Jisu Kim

Pum Jun Kim, Yoojin Jang, Jisu Kim et al.

We propose a robust and reliable evaluation metric for generative models by introducing topological and statistical treatments for rigorous support estimation. Existing metrics, such as Inception Score (IS), Frechet Inception Distance (FID), and the variants of Precision and Recall (P&R), heavily rely on supports that are estimated from sample features. However, the reliability of their estimation has not been seriously discussed (and overlooked) even though the quality of the evaluation entirely depends on it. In this paper, we propose Topological Precision and Recall (TopP&R, pronounced 'topper'), which provides a systematic approach to estimating supports, retaining only topologically and statistically important features with a certain level of confidence. This not only makes TopP&R strong for noisy features, but also provides statistical consistency. Our theoretical and experimental results show that TopP&R is robust to outliers and non-independent and identically distributed (Non-IID) perturbations, while accurately capturing the true trend of change in samples. To the best of our knowledge, this is the first evaluation metric focused on the robust estimation of the support and provides its statistical consistency under noise.

Hengrui Luo, Jisu Kim, Alice Patania et al.

Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal, we extend the framework of circular coordinates into a novel framework of mixed valued coordinates to take linear trends in the time series into consideration. One of the major challenges to learn from multiple time series effectively via a multiple output Gaussian process model is constructing a functional kernel. We propose to use topologically induced clustering to construct a cluster based kernel in a multiple output Gaussian process model. This kernel not only incorporates the topological structural information, but also allows us to put forward a unified framework using topological information in time and motion series.

Jisu Kim, Juhwan Lee

The rapid advancement of Large Language Models (LLMs) has improved text understanding and generation but poses challenges in computational resources. This study proposes a curriculum learning-inspired, data-centric training strategy that begins with simpler tasks and progresses to more complex ones, using criteria such as prompt length, attention scores, and loss values to structure the training data. Experiments with Mistral-7B (Jiang et al., 2023) and Gemma-7B (Team et al., 2024) models demonstrate that curriculum learning slightly improves performance compared to traditional random data shuffling. Notably, we observed that sorting data based on our proposed attention criteria generally led to better performance. This approach offers a sustainable method to enhance LLM performance without increasing model size or dataset volume, addressing scalability challenges in LLM training.

Keonvin Park, Jisu Kim, Jaemin Seo

This paper introduces PINT (Physics-Informed Neural Time Series Models), a framework that integrates physical constraints into neural time series models to improve their ability to capture complex dynamics. We apply PINT to the ERA5 WeatherBench dataset, focusing on long-term forecasting of 2m-temperature data. PINT incorporates the Simple Harmonic Oscillator Equation as a physics-informed prior, embedding its periodic dynamics into RNN, LSTM, and GRU architectures. This equation's analytical solutions (sine and cosine functions) facilitate rigorous evaluation of the benefits of incorporating physics-informed constraints. By benchmarking against a linear regression baseline derived from its exact solutions, we quantify the impact of embedding physical principles in data-driven models. Unlike traditional time series models that rely on future observations, PINT is designed for practical forecasting. Using only the first 90 days of observed data, it iteratively predicts the next two years, addressing challenges posed by limited real-time updates. Experiments on the WeatherBench dataset demonstrate PINT's ability to generalize, capture periodic trends, and align with physical principles. This study highlights the potential of physics-informed neural models in bridging machine learning and interpretable climate applications. Our models and datasets are publicly available on GitHub: https://github.com/KV-Park.

Eunhye Lee, Jeongmu Kim, Jisu Kim et al.

Recent image inpainting methods have shown promising results due to the power of deep learning, which can explore external information available from the large training dataset. However, many state-of-the-art inpainting networks are still limited in exploiting internal information available in the given input image at test time. To mitigate this problem, we present a novel and efficient self-supervised fine-tuning algorithm that can adapt the parameters of fully pre-trained inpainting networks without using ground-truth target images. We update the parameters of the pre-trained state-of-the-art inpainting networks by utilizing existing self-similar patches (i.e., self-exemplars) within the given input image without changing the network architecture and improve the inpainting quality by a large margin. Qualitative and quantitative experimental results demonstrate the superiority of the proposed algorithm, and we achieve state-of-the-art inpainting results on publicly available benchmark datasets.

Hengrui Luo, Alice Patania, Jisu Kim et al.

Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.

Shanxin Yuan, Radu Timofte, Ales Leonardis et al.

This paper reviews the Challenge on Image Demoireing that was part of the New Trends in Image Restoration and Enhancement (NTIRE) workshop, held in conjunction with CVPR 2020. Demoireing is a difficult task of removing moire patterns from an image to reveal an underlying clean image. The challenge was divided into two tracks. Track 1 targeted the single image demoireing problem, which seeks to remove moire patterns from a single image. Track 2 focused on the burst demoireing problem, where a set of degraded moire images of the same scene were provided as input, with the goal of producing a single demoired image as output. The methods were ranked in terms of their fidelity, measured using the peak signal-to-noise ratio (PSNR) between the ground truth clean images and the restored images produced by the participants' methods. The tracks had 142 and 99 registered participants, respectively, with a total of 14 and 6 submissions in the final testing stage. The entries span the current state-of-the-art in image and burst image demoireing problems.

Kwangho Kim, Jisu Kim, Manzil Zaheer et al.

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.

Jisu Kim, Young J. Kim

In this paper, we propose a novel penetration metric, called deformable penetration depth PDd, to define a measure of inter-penetration between two linearly deforming tetrahedra using the object norm. First of all, we show that a distance metric for a tetrahedron deforming between two configurations can be found in closed form based on object norm. Then, we show that the PDd between an intersecting pair of static and deforming tetrahedra can be found by solving a quadratic programming (QP) problem in terms of the distance metric with non-penetration constraints. We also show that the PDd between two, intersected, deforming tetrahedra can be found by solving a similar QP problem under some assumption on penetrating directions, and it can be also accelerated by an order of magnitude using pre-calculated penetration direction. We have implemented our algorithm on a standard PC platform using an off-the-shelf QP optimizer, and experimentally show that both the static/deformable and deformable/deformable tetrahedra cases can be solvable in from a few to tens of milliseconds. Finally, we demonstrate that our penetration metric is three-times smaller (or tighter) than the classical, rigid penetration depth metric in our experiments.

Milad Kiaee, Adam B Kashlak, Jisu Kim et al.

Obstructive sleep apnea is a serious condition causing a litany of health problems especially in the pediatric population. However, this chronic condition can be treated if diagnosis is possible. The gold standard for diagnosis is an overnight sleep study, which is often unobtainable by many potentially suffering from this condition. Hence, we attempt to develop a fast non-invasive diagnostic tool by training a classifier on 2D and 3D facial images of a patient to recognize facial features associated with obstructive sleep apnea. In this comparative study, we consider both persistent homology and geometric shape analysis from the field of computational topology as well as convolutional neural networks, a powerful method from deep learning whose success in image and specifically facial recognition has already been demonstrated by computer scientists.

Kwangho Kim, Jisu Kim, Alessandro Rinaldo

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the underlying dynamical system for an observed time series. The proposed methodology relies on the persistent landscapes and silhouette of the Rips complex obtained after a de-noising step based on principal components applied to a time-delayed embedding of a noisy, discrete time series sample. We analyze the stability properties of the proposed approach and show that the resulting TDA-based features are robust to sampling noise. Experiments on synthetic and real-world data demonstrate the effectiveness of our approach. We expect our method to provide new insights on feature extraction from granular, noisy time series data.

Jisu Kim, Yen-Chi Chen, Sivaraman Balakrishnan et al.

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by assessing the statistical significance of topological features of an empirical cluster tree. We first study a variety of metrics that can be used to compare different trees, analyze their properties and assess their suitability for inference. We then propose methods to construct and summarize confidence sets for the unknown true cluster tree. We introduce a partial ordering on cluster trees which we use to prune some of the statistically insignificant features of the empirical tree, yielding interpretable and parsimonious cluster trees. Finally, we illustrate the proposed methods on a variety of synthetic examples and furthermore demonstrate their utility in the analysis of a Graft-versus-Host Disease (GvHD) data set.