arXiv subjects

Jaeyong Bae

Publications and source records attributed to Jaeyong Bae.

6 recordsLinked to original sources

arXiv2026

Dataset Complexity Shapes Finite-Distance Loss Geometry in Neural Networks

Finite datasets can share the same size and low-order statistics while differing strongly in structural complexity. We connect this dataset complexity to loss-landscape geometry by pairing local label mixing across neighborhood scales with local entropy around trained neural-network solutions. Adapted from the Franz--Parisi construction in spin-glass theory, local entropy measures the effective volume of low-loss, solution-like parameter configurations at each distance from a reference. We estimate it in finite networks using adaptive sequential Monte Carlo. In a controlled synthetic sweep, greater dataset complexity produces a larger decrease in local entropy near the reference. Farther away, its radial derivative becomes weak and nearly common across conditions. Dataset complexity therefore changes where the effective solution volume contracts, rather than making it decrease uniformly faster. Experiments on real image data show the same qualitative trend, with label randomization further amplifying the effect. These results show that dataset structure shapes how low-loss neighborhoods are organized across finite distances from trained solutions.

cond-mat.dis-nn↗

arXiv2026

Opinion Formation in a Spatially Constrained Coevolving Nonlinear Voter Model

We investigate a spatially constrained coevolving nonlinear voter model. Using a random geometric graph, we constrain the interaction range of voter dynamics. If local rewiring is not possible, the discordant link is deleted. Our results reveal absorbing states that differ not only in magnetization and activity, but also in mean degree and spatial state organization. By exploring dynamical and structural observables, we found that distinct regimes from the existing coevolving nonlinear voter model are characterized by a reduced consensus region, spatially segregated fragmentation, and isolated node formation. Additionally, we develop a phenomenological description of the evolution of the mean degree and terminal non-conserved quantities that is consistent with the numerical results. Our model highlights how local geometric accessibility reshapes the structure of the absorbing states.

cond-mat.stat-mech↗

arXiv2025

Uncovering Spontaneous Physics Representations in In-Context Learning

In-context learning (ICL) lets large language models (LLMs) solve new tasks from prompts alone, across an ever-widening range of domains, yet the mechanisms underlying this ability remain poorly understood. Physical systems offer a controlled testbed for this question as they provide experimentally controllable data with structured dynamics grounded in fundamental principles. Here we study the ICL ability of LLMs, focusing on physical reasoning. Using dynamics forecasting as a proxy task, we first show that LLMs forecast physical dynamics in context, with accuracy improving as more history is provided. Analyzing the model's residual stream reveals internal activations that correlate with key physical quantities such as energy. These correlations strengthen gradually with context length, indicating that LLMs spontaneously form representations aligned with physical concepts without any physics-specific supervision. To assess whether these representations contribute to the model's predictions, we introduce a layer-wise gradient-based attribution analysis. We find that, residual directions more strongly correlated with energy also receive greater attribution to numerical predictions. This pattern is not observed for features correlated with directly observed quantities such as displacement, suggesting that the energy-related signal is not merely numerical information copied from the input. Our results broaden ICL analysis to structured physical dynamics and give a mechanistic account of how LLMs organize physical structure in context.

cs.CL↗

arXiv2024

Exploring how deep learning decodes anomalous diffusion via Grad-CAM

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at achieving explainable AI, namely the Gradient-weighted Class Activation Map (Grad-CAM), to investigate how deep learning (implemented by ResNets) recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data. Our results show that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion, which can be utilized to enhance the robustness of the trained classifier against the measurement noise. Moreover, we observe that deep learning distills unique statistical characteristics of different diffusion mechanisms at various spatiotemporal scales, with larger-scale (smaller-scale) features identified at higher (lower) layers.

cs.LG↗

arXiv2024

Gaussian Universality in Neural Network Dynamics with Generalized Structured Input Distributions

Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under the simplifying assumption of a Gaussian distribution. We extend this framework by modeling inputs as Gaussian mixtures to better represent complex, real-world data. Through empirical and theoretical investigation, we demonstrate that with proper standardization, the learning dynamics converges to the behavior seen in the simple Gaussian case. This finding exhibits a form of universality, where diverse structured distributions yield results consistent with Gaussian assumptions, thereby strengthening the theoretical understanding of deep learning models.

stat.ML↗

arXiv2023

Quantitative evaluation of methods to analyze motion changes in single-particle experiments

The analysis of live-cell single-molecule imaging experiments can reveal valuable information about the heterogeneity of transport processes and interactions between cell components. These characteristics are seen as motion changes in the particle trajectories. Despite the existence of multiple approaches to carry out this type of analysis, no objective assessment of these methods has been performed so far. Here, we report the results of a competition to characterize and rank the performance of these methods when analyzing the dynamic behavior of single molecules. To run this competition, we implemented a software library that simulates realistic data corresponding to widespread diffusion and interaction models, both in the form of trajectories and videos obtained in typical experimental conditions. The competition constitutes the first assessment of these methods, providing insights into the current limitations of the field, fostering the development of new approaches, and guiding researchers to identify optimal tools for analyzing their experiments.

cond-mat.soft↗