[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-02-05T09:23:25Z","arxiv":1,"scopus_import":"1","type":"conference","publication_status":"published","article_processing_charge":"No","quality_controlled":"1","citation":{"short":"D. Yao, D. Rancati, R. Cadei, M. Fumero, F. Locatello, in:, 13th International Conference on Learning Representations, ICLR, 2025.","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.","mla":"Yao, Dingling, et al. “Unifying Causal Representation Learning with the Invariance Principle.” <i>13th International Conference on Learning Representations</i>, ICLR, 2025.","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.","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.","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.","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."},"has_accepted_license":"1","oa_version":"Published Version","oa":1,"month":"01","title":"Unifying causal representation learning with the invariance principle","language":[{"iso":"eng"}],"conference":{"start_date":"2025-04-24","name":"ICLR: International Conference on Learning Representations","location":"Singapore","end_date":"2025-04-28"},"publication":"13th International Conference on Learning Representations","department":[{"_id":"FrLo"}],"day":"22","date_published":"2025-01-22T00:00:00Z","date_updated":"2026-02-09T05:52:14Z","external_id":{"arxiv":["2409.02772"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"status":"public","ddc":["000"],"year":"2025","file_date_updated":"2026-01-27T12:43:25Z","OA_type":"gold","publisher":"ICLR","author":[{"last_name":"Yao","id":"d3e02e50-48a8-11ee-8f62-c108061797fa","full_name":"Yao, Dingling","first_name":"Dingling"},{"first_name":"Dario","full_name":"Rancati, Dario","id":"feb58f2e-72ef-11ef-b75a-8f0894539cd0","last_name":"Rancati"},{"last_name":"Cadei","id":"0fa8b76f-72f0-11ef-b75a-a5da96e5ad6b","full_name":"Cadei, Riccardo","first_name":"Riccardo"},{"first_name":"Marco","full_name":"Fumero, Marco","last_name":"Fumero","id":"1c1593eb-393f-11ef-bb8e-ab4f1e979650"},{"last_name":"Locatello","orcid":"0000-0002-4850-0683","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","full_name":"Locatello, Francesco","first_name":"Francesco"}],"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."}],"_id":"19010","corr_author":"1","OA_place":"publisher","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.","file":[{"file_name":"4356_Unifying_Causal_Represent (1).pdf","success":1,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","date_updated":"2026-01-27T12:43:25Z","file_size":877014,"creator":"flocatel","date_created":"2026-01-27T12:43:25Z","checksum":"c4b5a4a644228c6d1b0283e1368bce9e","file_id":"21048"}]},{"corr_author":"1","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.","file":[{"file_name":"2506.01599v2.pdf","success":1,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":7749349,"date_updated":"2026-01-29T14:31:42Z","checksum":"b1a645418025f46394764cd16d0cb089","creator":"flocatel","date_created":"2026-01-29T14:31:42Z","file_id":"21075"}],"OA_place":"publisher","_id":"21074","publisher":"Neural Information Processing Systems Foundation","abstract":[{"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.","lang":"eng"}],"author":[{"last_name":"Yu","first_name":"Hanlin","full_name":"Yu, Hanlin"},{"last_name":"Inal","full_name":"Inal, Befrin","first_name":"Befrin"},{"full_name":"Arvanitidis, Georgios","first_name":"Georgios","last_name":"Arvanitidis"},{"last_name":"Hauberg","full_name":"Hauberg, Soren","first_name":"Soren"},{"orcid":"0000-0002-4850-0683","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","last_name":"Locatello","full_name":"Locatello, Francesco","first_name":"Francesco"},{"full_name":"Fumero, Marco","first_name":"Marco","last_name":"Fumero","id":"1c1593eb-393f-11ef-bb8e-ab4f1e979650"}],"year":"2025","OA_type":"gold","file_date_updated":"2026-01-29T14:31:42Z","date_updated":"2026-07-28T07:19:01Z","external_id":{"arxiv":["2506.01599"]},"ddc":["000"],"status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"day":"15","intvolume":"        38","date_published":"2025-12-15T00:00:00Z","department":[{"_id":"FrLo"}],"publication":"39th Annual Conference on Neural Information Processing Systems","das_tickbox":"1","conference":{"start_date":"2025-12-02","name":"NeurIPS: Neural Information Processing Systems","location":"San Diego, CA, United States","end_date":"2025-12-07"},"month":"12","title":"Connecting neural models latent geometries with relative geodesic representations","ec_funded":1,"language":[{"iso":"eng"}],"has_accepted_license":"1","alternative_title":["Advances in Neural Information Processing Systems"],"oa":1,"oa_version":"Published Version","quality_controlled":"1","article_processing_charge":"No","citation":{"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.","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.","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.","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.","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."