@inproceedings{19010,
  abstract     = {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.},
  author       = {Yao, Dingling and Rancati, Dario and Cadei, Riccardo and Fumero, Marco and Locatello, Francesco},
  booktitle    = {13th International Conference on Learning Representations},
  location     = {Singapore},
  publisher    = {ICLR},
  title        = {{Unifying causal representation learning with the invariance principle}},
  year         = {2025},
}

@inproceedings{20032,
  abstract     = {We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.},
  author       = {Chen, Jiale and Yao, Dingling and Pervez, Adeel A and Alistarh, Dan-Adrian and Locatello, Francesco},
  booktitle    = {13th International Conference on Learning Representations},
  isbn         = {9798331320850},
  location     = {Singapore, Singapore},
  pages        = {63716--63737},
  publisher    = {ICLR},
  title        = {{Scalable mechanistic neural networks}},
  year         = {2025},
}

@inproceedings{20592,
  abstract     = {Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical applications, however, the underlying dynamical system often contains uncertain parameters, requiring the propagation of this model uncertainty to the ODE solution. In this paper, we demonstrate that ODE filters, despite their probabilistic nature, do not automatically solve this uncertainty propagation problem. To address this limitation, we present a novel approach that combines ODE filters with numerical quadrature to properly marginalize over uncertain parameters, while accounting for both parameter uncertainty and numerical solver uncertainty. Experiments across multiple dynamical systems demonstrate that the resulting uncertainty estimates closely match reference solutions. Notably, we show
how the numerical uncertainty from the ODE solver can help prevent overconfidence in the propagated uncertainty estimates, especially when using larger step sizes. Our results illustrate that probabilistic numerical methods can effectively quantify both numerical and parametric uncertainty in dynamical systems. },
  author       = {Yao, Dingling and Tronarp, Filip and Bosch, Nathanael},
  booktitle    = {Proceedings of the 1st International Conference on Probabilistic Numerics},
  issn         = {2640-3498},
  location     = {Sophia Antipolis, France},
  publisher    = {ML Research Press},
  title        = {{Propagating model uncertainty through filtering-based probabilistic numerical ODE solvers}},
  volume       = {271},
  year         = {2025},
}

@inproceedings{21068,
  abstract     = {Causal reasoning and discovery, two fundamental tasks of causal analysis,
often face challenges in applications due to the complexity, noisiness, and highdimensionality of real-world data. Despite recent progress in identifying latent
causal structures using causal representation learning (CRL), what makes learned
representations useful for causal downstream tasks and how to evaluate them are
still not well understood. In this paper, we reinterpret CRL using a measurement
model framework, where the learned representations are viewed as proxy measurements of the latent causal variables. Our approach clarifies the conditions under
which learned representations support downstream causal reasoning and provides
a principled basis for quantitatively assessing the quality of representations using
a new Test-based Measurement EXclusivity (T-MEX) score. We validate T-MEX
across diverse causal inference scenarios, including numerical simulations and
real-world ecological video analysis, demonstrating that the proposed framework
and corresponding score effectively assess the identification of learned representations and their usefulness for causal downstream tasks. Reproducible code can
be found at https://github.com/shimenghuang/a-measurement-perspective-of-crl.},
  author       = {Yao, Dingling and Huang, Shimeng and Cadei, Riccardo and Zhang, Kun and Locatello, Francesco},
  booktitle    = {39th Annual Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {San Diego, CA, United States},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{The third pillar of causal analysis? A measurement perspective on causal representations}},
  volume       = {38},
  year         = {2025},
}

@inproceedings{14946,
  abstract     = {We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a nonlinear mixture of a subset of underlying latent variables, which can be causally related. We prove that the information shared across all subsets of any number of views can be learned up to a smooth bijection using contrastive learning and a single encoder per view. We also provide graphical criteria indicating which latent variables can be identified through a simple set of rules, which we refer to as identifiability algebra. Our general framework and theoretical results unify and extend several previous work on multi-view nonlinear ICA, disentanglement, and causal representation learning. We experimentally validate our claims on numerical, image, and multi-modal data sets. Further, we demonstrate that the performance of prior methods is recovered in different special cases of our setup. Overall, we find that access to multiple partial views offers unique opportunities for identifiable representation learning, enabling the discovery of latent structures from purely observational data.},
  author       = {Yao, Dingling and Xu, Danru and Lachapelle, Sébastien and Magliacane, Sara and Taslakian, Perouz and Martius, Georg and Kügelgen, Julius von and Locatello, Francesco},
  booktitle    = {12th International Conference on Learning Representations},
  location     = {Vienna, Austria},
  publisher    = {Curran Associates},
  title        = {{Multi-view causal representation learning with partial observability}},
  year         = {2024},
}

@inproceedings{19005,
  abstract     = {Causal representation learning promises to extend causal models to hidden causal
variables from raw entangled measurements. However, most progress has focused
on proving identifiability results in different settings, and we are not aware of any
successful real-world application. At the same time, the field of dynamical systems
benefited from deep learning and scaled to countless applications but does not allow
parameter identification. In this paper, we draw a clear connection between the two
and their key assumptions, allowing us to apply identifiable methods developed
in causal representation learning to dynamical systems. At the same time, we can
leverage scalable differentiable solvers developed for differential equations to build
models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream
tasks such as out-of-distribution classification or treatment effect estimation. We
experiment with a wind simulator with partially known factors of variation. We
also apply the resulting model to real-world climate data and successfully answer
downstream causal questions in line with existing literature on climate change.
Code is available at https://github.com/CausalLearningAI/crl-dynamical-systems.},
  author       = {Yao, Dingling and Muller, Caroline J and Locatello, Francesco},
  booktitle    = {38th Conference on Neural Information Processing Systems},
  location     = {Vancouver, Canada},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Marrying causal representation learning with dynamical systems for science}},
  volume       = {37},
  year         = {2024},
}

@inproceedings{14958,
  abstract     = {Causal representation learning (CRL) aims at identifying high-level causal variables from low-level data, e.g. images. Current methods usually assume that all causal variables are captured in the high-dimensional observations. In this work, we focus on learning causal representations from data under partial observability, i.e., when some of the causal variables are not observed in the measurements, and the set of masked variables changes across the different samples. We introduce some initial theoretical results for identifying causal variables under partial observability by exploiting a sparsity regularizer, focusing in particular on the linear and piecewise linear mixing function case. We provide a theorem that allows us to identify the causal variables up to permutation and element-wise linear transformations in the linear case and a lemma that allows us to identify causal variables up to linear transformation in the piecewise case. Finally, we provide a conjecture that would allow us to identify the causal variables up to permutation and element-wise linear transformations also in the piecewise linear case. We test the theorem and conjecture on simulated data, showing the effectiveness of our method.},
  author       = {Xu, Danru and Yao, Dingling and Lachapelle, Sebastien and Taslakian, Perouz and von Kügelgen, Julius and Locatello, Francesco and Magliacane, Sara},
  booktitle    = {Causal Representation Learning Workshop at NeurIPS 2023},
  location     = {New Orleans, LA, United States},
  publisher    = {OpenReview},
  title        = {{A sparsity principle for partially observable causal representation learning}},
  year         = {2023},
}