorfer, S. Cremer, C. Schmid,
    F. Locatello, in:, 39th Annual Conference on Neural Information Processing Systems,
    Neural Information Processing Systems Foundation, 2025.
conference:
  end_date: 2025-12-07
  location: San Diego, CA, United States
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2025-12-02
das_tickbox: '1'
date_created: 2026-01-29T14:35:11Z
date_published: 2025-12-15T00:00:00Z
date_updated: 2026-10-15T09:29:52Z
day: '15'
ddc:
- '000'
department:
- _id: FrLo
- _id: SyCr
doi: 10.52202/085713-2479
file:
- access_level: open_access
  checksum: 92467fa566cd36671a6a3b9e71ae0f71
  content_type: application/pdf
  creator: flocatel
  date_created: 2026-01-29T14:35:02Z
  date_updated: 2026-01-29T14:35:02Z
  file_id: '21077'
  file_name: 17546_Prediction_Powered_Causa.pdf
  file_size: 8489023
  relation: main_file
  success: 1
file_date_updated: 2026-01-29T14:35:02Z
fulldoi: https://doi.org/10.52202/085713-2479
has_accepted_license: '1'
intvolume: '        38'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 39th Annual Conference on Neural Information Processing Systems
publication_identifier:
  eissn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
status: public
title: Prediction-powered causal inferences
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '21068'
abstract:
- lang: eng
  text: "Causal reasoning and discovery, two fundamental tasks of causal analysis,\r\noften
    face challenges in applications due to the complexity, noisiness, and highdimensionality
    of real-world data. Despite recent progress in identifying latent\r\ncausal structures
    using causal representation learning (CRL), what makes learned\r\nrepresentations
    useful for causal downstream tasks and how to evaluate them are\r\nstill not well
    understood. In this paper, we reinterpret CRL using a measurement\r\nmodel framework,
    where the learned representations are viewed as proxy measurements of the latent
    causal variables. Our approach clarifies the conditions under\r\nwhich learned
    representations support downstream causal reasoning and provides\r\na principled
    basis for quantitatively assessing the quality of representations using\r\na new
    Test-based Measurement EXclusivity (T-MEX) score. We validate T-MEX\r\nacross
    diverse causal inference scenarios, including numerical simulations and\r\nreal-world
    ecological video analysis, demonstrating that the proposed framework\r\nand corresponding
    score effectively assess the identification of learned representations and their
    usefulness for causal downstream tasks. Reproducible code can\r\nbe found at https://github.com/shimenghuang/a-measurement-perspective-of-crl."
acknowledgement: "This research was funded in whole or in part by the Austrian Science
  Fund (FWF) 10.55776/COE12. For open access purposes, the author has applied a CC
  BY public copyright license to any accepted manuscript version arising from this
  submission.\r\n"
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Dingling
  full_name: Yao, Dingling
  id: d3e02e50-48a8-11ee-8f62-c108061797fa
  last_name: Yao
- first_name: Shimeng
  full_name: Huang, Shimeng
  id: 989c2a06-fb4e-11ef-a992-ab766442255b
  last_name: Huang
  orcid: 0000-0001-6919-821X
- first_name: Riccardo
  full_name: Cadei, Riccardo
  id: 0fa8b76f-72f0-11ef-b75a-a5da96e5ad6b
  last_name: Cadei
- first_name: Kun
  full_name: Zhang, Kun
  last_name: Zhang
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Yao D, Huang S, Cadei R, Zhang K, Locatello F. The third pillar of causal
    analysis? A measurement perspective on causal representations. In: <i>39th Annual
    Conference on Neural Information Processing Systems</i>. Vol 38. Neural Information
    Processing Systems Foundation; 2025. doi:<a href="https://doi.org/10.52202/085713-1444">10.52202/085713-1444</a>'
  apa: 'Yao, D., Huang, S., Cadei, R., Zhang, K., &#38; Locatello, F. (2025). The
    third pillar of causal analysis? A measurement perspective on causal representations.
