Junghyo Jo

Yong-Hyun Park, Mingi Kwon, Jaewoong Choi et al.

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach involves deriving the local latent basis within $\mathcal{X}$ by leveraging the pullback metric associated with their encoding feature maps. Remarkably, our discovered local latent basis enables image editing capabilities by moving $\mathbf{x}_t$, the latent space of DMs, along the basis vector at specific timesteps. We further analyze how the geometric structure of DMs evolves over diffusion timesteps and differs across different text conditions. This confirms the known phenomenon of coarse-to-fine generation, as well as reveals novel insights such as the discrepancy between $\mathbf{x}_t$ across timesteps, the effect of dataset complexity, and the time-varying influence of text prompts. To the best of our knowledge, this paper is the first to present image editing through $\mathbf{x}$-space traversal, editing only once at specific timestep $t$ without any additional training, and providing thorough analyses of the latent structure of DMs. The code to reproduce our experiments can be found at https://github.com/enkeejunior1/Diffusion-Pullback.

Yong-Hyun Park, Sangdoo Yun, Jin-Hwa Kim et al.

Recent advancements in text-to-image (T2I) models have unlocked a wide range of applications but also present significant risks, particularly in their potential to generate unsafe content. To mitigate this issue, researchers have developed unlearning techniques to remove the model's ability to generate potentially harmful content. However, these methods are easily bypassed by adversarial attacks, making them unreliable for ensuring the safety of generated images. In this paper, we propose Direct Unlearning Optimization (DUO), a novel framework for removing Not Safe For Work (NSFW) content from T2I models while preserving their performance on unrelated topics. DUO employs a preference optimization approach using curated paired image data, ensuring that the model learns to remove unsafe visual concepts while retaining unrelated features. Furthermore, we introduce an output-preserving regularization term to maintain the model's generative capabilities on safe content. Extensive experiments demonstrate that DUO can robustly defend against various state-of-the-art red teaming methods without significant performance degradation on unrelated topics, as measured by FID and CLIP scores. Our work contributes to the development of safer and more reliable T2I models, paving the way for their responsible deployment in both closed-source and open-source scenarios.

Yong-Hyun Park, Mingi Kwon, Junghyo Jo et al.

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an unsupervised method to discover interpretable editing directions for the latent variables $\mathbf{x}_t \in \mathcal{X}$ of DMs. Our method adopts Riemannian geometry between $\mathcal{X}$ and the intermediate feature maps $\mathcal{H}$ of the U-Nets to provide a deep understanding over the geometrical structure of $\mathcal{X}$. The discovered semantic latent directions mostly yield disentangled attribute changes, and they are globally consistent across different samples. Furthermore, editing in earlier timesteps edits coarse attributes, while ones in later timesteps focus on high-frequency details. We define the curvedness of a line segment between samples to show that $\mathcal{X}$ is a curved manifold. Experiments on different baselines and datasets demonstrate the effectiveness of our method even on Stable Diffusion. Our source code will be publicly available for the future researchers.

Hoyun Choi, Junghyo Jo, Deok-Sun Lee

How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties. Canonical approaches, formulated as exponential random graph models (ERGMs), enforce constraints only in expectation, allowing individual realizations to fluctuate around the target. Conversely, microcanonical ensembles impose hard constraints exactly, but practical sampling methods beyond fixing the degree sequence have remained out of reach. Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning (RL) framework that transforms any given graph through degree-preserving rewirings to exactly reach a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. Instead of relying on the entropically dominated Metropolis--Hastings dynamics of the ERGM, DMGG employs a policy-guided search that maximally alters the joint-degree matrix. This eliminates exhaustive parameter tuning and accelerates generation by at least an order of magnitude while preserving configurational diversity. As DMGG generalizes across various graph sizes, sparsities, and topologies, it provides exact null models that allow for the quantitative isolation of secondary observables, such as the clustering coefficient. These results establish RL as a practical and powerful paradigm for generating hard-constrained graphs, opening avenues to investigate structure-function relationships free from ensemble artifacts.

Gilhan Kim, Hojun Lee, Junghyo Jo et al.

Finding the optimal model complexity that minimizes the generalization error (GE) is a key issue of machine learning. For the conventional supervised learning, this task typically involves the bias-variance tradeoff: lowering the bias by making the model more complex entails an increase in the variance. Meanwhile, little has been studied about whether the same tradeoff exists for unsupervised learning. In this study, we propose that unsupervised learning generally exhibits a two-component tradeoff of the GE, namely the model error and the data error -- using a more complex model reduces the model error at the cost of the data error, with the data error playing a more significant role for a smaller training dataset. This is corroborated by training the restricted Boltzmann machine to generate the configurations of the two-dimensional Ising model at a given temperature and the totally asymmetric simple exclusion process with given entry and exit rates. Our results also indicate that the optimal model tends to be more complex when the data to be learned are more complex.

Hyungjoon Soh, Dongyeob Kim, Juno Hwang et al.

Mirror descent is an elegant optimization technique that leverages a dual space of parametric models to perform gradient descent. While originally developed for convex optimization, it has increasingly been applied in the field of machine learning. In this study, we propose a novel approach for utilizing mirror descent to initialize the parameters of neural networks. Specifically, we demonstrate that by using the Hopfield model as a prototype for neural networks, mirror descent can effectively train the model with significantly improved performance compared to traditional gradient descent methods that rely on random parameter initialization. Our findings highlight the potential of mirror descent as a promising initialization technique for enhancing the optimization of machine learning models.

Yong-Hyun Park, Junghoon Seo, Bomseok Park et al.

Identifying the relevant input features that have a critical influence on the output results is indispensable for the development of explainable artificial intelligence (XAI). Remove-and-Retrain (ROAR) is a widely accepted approach for assessing the importance of individual pixels by measuring changes in accuracy following their removal and subsequent retraining of the modified dataset. However, we uncover notable limitations in pixel-perturbation strategies. When viewed from a geometric perspective, we discover that these metrics fail to discriminate between differences among feature attribution methods, thereby compromising the reliability of the evaluation. To address this challenge, we introduce an alternative feature-perturbation approach named Geometric Remove-and-Retrain (GOAR). Through a series of experiments with both synthetic and real datasets, we substantiate that GOAR transcends the limitations of pixel-centric metrics.

Hoyun Choi, Sungyeop Lee, B. Kahng et al.

Neural networks have proven to be efficient surrogate models for tackling partial differential equations (PDEs). However, their applicability is often confined to specific PDEs under certain constraints, in contrast to classical PDE solvers that rely on numerical differentiation. Striking a balance between efficiency and versatility, this study introduces a novel approach called Graph Neural Runge-Kutta (GNRK), which integrates graph neural network modules with a recurrent structure inspired by the classical solvers. The GNRK operates on graph structures, ensuring its resilience to changes in spatial and temporal resolutions during domain discretization. Moreover, it demonstrates the capability to address general PDEs, irrespective of initial conditions or PDE coefficients. To assess its performance, we benchmark the GNRK against existing neural network based PDE solvers using the 2-dimensional Burgers' equation, revealing the GNRK's superiority in terms of model size and accuracy. Additionally, this graph-based methodology offers a straightforward extension for solving coupled differential equations, typically necessitating more intricate models.

Juno Hwang, Yong-Hyun Park, Junghyo Jo

Diffusion models have demonstrated superior performance across various generative tasks including images, videos, and audio. However, they encounter difficulties in directly generating high-resolution samples. Previously proposed solutions to this issue involve modifying the architecture, further training, or partitioning the sampling process into multiple stages. These methods have the limitation of not being able to directly utilize pre-trained models as-is, requiring additional work. In this paper, we introduce upsample guidance, a technique that adapts pretrained diffusion model (e.g., $512^2$) to generate higher-resolution images (e.g., $1536^2$) by adding only a single term in the sampling process. Remarkably, this technique does not necessitate any additional training or relying on external models. We demonstrate that upsample guidance can be applied to various models, such as pixel-space, latent space, and video diffusion models. We also observed that the proper selection of guidance scale can improve image quality, fidelity, and prompt alignment.

