I am a postdoctoral researcher at the Max Planck Institute for Intelligent Systems in the Empirical Inference Department, and I am supported by the Tübingen AI Center.

My main research interests are representation learning and causality. I did my PhD in mathematics at the University of Bonn, where I worked at the intersection of probability theory and statistical mechanics.

My email is sbuchholz at tue dot mpg dot de

Teaching

• Summer term 2024: Representations in Generative AI, block seminar at ETH together with Bernhard Schölkopf, Michel Besserve, Zhijing Jin

• Summer term 2024: Mathematical Foundations of Machine Learning

Publications and Preprints

Machine learning related:

• Simon Buchholz*, Goutham Rajendran*, Elan Rosenfeld, Bryon Aragam, Bernhard Schölkopf, and Pradeep Ravikumar, Learning Linear Causal Representations from Interventions under General Nonlinear Mixing, NeurIPS (oral), 2023. (arxiv)

• Jonas Wildberger*, Maximilian Dax*, Simon Buchholz*, Stephen Green, Jakob Macke, and Bernhard Schölkopf, Flow Matching for Scalable Simulation-Based Inference, NeurIPS, 

also at ICML 2023 Workshop on Structured Probabilistic Inference & Generative Modeling and 2nd ICML Workshop on Machine Learning for Astrophysics, 2023.  (arxiv)

• Wendong Liang, Armin Kekic, Julius von Kügelgen, Simon Buchholz, Michel Besserve, Luigi Gresele*, and Bernhard Schölkopf*, Causal Component Analysis, NeurIPS 2023. (arxiv)

• Junhyung Park, Simon Buchholz, Bernhard Schölkopf, and Krikamol Muandet, A Measure-Theoretic Axiomatisation of Causality, NeurIPS (oral), 2023. (arxiv)

• Simon Buchholz, Jonas Kübler, and Bernhard Schölkopf, Multi Armed Bandits and Quantum Channel Oracles, arXiv preprint arXiv:2301.08544, 2023.

• Simon Buchholz, Some Remarks on Identifiability of Independent Component Analysis in restricted Function Classes, Transactions on Machine Learning Research, 2023. (link)

• Simon Buchholz, Michel Besserve, and Bernhard Schölkopf, Function Classes for Identifiable Nonlinear Independent Component Analysis, NeurIPS, 2022. (link)

• Jonas Kübler, Vincent Stimper, Simon Buchholz, Krikamol Muandet, and Bernhard Schölkopf, AutoML Two-Sample Test, NeurIPS, 2022. (link)

• Simon Buchholz, Kernel interpolation in Sobolev spaces is not consistent in low dimensions, COLT, 2022. (link)

• Jonas Kübler*, Simon Buchholz*, and Bernhard Schölkopf, The Inductive Bias of Quantum Kernels, NeurIPS, 2021. (link)

Math related:

• Simon Buchholz and Codina Cotar, Aizenman-Wehr Argument for a Class of disordered Gradient Models, arXiv preprint arXiv:2309.12799, 2023.

• Stefan Adams, Simon Buchholz, Roman Kotecky, and Stefan Müller, Cauchy-Born Rule from Microscopic Models with non-convex Potentials, arXiv preprint arXiv:1910.13564, 2019.

• Simon Buchholz, Phase Transitions for a Class of Gradient Fields, Probability Theory and Related Fields, 179(3):969--1022, 2021. (link)

• Simon Buchholz, Jean-Dominique Deuschel, Noemi Kurt, and Florian Schweiger, Probability to be positive for the Membrane Model in Dimensions 2 and 3, Electronic Communications in Probability, 24:1 -- 14, 2019. (link)

• Simon Buchholz, Finite range decomposition for Gaussian measures with improved regularity, Journal of Functional Analysis, 275(7):1674--1711, 2018. (link)

• Simon Buchholz, Chiara Saffirio, and Benjamin Schlein, Multivariate Central Limit Theorem in Quantum Dynamics, Journal of Statistical Physics, 154(1):113--152, 2014. (link)