arXiv subjects

Junwon You

Publications and source records attributed to Junwon You.

4 recordsLinked to original sources

arXiv2026

Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning

Vision-language models have shown strong performance, but they often generalize poorly to specialized domains. While semi-supervised vision-language learning mitigates this limitation by leveraging a small set of labeled image-text pairs together with abundant unlabeled images, existing methods remain fundamentally pairwise and fail to model the global structure of multimodal representation manifolds. Existing topology-based alignment methods rely on persistence diagram matching, which neither guarantees geometric alignment nor utilizes the image-text pairing information central to vision-language learning. We propose Topology-Aware Multimodal Representation Alignment (ToMA), a framework that uses persistent homology to identify topologically salient edges and aligns them across modalities through available cross-modal correspondences. ToMA leverages both H_0-death edges and lightweight H_1-birth edges, allowing it to capture both connectivity and cycle structure without constructing 2-simplices. Experiments show that ToMA yields stable gains, with clear improvements on remote sensing and modest but consistent benefits on fashion retrieval. Additional analysis shows that ToMA is more stable than alternative topology-based objectives and that lightweight H_1-birth edges provide useful higher-order structural signals.

cs.CV↗

arXiv2026

Zipf-Mandelbrot Scaling in Korean Court Music: Universal Patterns in Music

Zipf's law, originally discovered in natural language and later generalized to the Zipf-Mandelbrot law, describes a power-law relationship between the frequency of a Zipfian element and its rank. Due to the semantic characteristics of this law, it has also been observed in musical data. However, most such studies have focused on Western music, and its applicability to non-Western music remains not well investigated. We analyzed 43 Korean court music pieces called Jeong-ak, spanning several centuries and written in the traditional Korean musical notation Jeongganbo. These pieces were transcribed into Western staff notation, and musical data such as pitch and duration were extracted. Using pitch, duration, and their paired combinations as Zipfian units, we found that Korean music also fits the Zipf-Mandelbrot law to a high degree, particularly for the paired pitch-duration unit. Korean music has evolved collectively over long periods, smoothing idiosyncratic variations and producing forms that are widely understandable among people. This collective evolution appears to have played a significant role in shaping the characteristics that lead to the satisfaction of Zipf-Mandelbrot law. Our findings provide additional evidence that Zipf-Mandelbrot scaling in musical data is universal across cultures. We further show that the joint distribution of two independent Zipfian data sets follows the Zipf-Mandelbrot law; in this sense, our result does not merely extend Zipf's law but deepens our understanding of how scaling laws behave under composition and interaction, offering a more unified perspective on rank-based statistical regularities.

stat.AP↗

arXiv2025

Topological Alignment of Shared Vision-Language Embedding Space

Contrastive Vision-Language Models (VLMs) have demonstrated strong zero-shot capabilities. However, their cross-modal alignment remains biased toward English due to limited multilingual multimodal data. Recent multilingual extensions have alleviated this gap but enforce instance-level alignment while neglecting the global geometry of the shared embedding space. We address this problem by introducing ToMCLIP (Topological Alignment for Multilingual CLIP), a topology-aware framework aligning embedding spaces with topology-preserving constraints. The proposed method applies persistent homology to define a topological alignment loss and approximates persistence diagram with theoretical error bounds using graph sparsification strategy. This work validates the proposed approach, showing enhanced structural coherence of multilingual representations, higher zero-shot accuracy on the CIFAR-100, and stronger multilingual retrieval performance on the xFlickr&CO. Beyond VLMs, the proposed approach provides a general method for incorporating topological alignment into representation learning. Code is available at https://github.com/junwon0/ToMCLIP.git.

cs.CV↗

arXiv2024

PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction

Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models have achieved high performance in LP, understanding why they perform well is challenging because most comprise complex neural networks. We employ persistent homology (PH), a topological data analysis method that helps analyze the topological information of graphs, to interpret the features used for prediction. We propose a novel method that employs PH for LP (PHLP) focusing on how the presence or absence of target links influences the overall topology. The PHLP utilizes the angle hop subgraph and new node labeling called degree double radius node labeling (Degree DRNL), distinguishing the information of graphs better than DRNL. Using only a classifier, PHLP performs similarly to state-of-the-art (SOTA) models on most benchmark datasets. Incorporating the outputs calculated using PHLP into the existing GNN-based SOTA models improves performance across all benchmark datasets. To the best of our knowledge, PHLP is the first method of applying PH to LP without GNNs. The proposed approach, employing PH while not relying on neural networks, enables the identification of crucial factors for improving performance.

cs.LG↗