Publication Archive

As a company positioned in the forefront of machine learning research in Germany, we collaborate with scientists and internationally established institutions. A a full list of our publication online history can be found below.


Improved sampling via learned diffusions (2024)

  • Generative modeling
  • Sampling

Lorenz Richter, Julius Berner, Guan-Horng Liu

Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.

An optimal control perspective on diffusion-based generative modeling (2024)

  • Generative modeling
  • Sampling

Julius Berner, Lorenz Richter, Karen Ullrich

We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based generative modeling as a minimization of the Kullback-Leibler divergence between suitable measures in path space. Finally, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. We demonstrate that our time-reversed diffusion sampler (DIS) can outperform other diffusion-based sampling approaches on multiple numerical examples.


Separation, Characterization, and Handling of Microalgae by Dielectrophoresis (2023)

  • Biotechnology
  • Bioelectronics

Vinzenz Abt, Fabian Gringel, Arum Han, Peter Neubauer, Mario Birkholz

Microalgae biotechnology has a high potential for sustainable bioproduction of diverse high-value biomolecules. Some of the main bottlenecks in cell-based bioproduction, and more specifically in microalgae-based bioproduction, are due to insufficient methods for rapid and efficient cell characterization, which contributes to having only a few industrially established microalgal species in commercial use.

Solving Inverse Problems With Deep Neural Networks - Robustness Included? (2023)

  • Image processing
  • Inverse problems

Martin Genzel, Jan Macdonald, Maximilian März

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks.

Let's Enhance: A Deep Learning Approach to Extreme Deblurring of Text Images (2023)

  • Image processing
  • Inverse problems

Theophil Trippe, Martin Genzel, Jan Macdonald, Maximilian März

This work presents a novel deep-learning-based pipeline for the inverse problem of image deblurring, leveraging augmentation and pre-training with synthetic data. Our results build on our winning submission to the recent Helsinki Deblur Challenge 2021, whose goal was to explore the limits of state-of-the-art deblurring algorithms in a real-world data setting.

Early Crop Classification via Multi-Modal Satellite Data Fusion and Temporal Attention (2023)

  • Remote Sensing

Frank Weilandt, Robert Behling, Romulo Goncalves, Arash Madadi, Lorenz Richter, Tiago Sanona, Daniel Spengler, Jona Welsch

In this article, we propose a deep learning-based algorithm for the classification of crop types from Sentinel-1 and Sentinel-2 time series data which is based on the celebrated transformer architecture. Crucially, we enable our algorithm to do early classification, i.e., predict crop types at arbitrary time points early in the year with a single trained model (progressive intra-season classification). Such early season predictions are of practical relevance for instance for yield forecasts or the modeling of agricultural water balances, therefore being important for the public as well as the private sector. Furthermore, we improve the mechanism of combining different data sources for the prediction task, allowing for both optical and radar data as inputs (multi-modal data fusion) without the need for temporal interpolation. We can demonstrate the effectiveness of our approach on an extensive data set from three federal states of Germany reaching an average F1 score of 0.920.92 using data of a complete growing season to predict the eight most important crop types and an F1 score above 0.80.8 when doing early classification at least one month before harvest time. In carefully chosen experiments, we can show that our model generalizes well in time and space.

Computer Simulations of Causal Sets (2023)

  • Quantum Gravity

Liel Glaser

This review introduces Markov Chain Monte Carlo simulations in causal set theory, with a focus on the study of the 2d orders. It will first introduce the Benincasa-Dowker action on causal sets, and cover some musings on the philosophy of computer simulations. And then proceed to review results from the study of the 2d orders, first their general phase transition and scaling behavior and then results on defining a wave function of the universe using these orders and on coupling the 2d orders to an Ising like model.

