Fourier Neural Operators for Non-Markovian Processes:Approximation Theorems and Experiments

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror padding, enabling it to handle non-periodic inputs. We rigorously prove that MFNOs can approximate solutions of path-dependent stochastic differential equations and Lipschitz transformations of fractional Brownian motions to an arbitrary degree of accuracy. Our theoretical analysis builds on Wong--Zakai type theorems and various approximation techniques. Empirically, the MFNO exhibits strong resolution generalization--a property rarely seen in standard architectures such as LSTMs, TCNs, and DeepONet. Furthermore, our model achieves performance that is comparable or superior to these baselines while offering significantly faster sample path generation than classical numerical schemes.

Diversity and stylization of the contemporary user-generated visual arts in the complexity-entropy plane

The advent of computational and numerical methods in recent times has provided new avenues for analyzing art historiographical narratives and tracing the evolution of art styles therein. Here, we investigate an evolutionary process underpinning the emergence and stylization of contemporary user-generated visual art styles using the complexity-entropy (C-H) plane, which quantifies local structures in paintings. Informatizing 149,780 images curated in DeviantArt and Behance platforms from 2010 to 2020, we analyze the relationship between local information of the C-H space and multi-level image features generated by a deep neural network and a feature extraction algorithm. The results reveal significant statistical relationships between the C-H information of visual artistic styles and the dissimilarities of the multi-level image features over time within groups of artworks. By disclosing a particular C-H region where the diversity of image representations is noticeably manifested, our analyses reveal an empirical condition of emerging styles that are both novel in the C-H plane and characterized by greater stylistic diversity. Our research shows that visual art analyses combined with physics-inspired methodologies and machine learning, can provide macroscopic insights into quantitatively mapping relevant characteristics of an evolutionary process underpinning the creative stylization of uncharted visual arts of given groups and time.

HyperCLOVA X Technical Report

We introduce HyperCLOVA X, a family of large language models (LLMs) tailored to the Korean language and culture, along with competitive capabilities in English, math, and coding. HyperCLOVA X was trained on a balanced mix of Korean, English, and code data, followed by instruction-tuning with high-quality human-annotated datasets while abiding by strict safety guidelines reflecting our commitment to responsible AI. The model is evaluated across various benchmarks, including comprehensive reasoning, knowledge, commonsense, factuality, coding, math, chatting, instruction-following, and harmlessness, in both Korean and English. HyperCLOVA X exhibits strong reasoning capabilities in Korean backed by a deep understanding of the language and cultural nuances. Further analysis of the inherent bilingual nature and its extension to multilingualism highlights the model's cross-lingual proficiency and strong generalization ability to untargeted languages, including machine translation between several language pairs and cross-lingual inference tasks. We believe that HyperCLOVA X can provide helpful guidance for regions or countries in developing their sovereign LLMs.