Juno Hwang, Yong-Hyun Park, Junghyo Jo

Diffusion models generate high-resolution images through iterative stochastic processes. In particular, the denoising method is one of the most popular approaches that predicts the noise in samples and denoises it at each time step. It has been commonly observed that the resolution of generated samples changes over time, starting off blurry and coarse, and becoming sharper and finer. In this paper, we introduce "resolution chromatography" that indicates the signal generation rate of each resolution, which is very helpful concept to mathematically explain this coarse-to-fine behavior in generation process, to understand the role of noise schedule, and to design time-dependent modulation. Using resolution chromatography, we determine which resolution level becomes dominant at a specific time step, and experimentally verify our theory with text-to-image diffusion models. We also propose some direct applications utilizing the concept: upscaling pre-trained models to higher resolutions and time-dependent prompt composing. Our theory not only enables a better understanding of numerous pre-existing techniques for manipulating image generation, but also suggests the potential for designing better noise schedules.

Kanghun Lee, Hyungjoon Soh, Junghyo Jo

Sparse regularization plays a central role in solving inverse problems arising from incomplete or corrupted measurements. Different regularizers correspond to different prior assumptions about the structure of the unknown signal, and reconstruction performance depends on how well these priors match the intrinsic sparsity of the data. This work investigates the effect of sparsity priors in inverse problems by comparing conventional L1 regularization with the Variational Garrote (VG), a probabilistic method that approximates L0 sparsity through variational binary gating variables. A unified experimental framework is constructed across multiple reconstruction tasks including signal resampling, signal denoising, and sparse-view computed tomography. To enable consistent comparison across models with different parameterizations, regularization strength is swept across wide ranges and reconstruction behavior is analyzed through train-generalization error curves. Experiments reveal characteristic bias-variance tradeoff patterns across tasks and demonstrate that VG frequently achieves lower minimum generalization error and improved stability in strongly underdetermined regimes where accurate support recovery is critical. These results suggest that sparsity priors closer to spike-and-slab structure can provide advantages when the underlying coefficient distribution is strongly sparse. The study highlights the importance of prior-data alignment in sparse inverse problems and provides empirical insights into the behavior of variational L0-type methods across different information bottlenecks.

Hyungjoon Soh, Junghyo Jo

We formulate an attention mechanism for continuous and ordered sequences that explicitly functions as an alignment model, which serves as the core of many sequence-to-sequence tasks. Standard scaled dot-product attention relies on positional encodings and masks but does not enforce continuity or monotonicity, which are crucial for frame-synchronous targets. We propose learned nonnegative \emph{clocks} to source and target and model attention as the meeting probability of these clocks; a path-integral derivation yields a closed-form, Gaussian-like scoring rule with an intrinsic bias toward causal, smooth, near-diagonal alignments, without external positional regularizers. The framework supports two complementary regimes: normalized clocks for parallel decoding when a global length is available, and unnormalized clocks for autoregressive decoding -- both nearly-parameter-free, drop-in replacements. In a Transformer text-to-speech testbed, this construction produces more stable alignments and improved robustness to global time-scaling while matching or improving accuracy over scaled dot-product baselines. We hypothesize applicability to other continuous targets, including video and temporal signal modeling.

Hyungjoon Soh, Dongha Lee, Vipul Periwal et al.

Selecting key variables from high-dimensional data is increasingly important in the era of big data. Sparse regression serves as a powerful tool for this purpose by promoting model simplicity and explainability. In this work, we revisit a valuable yet underutilized method, the statistical physics-based Variational Garrote (VG), which introduces explicit feature selection spin variables and leverages variational inference to derive a tractable loss function. We enhance VG by incorporating modern automatic differentiation techniques, enabling scalable and efficient optimization. We evaluate VG on both fully controllable synthetic datasets and complex real-world datasets. Our results demonstrate that VG performs especially well in highly sparse regimes, offering more consistent and robust variable selection than Ridge and LASSO regression across varying levels of sparsity. We also uncover a sharp transition: as superfluous variables are admitted, generalization degrades abruptly and the uncertainty of the selection variables increases. This transition point provides a practical signal for estimating the correct number of relevant variables, an insight we successfully apply to identify key predictors in real-world data. We expect that VG offers strong potential for sparse modeling across a wide range of applications, including compressed sensing and model pruning in machine learning.

Yechan Lim, Sangwon Lee, Junghyo Jo

Identifying model parameters from observed configurations poses a fundamental challenge in data science, especially with limited data. Recently, diffusion models have emerged as a novel paradigm in generative machine learning, capable of producing new samples that closely mimic observed data. These models learn the gradient of model probabilities, bypassing the need for cumbersome calculations of partition functions across all possible configurations. We explore whether diffusion models can enhance parameter inference by augmenting small datasets. Our findings demonstrate this potential through a synthetic task involving inverse Ising inference and a real-world application of reconstructing missing values in neural activity data. This study serves as a proof-of-concept for using diffusion models for data augmentation in physics-related problems, thereby opening new avenues in data science.

Han Kim, Hyungjoon Soh, Vipul Periwal et al.

Efficient training of artificial neural networks remains a key challenge in deep learning. Backpropagation (BP), the standard learning algorithm, relies on gradient descent and typically requires numerous iterations for convergence. In this study, we introduce Expectation Reflection (ER), a novel learning approach that updates weights multiplicatively based on the ratio of observed to predicted outputs. Unlike traditional methods, ER maintains consistency without requiring ad hoc loss functions or learning rate hyperparameters. We extend ER to multilayer networks and demonstrate its effectiveness in performing image classification tasks. Notably, ER achieves optimal weight updates in a single iteration. Additionally, we reinterpret ER as a modified form of gradient descent incorporating the inverse mapping of target propagation. These findings suggest that ER provides an efficient and scalable alternative for training neural networks.

Hoyun Choi, Sungyeop Lee, B. Kahng et al.

Numerical simulation is a predominant tool for studying the dynamics in complex systems, but large-scale simulations are often intractable due to computational limitations. Here, we introduce the Neural Graph Simulator (NGS) for simulating time-invariant autonomous systems on graphs. Utilizing a graph neural network, the NGS provides a unified framework to simulate diverse dynamical systems with varying topologies and sizes without constraints on evaluation times through its non-uniform time step and autoregressive approach. The NGS offers significant advantages over numerical solvers by not requiring prior knowledge of governing equations and effectively handling noisy or missing data with a robust training scheme. It demonstrates superior computational efficiency over conventional methods, improving performance by over $10^5$ times in stiff problems. Furthermore, it is applied to real traffic data, forecasting traffic flow with state-of-the-art accuracy. The versatility of the NGS extends beyond the presented cases, offering numerous potential avenues for enhancement.

Sungyeop Lee, Junghyo Jo

The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency of internal codes or labels follows power laws in both supervised and unsupervised learning models. This scale-invariant distribution implies that machine learning largely compresses frequent typical data, and simultaneously, differentiates many atypical data as outliers. In this study, we derive the process by which these power laws can naturally arise in machine learning. In terms of information theory, the scale-invariant representation corresponds to a maximally uncertain data grouping among possible representations that guarantee a given learning accuracy.

Sungyeop Lee, Junghyo Jo

The outstanding performance of deep learning in various fields has been a fundamental query, which can be potentially examined using information theory that interprets the learning process as the transmission and compression of information. Information plane analyses of the mutual information between the input-hidden-output layers demonstrated two distinct learning phases of fitting and compression. It is debatable if the compression phase is necessary to generalize the input-output relations extracted from training data. In this study, we investigated this through experiments with various species of autoencoders and evaluated their information processing phase with an accurate kernel-based estimator of mutual information. Given sufficient training data, vanilla autoencoders demonstrated the compression phase, which was amplified after imposing sparsity regularization for hidden activities. However, we found that the compression phase is not universally observed in different species of autoencoders, including variational autoencoders, that have special constraints on network weights or manifold of hidden space. These types of autoencoders exhibited perfect generalization ability for test data without requiring the compression phase. Thus, we conclude that the compression phase is not necessary for generalization in representation learning.

Sangwon Lee, Vipul Periwal, Junghyo Jo

Inferring dynamics from time series is an important objective in data analysis. In particular, it is challenging to infer stochastic dynamics given incomplete data. We propose an expectation maximization (EM) algorithm that iterates between alternating two steps: E-step restores missing data points, while M-step infers an underlying network model of restored data. Using synthetic data generated by a kinetic Ising model, we confirm that the algorithm works for restoring missing data points as well as inferring the underlying model. At the initial iteration of the EM algorithm, the model inference shows better model-data consistency with observed data points than with missing data points. As we keep iterating, however, missing data points show better model-data consistency. We find that demanding equal consistency of observed and missing data points provides an effective stopping criterion for the iteration to prevent overshooting the most accurate model inference. Armed with this EM algorithm with this stopping criterion, we infer missing data points and an underlying network from a time-series data of real neuronal activities. Our method recovers collective properties of neuronal activities, such as time correlations and firing statistics, which have previously never been optimized to fit.

Juno Hwang, Wonseok Hwang, Junghyo Jo

The restricted Boltzmann machine (RBM) is a representative generative model based on the concept of statistical mechanics. In spite of the strong merit of interpretability, unavailability of backpropagation makes it less competitive than other generative models. Here we derive differentiable loss functions for both binary and multinary RBMs. Then we demonstrate their learnability and performance by generating colored face images.

Woo Seok Lee, Junghyo Jo, Taegeun Song

Machine learning shows remarkable success for recognizing patterns in data. Here we apply the machine learning (ML) for the diagnosis of early stage diabetes, which is known as a challenging task in medicine. Blood glucose levels are tightly regulated by two counter-regulatory hormones, insulin and glucagon, and the failure of the glucose homeostasis leads to the common metabolic disease, diabetes mellitus. It is a chronic disease that has a long latent period the complicates detection of the disease at an early stage. The vast majority of diabetics result from that diminished effectiveness of insulin action. The insulin resistance must modify the temporal profile of blood glucose. Thus we propose to use ML to detect the subtle change in the temporal pattern of glucose concentration. Time series data of blood glucose with sufficient resolution is currently unavailable, so we confirm the proposal using synthetic data of glucose profiles produced by a biophysical model that considers the glucose regulation and hormone action. Multi-layered perceptrons, convolutional neural networks, and recurrent neural networks all identified the degree of insulin resistance with high accuracy above $85\%$.

Junghyo Jo, Danh-Tai Hoang, Vipul Periwal

Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of partition functions summing over all configurations, both observed and unobserved. We present here a conceptually and computationally transparent data-driven approach to system inference that is based on the simple question: How should the Boltzmann weights of observed configurations be modified to make the probability distribution of observed configurations close to a flat distribution? This algorithm gives accurate inference by using only observed configurations for systems with a large number of degrees of freedom where other approaches are intractable.

Juyong Song, Matteo Marsili, Junghyo Jo

Deep learning has been successfully applied to various tasks, but its underlying mechanism remains unclear. Neural networks associate similar inputs in the visible layer to the same state of hidden variables in deep layers. The fraction of inputs that are associated to the same state is a natural measure of similarity and is simply related to the cost in bits required to represent these inputs. The degeneracy of states with the same information cost provides instead a natural measure of noise and is simply related the entropy of the frequency of states, that we call relevance. Representations with minimal noise, at a given level of similarity (resolution), are those that maximise the relevance. A signature of such efficient representations is that frequency distributions follow power laws. We show, in extensive numerical experiments, that deep neural networks extract a hierarchy of efficient representations from data, because they i) achieve low levels of noise (i.e. high relevance) and ii) exhibit power law distributions. We also find that the layer that is most efficient to reliably generate patterns of training data is the one for which relevance and resolution are traded at the same price, which implies that frequency distribution follows Zipf's law.

Marissa Pastor, Juyong Song, Danh-Tai Hoang et al.

Feedforward neural networks have been investigated to understand learning and memory, as well as applied to numerous practical problems in pattern classification. It is a rule of thumb that more complex tasks require larger networks. However, the design of optimal network architectures for specific tasks is still an unsolved fundamental problem. In this study, we consider three-layered neural networks for memorizing binary patterns. We developed a new complexity measure of binary patterns, and estimated the minimal network size for memorizing them as a function of their complexity. We formulated the minimal network size for regular, random, and complex patterns. In particular, the minimal size for complex patterns, which are neither ordered nor disordered, was predicted by measuring their Hamming distances from known ordered patterns. Our predictions agreed with simulations based on the back-propagation algorithm.