    In <i>39th Annual Conference on Neural Information Processing Systems</i> (Vol.
    38). San Diego, CA, United States: Neural Information Processing Systems Foundation.
    <a href="https://doi.org/10.52202/085713-1444">https://doi.org/10.52202/085713-1444</a>'
  chicago: Yao, Dingling, Shimeng Huang, Riccardo Cadei, Kun Zhang, and Francesco
    Locatello. “The Third Pillar of Causal Analysis? A Measurement Perspective on
    Causal Representations.” In <i>39th Annual Conference on Neural Information Processing
    Systems</i>, Vol. 38. Neural Information Processing Systems Foundation, 2025.
    <a href="https://doi.org/10.52202/085713-1444">https://doi.org/10.52202/085713-1444</a>.
  ieee: D. Yao, S. Huang, R. Cadei, K. Zhang, and F. Locatello, “The third pillar
    of causal analysis? A measurement perspective on causal representations,” in <i>39th
    Annual Conference on Neural Information Processing Systems</i>, San Diego, CA,
    United States, 2025, vol. 38.
  ista: 'Yao D, Huang S, Cadei R, Zhang K, Locatello F. 2025. The third pillar of
    causal analysis? A measurement perspective on causal representations. 39th Annual
    Conference on Neural Information Processing Systems. NeurIPS: Neural Information
    Processing Systems, Advances in Neural Information Processing Systems, vol. 38.'
  mla: Yao, Dingling, et al. “The Third Pillar of Causal Analysis? A Measurement Perspective
    on Causal Representations.” <i>39th Annual Conference on Neural Information Processing
    Systems</i>, vol. 38, Neural Information Processing Systems Foundation, 2025,
    doi:<a href="https://doi.org/10.52202/085713-1444">10.52202/085713-1444</a>.
  short: D. Yao, S. Huang, R. Cadei, K. Zhang, F. Locatello, in:, 39th Annual Conference
    on Neural Information Processing Systems, Neural Information Processing Systems
    Foundation, 2025.
conference:
  end_date: 2025-12-07
  location: San Diego, CA, United States
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2025-12-02
corr_author: '1'
das_tickbox: '1'
date_created: 2026-01-29T14:24:56Z
date_published: 2025-12-15T00:00:00Z
date_updated: 2026-10-15T09:31:39Z
day: '15'
ddc:
- '000'
department:
- _id: FrLo
doi: 10.52202/085713-1444
external_id:
  arxiv:
  - '2505.17708'
fulldoi: https://doi.org/10.52202/085713-1444
has_accepted_license: '1'
intvolume: '        38'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2505.17708
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 39th Annual Conference on Neural Information Processing Systems
publication_identifier:
  eissn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/shimenghuang/a-measurement-perspective-of-crl
status: public
title: The third pillar of causal analysis? A measurement perspective on causal representations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '21070'
abstract:
- lang: eng
  text: 'Deep learning systems deployed in real-world applications often encounter
    data that is different from their in-distribution (ID). A reliable model should
    ideally abstain from making decisions in this out-of-distribution (OOD) setting.
    Existing state-of-the-art methods primarily focus on feature distances, such as
    k-th nearest neighbors and distances to decision boundaries, either overlooking
    or ineffectively using in-distribution statistics. In this work, we propose a
    novel angle-based metric for OOD detection that is computed relative to the in-distribution
    structure. We demonstrate that the angles between feature representations and
    decision boundaries, viewed from the mean of in-distribution features, serve as
    an effective discriminative factor between ID and OOD data. We evaluate our method
    on nine ImageNet-pretrained models. Our approach achieves the lowest FPR in 5
    out of 9 ImageNet models, obtains the best average FPR overall, and consistently
    ranking among the top 3 across all evaluated models. Furthermore, we highlight
    the benefits of contrastive representations by showing strong performance with
    ResNet SCL and CLIP architectures. Finally, we demonstrate that the scale-invariant
    nature of our score enables an ensemble strategy via simple score summation. '
acknowledgement: "This research was funded in whole or in part by the Austrian Science
  Fund (FWF) 10.55776/COE12. For open access purposes, the author has applied a CC
  BY public copyright license to any accepted manuscript version arising from this
  submission.\r\n"
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Berker
  full_name: Demirel, Berker
  id: 8b4bc47f-3200-11ee-973b-8f0e7be21a9f
  last_name: Demirel
- first_name: 'Marco '
  full_name: 'Fumero, Marco '
  last_name: Fumero
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
citation:
  ama: 'Demirel B, Fumero M, Locatello F. Out-of-Distribution detection with relative
    angles. In: <i>39th Annual Conference on Neural Information Processing Systems</i>.
    Vol 38. Neural Information Processing Systems Foundation; 2025. doi:<a href="https://doi.org/10.52202/085713-3125">10.52202/085713-3125</a>'
  apa: 'Demirel, B., Fumero, M., &#38; Locatello, F. (2025). Out-of-Distribution detection
    with relative angles. In <i>39th Annual Conference on Neural Information Processing
    Systems</i> (Vol. 38). San Diego, CA, United States: Neural Information Processing
    Systems Foundation. <a href="https://doi.org/10.52202/085713-3125">https://doi.org/10.52202/085713-3125</a>'
  chicago: Demirel, Berker, Marco  Fumero, and Francesco Locatello. “Out-of-Distribution
    Detection with Relative Angles.” In <i>39th Annual Conference on Neural Information
    Processing Systems</i>, Vol. 38. Neural Information Processing Systems Foundation,
    2025. <a href="https://doi.org/10.52202/085713-3125">https://doi.org/10.52202/085713-3125</a>.
  ieee: B. Demirel, M. Fumero, and F. Locatello, “Out-of-Distribution detection with
    relative angles,” in <i>39th Annual Conference on Neural Information Processing
    Systems</i>, San Diego, CA, United States, 2025, vol. 38.
  ista: 'Demirel B, Fumero M, Locatello F. 2025. Out-of-Distribution detection with
    relative angles. 39th Annual Conference on Neural Information Processing Systems.
    NeurIPS: Neural Information Processing Systems, Advances in Neural Information
    Processing Systems, vol. 38.'
  mla: Demirel, Berker, et al. “Out-of-Distribution Detection with Relative Angles.”
    <i>39th Annual Conference on Neural Information Processing Systems</i>, vol. 38,
    Neural Information Processing Systems Foundation, 2025, doi:<a href="https://doi.org/10.52202/085713-3125">10.52202/085713-3125</a>.
  short: B. Demirel, M. Fumero, F. Locatello, in:, 39th Annual Conference on Neural
    Information Processing Systems, Neural Information Processing Systems Foundation,
    2025.
conference:
  end_date: 2025-12-07
  location: San Diego, CA, United States
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2025-12-02
corr_author: '1'
das_tickbox: '1'
date_created: 2026-01-29T14:26:47Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-10-15T09:32:34Z
day: '01'
ddc:
- '000'
department:
- _id: FrLo
doi: 10.52202/085713-3125
external_id:
  arxiv:
  - '2410.04525'
fulldoi: https://doi.org/10.52202/085713-3125
has_accepted_license: '1'
intvolume: '        38'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2410.04525
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: a392d8f0-b034-11f1-b88e-d3025c6734f6
  grant_number: COE12
  name: Bilateral Artificial Intelligence (Locatello)
publication: 39th Annual Conference on Neural Information Processing Systems
publication_identifier:
  eissn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/berkerdemirel/ORA-OOD-Detection-with-Relative-Angles
status: public
title: Out-of-Distribution detection with relative angles
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...