The 9th International Conference on the Dynamics of Information Systems (DIS 2026)

Panos M. Pardalos, University of Florida, USA

Title: A New Frontier: From a Single Network to a Network of Networks

Abstract: This lecture examines the fundamental shift from isolated, monolithic systems to the expansive “Network of Networks” architecture that underpins modern global infrastructure. We move beyond traditional single-layer analysis to explore the intricate interdependencies among critical domains—for example, the Energy–Financial nexus, where real-time market signals influence grid stability, and the Transportation–Digital nexus, where autonomous logistics depend on ubiquitous communication.

Problems in networks of networks are far more complex than those in single networks. For example, in a single network, the propagation of failures can often be predicted and contained. In contrast, within a “Network of Networks,” such failures become exponentially more difficult to anticipate due to hidden interdependencies—connections that remain invisible until they trigger cascading and often unpredictable effects.

Biography: Panos Pardalos received his PhD (Computes and Information Sciences) from the University of Minnesota. He is an Emeritus Distinguished Professor in the Department of Industrial and Systems Engineering at the University of Florida, and an affiliated faculty of Biomedical Engineering and Computer Science & Information & Engineering departments.

Panos Pardalos is a world-renowned leader in Global Optimization, Mathematical Modeling, Energy Systems, Financial applications, and Data Sciences. He is a Fellow of AAAS, AAIA, AIMBE, EUROPT, and INFORMS and was awarded the 2013 Constantin Caratheodory Prize of the International Society of Global Optimization. In addition, Panos Pardalos has been awarded the 2013 EURO Gold Medal prize bestowed by the Association for European Operational Research Societies. This medal is the preeminent European award given to Operations Research (OR) professionals for “scientific contributions that stand the test of time.”

Panos Pardalos has been awarded a prestigious Humboldt Research Award (2018-2019). The Humboldt Research Award is granted in recognition of a researcher’s entire achievements to date – fundamental discoveries, new theories, insights that have had significant impact on their discipline.

Panos Pardalos is also a Member of several Academies of Sciences, and he holds several honorary PhD degrees and affiliations. He is the Founding Editor of Optimization Letters, Energy Systems, and Co-Founder of the International Journal of Global Optimization, Computational Management Science, and Springer Nature Operations Research Forum. He has published over 600 journal papers, and edited/authored over 200 books. He is one of the most cited authors and has graduated 71 PhD students so far. Details can be found in www.ise.ufl.edu/pardalos

Panos Pardalos has lectured and given invited keynote addresses worldwide in countries including Austria, Australia, Azerbaijan, Belgium, Brazil, Canada, Chile, China, Czech Republic, Cyprus, Denmark, Egypt, England, France, Finland, Germany, Greece, Holland, Hong Kong, Hungary, Iceland, Ireland, Italy, Japan, Lithuania, Mexico, Mongolia, Montenegro, New Zealand, Norway, Peru, Portugal, Russia, South Korea, Singapore, Serbia, South Africa, Spain, Sweden, Switzerland, Taiwan, Turkey, Ukraine, United Arab Emirates, and the USA.

Peter Richtárik, KAUST, Saudi Arabia

Title: From the Ball-proximal (Broximal) Point Method to Efficient Training of Large Language Models

Abstract: Non-smooth and non-convex global optimization poses significant challenges across various applications, where standard gradient-based methods often struggle. We propose the Ball-Proximal Point Method, Broximal Point Method, or Ball Point Method (BPM) for short – a novel algorithmic framework inspired by the classical Proximal Point Method (PPM) [8], which, as we show, sheds new light on several foundational optimization paradigms and phenomena, including non-convex and non-smooth optimization, acceleration, smoothing, adaptive stepsize selection, and trust-region methods. At the core of BPM lies the ball-proximal (“broximal”) operator, which arises from the classical proximal operator by replacing the quadratic distance penalty by a ball constraint. Surprisingly, and in sharp contrast with the sublinear rate of PPM in the nonsmooth convex regime, we prove that BPM converges linearly and in a finite number of steps in the same regime. Furthermore, by introducing the concept of ball-convexity, we prove that BPM retains the same global convergence guarantees under weaker assumptions, making it a powerful tool for a broader class of potentially non-convex optimization problems. Just like PPM plays the role of a conceptual method inspiring the development of practically efficient algorithms and algorithmic elements, e.g., gradient descent, adaptive step sizes, acceleration [1], and “W” in AdamW [9], we believe that BPM should be understood in the same manner: as a blueprint and inspiration for further development. Generalization non-Euclidean ball constraints can be found in the follow-up work [3].

The Broximal Point Method (BPM) [2] offers an idealized optimization framework based on iteratively minimizing the objective function over norm balls centered at the current iterate. It enjoys striking global convergence guarantees, converging linearly and in a finite number of steps for proper, closed and convex functions. However, its theoretical analysis has so far been confined to the Euclidean geometry. At the same time, emerging trends in deep learning optimization, exemplified by algorithms such as Muon [4] and Scion [6], demonstrate the practical advantages of minimizing over balls defined via non-Euclidean norms which better align with the underlying geometry of the associated loss landscapes. We ask whether the convergence theory of BPM can be extended to this more general, non-Euclidean setting. We give a positive answer, showing that most of the elegant guarantees of the original method carry over to arbitrary norm geometries. Along the way, we clarify which properties are preserved and which necessarily break down when leaving the Euclidean realm. Our analysis positions Non-Euclidean BPM as a conceptual blueprint for understanding a broad class of geometry-aware optimization algorithms, shedding light on the principles behind their practical effectiveness.

Latest developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as Muon [4] and Scion [6]. After over a decade of Adam’s [5] dominance, these LMO-based methods are emerging as viable replacements, offering several practical advantages such as improved memory efficiency, better hyperparameter transferability, and most importantly, superior empirical performance on large-scale tasks, including LLM training. However, a significant gap remains between their practical use and our current theoretical understanding: prior analyses (1) overlook the layer-wise LMO application of these optimizers in practice, and (2) rely on an unrealistic smoothness assumption, leading to impractically small stepsizes. To address both, we propose a new LMO-based method called Gluon, capturing prior theoretically analyzed methods as special cases, and introduce a new refined generalized smoothness model that captures the layer-wise geometry of neural networks, matches the layer-wise practical implementation of Muon and Scion, and leads to con- vergence guarantees with strong practical predictive power. Unlike prior results, our theoretical stepsizes closely match the fine-tuned values reported in [6]. Our experiments with NanoGPT and CNN confirm that our assumption holds along the optimization trajectory, ultimately closing the gap between theory and practice.

Recent optimizers like Muon [4], Scion [6], and Gluon [7] have pushed the frontier of large-scale deep learning by exploiting layer-wise linear minimization oracles (LMOs) over non-Euclidean norm balls, capturing neural network structure in ways traditional algorithms cannot. Yet, no principled distributed framework exists for these methods, and communication bottlenecks remain unaddressed. The very few distributed variants are heuristic, with no convergence guarantees in sight. We introduce EF21-Muon, the first communication-efficient, non-Euclidean LMO-based optimizer with rigorous convergence guarantees. EF21-Muon supports stochastic gradients, momentum, and bidirectional compression with error feedback-marking the first extension of error feedback beyond the Euclidean setting. It recovers Muon/Scion/Gluon when compression is off and specific norms are chosen, providing the first efficient distributed implementation of this powerful family. Our theory covers non-Euclidean smooth and the more general communication savings with no accuracy degradation.

References

[1] Kwangjun Ahn and Suvrit Sra. “Understanding Nesterov’s Acceleration via Proximal Point Method”. Symposium on Simplicity in Algorithms (SOSA), 2022, pp. 117–130.

[2] Kaja Gruntkowska, Hanmin Li, Aadi Rane, and Peter Richtárik. “The ball-proximal (=”broximal”) point method: a new algorithm, convergence theory, and applications”. arXiv preprint arXiv:2502.02002, 2025.

[3] Kaja Gruntkowska and Peter Richtárik. Non-Euclidean broximal point method: a blueprint for geometry-aware optimization. arXiv preprint arXiv:2510.00823, 2025

[4] Keller Jordan, Yuchen Jin, Vlado Boza, Jiacheng You, Franz Cesista, Laker Newhouse, and Jeremy Bernstein. Muon: An optimizer for hidden layers in neural networks, 2024.

[5] Diederik P. Kingma and Jimmy Ba. “Adam: A method for stochastic optimization”. In: arXiv preprint arXiv:1412.6980 (2014).

[6] Thomas Pethick, Wanyun Xie, Kimon Antonakopoulos, Zhenyu Zhu, Antonio Silveti-Falls, and Volkan Cevher. “Training deep learning models with norm-constrained LMOs”. arXiv preprint arXiv:2502.07529 (2025).

[7] Artem Riabinin, Kaja Gruntkowska, Egor Shulgin, and Peter Richtárik. “Gluon: Making Muon and Scion great again! (Bridging theory and practice of LMO-based optimizers for LLMs)”. arXiv preprint arXiv:2505.13416 (2025).

[8] R. T Rockafellar. “Monotone operators and the proximal point algorithm”. In: SIAM Journal on Control and Optimization 14.5 (1976), pp. 877–898.

[9] Z. Zhuang, M. Liu, A. Cutkosky, and F. Orabona. “Understanding AdamW through proximal methods and scale-freeness”. Transactions on Machine Learning Research (2022).

[10] Kaja Gruntkowska, Yassine Maziane, Zheng Qu, and Peter Richtárik. Drop-Muon: Update less, converge faster, arXiv preprint arXiv:2510.02239, 2025.

[11] Kaja Gruntkowska, Alexander Gaponov, Zhirayr Tovmasyan, and Peter Richtárik. Error feedback for Muon and friends, 14th International Conference on Learning Representations (ICLR 2026).

Biography: Peter Richtárik is a professor of Computer Science at the King Abdullah University of Science and Technology (KAUST), Saudi Arabia, where he leads the Optimization and Machine Learning Lab . His research interests lie at the intersection of mathematics, computer science, machine learning, optimization, numerical linear algebra, and high-performance computing. Through his work on randomized and distributed optimization algorithms, he has contributed to the foundations of machine learning, optimization and randomized numerical linear algebra. He is one of the original developers of Federated Learning. Prof Richtárik’s works attracted international awards, including the Charles Broyden Prize, SIAM SIGEST Best Paper Award, Distinguished Speaker Award at the 2019 International Conference on Continuous Optimization, the IMA Leslie Fox Prize (three times), and a Best Paper Award at the NeurIPS 2020 Workshop on Scalability, Privacy, and Security in Federated Learning. Several of his works are among the most read papers published by the SIAM Journal on Optimization and the SIAM Journal on Matrix Analysis and Applications. Prof Richtárik serves as an Area Chair for leading machine learning conferences, including NeurIPS, ICML and ICLR, and is an Action Editor of JMLR, and Associate Editor of Numerische Mathematik and Optimization Methods and Software. In the past, he served as an Action Editor of TMLR and an Area Editor of JOTA.

Roman Belavkin, Middlesex University, UK

Title: Value of Information and Entropic Optimal Transport

Abstract: The optimal transport theory pioneered by Gaspar Monge and developed in probabilistic setting by Leonid Kantorovich has gained popularity recently in the context of machine learning and statistical applications due to the appearance of new algorithms (e.g. Sinkhorn) that simplify computations using entropic regularization. These methods allow for more efficient estimations of transport metrics (aka the Kantorovich or Wasserstein metric) to compare distributions. It was shown in 2018 that optimal transport with entropic regularization is closely related to the value of Shannon’s information, and that the latter is a relaxed version of the former. Therefore, many solutions and examples developed by Stratonovich and his colleagues in the 1960s for the value of information can be readily used as lower bounds on the optimal transport costs. I will discuss further generalizations of these concepts by considering other types of information.

Biography: Roman Belavkin obtained MSc in Physics from the Moscow State University and PhD in Computer Science from the University of Nottingham.  His research interests span several areas including geometric analysis of optimal and learning systems, dynamics of information, value of information, quantum information, topology of information, geometry and combinatorics of mutation and recombination of sequences, optimal control of evolutionary algorithms, cognitive modelling.  Roman joined Middlesex University in 2002, where he participated in several research projects and organized research seminars of the Artificial Intelligence group.  From 2009 Roman has been the Principle Investigator of the EPSRC project `SANDPIT: Evolution as an Information Dynamic System’, which was led by Middlesex University in collaboration with Universities of Manchester, Keele and Warwick.  In this project, Roman developed a theory of optimal control of mutation rate in evolutionary systems, and the team discovered plastic mutation rates in microbes (http://doi.org/skb, http://doi.org/cb9s).  Roman‘s current work is on geometric and dynamic value of information theory, which has applications in parameter control and optimization of learning, adaptive and evolving systems.  Roman has many international collaborations: He has been an associate member of the `Centre of Applied Optimization’ in the University of Florida, USA; his collaboration with Tokyo University of Science was recognized in 2014 by the award from the university’s president Professor Akira Fujishima.  Roman has been a keynote speaker at many international conferences, workshops and research seminars.  He also serves on the editorial board of the `Optimization Letters’ and `SN Operations Research Forum’ journals.

Zbyšek Posel, Jan Evangelista Purkyně University, Czech Republic

Title: AI-Driven Labeling and Data Augmentation for ICU Monitoring

Abstract: Continuous monitoring of patients’ vital functions in intensive care units (ICUs) generates high-frequency physiological signals. Among these, electrocardiography (ECG), arterial blood pressure (ABP), and intracranial pressure (ICP) are routinely recorded, particularly in patients with traumatic brain injury. In addition, clinically relevant indices such as the pressure reactivity index and cerebral perfusion pressure are derived from these signals to assess patient status.

However, raw recordings are frequently contaminated by anomalies arising from patient movement, sensor manipulation, device malfunction, and routine clinical interventions. Robust detection and management of such artifacts are essential to ensure data integrity, enable reliable derivation of physiological parameters, and reduce the risk of misclassification of clinically significant events. Recent approaches increasingly rely on machine learning to automate anomaly detection and handling, reflecting the recognition that artifacts are ubiquitous in continuous neuromonitoring and cannot be reliably addressed through manual or ad hoc methods alone. Despite this progress, human annotation remains the ground truth for both model training and evaluation, and together with data availability, defines the upper bound of achievable performance. While several physiological signal databases are publicly available, none provide sufficiently reliable anomaly labels, limiting the development and benchmarking of new methods. To address this limitation, we propose an AI-assisted framework for rapid waveform pre-labeling, enabling efficient human validation and curation. The framework is designed to facilitate the creation of large-scale, multicentric labeled datasets for anomaly detection in physiological signals.

A further challenge lies in the high inter- and intra-patient variability of ICU physiological signals, which complicates the generalization of anomaly detection models. Signal characteristics may vary not only across patients but also due to differences in acquisition methods and treatment conditions over time. To mitigate these challenges and alleviate data scarcity, we also introduce a method for extending real ABP datasets through synthetic signal generation. The proposed approach embeds hemodynamic envelope dynamics and links them with fast signal components such as heart rate variability and waveform morphology. By coupling envelope properties across nearest neighbors in the embedded space, the method produces realistic synthetic ABP signals that closely resemble true physiological recordings.

Biography: Zbyšek Posel is the Deputy Head of the Department and Head of the Data Analysis and Simulation Unit at the Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem. His research focuses on computational modeling, computer analysis of electro-physiological signals (EEG, EKG, EMG), image analysis of biological and material systems, and mesoscale simulations of polymers and complex materials. He combines classical algorithms with modern machine learning approaches to address challenges in biomedical data analysis, materials science, and complex system simulations. Dr. Posel has led and contributed to numerous international and national projects, including FP6 MULTIPRO, H2020 VIMMP, TA ČR METAMORPH, and OP JAK DIGITECH, and has conducted extended research stays at the University of Trieste. He teaches a wide range of courses in data analysis, signal and image processing, parallel programming, and system simulation, and supervises research on anomaly detection in physiological signals, polymer self-organization, and artificial signal generation. His work has been published in leading journals such as Polymers, ACS Nano, Langmuir, and Soft Matter, and he maintains scientific collaborations with hospitals, research centers, and universities across Europe.