arXiv subjects

Jiyun Park

Publications and source records attributed to Jiyun Park.

11 recordsLinked to original sources

arXiv2026

Inverting Data Transformations via Diffusion Sampling

We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such unknown transformations arise widely in machine learning and scientific modeling, where they can significantly distort observations. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on the data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie algebra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines. Code is available at https://github.com/jw9730/tied.

cs.LG↗

arXiv2026

Size of exceptional sets in weakly mixing systems

We study exceptional sets for the Chacon transformation and, more generally, for a class of cutting-and-stacking transformations called restrictive tight maps. For these systems we explicitly construct a universal exceptional set $J\subseteq\mathbb{N}$, valid uniformly for all measurable pairs $A,B\in\mathscr{B}$, such that for every increasing function $h:\mathbb{N}\to\mathbb{R}_{>0}$ diverging to infinity, $|J\cap[0,n]|\le(\log n)^{h(n)}$ for all sufficiently large $n$. The Chacon transformation considered in this paper belongs to this class, giving a logarithmic-scale universal exceptional set for Chacon. We also prove that this logarithmic scale is essentially sharp at the level of pairwise obstructions: for every tight map with no spacers above the last subcolumn, i.e. $s_{m-1}=0$, and every $t>0$, there exist measurable sets $A,B$ such that every exceptional set $J$ for $(A,B)$ satisfies $|J\cap[0,n]|\ge(\log n)^t$ for all sufficiently large $n$. The construction is based on recursive formulas for return-time distributions arising from the cutting-and-stacking structure. As a complementary quantitative principle, we show that if the corresponding $p$-th Cesàro weak-mixing averages satisfy a rate $o(b_N)$, then $J_{A,B}$ may be chosen so that $|J_{A,B}\cap[0,N]|=o(Nb_N)$. We apply this rate-to-exceptional-set principle to several weakly mixing models, including interval exchange transformations, translation flows, and substitution dynamical systems, under the regularity assumptions of the available quantitative estimates. We also construct a separate weakly mixing one-spacer rank-one example in which exceptional-set obstructions have polynomial lower growth.

math.DS↗

arXiv2026

Asymptotics of Brownian occupation measures with unusually large intersections

We prove that the occupation measures of Brownian motions conditioned to have large intersections converge weakly, up to spatial shifts, to the measure whose density is the square of an optimizer of the Gagliardo-Nirenberg inequality. We do so by proving a large deviation principle (LDP) for Brownian occupation measures conditioned either on large self-intersections or large mutual intersections. To this end, we derive a compact LDP for unconditioned Brownian occupation measures, generalizing the work of Mukherjee and Varadhan. We also prove the LDP for Brownian occupation measures tilted by their intersections in the same topology. A key tool of independent interest is an exponentially good approximation of the intersection measure tested against all bounded measurable functions, from which we further get the LDP for the intersection measure of independent Brownian motions.

math.PR↗

arXiv2025

Capacity of the range of random walk: Moderate deviations in dimensions 4 and 5

We prove a moderate deviation principle for the capacity of the range of random walk in $\mathbb{Z}^5$. Depending on the scale of deviation, we get two different regimes. We observe Gaussian tails when the deviation scale is smaller than $n^{1/2} (\log n)^{3/4}$. Otherwise, we get non-Gaussian tails with a constant arising from a generalized Gagliardo-Nirenberg inequality. This is analogous to the behavior of the volume of the random walk range in $\mathbb{Z}^3$. Our methods can also be applied to the $d = 4$ case to prove the moderate deviation principle in almost the full range of interest. This extends the work of Okada and the first author \cite{AdhikariOkada2023}, where they showed moderate deviations up to a deviation scale of $\log \log n$ times the standard deviation.

math.PR↗

arXiv2025

MemEIC: A Step Toward Continual and Compositional Knowledge Editing

The dynamic nature of information necessitates continuously updating large vision-language models (LVLMs). While recent knowledge editing techniques hint at promising directions, they often focus on editing a single modality (vision or language) in isolation. This prevalent practice neglects the inherent multimodality of LVLMs and the continuous nature of knowledge updates, potentially leading to suboptimal editing outcomes when considering the interplay between modalities and the need for ongoing knowledge refinement. To address these limitations, we propose MemEIC, a novel method for Continual and Compositional Knowledge Editing (CCKE) in LVLMs. MemEIC enables compositional editing of both visual and textual knowledge sequentially. Our approach employs a hybrid external-internal editor featuring a dual external memory for cross-modal evidence retrieval and dual LoRA adapters that facilitate disentangled parameter updates for each modality. A key component is a brain-inspired knowledge connector, activated selectively for compositional reasoning, that integrates information across different modalities. Experiments demonstrate that MemEIC significantly improves performance on complex multimodal questions and effectively preserves prior edits, setting a new benchmark for CCKE in LVLMs.

cs.LG↗

arXiv2025

Matchmaker: An Open-source Library for Real-time Piano Score Following and Systematic Evaluation

Real-time music alignment, also known as score following, is a fundamental MIR task with a long history and is essential for many interactive applications. Despite its importance, there has not been a unified open framework for comparing models, largely due to the inherent complexity of real-time processing and the language- or system-dependent implementations. In addition, low compatibility with the existing MIR environment has made it difficult to develop benchmarks using large datasets available in recent years. While new studies based on established methods (e.g., dynamic programming, probabilistic models) have emerged, most evaluations compare models only within the same family or on small sets of test data. This paper introduces Matchmaker, an open-source Python library for real-time music alignment that is easy to use and compatible with modern MIR libraries. Using this, we systematically compare methods along two dimensions: music representations and alignment methods. We evaluated our approach on a large test set of solo piano music from the (n)ASAP, Batik, and Vienna4x22 datasets with a comprehensive set of metrics to ensure robust assessment. Our work aims to establish a benchmark framework for score-following research while providing a practical tool that developers can easily integrate into their applications.

cs.SD↗

arXiv2024

Upper tails of subgraph counts in directed random graphs

The upper tail problem in a sparse Erdős-Rényi graph asks for the probability that the number of copies of some fixed subgraph exceeds its expected value by a constant factor. We study the analogous problem for oriented subgraphs in directed random graphs. By adapting the proof of Cook, Dembo, and Pham, we reduce this upper tail problem to the asymptotic of a certain variational problem over edge weighted directed graphs. We give upper and lower bounds for the solution to the corresponding variational problem, which differ by a constant factor of at most $2$. We provide a host of subgraphs where the upper and lower bounds coincide, giving the solution to the upper tail problem. Examples of such digraphs include triangles, stars, directed $k$-cycles, and balanced digraphs.

math.PR↗

arXiv2024

A Real-Time Lyrics Alignment System Using Chroma And Phonetic Features For Classical Vocal Performance

The goal of real-time lyrics alignment is to take live singing audio as input and to pinpoint the exact position within given lyrics on the fly. The task can benefit real-world applications such as the automatic subtitling of live concerts or operas. However, designing a real-time model poses a great challenge due to the constraints of only using past input and operating within a minimal latency. Furthermore, due to the lack of datasets for real-time models for lyrics alignment, previous studies have mostly evaluated with private in-house datasets, resulting in a lack of standard evaluation methods. This paper presents a real-time lyrics alignment system for classical vocal performances with two contributions. First, we improve the lyrics alignment algorithm by finding an optimal combination of chromagram and phonetic posteriorgram (PPG) that capture melodic and phonetics features of the singing voice, respectively. Second, we recast the Schubert Winterreise Dataset (SWD) which contains multiple performance renditions of the same pieces as an evaluation set for the real-time lyrics alignment.

cs.SD↗

arXiv2023

A study of audio mixing methods for piano transcription in violin-piano ensembles

While piano music transcription models have shown high performance for solo piano recordings, their performance degrades when applied to ensemble recordings. This study aims to analyze the impact of different data augmentation methods on piano transcription performance, specifically focusing on mixing techniques applied to violin-piano ensembles. We apply mixing methods that consider both harmonic and temporal characteristics of the audio. To create datasets for this study, we generated the PFVN-synth dataset, which contains 7 hours of violin-piano ensemble audio by rendering MIDI files and corresponding labels, and also collected unaccompanied violin recordings and mixed them with the MAESTRO dataset. We evaluated the transcription results on both synthesized and real audio recordings datasets.

cs.SD↗

arXiv2023

Six dimensional almost complex torus manifolds with Euler number six

An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $χ_y$-genus of $M$.

math.AT↗

arXiv2022

Compositionally Complex Perovskite Oxides for Solar Thermochemical Water Splitting

Solar thermochemical hydrogen generation (STCH) is a promising approach for eco-friendly H2 production, but conventional STCH redox compounds often suffer from thermodynamic and kinetic limitations with limited tunability. Expanding from the nascent high-entropy ceramics field, this study explores a new class of compositionally complex perovskite oxides (La0.8Sr0.2)(Mn(1-x)/3Fe(1-x)/3CoxAl(1-x)/3)O3 for STCH. In situ X-ray diffraction demonstrates the phase stability during redox cycling and in situ X-ray photoelectron spectroscopy shows preferential redox of Co. The extent of reduction increases, but the intrinsic kinetics decreases, with increased Co content. Consequently, (La0.8Sr0.2)(Mn0.2Fe0.2Co0.4Al0.2)O3-δ achieves an optimal balance between the thermodynamics and kinetics properties. The combination of a moderate enthalpy of reduction, high entropy of reduction, and preferable surface oxygen exchange kinetics enables a maximum H2 yield of 395 +- 11 μmol g-1 in a short 1-hour redox duration. Entropy stabilization expectedly contributes to the structure stability during redox without phase transformation, which enables an exceptional STCH stability for >50 cycles under harsh interrupted conditions. The underlying redox mechanism is further elucidated by the density functional theory based parallel Monte Carlo computation, which represents a new computation paradigm first established here. This study suggests a new class of non-equimolar compositionally complex ceramics for STCH and chemical looping.

cond-mat.mtrl-sci↗