Environmental sustainability in basic research: a perspective from HECAP+ (2023)

  • Physics and Society

Liel Glaser, Sustainable HECAP+ Initiative: Shankha Banerjee, Thomas Y. Chen, Claire David, Michael Düren, Harold Erbin, Jacopo Ghiglieri, Mandeep S. S. Gill, Christian Gütschow, Jack Joseph Hall, Johannes Hampp, Patrick Koppenburg, Matthias Koschnitzke, Kristin Lohwasser, Rakhi Mahbubani, Viraf Mehta, Peter Millington, Ayan Paul, Frauke Poblotzki, Karolos Potamianos, Nikolina Šarčević, Rajeev Singh, Hannah Wakeling, Rodney Walker, Matthijs van der Wild, Pia Zurita

The climate crisis and the degradation of the world's ecosystems require humanity to take immediate action. The international scientific community has a responsibility to limit the negative environmental impacts of basic research. The HECAP+ communities (High Energy Physics, Cosmology, Astroparticle Physics, and Hadron and Nuclear Physics) make use of common and similar experimental infrastructure, such as accelerators and observatories, and rely similarly on the processing of big data.

Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers (2023)

  • Semiconductor Manufacture

Christof Zink, Michael Ekterai, Dominik Martin, William Clemens, Angela Maennel, Konrad Mundinger, Lorenz Richter, Paul Crump, Andrea Knigge

The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development.


Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings (2022)

  • Explainable AI
  • Non-convex optimization

Jan Macdonald, Mathieu Besançon, Sebastian Pokutta

We study the effects of constrained optimization formulations and Frank-Wolfe algorithms for obtaining interpretable neural network predictions. Reformulating the Rate-Distortion Explanations (RDE) method for relevance attribution as a constrained optimization problem provides precise control over the sparsity of relevance maps.

Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning (2022)

  • Stochastic processes
  • PDEs

Lorenz Richter, Julius Berner

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods.

Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics (2022)

  • Monte Carlo methods
  • Stochastic processes

Enric Ribera Borrell, Jannes Quer, Lorenz Richter, Christof Schütte

Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty.

The perfection of local semi-flows and local random dynamical systems with applications to SDEs (2022)

  • Stochastic processes
  • Dynamical Systems

Chengcheng Ling, Michael Scheutzow, Isabell Vorkastner

We provide a rather general perfection result for crude local semi-flows taking values in a Polish space showing that a crude semi-flow has a modification which is a (perfect) local semi-flow which is invariant under a suitable metric dynamical system. Such a (local) semi-flow induces a (local) random dynamical system.


Noncommutative differential K-theory (2021)

  • Differential geometry

Byungdo Park, Arthur J. Parzygnat, Corbett Redden, Augusto Stoffel

We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression forms as well as a differential refinement of the smooth Serre--Swan correspondence. Our construction subsumes the differential K-theory of a smooth manifold when the algebra is complex-valued smooth functions.

Nonasymptotic bounds for suboptimal importance sampling (2021)

  • Monte Carlo methods
  • Stochastic processes

Carsten Hartmann, Lorenz Richter

Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention.

G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality (2021)

  • String Theory

Mark Bugden, Ondrej Hulik, Fridrich Valach, Daniel Waldram

We introduce the notion of G-algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in En(n) × + exceptional generalised geometry for n∈{3,…,6}. Focusing on the exceptional case, we prove a classification of "exact" algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem.

Exceptional algebroids and type IIB superstrings (2021)

  • String Theory

Mark Bugden, Ondrej Hulik, Fridrich Valach, Daniel Waldram

In this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB-exact exceptional algebroid locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat gl(2,R)-connection, a covariantly closed pair of 3-forms, and a 5-form, and comment on their physical interpretation.

The Computational Complexity of Understanding Binary Classifier Decisions (2021)

  • Machine Learning Theory
  • Explainable AI

Stephan Wäldchen, Jan Macdonald, Sascha Hauch, Gitta Kutyniok

For a d-ary Boolean function Φ: {0, 1}d → {0, 1} and an assignment to its variables x = (x1, x2, . . . , xd) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean circuits, which can be seen as special cases of neural networks.

Detecting Failure Modes in Image Reconstructions with Interval Neural Network Uncertainty (2021)

  • Image processing
  • Uncertainty Quantification

Luis Oala, Cosmas Heiß, Jan Macdonald, Maximilian März, Gitta Kutyniok, Wojciech Samek

The quantitative detection of failure modes is important for making deep neural networks reliable and usable at scale. We consider three examples for common failure modes in image reconstruction and demonstrate the potential of uncertainty quantification as a fine-grained alarm system.


VarGrad: A Low-Variance Gradient Estimator for Variational Inference (2020)

  • Statistics
  • Machine Learning Theory

Lorenz Richter, Ayman Boustati, Nikolas Nüsken, Francisco J. R. Ruiz, Ömer Deniz Akyildiz

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the log-variance loss.

Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space (2020)

  • Stochastic processes
  • Optimal Control
  • PDEs

Nikolas Nüsken, Lorenz Richter

Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the potential of iterative diffusion optimisation techniques.

A framework for geometric field theories and their classification in dimension one (2020)

  • Algebraic topology

Matthias Ludewig, Augusto Stoffel

In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory to depend smoothly on the input.

On the approaching time towards the attractor of differential equations perturbed by small noise (2020)

  • Stochastic processes
  • Dynamical Systems

Isabell Vorkastner

We estimate the time a point or set, respectively, requires to approach the attractor of a radially symmetric gradient type stochastic differential equation driven by small noise. Here, both of these times tend to infinity as the noise gets small. However, the rates at which they go to infinity differ significantly. In the case of a set approaching the attractor, we use large deviation techniques to show that this time increases exponentially.


Quantum rolling friction (2019)

  • Quantum physics

Francesco Intravaia, Marty Oelschläger, Daniel Reiche, Diego A. R. Dalvit, Kurt Busch

An atom moving in a vacuum at constant velocity and parallel to a surface experiences a frictional force induced by the dissipative interaction with the quantum fluctuations of the electromagnetic field. We show that the combination of nonequilibrium dynamics, anomalous Doppler effect and spin-momentum locking of light mediates an intriguing interplay between the atom's translational and rotational motion.

Variational approach to rare event simulation using least-squares regression (2019)

  • Statistical physics

Carsten Hartmann, Omar Kebiri, Lara Neureither, Lorenz Richter

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e., zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem.


Holographic Gauged NJL Model: the Conformal Window and Ideal Walking (2018)

  • Theoretical physics

Kazem Bitaghsir Fadafan, William Clemens, Nick Evans

We study the holographic Dynamic AdS/QCD description of a SU(Nc) non-abelian gauge theory with Nf fermions in the fundamental representation which also have Nambu-Jona-Lasinio interactions included using Witten's multi-trace prescription. In particular here we study aspects of the dynamics in and near the conformal window of the gauge theory as described by the two loop running of the gauge theory.

Noise dependent synchronization of a degenerate SDE (2018)

  • Stochastic processes
  • Dynamical Systems

Isabell Vorkastner

We provide an example of an SDE with degenerate additive noise where synchronization depends on the strength of noise and the number of directions in which the noise acts. Here, synchronization means that the weak random attractor consists of a single random point. Indicated by a change of sign of the top Lyapunov exponent, we prove synchronization respectively no (weak) synchronization.

Connectedness of random set attractors (2018)

  • Stochastic processes
  • Dynamical Systems

Isabell Vorkastner, Michael Scheutzow

We examine the question whether random set attractors for continuous-time random dynamical systems on a connected state space are connected. In the deterministic case, these attractors are known to be connected. In the probabilistic setup, however, connectedness has only been shown under stronger connectedness assumptions on the state space. Under a weak continuity condition on the random dynamical system we prove connectedness of the pullback attractor on a connected space. Additionally, we provide an example of a weak random set attractor of a random dynamical system with even more restrictive continuity assumptions on an even path-connected space which even attracts all bounded sets and which is not connected.