},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"publication_status":"published","arxiv":1,"volume":38,"type":"conference","date_created":"2026-01-29T14:31:52Z","publication_identifier":{"issn":["1049-5258"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_published":"2024-12-20T00:00:00Z","intvolume":"        37","day":"20","status":"public","external_id":{"arxiv":["2406.14183"]},"date_updated":"2025-05-14T11:36:51Z","conference":{"name":"NeurIPS: Neural Information Processing Systems","start_date":"2024-12-09","location":"Vancouver, Canada","end_date":"2024-12-15"},"publication":"38th Conference on Neural Information Processing Systems","department":[{"_id":"FrLo"}],"_id":"19515","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.","OA_place":"repository","corr_author":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.14183","open_access":"1"}],"OA_type":"green","year":"2024","abstract":[{"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","lang":"eng"}],"author":[{"full_name":"Fumero, Marco","first_name":"Marco","id":"1c1593eb-393f-11ef-bb8e-ab4f1e979650","last_name":"Fumero"},{"last_name":"Pegoraro","full_name":"Pegoraro, Marco","first_name":"Marco"},{"full_name":"Maiorca, Valentino","first_name":"Valentino","last_name":"Maiorca"},{"full_name":"Locatello, Francesco","first_name":"Francesco","last_name":"Locatello","orcid":"0000-0002-4850-0683","id":"26cfd52f-2483-11ee-8040-88983bcc06d4"},{"full_name":"Rodolà, Emanuele","first_name":"Emanuele","last_name":"Rodolà"}],"publisher":"Neural Information Processing Systems Foundation","date_created":"2025-04-06T22:01:32Z","type":"conference","scopus_import":"1","volume":37,"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1049-5258"]},"oa":1,"oa_version":"Preprint","alternative_title":["Advances in Neural Information Processing Systems"],"language":[{"iso":"eng"}],"ec_funded":1,"title":"Latent functional maps: A spectral framework for representation alignment","month":"12","publication_status":"published","citation":{"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.","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.","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.","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.","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.","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."},"project":[{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}],"quality_controlled":"1","article_processing_charge":"No"},{"publication_status":"published","quality_controlled":"1","article_processing_charge":"No","project":[{"call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"citation":{"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.","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.","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.","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.","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.","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.","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."},"alternative_title":["Advances in Neural Information Processing Systems"],"oa_version":"Preprint","oa":1,"month":"12","title":"C2M3: Cycle-consistent multi-model merging","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1049-5258"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2025-04-06T22:01:32Z","volume":37,"arxiv":1,"scopus_import":"1","type":"conference","year":"2024","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.17897"}],"OA_type":"green","publisher":"Neural Information Processing Systems Foundation","author":[{"last_name":"Crisostomi","first_name":"Donato","full_name":"Crisostomi, Donato"},{"id":"1c1593eb-393f-11ef-bb8e-ab4f1e979650","last_name":"Fumero","first_name":"Marco","full_name":"Fumero, Marco"},{"first_name":"Daniele","full_name":"Baieri, Daniele","last_name":"Baieri"},{"first_name":"Florian","full_name":"Bernard, Florian","last_name":"Bernard"},{"last_name":"Rodolà","full_name":"Rodolà, Emanuele","first_name":"Emanuele"}],"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."}],"_id":"19517","corr_author":"1","OA_place":"repository","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.","conference":{"end_date":"2024-12-15","location":"Vancouver, Canada","start_date":"2024-12-09","name":"NeurIPS: Neural Information Processing Systems"},"department":[{"_id":"FrLo"}],"publication":"38th Conference on Neural Information Processing Systems","intvolume":"        37","day":"20","date_published":"2024-12-20T00:00:00Z","external_id":{"arxiv":["2405.17897"]},"date_updated":"2025-05-14T11:36:59Z","status":"public"}]