arXiv subjects

Jiwoo Song

Publications and source records attributed to Jiwoo Song.

8 recordsLinked to original sources

arXiv2026

Diffusion Maps Kernel Ridge Regression

In this paper, we study kernel ridge regression using the data-driven diffusion maps (DM) kernel, which is constructed through algebraic manipulations of the diffusion maps algorithm. Under the assumptions that the data lie on a manifold and are sampled uniformly, we prove that the appropriately scaled DM kernel converges uniformly to the heat kernel on the manifold for sufficiently large times as the dataset size increases and the kernel bandwidth is scaled appropriately. Consequently, the limiting Reproducing Kernel Hilbert Space (RKHS) induced by the DM kernel coincides with the RKHS associated with the heat kernel on the manifold. We further show that the RKHS induced by the DM kernel is isometrically isomorphic to the RKHS of the Gaussian kernel, which is continuously embedded in the RKHS of a Mat\'ern kernel whose norm is equivalent to an appropriate Sobolev norm. This result implies that standard risk bounds for kernel ridge regression applicable to Mat\'ern kernels also apply to the DM kernel. Finally, we provide numerical results that (1) validate the convergence of the heat kernel approximation, (2) demonstrate the greater expressiveness of the DM kernel compared to the Gaussian kernel for supervised learning over a larger class of functions on manifolds with boundary, and (3) demonstrate the advantage of the DM kernel over the Gaussian kernel in learning functions with varying frequencies and co-dimensions.

math.NA↗

arXiv2026

CORAL: Adaptive Retrieval Loop for Culturally-Aligned Multilingual RAG

Multilingual retrieval-augmented generation (mRAG) is often implemented within a fixed retrieval space, typically via query or document translation or multilingual embedding vector representations. However, this approach may be inadequate for culturally grounded queries, in which retrieval-condition misalignment may occur. Even strong retrievers and generators may struggle to produce culturally relevant answers when sourcing evidence from inappropriate linguistic or regional contexts. To this end, we introduce CORAL (COntext-aware Retrieval with Agentic Loop, an adaptive retrieval methodology for mRAG that enables iterative refinement of both the retrieval space (corpora) and the retrieval probe (query) based on the quality of the evidence. The overall process includes: (1) selecting corpora, (2) retrieving documents, (3) critiquing evidence for relevance and cultural alignment, and (4) checking sufficiency. If the retrieved documents are insufficient to answer the query correctly, the system (5) reselects corpora and rewrites the query. Across two cultural QA benchmarks, CORAL achieves up to a 3.58%p accuracy improvement on low-resource languages relative to the strongest baselines.

cs.CL↗

arXiv2025

Learning solution operator of dynamical systems with diffusion maps kernel ridge regression

In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the proposed Diffusion Maps Kernel Ridge Regression (DM-KRR) method implicitly adapts to the intrinsic geometry of the system's invariant set, without requiring explicit manifold reconstruction or attractor modeling, procedures that often limit predictive performance. Across a broad range of systems, including smooth manifolds, chaotic attractors, and high-dimensional spatiotemporal flows, DM-KRR consistently outperforms state-of-the-art random feature, neural-network and operator-learning methods in both accuracy and data efficiency. These findings underscore that long-term predictive skill depends not only on model expressiveness, but critically on respecting the geometric constraints encoded in the data through dynamically consistent model selection. Together, simplicity, geometry awareness, and strong empirical performance point to a promising path for reliable and efficient learning of complex dynamical systems.

cs.LG↗

arXiv2025

ATAS: Any-to-Any Self-Distillation for Enhanced Open-Vocabulary Dense Prediction

Vision-language models such as CLIP have recently propelled open-vocabulary dense prediction tasks by enabling recognition of a broad range of visual concepts. However, CLIP still struggles with fine-grained, region-level understanding, hindering its effectiveness on these dense prediction tasks. We identify two pivotal factors required to address this limitation: semantic coherence and fine-grained vision-language alignment. Current adaptation methods often improve fine-grained alignment at the expense of semantic coherence, and often rely on extra modules or supervised fine-tuning. To overcome these issues, we propose Any-to-Any Self-Distillation (ATAS), a novel approach that simultaneously enhances semantic coherence and fine-grained alignment by leveraging own knowledge of a model across all representation levels. Unlike prior methods, ATAS uses only unlabeled images and an internal self-distillation process to refine representations of CLIP vision encoders, preserving local semantic consistency while sharpening local detail recognition. On open-vocabulary object detection and semantic segmentation benchmarks, ATAS achieves substantial performance gains, outperforming baseline CLIP models. These results validate the effectiveness of our approach and underscore the importance of jointly maintaining semantic coherence and fine-grained alignment for advanced open-vocabulary dense prediction.

cs.CV↗

arXiv2025

Global Description of Flutter Dynamics via Koopman Theory

This paper presents a novel parametrization approach for aeroelastic systems utilizing Koopman theory, specifically leveraging the Koopman Bilinear Form (KBF) model. To address the limitations of linear parametric dependence in the KBF model, we introduce the Extended KBF (EKBF) model, which enables a global linear representation of aeroelastic dynamics while capturing stronger nonlinear dependence on, e.g., the flutter parameter. The effectiveness of the proposed methodology is demonstrated through two case studies: a 2D academic example and a panel flutter problem. Results show that EKBF effectively interpolates and extrapolates principal eigenvalues, capturing flutter mechanisms, and accurately predicting the flutter boundary even when the data is corrupted by noise. Furthermore, parameterized isostable and isochron identified by EKBF provides valuable insights into the nonlinear flutter system.

physics.flu-dyn↗

arXiv2024

Model-based Preference Optimization in Abstractive Summarization without Human Feedback

In abstractive summarization, the challenge of producing concise and accurate summaries arises from the vast amount of information contained in the source document. Consequently, although Large Language Models (LLMs) can generate fluent text, they often introduce inaccuracies by hallucinating content not found in the original source. While supervised fine-tuning methods that maximize likelihood contribute to this issue, they do not consistently enhance the faithfulness of the summaries. Preference-based optimization methods, such as Direct Preference Optimization (DPO), can further refine the model to align with human preferences. However, these methods still heavily depend on costly human feedback. In this work, we introduce a novel and straightforward approach called Model-based Preference Optimization (MPO) to fine-tune LLMs for improved summarization abilities without any human feedback. By leveraging the model's inherent summarization capabilities, we create a preference dataset that is fully generated by the model using different decoding strategies. Our experiments on standard summarization datasets and various metrics demonstrate that our proposed MPO significantly enhances the quality of generated summaries without relying on human feedback.

cs.CL↗

arXiv2024

ISLES'24: Final Infarct Prediction with Multimodal Imaging and Clinical Data. Where Do We Stand?

Accurate estimation of brain infarction (i.e., irreversibly damaged tissue) is critical for guiding treatment decisions in acute ischemic stroke. Reliable infarct prediction informs key clinical interventions, including the need for patient transfer to comprehensive stroke centers, the potential benefit of additional reperfusion attempts during mechanical thrombectomy, decisions regarding secondary neuroprotective treatments, and ultimately, prognosis of clinical outcomes. This work introduces the Ischemic Stroke Lesion Segmentation (ISLES) 2024 challenge, which focuses on the prediction of final infarct volumes from pre-interventional acute stroke imaging and clinical data. ISLES24 provides a comprehensive, multimodal setting where participants can leverage all clinically and practically available data, including full acute CT imaging, sub-acute follow-up MRI, and structured clinical information, across a train set of 150 cases. On the hidden test set of 98 cases, the top-performing model, a multimodal nnU-Net-based architecture, achieved a Dice score of 0.285 (+/- 0.213) and an absolute volume difference of 21.2 (+/- 37.2) mL, underlining the significant challenges posed by this task and the need for further advances in multimodal learning. This work makes two primary contributions: first, we establish a standardized, clinically realistic benchmark for post-treatment infarct prediction, enabling systematic evaluation of multimodal algorithmic strategies on a longitudinal stroke dataset; second, we analyze current methodological limitations and outline key research directions to guide the development of next-generation infarct prediction models.

eess.IV↗

arXiv2024

Modal Analysis of Spatiotemporal Data via Multivariate Gaussian Process Regression

Modal analysis has become an essential tool to understand the coherent structure of complex flows. The classical modal analysis methods, such as dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), rely on a sufficient amount of data that is regularly sampled in time. However, often one needs to deal with sparse temporally irregular data, e.g., due to experimental measurements and simulation algorithm. To overcome the limitations of data scarcity and irregular sampling, we propose a novel modal analysis technique using multi-variate Gaussian process regression (MVGPR). We first establish the connection between MVGPR and the existing modal analysis techniques, DMD and SPOD, from a linear system identification perspective. Next, leveraging this connection, we develop a MVGPR-based modal analysis technique that addresses the aforementioned limitations. The capability of MVGPR is endowed by its judiciously designed kernel structure for correlation function, that is derived from the assumed linear dynamics. Subsequently, the proposed MVGPR method is benchmarked against DMD and SPOD on a range of examples, from academic and synthesized data to unsteady airfoil aerodynamics. The results demonstrate MVGPR as a promising alternative to classical modal analysis methods, especially in the scenario of scarce and temporally irregular data.

stat.ME↗