Synchronization, Lyapunov exponents and stable manifolds for random dynamical systems (2018)

  • Stochastic processes
  • Dynamical Systems

Isabell Vorkastner, Michael Scheutzow

During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and Röckner. Recently some authors investigated sufficient conditions which guarantee synchronization, i.e. existence of a random attractor which is a singleton. It is reasonable to conjecture that synchronization and negativity (or non-positivity) of the top Lyapunov exponent of the system should be closely related since both mean that the system is contracting in some sense.


Variational characterization of free energy: Theory and algorithms (2017)

  • Statistical physics

Carsten Hartmann, Lorenz Richter, Christof Schütte, Wei Zhang

The article surveys and extends variational formulations of the thermodynamic free energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations.

A Holographic Study of the Gauged NJL Model (2017)

  • Theoretical physics

William Clemens, Nick Evans

The Nambu Jona-Lasinio model of chiral symmetry breaking predicts a second order chiral phase transition. If the fermions in addition have non-abelian gauge interactions then the transition is expected to become a crossover as the NJL term enhances the IR chiral symmetry breaking of the gauge theory. We study this behaviour in the holographic Dynamic AdS/QCD description of a non-abelian gauge theory with the NJL interaction included using Witten's multi-trace prescription.

Holograms of a Dynamical Top Quark (2017)

  • Theoretical physics

William Clemens, Nick Evans, Marc Scott

We present holographic desciptions of dynamical electroweak symmetry breaking models that incorporate the top mass generation mechanism. The models allow computation of the spectrum in the presence of large anomalous dimensions due to walking and strong NJL interactions. Technicolour and QCD dynamics are described by the bottom-up Dynamic AdS/QCD model for arbitrary gauge groups and numbers of quark flavours.

Tilted disordered Weyl semimetals (2017)

  • Theoretical condensed matter physics

Maximilian Trescher, Björn Sbierski, Piet W. Brouwer, Emil J. Bergholtz

Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder.

Charge density wave instabilities of type-II Weyl semimetals in a strong magnetic field (2017)

  • Theoretical condensed matter physics

Maximilian Trescher, Emil J. Bergholtz, Masafumi Udagawa, Johannes Knolle

Shortly after the discovery of Weyl semimetals, properties related to the topology of their bulk band structure have been observed, e.g., signatures of the chiral anomaly and Fermi arc surface states. These essentially single particle phenomena are well understood, but whether interesting many-body effects due to interactions arise in Weyl systems remains much less explored.

Anatomy of topological surface states: Exact solutions from destructive interference on frustrated lattices (2017)

  • Theoretical condensed matter physics

Flore K. Kunst, Maximilian Trescher, Emil J. Bergholtz

The hallmark of topological phases is their robust boundary signature whose intriguing properties—such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals—are impossible to realize on the surface alone.


Onset of time dependence in ensembles of excitable elements with global repulsive coupling (2016)

  • Nonlinear dynamics

Michael A. Zaks, Petar Tomov

We consider the effect of global repulsive coupling on an ensemble of identical excitable elements. An increase of the coupling strength destabilizes the synchronous equilibrium and replaces it with many attracting oscillatory states, created in the transcritical heteroclinic bifurcation. The period of oscillations is inversely proportional to the distance from the critical parameter value.

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators (2016)

  • Theoretical condensed matter physics

Frédéric Combes, Maximilian Trescher, Frédéric Piéchon, Jean-Noël Fuchs

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling.

Mechanisms of self-sustained oscillatory states in hierarchical modular networks with mixtures of electrophysiological cell types (2016)

  • Computational Neuroscience

Petar Tomov, Rodrigo F. O. Pena, Antonio C. Roque, Michael A. Zaks

In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics “up” and “down” states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons.