J. Jon Ryu

J. Jon Ryu, Abhin Shah, Gregory W. Wornell

This paper studies a family of estimators based on noise-contrastive estimation (NCE) for learning unnormalized distributions. The main contribution of this work is to provide a unified perspective on various methods for learning unnormalized distributions, which have been independently proposed and studied in separate research communities, through the lens of NCE. This unified view offers new insights into existing estimators. Specifically, for exponential families, we establish the finite-sample convergence rates of the proposed estimators under a set of regularity assumptions, most of which are new.

J. Jon Ryu, Pavan Yeddanapudi, Xiangxiang Xu et al.

The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE should not be regarded as a valid MI estimator, and we introduce a simple modification, which we refer to as InfoNCE-anchor, for accurate MI estimation. Our modification introduces an auxiliary anchor class, enabling consistent density ratio estimation and yielding a plug-in MI estimator with significantly reduced bias. Beyond this, we generalize our framework using proper scoring rules, which recover InfoNCE-anchor as a special case when the log score is employed. This formulation unifies a broad spectrum of contrastive objectives, including NCE, InfoNCE, and $f$-divergence variants, under a single principled framework. Empirically, we find that InfoNCE-anchor with the log score achieves the most accurate MI estimates; however, in self-supervised representation learning experiments, we find that the anchor does not improve the downstream task performance. These findings corroborate that contrastive representation learning benefits not from accurate MI estimation per se, but from the learning of structured density ratios.

J. Jon Ryu, Xiangxiang Xu, H. S. Melihcan Erol et al.

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called \emph{nesting} for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.

Maohao Shen, J. Jon Ryu, Soumya Ghosh et al.

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called \emph{evidential deep learning} (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their perceived strong empirical performance on downstream tasks, a line of recent studies by Bengs et al. identify limitations of the existing methods to conclude their learned epistemic uncertainties are unreliable, e.g., in that they are non-vanishing even with infinite data. Building on and sharpening such analysis, we 1) provide a sharper understanding of the asymptotic behavior of a wide class of EDL methods by unifying various objective functions; 2) reveal that the EDL methods can be better interpreted as an out-of-distribution detection algorithm based on energy-based-models; and 3) conduct extensive ablation studies to better assess their empirical effectiveness with real-world datasets. Through all these analyses, we conclude that even when EDL methods are empirically effective on downstream tasks, this occurs despite their poor uncertainty quantification capabilities. Our investigation suggests that incorporating model uncertainty can help EDL methods faithfully quantify uncertainties and further improve performance on representative downstream tasks, albeit at the cost of additional computational complexity.

Maohao Shen, Kaiwen Zha, Zexue He et al.

There is growing interest in improving LLMs without updating model parameters. One well-established direction is test-time scaling, where increased inference-time computation (e.g., longer reasoning, sampling, or search) is used to improve performance. However, for complex reasoning and agentic tasks, naively scaling test-time compute can substantially increase cost and still lead to wasted budget on suboptimal exploration. In this paper, we explore \emph{context} as a complementary scaling axis for improving LLM performance, and systematically study how to construct better inputs that guide reasoning through \emph{experience}. We show that effective context construction critically depends on \emph{decocted experience}. We present a detailed analysis of experience-augmented agents, studying how to derive context from experience, how performance scales with accumulated experience, what characterizes good context, and which data structures best support context construction. We identify \emph{decocted experience} as a key mechanism for effective context construction: extracting essence from experience, organizing it coherently, and retrieving salient information to build effective context. We validate our findings across reasoning and agentic tasks, including math reasoning, web browsing, and software engineering.

J. Jon Ryu, Jeongyeol Kwon, Benjamin Koppe et al.

We consider off-policy selection and learning in contextual bandits, where the learner aims to select or train a reward-maximizing policy using data collected by a fixed behavior policy. Our contribution is two-fold. First, we propose a novel off-policy selection method that leverages a new betting-based confidence bound applied to an inverse propensity weight sequence. Our theoretical analysis reveals that this method achieves a significantly improved, variance-adaptive guarantee over prior work. Second, we propose a novel and generic condition on the optimization objective for off-policy learning that strikes a different balance between bias and variance. One special case, which we call freezing, tends to induce low variance, which is preferred in small-data regimes. Our analysis shows that it matches the best existing guarantees. In our empirical study, our selection method outperforms existing methods, and freezing exhibits improved performance in small-sample regimes.

Minchan Jeong, J. Jon Ryu, Se-Young Yun et al.

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify dominant modes of a system in a data-driven manner. Building on this idea, deep learning methods such as VAMPnet and DPNet have been proposed to learn the leading singular subspaces of the Koopman operator. However, these methods require backpropagation through potentially numerically unstable operations on empirical second moment matrices, such as singular value decomposition and matrix inversion, during objective computation, which can introduce biased gradient estimates and hinder scalability to large systems. In this work, we propose a scalable and conceptually simple method for learning the top-$k$ singular functions of the Koopman operator for stochastic dynamical systems based on the idea of low-rank approximation. Our approach eliminates the need for unstable linear-algebraic operations and integrates easily into modern deep learning pipelines. Empirical results demonstrate that the learned singular subspaces are both reliable and effective for downstream tasks such as eigen-analysis and multi-step prediction.

