---
OA_place: publisher
OA_type: gold
_id: '19010'
abstract:
- lang: eng
  text: Causal representation learning aims at recovering latent causal variables
    from high-dimensional observations to solve causal downstream tasks, such as predicting
    the effect of new interventions or more robust classification. A plethora of methods
    have been developed, each tackling carefully crafted problem settings that lead
    to different types of identifiability. The folklore is that these different settings
    are important, as they are often linked to different rungs of Pearl's causal hierarchy,
    although not all neatly fit. Our main contribution is to show that many existing
    causal representation learning approaches methodologically align the representation
    to known data symmetries. Identification of the variables is guided by equivalence
    classes across different "data pockets" that are not necessarily causal. This
    result suggests important implications, allowing us to unify many existing approaches
    in a single method that can mix and match different assumptions, including non-causal
    ones, based on the invariances relevant to our application. It also significantly
    benefits applicability, which we demonstrate by improving treatment effect estimation
    on real-world high-dimensional ecological data. Overall, this paper clarifies
    the role of causality assumptions in the discovery of causal variables and shifts
    the focus to preserving data symmetries.
acknowledgement: "We thank Jiaqi Zhang, Francesco Montagna, David Lopez-Paz, Kartik
  Ahuja, Thomas Kipf, Sara\r\nMagliacane, Julius von Kügelgen, Kun Zhang, and Bernhard
  Schölkopf for extremely helpful discussion. Riccardo Cadei was supported by a Google
  Research Scholar Award to Francesco Locatello. We acknowledge the Third Bellairs
  Workshop on Causal Representation Learning held at the Bellairs Research Institute,
  February 9/16, 2024, and a debate on the difference between interventions and counterfactuals
  in disentanglement and CRL that took place during Dhanya Sridhar’s lecture, which
  motivated us to significantly broaden the scope of the paper. We thank Dhanya and
  all participants of the workshop."
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: Dario
  full_name: Rancati, Dario
  id: feb58f2e-72ef-11ef-b75a-8f0894539cd0
  last_name: Rancati
- first_name: Riccardo
  full_name: Cadei, Riccardo
  id: 0fa8b76f-72f0-11ef-b75a-a5da96e5ad6b
  last_name: Cadei
- first_name: Marco
  full_name: Fumero, Marco
  id: 1c1593eb-393f-11ef-bb8e-ab4f1e979650
  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: 'Yao D, Rancati D, Cadei R, Fumero M, Locatello F. Unifying causal representation
    learning with the invariance principle. In: <i>13th International Conference on
    Learning Representations</i>. ICLR; 2025.'
  apa: 'Yao, D., Rancati, D., Cadei, R., Fumero, M., &#38; Locatello, F. (2025). Unifying
    causal representation learning with the invariance principle. In <i>13th International
    Conference on Learning Representations</i>. Singapore: ICLR.'
  chicago: Yao, Dingling, Dario Rancati, Riccardo Cadei, Marco Fumero, and Francesco
    Locatello. “Unifying Causal Representation Learning with the Invariance Principle.”
    In <i>13th International Conference on Learning Representations</i>. ICLR, 2025.
  ieee: D. Yao, D. Rancati, R. Cadei, M. Fumero, and F. Locatello, “Unifying causal
    representation learning with the invariance principle,” in <i>13th International
    Conference on Learning Representations</i>, Singapore, 2025.
  ista: 'Yao D, Rancati D, Cadei R, Fumero M, Locatello F. 2025. Unifying causal representation
    learning with the invariance principle. 13th International Conference on Learning
    Representations. ICLR: International Conference on Learning Representations.'
  mla: Yao, Dingling, et al. “Unifying Causal Representation Learning with the Invariance
    Principle.” <i>13th International Conference on Learning Representations</i>,
    ICLR, 2025.
  short: D. Yao, D. Rancati, R. Cadei, M. Fumero, F. Locatello, in:, 13th International
    Conference on Learning Representations, ICLR, 2025.
