TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning

Shicheng Fan, Kun Zhang, Lu Cheng
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:28932-28959, 2026.

Abstract

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle’s dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling test-time recovery of mechanism trajectories, including intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-fan26i, title = {{TRACE}: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning}, author = {Fan, Shicheng and Zhang, Kun and Cheng, Lu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {28932--28959}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/fan26i/fan26i.pdf}, url = {https://proceedings.mlr.press/v306/fan26i.html}, abstract = {Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle’s dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling test-time recovery of mechanism trajectories, including intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.} }
Endnote
%0 Conference Paper %T TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning %A Shicheng Fan %A Kun Zhang %A Lu Cheng %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-fan26i %I PMLR %P 28932--28959 %U https://proceedings.mlr.press/v306/fan26i.html %V 306 %X Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle’s dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling test-time recovery of mechanism trajectories, including intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.
APA
Fan, S., Zhang, K. & Cheng, L.. (2026). TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:28932-28959 Available from https://proceedings.mlr.press/v306/fan26i.html.

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