arXiv subjects

Johannes Berger

Publications and source records attributed to Johannes Berger.

11 recordsLinked to original sources

arXiv2026

RLLBC-Lib: An Educational Code Library for Reinforcement Learning and Learning-Based Control

Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.

cs.LG↗

arXiv2026

Going Beyond the Edge: Distributed Inference of Transformer Models on Ultra-Low-Power Wireless Devices

Transformer models are rapidly becoming a cornerstone of modern Internet of Things (IoT) applications, yet their computational and memory demands far exceed the capabilities of a single typical ultra-low-power IoT device. We present CATS, a framework for distributed transformer inference on ultra-low-power wireless devices, enabling multiple devices to collaboratively execute models far larger than what a single device can sustain. At its core, CATS is a communication-aware distributed transformer inference scheme co-designed across transformer partitioning, wireless communication and training. It employs SomeGather, a new pruned communication primitive that selectively broadcasts activation columns to reduce communication bandwidth and RAM usage without sacrificing model accuracy. Building on SomeGather, we design a partitioning method that exploits this primitive for efficient model parallelism. To cope with unreliable wireless communication, CATS employs message-dropout during training, which mimics packet losses and yields models that are robust to message loss during inference. In real-world experiments, we show that CATS brings distributed transformer inference to ultra-low-power wireless devices for the first time, with deployments on up to 16 devices that collaboratively execute transformer models up to 14 times larger than what a single device can run.

cs.LG↗

arXiv2026

Non-semisimple link and manifold invariants for symplectic fermions

We consider the link and three-manifold invariants from arXiv:1912.02063, which are defined in terms of certain non-semisimple finite ribbon categories $\mathcal{C}$ together with a choice of tensor ideal and modified trace. If the ideal is all of $\mathcal{C}$, these invariants agree with those defined by Lyubashenko in the 90's. We show that in that case the invariants depend on the objects labelling the link only through their simple composition factors, so that in order to detect non-trivial extensions one needs to pass to proper ideals. We compute examples of link and three-manifold invariants for $\mathcal{C}$ being the category of $N$ pairs of symplectic fermions. Using a quasi-Hopf algebra realisation of $\mathcal{C}$, we find that the Lyubashenko-invariant of a lens space is equal to the order of its first homology group to the power $N$, a relation we conjecture to hold for all rational homology spheres. For $N \ge 2$, $\mathcal{C}$ allows for tensor ideals $\mathcal{I}$ with a modified trace which are different from all of $\mathcal{C}$ and from the projective ideal. Using the theory of pull-back traces and symmetrised cointegrals, we show that the link invariant obtained from $\mathcal{I}$ can distinguish a continuum of indecomposable but reducible objects which all have the same composition series.

math.QA↗

arXiv2026

Optically detected and radio wave-controlled spin chemistry in flavoproteins

Optically addressable spin systems, such as nitrogen-vacancy centers in diamond, have been widely studied for quantum sensing applications. In this work, we demonstrate that certain flavoproteins, specifically cryptochrome and iLOV, which generate spin correlated radical pairs upon optical excitation, also exhibit optically detected magnetic resonance (ODMR). Remarkably, the iLOV protein, commonly used in cellular imaging, displays ODMR contrast approaching 50%. We present initial applications including widefield magnetic field sensing and spatial modulation of photoluminescence using radiofrequency pulses and magnetic field gradients. Our results establish radical pairs in proteins as a novel platform for optically addressable spin systems, offering the key advantages of molecular designability and genetic encodability. Moreover, due to the spin-selective nature of radical pair chemistry, the results lay the groundwork for future radiofrequency-based manipulation of biological systems.

quant-ph↗

arXiv2023

Everybody knows what a normal gabi-algebra is

Let A be a k-algebra over a commutative ring k. By the renowned Tannaka-Krein reconstruction, liftings of the monoidal structure from k-modules to A-modules correspond to bialgebra structures on A and liftings of the closed monoidal structure correspond to Hopf algebra structures on A. In this paper, we determine conditions on A that correspond to liftings of the closed structure alone, i.e. without considering the monoidal one, which lead to the notion of what we call a gabi-algebra. First, we tackle the question from the general perspective of monads, then we focus on the set-theoretic and the linear setting. Our main and most surprising result is that a normal gabi-algebra, that is an algebra A whose category of modules is (associative and unital normal) closed with closed forgetful functor to k-modules, is automatically a Hopf algebra (thus justifying our title).