conference:
  end_date: 2025-04-28
  location: Singapore
  name: 'ICLR: International Conference on Learning Representations'
  start_date: 2025-04-24
corr_author: '1'
date_created: 2025-02-05T09:23:25Z
date_published: 2025-01-22T00:00:00Z
date_updated: 2026-02-09T05:52:14Z
day: '22'
ddc:
- '000'
department:
- _id: FrLo
external_id:
  arxiv:
  - '2409.02772'
file:
- access_level: open_access
  checksum: c4b5a4a644228c6d1b0283e1368bce9e
  content_type: application/pdf
  creator: flocatel
  date_created: 2026-01-27T12:43:25Z
  date_updated: 2026-01-27T12:43:25Z
  file_id: '21048'
  file_name: 4356_Unifying_Causal_Represent (1).pdf
  file_size: 877014
  relation: main_file
  success: 1
file_date_updated: 2026-01-27T12:43:25Z
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
publication: 13th International Conference on Learning Representations
publication_status: published
publisher: ICLR
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unifying causal representation learning with the invariance principle
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
year: '2025'
...
---
OA_place: publisher
OA_type: gold
_id: '21074'
abstract:
- lang: eng
  text: Neural models learn representations of high-dimensional data on low-dimensional
    manifolds. Multiple factors, including stochasticities in the training process,
    model architectures, and additional inductive biases, may induce different representations,
    even when learning the same task on the same data. However, it has recently been
    shown that when a latent structure is shared between distinct latent spaces, relative
    distances between representations can be preserved, up to distortions. Building
    on this idea, we demonstrate that exploiting the differential-geometric structure
    of latent spaces of neural models, it is possible to capture precisely the transformations
    between representational spaces trained on similar data distributions. Specifically,
    we assume that distinct neural models parametrize approximately the same underlying
    manifold, and introduce a representation based on the pullback metric that captures
    the intrinsic structure of the latent space, while scaling efficiently to large
    models. We validate experimentally our method on model stitching and retrieval
    tasks, covering autoencoders and vision foundation discriminative models, across
    diverse architectures, datasets, pretraining schemes and modalities. Code is available
    at the following link.
acknowledgement: 'We thank Gregor Krzmanc, German Magai, Vital Fernandez for insightful
  discussions in the early stages of the project. HY was supported by the Research
  Council of Finland Flagship programme: Finnish Center for Artificial Intelligence
  FCAI. HY wishes to acknowledge CSC - IT Center for Science, Finland, for computational
  resources. GA was supported by the DFF Sapere Aude Starting Grant “GADL”. SH was
  supported by a research grant (42062) from VILLUM FONDEN and partly funded by the
  Novo Nordisk Foundation through the Center for Basic Research in Life Science (NNF20OC0062606).
  SH received funding from the European Research Council (ERC) under the European
  Union’s Horizon Programme (grant agreement 101125003). MF is supported by the MSCA
  IST-Bridge fellowship which has received funding from the European Union’s Horizon
  2020 research and innovation program under the Marie Skłodowska-Curie grant agreement
  No 101034413.'
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Hanlin
  full_name: Yu, Hanlin
  last_name: Yu
- first_name: Befrin
  full_name: Inal, Befrin
  last_name: Inal
- first_name: Georgios
  full_name: Arvanitidis, Georgios
  last_name: Arvanitidis
- first_name: Soren
  full_name: Hauberg, Soren
  last_name: Hauberg
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
- first_name: Marco
  full_name: Fumero, Marco
  id: 1c1593eb-393f-11ef-bb8e-ab4f1e979650
  last_name: Fumero
citation:
  ama: 'Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. Connecting
    neural models latent geometries with relative geodesic representations. In: <i>39th
    Annual Conference on Neural Information Processing Systems</i>. Vol 38. Neural
    Information Processing Systems Foundation; 2025.'
  apa: 'Yu, H., Inal, B., Arvanitidis, G., Hauberg, S., Locatello, F., &#38; Fumero,
    M. (2025). Connecting neural models latent geometries with relative geodesic representations.
    In <i>39th Annual Conference on Neural Information Processing Systems</i> (Vol.
    38). San Diego, CA, United States: Neural Information Processing Systems Foundation.'
  chicago: Yu, Hanlin, Befrin Inal, Georgios Arvanitidis, Soren Hauberg, Francesco
    Locatello, and Marco Fumero. “Connecting Neural Models Latent Geometries with
    Relative Geodesic Representations.” In <i>39th Annual Conference on Neural Information
    Processing Systems</i>, Vol. 38. Neural Information Processing Systems Foundation,
    2025.
  ieee: H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, and M. Fumero, “Connecting
    neural models latent geometries with relative geodesic representations,” in <i>39th
    Annual Conference on Neural Information Processing Systems</i>, San Diego, CA,
    United States, 2025, vol. 38.
  ista: 'Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. 2025. Connecting
    neural models latent geometries with relative geodesic representations. 39th Annual
    Conference on Neural Information Processing Systems. NeurIPS: Neural Information
    Processing Systems, Advances in Neural Information Processing Systems, vol. 38.'
  mla: Yu, Hanlin, et al. “Connecting Neural Models Latent Geometries with Relative
    Geodesic Representations.” <i>39th Annual Conference on Neural Information Processing
    Systems</i>, vol. 38, Neural Information Processing Systems Foundation, 2025.
  short: H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, M. Fumero, 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'
date_created: 2026-01-29T14:31:52Z
date_published: 2025-12-15T00:00:00Z
date_updated: 2026-02-11T09:03:37Z
day: '15'
ddc:
- '000'
department:
- _id: FrLo
ec_funded: 1
external_id:
  arxiv:
  - '2506.01599'
file:
- access_level: open_access
  checksum: b1a645418025f46394764cd16d0cb089
  content_type: application/pdf
  creator: flocatel
  date_created: 2026-01-29T14:31:42Z
  date_updated: 2026-01-29T14:31:42Z
  file_id: '21075'
  file_name: 2506.01599v2.pdf
  file_size: 7749349
  relation: main_file
  success: 1
file_date_updated: 2026-01-29T14:31:42Z
has_accepted_license: '1'
intvolume: '        38'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: 39th Annual Conference on Neural Information Processing Systems
publication_identifier:
  issn:
  - 1049-5258
publication_status: epub_ahead
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
status: public
title: Connecting neural models latent geometries with relative geodesic 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: '19515'
abstract:
- lang: eng
  text: "Neural models learn data representations that lie on low-dimensional manifolds,\r\nyet
    modeling the relation between these representational spaces is an ongoing challenge.
    By integrating spectral geometry principles into neural modeling, we show\r\nthat
    this problem can be better addressed in the functional domain, mitigating complexity,
    while enhancing interpretability and performances on downstream tasks.\r\nTo this
    end, we introduce a multi-purpose framework to the representation learning\r\ncommunity,
    which allows to: (i) compare different spaces in an interpretable way\r\nand measure
    their intrinsic similarity; (ii) find correspondences between them, both\r\nin
    unsupervised and weakly supervised settings, and (iii) to effectively transfer\r\nrepresentations
    between distinct spaces. We validate our framework on various\r\napplications,
    ranging from stitching to retrieval tasks, and on multiple modalities,\r\ndemonstrating
    that Latent Functional Maps can serve as a swiss-army knife for\r\nrepresentation
    alignment"
acknowledgement: MF is supported by the MSCA IST-Bridge fellowship which has received
  funding from the European Union’s Horizon 2020 research and innovation program under
  the Marie Skłodowska-Curie grant agreement No 101034413. ER and VM are supported
  by the PNRR MUR project PE0000013-FAIR. MP is supported by the Sapienza grant "Predicting
  and Explaining Clinical Trial Outcomes", prot. RG12218166FA3F13.
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Marco
  full_name: Fumero, Marco
  id: 1c1593eb-393f-11ef-bb8e-ab4f1e979650
  last_name: Fumero
- first_name: Marco
  full_name: Pegoraro, Marco
  last_name: Pegoraro
- first_name: Valentino
  full_name: Maiorca, Valentino
  last_name: Maiorca
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
- first_name: Emanuele
  full_name: Rodolà, Emanuele
  last_name: Rodolà
citation:
  ama: 'Fumero M, Pegoraro M, Maiorca V, Locatello F, Rodolà E. Latent functional
    maps: A spectral framework for representation alignment. In: <i>38th Conference
    on Neural Information Processing Systems</i>. Vol 37. Neural Information Processing
    Systems Foundation; 2024.'
  apa: 'Fumero, M., Pegoraro, M., Maiorca, V., Locatello, F., &#38; Rodolà, E. (2024).
    Latent functional maps: A spectral framework for representation alignment. In
    <i>38th Conference on Neural Information Processing Systems</i> (Vol. 37). Vancouver,
    Canada: Neural Information Processing Systems Foundation.'
  chicago: 'Fumero, Marco, Marco Pegoraro, Valentino Maiorca, Francesco Locatello,
    and Emanuele Rodolà. “Latent Functional Maps: A Spectral Framework for Representation
    Alignment.” In <i>38th Conference on Neural Information Processing Systems</i>,
    Vol. 37. Neural Information Processing Systems Foundation, 2024.'
  ieee: 'M. Fumero, M. Pegoraro, V. Maiorca, F. Locatello, and E. Rodolà, “Latent
    functional maps: A spectral framework for representation alignment,” in <i>38th
    Conference on Neural Information Processing Systems</i>, Vancouver, Canada, 2024,
    vol. 37.'
  ista: 'Fumero M, Pegoraro M, Maiorca V, Locatello F, Rodolà E. 2024. Latent functional
    maps: A spectral framework for representation alignment. 38th Conference on Neural
    Information Processing Systems. NeurIPS: Neural Information Processing Systems,
    Advances in Neural Information Processing Systems, vol. 37.'
  mla: 'Fumero, Marco, et al. “Latent Functional Maps: A Spectral Framework for Representation
    Alignment.” <i>38th Conference on Neural Information Processing Systems</i>, vol.
    37, Neural Information Processing Systems Foundation, 2024.'
  short: M. Fumero, M. Pegoraro, V. Maiorca, F. Locatello, E. Rodolà, in:, 38th Conference
    on Neural Information Processing Systems, Neural Information Processing Systems
    Foundation, 2024.
conference:
  end_date: 2024-12-15
  location: Vancouver, Canada
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2024-12-09
corr_author: '1'
date_created: 2025-04-06T22:01:32Z
date_published: 2024-12-20T00:00:00Z
date_updated: 2025-05-14T11:36:51Z
day: '20'
department:
- _id: FrLo
ec_funded: 1
external_id:
  arxiv:
  - '2406.14183'
intvolume: '        37'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2406.14183
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: 38th Conference on Neural Information Processing Systems
publication_identifier:
  issn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Latent functional maps: A spectral framework for representation alignment'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '19517'
abstract:
- lang: eng
  text: "In this paper, we present a novel data-free method for merging neural networks
    in weight space. Differently from most existing works, our method optimizes for
    the permutations of network neurons globally across all layers. This allows us
    to enforce cycle consistency of the permutations when merging n ≥ 3 models, allowing
    circular compositions of permutations to be computed without accumulating error
    along the path. We qualitatively and quantitatively motivate the need for such
    a constraint, showing its benefits when merging sets of models in scenarios spanning
    varying architectures and datasets. We finally show that, when coupled\r\nwith
    activation renormalization, our approach yields the best results in the task."
acknowledgement: "This work is supported by the ERC grant no.802554 (SPECGEO), PRIN
  2020 project\r\nno.2020TA3K9N (LEGO.AI), and PNRR MUR project PE0000013-FAIR. Marco
  Fumero is supported by the MSCA IST-Bridge fellowship which has received funding
  from the European Union’s Horizon 2020 research and innovation program under the
  Marie Skłodowska-Curie grant agreement No 101034413. We thank Simone Scardapane
  for the helpful feedback on the paper."
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Donato
  full_name: Crisostomi, Donato
  last_name: Crisostomi
- first_name: Marco
  full_name: Fumero, Marco
  id: 1c1593eb-393f-11ef-bb8e-ab4f1e979650
  last_name: Fumero
- first_name: Daniele
  full_name: Baieri, Daniele
  last_name: Baieri
- first_name: Florian
  full_name: Bernard, Florian
  last_name: Bernard
- first_name: Emanuele
  full_name: Rodolà, Emanuele
  last_name: Rodolà
citation:
  ama: 'Crisostomi D, Fumero M, Baieri D, Bernard F, Rodolà E. C2M3: Cycle-consistent
    multi-model merging. In: <i>38th Conference on Neural Information Processing Systems</i>.
    Vol 37. Neural Information Processing Systems Foundation; 2024.'
  apa: 'Crisostomi, D., Fumero, M., Baieri, D., Bernard, F., &#38; Rodolà, E. (2024).
    C2M3: Cycle-consistent multi-model merging. In <i>38th Conference on Neural Information
    Processing Systems</i> (Vol. 37). Vancouver, Canada: Neural Information Processing
    Systems Foundation.'
  chicago: 'Crisostomi, Donato, Marco Fumero, Daniele Baieri, Florian Bernard, and
    Emanuele Rodolà. “C2M3: Cycle-Consistent Multi-Model Merging.” In <i>38th Conference
    on Neural Information Processing Systems</i>, Vol. 37. Neural Information Processing
    Systems Foundation, 2024.'
  ieee: 'D. Crisostomi, M. Fumero, D. Baieri, F. Bernard, and E. Rodolà, “C2M3: Cycle-consistent
    multi-model merging,” in <i>38th Conference on Neural Information Processing Systems</i>,
    Vancouver, Canada, 2024, vol. 37.'
  ista: 'Crisostomi D, Fumero M, Baieri D, Bernard F, Rodolà E. 2024. C2M3: Cycle-consistent
    multi-model merging. 38th Conference on Neural Information Processing Systems.
    NeurIPS: Neural Information Processing Systems, Advances in Neural Information
    Processing Systems, vol. 37.'
  mla: 'Crisostomi, Donato, et al. “C2M3: Cycle-Consistent Multi-Model Merging.” <i>38th
    Conference on Neural Information Processing Systems</i>, vol. 37, Neural Information
    Processing Systems Foundation, 2024.'
  short: D. Crisostomi, M. Fumero, D. Baieri, F. Bernard, E. Rodolà, in:, 38th Conference
    on Neural Information Processing Systems, Neural Information Processing Systems
    Foundation, 2024.
conference:
  end_date: 2024-12-15
  location: Vancouver, Canada
  name: 'NeurIPS: Neural Information Processing Systems'
  start_date: 2024-12-09
corr_author: '1'
date_created: 2025-04-06T22:01:32Z
date_published: 2024-12-20T00:00:00Z
date_updated: 2025-05-14T11:36:59Z
day: '20'
department:
- _id: FrLo
ec_funded: 1
external_id:
  arxiv:
  - '2405.17897'
intvolume: '        37'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2405.17897
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: 38th Conference on Neural Information Processing Systems
publication_identifier:
  issn:
  - 1049-5258
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'C2M3: Cycle-consistent multi-model merging'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2024'
...