I am a postdoctoral researcher in the Empirical Inference Department at the Max Planck Institute for Intelligent Systems, supported by the Tübingen AI Center. This fall, I will start an Emmy Noether Research Group at the Technical University of Munich, where I have open PhD positions for students working at the intersection of statistics and machine learning. I am also happy to supervise Bachelor's and Master's theses. If you are interested in working with me, feel free to get in touch.
My main research interests are representation learning and causality. I completed my PhD in mathematics at the University of Bonn, focusing on probability theory and statistical mechanics.
My email is sbuchholz at tue dot mpg dot de.
Pattern matching beyond i.i.d. data
Block seminar at ETH, Summer term 2025 (with Bernhard Schölkopf, Antonio Orvieto, and Siyuan Guo)
Representations in Generative AI
Block seminar at ETH, Summer term 2024 (with Bernhard Schölkopf, Michel Besserve, and Zhijing Jin)
Mathematical Foundations of Machine Learning
Summer term 2024
* denotes equal contribution; † denotes joint supervision.
Pion: A spectrum-preserving optimizer via orthogonal equivalence transformation
Kexuan Shi, Hanxuan Li, Zeju Qiu, Yandong Wen, Simon Buchholz, and Weiyang Liu
Preprint, 2026 (arXiv)
Is generation required for data-efficient perception?
Jack Brady, Bernhard Schölkopf, Thomas Kipf, Simon Buchholz*, and Wieland Brendel*
Accepted at ICML, 2026 (arXiv)
Logit distance bounds representational similarity
Beatrix M. G. Nielsen*, Emanuele Marconato*, Luigi Gresele†, Andrea Dittadi†, and Simon Buchholz†
Accepted at ICML, 2026 (arXiv)
Reparameterized LLM training via orthogonal equivalence transformation
Zeju Qiu, Simon Buchholz, Tim Z. Xiao, Maximilian Dax, Bernhard Schölkopf, and Weiyang Liu
NeurIPS, 2025 (proceedings)
Interaction asymmetry: A unified principle for learning compositional abstractions
Jack Brady, Sébastien Lachapelle, Julius von Kügelgen, Simon Buchholz, Thomas Kipf*, and Wieland Brendel*
ICLR, 2025 (also at the NeurIPS 2025 Workshops on Causal Representation Learning and Compositional Learning) (proceedings)
Multi-armed bandits and quantum channel oracles
Simon Buchholz, Jonas Kübler, and Bernhard Schölkopf
Quantum, 2025 (arXiv, journal)
Learning partitions from context
Simon Buchholz
NeurIPS, 2024 (proceedings)
From causal to concept-based representation learning
Goutham Rajendran*, Simon Buchholz*, Bryon Aragam, Bernhard Schölkopf, and Pradeep Ravikumar
NeurIPS, 2024 (also at CALM: First Workshop on Causality and Large Models, oral) (arXiv, proceedings)
Robustness of nonlinear representation learning
Simon Buchholz and Bernhard Schölkopf
ICML (oral), 2024 (proceedings)
Products, abstractions and inclusions of causal spaces
Simon Buchholz*, Junhyung Park*, and Bernhard Schölkopf
UAI, 2024 (proceedings)
Learning linear causal representations from interventions under general nonlinear mixing
Simon Buchholz*, Goutham Rajendran*, Elan Rosenfeld, Bryon Aragam, Bernhard Schölkopf, and Pradeep Ravikumar
NeurIPS (oral), 2023 (arXiv, proceedings)
Flow matching for scalable simulation-based inference
Jonas Wildberger*, Maximilian Dax*, Simon Buchholz*, Stephen Green, Jakob Macke, and Bernhard Schölkopf
NeurIPS, 2023 (also at the 2nd ICML 2023 Workshop on Machine Learning for Astrophysics, workshop oral)(arXiv, proceedings)
Causal component analysis
Wendong Liang, Armin Kekić, Julius von Kügelgen, Simon Buchholz, Michel Besserve, Luigi Gresele*, and Bernhard Schölkopf*
NeurIPS, 2023 (arXiv, proceedings)
A measure-theoretic axiomatisation of causality
Junhyung Park, Simon Buchholz, Bernhard Schölkopf, and Krikamol Muandet
NeurIPS (oral), 2023 (arXiv, proceedings)
Some remarks on identifiability of independent component analysis in restricted function classes
Simon Buchholz
Transactions on Machine Learning Research, 2023 (journal)
Function classes for identifiable nonlinear independent component analysis
Simon Buchholz, Michel Besserve, and Bernhard Schölkopf
NeurIPS, 2022 (proceedings)
AutoML two-sample test
Jonas Kübler, Vincent Stimper, Simon Buchholz, Krikamol Muandet, and Bernhard Schölkopf
NeurIPS, 2022 (proceedings)
Kernel interpolation in Sobolev spaces is not consistent in low dimensions
Simon Buchholz
COLT, 2022 (proceedings)
The inductive bias of quantum kernels
Jonas Kübler*, Simon Buchholz*, and Bernhard Schölkopf
NeurIPS, 2021 (proceedings)
Authors are listed in alphabetical order.
Aizenman–Wehr argument for a class of disordered gradient models
Simon Buchholz and Codina Cotar
Accepted in Annals of Applied Probability, 2023 (arXiv)
Phase transitions for a class of gradient fields
Simon Buchholz
Probability Theory and Related Fields, 179(3):969–1022, 2021 (journal)
Cauchy–Born rule from microscopic models with non-convex potentials
Stefan Adams, Simon Buchholz, Roman Kotecký, and Stefan Müller
Accepted in Memoirs of the AMS, 2019 (arXiv)
Probability to be positive for the membrane model in dimensions 2 and 3
Simon Buchholz, Jean-Dominique Deuschel, Noemi Kurt, and Florian Schweiger
Electronic Communications in Probability, 24:1–14, 2019 (journal)
Finite range decomposition for Gaussian measures with improved regularity
Simon Buchholz
Journal of Functional Analysis, 275(7):1674–1711, 2018 (journal)
Multivariate central limit theorem in quantum dynamics
Simon Buchholz, Chiara Saffirio, and Benjamin Schlein
Journal of Statistical Physics, 154(1):113–152, 2014 (journal)