Related papers: HyCOP: Hybrid Composition Operators for Interpreta…

Multiscale partial differential equations (PDEs) arise in various applications, and several schemes have been developed to solve them efficiently. Homogenization theory is a powerful methodology that eliminates the small-scale dependence,…

To apply neural sequence models such as the Transformers to music generation tasks, one has to represent a piece of music by a sequence of tokens drawn from a finite set of pre-defined vocabulary. Such a vocabulary usually involves tokens…

Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces…

Complex systems are often composed of many small communicating components called modules. We investigate the synthesis of supervisory controllers for modular systems under partial observation that, as the closed-loop system, realize the…

In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…

There are two main lines of research on visual question answering (VQA): compositional model with explicit multi-hop reasoning, and monolithic network with implicit reasoning in the latent feature space. The former excels in…

Transformers rely on explicit positional encoding to model structure in data. While Rotary Position Embedding (RoPE) excels in 1D domains, its application to image generation reveals significant limitations such as fine-grained spatial…

Scientific machine learning often requires combining known physics with unknown parameters or correction terms learned from data. Existing approaches either ignore known structure, encode it as a soft penalty, or require hand-written…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions…

Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning…

This paper introduces HiKO (Hierarchical Kronecker Operation), a novel framework for training high-rate neural error-correcting codes that enables KO codes to outperform Reed-Muller codes beyond second order. To our knowledge, this is the…

While existing image-guided composition methods may help insert a foreground object onto a user-specified region of a background image, achieving natural blending inside the region with the rest of the image unchanged, we observe that these…

Large Language Models are increasingly deployed inside agentic systems, where they must follow structured protocols, adapt to evolving states, and operate under memory, latency, and cost constraints. In such regimes, prompt extension is…

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved…

We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks. While deep learning has proven effective at modeling complex relationships from data, compositional couplings…

Retrieval-augmented generation (RAG) remains brittle on multi-step questions and heterogeneous evidence sources, trading accuracy against latency and token/tool budgets. This paper introduces RELOOP, a structure aware framework using…