math.RA↗

arXiv2021

Monadic cointegrals and applications to quasi-Hopf algebras

For $\mathcal{C}$ a finite tensor category we consider four versions of the central monad, $A_1, \dots, A_4$ on $\mathcal{C}$. Two of them are Hopf monads, and for $\mathcal{C}$ pivotal, so are the remaining two. In that case all $A_i$ are isomorphic as Hopf monads. We define a monadic cointegral for $A_i$ to be an $A_i$-module morphism $\mathbf{1} \to A_i(D)$, where $D$ is the distinguished invertible object of $\mathcal{C}$. We relate monadic cointegrals to the categorical cointegral introduced by Shimizu (2019), and, in case $\mathcal{C}$ is braided, to an integral for the braided Hopf algebra $\mathcal{L} = \int^X X^\vee \otimes X$ in $\mathcal{C}$ studied by Lyubashenko (1995). Our main motivation stems from the application to finite dimensional quasi-Hopf algebras $H$. For the category of finite-dimensional $H$-modules, we relate the four monadic cointegrals (two of which require $H$ to be pivotal) to four existing notions of cointegrals for quasi-Hopf algebras: the usual left/right cointegrals of Hausser and Nill (1994), as well as so-called $γ$-symmetrised cointegrals in the pivotal case, for $γ$ the modulus of $H$. For (not necessarily semisimple) modular tensor categories $\mathcal{C}$, Lyubashenko gave actions of surface mapping class groups on certain Hom-spaces of $\mathcal{C}$, in particular of $SL(2,\mathbb{Z})$ on $\mathcal{C}(\mathcal{L},\mathbf{1})$. In the case of a factorisable ribbon quasi-Hopf algebra, we give a simple expression for the action of $S$ and $T$ which uses the monadic cointegral.

math.QA↗

arXiv2019

Modified traces for quasi-Hopf algebras

Let H be a finite-dimensional unimodular pivotal quasi-Hopf algebra over a field k, and let H-mod be the pivotal tensor category of finite-dimensional H-modules. We give a bijection between left (resp. right) modified traces on the tensor ideal H-pmod of projective modules and left (resp. right) cointegrals for H. The non-zero left/right modified traces are non-degenerate, and we show that non-degenerate left/right modified traces can only exist for unimodular H. This generalises results of Beliakova, Blanchet, and Gainutdinov from Hopf algebras to quasi-Hopf algebras. As an example we compute cointegrals and modified traces for the family of symplectic fermion quasi-Hopf algebras.

math.QA↗

arXiv2018

Perfect tangles

We introduce perfect tangles for modular tensor categories. These are intended to generalise the perfect tensors first introduced in the context of a toy model for the AdS/CFT correspondence. We construct perfect tangles for several categories of relevance for topological quantum computation, including the Temperley-Lieb, Fibonacci, Kuperberg spider, and Haagerup planar algebras. A general inductive construction proposed by Vaughan Jones for perfect tangles is also described.

quant-ph↗

arXiv2016

Joint Recursive Monocular Filtering of Camera Motion and Disparity Map

Monocular scene reconstruction is essential for modern applications such as robotics or autonomous driving. Although stereo methods usually result in better accuracy than monocular methods, they are more expensive and more difficult to calibrate. In this work, we present a novel second order optimal minimum energy filter that jointly estimates the camera motion, the disparity map and also higher order kinematics recursively on a product Lie group containing a novel disparity group. This mathematical framework enables to cope with non-Euclidean state spaces, non-linear observations and high dimensions which is infeasible for most classical filters. To be robust against outliers, we use a generalized Charbonnier energy function in this framework rather than a quadratic energy function as proposed in related work. Experiments confirm that our method enables accurate reconstructions on-par with state-of-the-art.

cs.CV↗

arXiv2015

Second-Order Recursive Filtering on the Rigid-Motion Lie Group SE(3) Based on Nonlinear Observations

Camera motion estimation from observed scene features is an important task in image processing to increase the accuracy of many methods, e.g. optical flow and structure-from-motion. Due to the curved geometry of the state space SE(3) and the non-linear relation to the observed optical flow, many recent filtering approaches use a first-order approximation and assume a Gaussian a posteriori distribution or restrict the state to Euclidean geometry. The physical model is usually also limited to uniform motions. We propose a second-order minimum energy filter with a generalized kinematic model that copes with the full geometry of SE(3) as well as with the nonlinear dependencies between the state space and observations. The derived filter enables reconstructing motions correctly for synthetic and real scenes, e.g. from the KITTI benchmark. Our experiments confirm that the derived minimum energy filter with higher-order state differential equation copes with higher-order kinematics and is also able to minimize model noise. We also show that the proposed filter is superior to state-of-the-art extended Kalman filters on Lie groups in the case of linear observations and that our method reaches the accuracy of modern visual odometry methods.

math.OC↗

arXiv2015

Second Order Minimum Energy Filtering on $\operatorname{SE}_3$ with Nonlinear Measurement Equations

Accurate camera motion estimation is a fundamental building block for many Computer Vision algorithms. For improved robustness, temporal consistency of translational and rotational camera velocity is often assumed by propagating motion information forward using stochastic filters. Classical stochastic filters, however, use linear approximations for the non-linear observer model and for the non-linear structure of the underlying Lie Group $\operatorname{SE}_3$ and have to approximate the unknown posteriori distribution. In this paper we employ a non-linear measurement model for the camera motion estimation problem that incorporates multiple observation equations. We solve the underlying filtering problem using a novel Minimum Energy Filter on $\operatorname{SE}_3$ and give explicit expressions for the optimal state variables. Experiments on the challenging KITTI benchmark show that, although a simple motion model is only employed, our approach improves rotational velocity estimation and otherwise is on par with the state-of-the-art.

math.OC↗