Degrees

MSc in mathematics, Department of Mathematics, University of Osijek, Croatia, 2022.

BSc in mathematics, Department of Mathematics, University of Osijek, Croatia, 2020.

Publications

1. S. Canzar, V. Hoan Do, S. Jelić, S. Laue, D. Matijević, T. Prusina, Metric multidimensional scaling for large single-cell datasets using neural networks, Algorithms for Molecular Biology 19/21 (2024)
   Abstract

   Metric multidimensional scaling is one of the classical methods for embedding data into low-dimensional Euclidean space. It creates the low-dimensional embedding by approximately preserving the pairwise distances between the input points. However, current state-of-the-art approaches only scale to a few thousand data points. For larger data sets such as those occurring in single-cell RNA sequencing experiments, the running time becomes prohibitively large and thus alternative methods such as PCA are widely used instead. Here, we propose a simple neural network-based approach for solving the metric multidimensional scaling problem that is orders of magnitude faster than previous state-of-the-art approaches, and hence scales to data sets with up to a few million cells. At the same time, it provides a non-linear mapping between high- and low-dimensional space that can place previously unseen cells in the same embedding.
2. D. Ševerdija, T. Prusina, L. Borozan, D. Matijević, Efficient Sentence Representation Learning via Knowledge Distillation with Maximum Coding Rate Reduction, CIT. Journal of Computing and Information Technology 31/4 (2023)
   Abstract

   Addressing the demand for effective sentence representation in natural language inference problems, this paper explores the utility of pre-trained large language models in computing such representations. Although these models generate high-dimensional sentence embeddings, a noticeable performance disparity arises when they are compared to smaller models. The hardware limitations concerning space and time necessitate the use of smaller, distilled versions of large language models. In this study, we investigate the knowledge distillation of Sentence-BERT, a sentence representation model, by introducing an additional projection layer trained on the novel Maximum Coding Rate Reduction (MCR2) objective designed for general-purpose manifold clustering. Our experiments demonstrate that the distilled language model, with reduced complexity and sentence embedding size, can achieve comparable results on semantic retrieval benchmarks, providing a promising solution for practical applications.

1. S. Laue, T. Prusina, Efficient Line Search Method Based on Regression and Uncertainty, 18th Learning and Intelligent Optimization Conference, Ischia, Italy, 2024, 361-370
   Abstract

   Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach. Traditional line search methods, aimed at determining optimal step lengths, often discard valuable data from the search process and focus on refining step length intervals. This paper proposes a more efficient method using Bayesian optimization, which utilizes all available data points, i.e., function values and gradients, to guide the search towards a potential global minimum. This new approach more effectively explores the search space, leading to better solution quality. It is also easy to implement and integrate into existing frameworks. Tested on the challenging CUTEst test set, it demonstrates superior performance compared to existing state-of-the-art methods, solving more problems to optimality with equivalent resource usage.
2. D. Ševerdija, T. Prusina, A. Jovanović, L. Borozan, J. Maltar, D. Matijević, Compressing Sentence Representation with Maximum Coding Rate Reduction (Best paper award in AIS - Artificial Intelligence Systems track), ICT and Electronics Convention (MIPRO), 2023 46th MIPRO, Opatija, Hrvatska, 2023
   Abstract

   In most natural language inference problems, sentence representation is needed for semantic retrieval tasks. In recent years, pre-trained large language models have been quite effective for computing such representations. These models produce high-dimensional sentence embeddings. An evident performance gap between large and small models exists in practice. Hence, due to space and time hardware limitations, there is a need to attain comparable results when using the smaller model, which is usually a distilled version of the large language model. In this paper, we assess the model distillation of the sentence representation model Sentence-BERT by augmenting the pre-trained distilled model with a projection layer additionally learned on the Maximum Coding Rate Reduction (MCR2) objective, a novel approach developed for general purpose manifold clustering. We demonstrate that the new language model with reduced complexity and sentence embedding size can achieve comparable results on semantic retrieval benchmarks.