26 citations · 69 across the 20 of their papers we have counts for
23 papers
Gradient Gibbs measures with non-convex potentials and the universality class of the Gaussian Free Field
Simon Buchholz, Codina Cotar, Florian Schweiger
We study a general class of gradient interface models with Hamiltonian , , assuming essentially that the potential is even, on $[0,\infty…
Linear Independent Component Analysis via Optimal Transport
Ashutosh Jha, Michel Besserve, Simon Buchholz
Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize no…
Logit Distance Bounds Representational Similarity
Beatrix M. G. Nielsen, Emanuele Marconato, Luigi Gresele +2
For a broad family of discriminative models that includes autoregressive language models, identifiability results imply that if two models induce the same conditional distributions…
Reparameterized LLM Training via Orthogonal Equivalence Transformation
Zeju Qiu, Simon Buchholz, Tim Z. Xiao +3
While large language models (LLMs) are driving the rapid advancement of artificial intelligence, effectively and reliably training these large models remains one of the field's mos…
Algorithmic causal structure emerging through compression
Liang Wendong, Simon Buchholz, Bernhard Schölkopf
We explore the relationship between causality, symmetry, and compression. We build on and generalize the known connection between learning and compression to a setting where causal…
Robustness of Nonlinear Representation Learning
Simon Buchholz, Bernhard Schölkopf
We study the problem of unsupervised representation learning in slightly misspecified settings, and thus formalize the study of robustness of nonlinear representation learning. We…
Products, Abstractions and Inclusions of Causal Spaces
Simon Buchholz, Junhyung Park, Bernhard Schölkopf
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as st…
Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models
Goutham Rajendran, Simon Buchholz, Bryon Aragam +2
To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causa…
Aizenman-Wehr argument for a class of disordered gradient models
Simon Buchholz, Codina Cotar
We consider random gradient fields with disorder where the interaction potential on an edge can be expressed as $e^{-V_e(s)} = \int ρ(\mathrm{d}κ)\, e^{-κξ_e} e^{-\frac{κ…
Learning Linear Causal Representations from Interventions under General Nonlinear Mixing
Simon Buchholz, Goutham Rajendran, Elan Rosenfeld +3
We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function i…
Causal Component Analysis
Liang Wendong, Armin Kekić, Julius von Kügelgen +4
Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causall…
Flow Matching for Scalable Simulation-Based Inference
Maximilian Dax, Jonas Wildberger, Simon Buchholz +3
Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional pro…
A Measure-Theoretic Axiomatisation of Causality
Junhyung Park, Simon Buchholz, Bernhard Schölkopf +1
Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of pr…
Multi-Armed Bandits and Quantum Channel Oracles
Simon Buchholz, Jonas M. Kübler, Bernhard Schölkopf
Multi-armed bandits are one of the theoretical pillars of reinforcement learning. Recently, the investigation of quantum algorithms for multi-armed bandit problems was started, and…
Function Classes for Identifiable Nonlinear Independent Component Analysis
Simon Buchholz, Michel Besserve, Bernhard Schölkopf
Unsupervised learning of latent variable models (LVMs) is widely used to represent data in machine learning. When such models reflect the ground truth factors and the mechanisms ma…
AutoML Two-Sample Test
Jonas M. Kübler, Vincent Stimper, Simon Buchholz +2
Two-sample tests are important in statistics and machine learning, both as tools for scientific discovery as well as to detect distribution shifts. This led to the development of m…
The Inductive Bias of Quantum Kernels
Jonas M. Kübler, Simon Buchholz, Bernhard Schölkopf
It has been hypothesized that quantum computers may lend themselves well to applications in machine learning. In the present work, we analyze function classes defined via quantum k…
Assaying Large-scale Testing Models to Interpret COVID-19 Case Numbers
Michel Besserve, Simon Buchholz, Bernhard Schölkopf
Large-scale testing is considered key to assess the state of the current COVID-19 pandemic. Yet, the link between the reported case numbers and the true state of the pandemic remai…
Cauchy-Born Rule from Microscopic Models with Non-convex Potentials
Stefan Adams, Simon Buchholz, Roman Kotecký +1
We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In parti…
Phase transitions for a class of gradient fields
Simon Buchholz
We consider gradient fields on for potentials that can be expressed as This representation allows us…
Probability to be positive for the membrane model in dimensions 2 and 3
Simon Buchholz, Jean-Dominique Deuschel, Noemi Kurt +1
We consider the membrane model on a box of size with zero boundary condition in the subcritical dimensions and . We show optimal est…
Finite Range Decomposition for Gaussian Measures with Improved Regularity
Simon Buchholz
We consider a family of gradient Gaussian vector fields on the torus . Adams, Kotecký, Müller and independently Bauerschmidt established the existence…
Multivariate Central Limit Theorem in Quantum Dynamics
Simon Buchholz, Chiara Saffirio, Benjamin Schlein
We consider the time evolution of bosons in the mean field regime for factorized initial data. In the limit of large , the many body evolution can be approximated by the non…