@inproceedings{20817,
  abstract     = {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.},
  author       = {Pervez, Adeel A and Gavves, Efstratios and Locatello, Francesco},
  booktitle    = {42nd International Conference on Machine Learning},
  issn         = {2640-3498},
  location     = {Vancouver, Canada},
  pages        = {48962--48973},
  publisher    = {ML Research Press},
  title        = {{Mechanistic PDE networks for discovery of governing equations}},
  volume       = {267},
  year         = {2025},
}

@inproceedings{22832,
  abstract     = {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.},
  author       = {Cadei, Riccardo and Demirel, Ilker and De Bartolomeis, Piersilvio and Lindorfer, Lukas and Cremer, Sylvia and Schmid, Cordelia and Locatello, Francesco},
  booktitle    = {39th Conference on Neural Information Processing Systems},
  isbn         = {9798331338275},
  issn         = {1049-5258},
  location     = {San Diego, CA, United States},
  pages        = {82200--82229},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Prediction-Powered Causal Inferences}},
  doi          = {10.52202/085713-2479},
  volume       = {38},
  year         = {2025},
}

@inproceedings{21076,
  abstract     = {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.},
  author       = {Cadei, Riccardo and Demirel, Ilker and De Bartolomeis, Piersilvio and Lindorfer, Lukas and Cremer, Sylvia and Schmid, Cordelia 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        = {{Prediction-powered causal inferences}},
  doi          = {10.52202/085713-2479},
  volume       = {38},
  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}},
  doi          = {10.52202/085713-1444},
  volume       = {38},
  year         = {2025},
}

@inproceedings{21070,
  abstract     = {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. },
  author       = {Demirel, Berker and Fumero, Marco  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        = {{Out-of-Distribution detection with relative angles}},
  doi          = {10.52202/085713-3125},
  volume       = {38},
  year         = {2025},
}