Verena Wolf

Thomas A. Henzinger, Maria Mateescu, Linar Mikeev et al.

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient probability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We implemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.

Tugrul Dayar, Holger Hermanns, David Spieler et al.

Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its function as a biological switch. Unfortunately, the state space of these systems is infinite in most cases, preventing the use of traditional steady state solution techniques. In this paper we develop a new approach to tackle this problem by first retrieving geometric bounds enclosing a major part of the steady state probability mass, followed by a more detailed analysis revealing state-wise bounds.

Julius Gabelmann, Felix Jahn, Kevin Baum et al.

The widespread adoption of AI chatbots in education will drastically change learning, making responsible deployment a critical concern. While large language models (LLMs) might have access to sources discussing insights from educational sciences, they are not particularly inclined to adhere to pedagogical concepts, risking negative effects on the learning process, such as a loss of transfer capabilities, critical thinking, or creativity. In this paper, we introduce an agentic AI chatbot architecture assisting students with exercise solving, specifically designed to contribute to more responsible AI use in education. We base our conceptual development on the identification of several desiderata for responsible LLM-based educational systems, argue for the structural shortcomings inherent in monolithic, out-of-the-box solutions, and instead suggest modularizing the agentic architecture. We propose specific modules for different stages of exercise solving, enabling incorporation of targeted pedagogical advice, guiding students through the learning process in a more controllable, transparent, and overseeable manner.

Aleksandr Andreychenko, Pepijn Crouzen, Linar Mikeev et al.

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique.

Alexander Andreychenko, Linar Mikeev, Verena Wolf

The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.

Joschka Groß, Mohammad Shaique Solanki, Verena Wolf

We introduce B-cos GNNs, an inherently explainable class of graph neural networks whose predictions decompose exactly into per-node, per-feature contributions via a single input-dependent linear map. B-cos GNNs use linear (sum-based) aggregation and replace non-linear message and update functions with B-cos transforms. This induces meaningful, task-specific weight-input alignment that is directly accessible through the model's dynamic linearity. Instance-level explanations follow from a single forward and backward pass, requiring no auxiliary explainer, modified learning objective, or perturbation procedure. Instantiated as a GIN, our approach trades small losses in predictive accuracy for state-of-the-art explainability across diverse synthetic and real-world benchmarks, producing explanations orders of magnitude faster than post-hoc baselines.

Kevin Baum, Lisa Dargasz, Felix Jahn et al.

We propose an extension of the reinforcement learning architecture that enables moral decision-making of reinforcement learning agents based on normative reasons. Central to this approach is a reason-based shield generator yielding a moral shield that binds the agent to actions that conform with recognized normative reasons so that our overall architecture restricts the agent to actions that are (internally) morally justified. In addition, we describe an algorithm that allows to iteratively improve the reason-based shield generator through case-based feedback from a moral judge.

Prashanth Pombala, Gerrit Grossmann, Verena Wolf

Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs, graph neural networks (GNNs) as a diffusion backbone have achieved impressive results. Latent space diffusion, where diffusion occurs in a low-dimensional space via an autoencoder, has demonstrated computational efficiency. However, the literature on latent space diffusion for molecular graphs is scarce, and no commonly accepted best practices exist. In this work, we explore different approaches and hyperparameters, contrasting generative flow models (denoising diffusion, flow matching, heat dissipation) and architectures (GNNs and E(3)-equivariant GNNs). Our experiments reveal a high sensitivity to the choice of approach and design decisions. Code is made available at github.com/Prashanth-Pombala/Molecule-Generation-using-Latent-Space-Graph-Diffusion.

Timo P. Gros, Nicola J. Müller, Daniel Fiser et al.

Recent work has shown that successful per-domain generalizing action policies can be learned. Scaling behavior, from small training instances to large test instances, is the key objective; and the use of validation instances larger than training instances is one key to achieve it. Prior work has used fixed validation sets. Here, we introduce a method generating the validation set dynamically, on the fly, increasing instance size so long as informative and feasible.We also introduce refined methodology for evaluating scaling behavior, generating test instances systematically to guarantee a given confidence in coverage performance for each instance size. In experiments, dynamic validation improves scaling behavior of GNN policies in all 9 domains used.

Zhifei Li, Gerrit Großmann, Verena Wolf

In recent years, a wide variety of graph neural network (GNN) architectures have emerged, each with its own strengths, weaknesses, and complexities. Various techniques, including rewiring, lifting, and node annotation with centrality values, have been employed as pre-processing steps to enhance GNN performance. However, there are no universally accepted best practices, and the impact of architecture and pre-processing on performance often remains opaque. This study systematically explores the impact of various graph transformations as pre-processing steps on the performance of common GNN architectures across standard datasets. The models are evaluated based on their ability to distinguish non-isomorphic graphs, referred to as expressivity. Our findings reveal that certain transformations, particularly those augmenting node features with centrality measures, consistently improve expressivity. However, these gains come with trade-offs, as methods like graph encoding, while enhancing expressivity, introduce numerical inaccuracies widely-used python packages. Additionally, we observe that these pre-processing techniques are limited when addressing complex tasks involving 3-WL and 4-WL indistinguishable graphs.

Gerrit Großmann, Julian Zimmerlin, Michael Backenköhler et al.

Dynamical systems in which local interactions among agents give rise to complex emerging phenomena are ubiquitous in nature and society. This work explores the problem of inferring the unknown interaction structure (represented as a graph) of such a system from measurements of its constituent agents or individual components (represented as nodes). We consider a setting where the underlying dynamical model is unknown and where different measurements (i.e., snapshots) may be independent (e.g., may stem from different experiments). We propose GINA (Graph Inference Network Architecture), a graph neural network (GNN) to simultaneously learn the latent interaction graph and, conditioned on the interaction graph, the prediction of a node's observable state based on adjacent vertices. GINA is based on the hypothesis that the ground truth interaction graph -- among all other potential graphs -- allows to predict the state of a node, given the states of its neighbors, with the highest accuracy. We test this hypothesis and demonstrate GINA's effectiveness on a wide range of interaction graphs and dynamical processes.

Michael Backenköhler, Luca Bortolussi, Gerrit Großmann et al.

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method's applicability to a wide range of non-linear problems with complex stationary behaviors.

Timo P. Gros, Daniel Höller, Jörg Hoffmann et al.

Learning-based approaches for solving large sequential decision making problems have become popular in recent years. The resulting agents perform differently and their characteristics depend on those of the underlying learning approach. Here, we consider a benchmark planning problem from the reinforcement learning domain, the Racetrack, to investigate the properties of agents derived from different deep (reinforcement) learning approaches. We compare the performance of deep supervised learning, in particular imitation learning, to reinforcement learning for the Racetrack model. We find that imitation learning yields agents that follow more risky paths. In contrast, the decisions of deep reinforcement learning are more foresighted, i.e., avoid states in which fatal decisions are more likely. Our evaluations show that for this sequential decision making problem, deep reinforcement learning performs best in many aspects even though for imitation learning optimal decisions are considered.

Alexander Andreychenko, Luca Bortolussi, Ramon Grima et al.

The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach relies on an analytical approximation of the probability distribution of the CME using the system size expansion, considering higher-order terms than the linear noise approximation. We consider gene expression networks with unimodal and multimodal protein distributions to compare the accuracy of the two approaches. We find that both methods provide accurate approximations to the distributions of the CME while having different benefits and limitations in applications.

Alexander Andreychenko, Linar Mikeev, Verena Wolf

The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state space, analysis techniques based on an exploration of the state space are often not feasible and the integration of the moments of the underlying probability distribution has become a very popular alternative. In this paper the focus is on a comparison of reconstructed distributions from their moments obtained by two different moment-based analysis methods, the method of moments (MM) and the method of conditional moments (MCM). We use the maximum entropy principle to derive a distribution that fits best to a given sequence of (conditional) moments. For the two gene regulatory networks that we consider we find that the MCM approach is more suitable to describe multimodal distributions and that the reconstruction is more accurate if conditional distributions are considered.