Ioannis Kordonis

Ioannis Kordonis, Petros Maragos, George P. Papavassilopoulos

We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability. The results for the Max-Product systems are then applied to Max-Plus systems with Markovian Jumps, using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained. A numerical example illustrating the application of the stability results on a production system is also given.

Ioannis Kordonis, Petros Maragos

Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This paper presents a new look at the problem of tropical polynomial division and its application to the simplification of neural networks. We analyze tropical polynomials with real coefficients, extending earlier ideas and methods developed for polynomials with integer coefficients. We first prove the existence of a unique quotient-remainder pair and characterize the quotient in terms of the convex bi-conjugate of a related function. Interestingly, the quotient of tropical polynomials with integer coefficients does not necessarily have integer coefficients. Furthermore, we develop a relationship of tropical polynomial division with the computation of the convex hull of unions of convex polyhedra and use it to derive an exact algorithm for tropical polynomial division. An approximate algorithm is also presented, based on an alternation between data partition and linear programming. We also develop special techniques to divide composite polynomials, described as sums or maxima of simpler ones. Finally, we present some numerical results to illustrate the efficiency of the algorithms proposed, using the MNIST handwritten digit and CIFAR-10 datasets.

Ioannis Kordonis, Emmanouil Theodosis, George Retsinas et al.

Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the recent successes of tropical algebra and geometry in machine learning, we investigate two problems involving matrix factorization over the tropical algebra. For the first problem, Tropical Matrix Factorization (TMF), which has been studied already in the literature, we propose an improved algorithm that avoids many of the local optima. The second formulation considers the approximate decomposition of a given matrix into the product of three matrices where a usual matrix product is followed by a tropical product. This formulation has a very interesting interpretation in terms of the learning of the utility functions of multiple users. We also present numerical results illustrating the effectiveness of the proposed algorithms, as well as an application to recommendation systems with promising results.

Stelios Zarifis, Ioannis Kordonis, Petros Maragos

We propose Diffusion-Informed Model Predictive Control (D-I MPC), a generic framework for uncertainty-aware prediction and decision-making in partially observable stochastic systems by integrating diffusion-based time series forecasting models in Model Predictive Control algorithms. In our approach, a diffusion-based time series forecasting model is used to probabilistically estimate the evolution of the system's stochastic components. These forecasts are then incorporated into MPC algorithms to estimate future trajectories and optimize action selection under the uncertainty of the future. We evaluate the framework on the task of energy arbitrage, where a Battery Energy Storage System participates in the day-ahead electricity market of the New York state. Experimental results indicate that our model-based approach with a diffusion-based forecaster significantly outperforms both implementations with classical forecasting methods and model-free reinforcement learning baselines.

Nikolas Chatzis, Ioannis Kordonis, Manos Theodosis et al.

Expanding neural networks during training is a promising way to augment capacity without retraining larger models from scratch. However, newly added neurons often fail to adjust to a trained network and become inactive, providing no contribution to capacity growth. We propose the Shared-Weights Extender (SWE), a novel method explicitly designed to prevent inactivity of new neurons by coupling them with existing ones for smooth integration. In parallel, we introduce the Steepest Voting Distributor (SVoD), a gradient-based method for allocating neurons across layers during deep network expansion. Our extensive benchmarking on four datasets shows that our method can effectively suppress neuron inactivity and achieve better performance compared to other expanding methods and baselines.

Petros Georgoulas Wraight, Giorgos Sfikas, Ioannis Kordonis et al.

Handwritten Text Recognition (HTR) is a task of central importance in the field of document image understanding. State-of-the-art methods for HTR require the use of extensive annotated sets for training, making them impractical for low-resource domains like historical archives or limited-size modern collections. This paper introduces a novel framework that, unlike the standard HTR model paradigm, can leverage mild prior knowledge of lexical characteristics; this is ideal for scenarios where labeled data are scarce. We propose an iterative bootstrapping approach that aligns visual features extracted from unlabeled images with semantic word representations using Optimal Transport (OT). Starting with a minimal set of labeled examples, the framework iteratively matches word images to text labels, generates pseudo-labels for high-confidence alignments, and retrains the recognizer on the growing dataset. Numerical experiments demonstrate that our iterative visual-semantic alignment scheme significantly improves recognition accuracy on low-resource HTR benchmarks.

Stelios Zarifis, Ioannis Kordonis, Petros Maragos

Stochastic forecasting is critical for efficient decision-making in uncertain systems, such as energy markets and finance, where estimating the full distribution of future scenarios is essential. We propose Diffusion Scenario Tree (DST), a general framework for constructing scenario trees for multivariate prediction tasks using diffusion-based probabilistic forecasting models. DST recursively samples future trajectories and organizes them into a tree via clustering, ensuring non-anticipativity (decisions depending only on observed history) at each stage. We evaluate the framework on the optimization task of energy arbitrage in New York State's day-ahead electricity market. Experimental results show that our approach consistently outperforms the same optimization algorithms that use scenario trees from more conventional models and Model-Free Reinforcement Learning baselines. Furthermore, using DST for stochastic optimization yields more efficient decision policies, achieving higher performance by better handling uncertainty than deterministic and stochastic MPC variants using the same diffusion-based forecaster.