Tejas Jayashankar, J. Jon Ryu, Gregory Wornell

We propose Score-of-Mixture Training (SMT), a novel framework for training one-step generative models by minimizing a class of divergences called the $α$-skew Jensen--Shannon divergence. At its core, SMT estimates the score of mixture distributions between real and fake samples across multiple noise levels. Similar to consistency models, our approach supports both training from scratch (SMT) and distillation using a pretrained diffusion model, which we call Score-of-Mixture Distillation (SMD). It is simple to implement, requires minimal hyperparameter tuning, and ensures stable training. Experiments on CIFAR-10 and ImageNet 64x64 show that SMT/SMD are competitive with and can even outperform existing methods.

J. Jon Ryu, Samuel Zhou, Gregory W. Wornell

Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable approaches to representation learning, dynamical systems, and partial differential equations (PDEs). In this paper, we revisit a classical optimization framework from the computational physics literature known as the \emph{orbital minimization method} (OMM), originally proposed in the 1990s for solving eigenvalue problems in computational chemistry. We provide a simple linear-algebraic proof of the consistency of the OMM objective, and reveal connections between this method and several ideas that have appeared independently across different domains. Our primary goal is to justify its broader applicability in modern learning pipelines. We adapt this framework to train neural networks to decompose positive semidefinite operators, and demonstrate its practical advantages across a range of benchmark tasks. Our results highlight how revisiting classical numerical methods through the lens of modern theory and computation can provide not only a principled approach for deploying neural networks in numerical simulation, but also effective and scalable tools for machine learning.

J. Jon Ryu, Young-Han Kim

This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into smaller groups, where the $k$-NNs are found for a query point with respect to each subset of data. We propose \emph{optimal} rules to aggregate the fixed-$k$-NN information for classification, regression, and density estimation that achieve minimax optimal rates for the respective problems. We show that the distributed algorithm with a fixed $k$ over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions. Roughly speaking, distributed $k$-NN rules with $M$ groups has a performance comparable to the standard $Θ(kM)$-NN rules even for fixed $k$.

J. Jon Ryu, Alankrita Bhatt, Young-Han Kim

A class of parameter-free online linear optimization algorithms is proposed that harnesses the structure of an adversarial sequence by adapting to some side information. These algorithms combine the reduction technique of Orabona and P{á}l (2016) for adapting coin betting algorithms for online linear optimization with universal compression techniques in information theory for incorporating sequential side information to coin betting. Concrete examples are studied in which the side information has a tree structure and consists of quantized values of the previous symbols of the adversarial sequence, including fixed-order and variable-order Markov cases. By modifying the context-tree weighting technique of Willems, Shtarkov, and Tjalkens (1995), the proposed algorithm is further refined to achieve the best performance over all adaptive algorithms with tree-structured side information of a given maximum order in a computationally efficient manner.

Yang Yang, Guillaume Sautière, J. Jon Ryu et al.

In this work, we propose a new recurrent autoencoder architecture, termed Feedback Recurrent AutoEncoder (FRAE), for online compression of sequential data with temporal dependency. The recurrent structure of FRAE is designed to efficiently extract the redundancy along the time dimension and allows a compact discrete representation of the data to be learned. We demonstrate its effectiveness in speech spectrogram compression. Specifically, we show that the FRAE, paired with a powerful neural vocoder, can produce high-quality speech waveforms at a low, fixed bitrate. We further show that by adding a learned prior for the latent space and using an entropy coder, we can achieve an even lower variable bitrate.

J. Jon Ryu, Yoojin Choi, Young-Han Kim et al.

A new bimodal generative model is proposed for generating conditional and joint samples, accompanied with a training method with learning a succinct bottleneck representation. The proposed model, dubbed as the variational Wyner model, is designed based on two classical problems in network information theory -- distributed simulation and channel synthesis -- in which Wyner's common information arises as the fundamental limit on the succinctness of the common representation. The model is trained by minimizing the symmetric Kullback--Leibler divergence between variational and model distributions with regularization terms for common information, reconstruction consistency, and latent space matching terms, which is carried out via an adversarial density ratio estimation technique. The utility of the proposed approach is demonstrated through experiments for joint and conditional generation with synthetic and real-world datasets, as well as a challenging zero-shot image retrieval task.

J. Jon Ryu, Shouvik Ganguly, Young-Han Kim et al.

A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a $k$-nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function $f.$ Some instantiations of the proposed estimator recover existing $k$-nearest neighbor based estimators of Shannon and Rényi entropies and Kullback--Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The $L_2$-consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities.