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Jae Oh Woo

Publications and source records attributed to Jae Oh Woo.

18 recordsLinked to original sources
arXiv2026

Rényi stability of $B_h$ sets: a two-order phase diagram and sharp deletion principles

A set $B$ in an abelian group is a $B_h$ set if every $h$-term sum has a unique representation up to permutation; for $h=2$ these are the Sidon sets. We study a weighted removal problem for this collision-free property: if the $h$-fold sum map has small Rényi entropy loss, how much probability mass must be deleted so that the remaining support is a $B_h$ set? Two Rényi orders arise: $α$ is the order at which the coarsening loss is measured, whereas $β$ is the order of the entropy constraint. The diagonal specialization $β=α$ ties the two roles together. We determine the resulting stability problem on the positive $(α,β)$-quadrant. Stability holds exactly when $β\le1$ and $α\geβ$. Inside this region the optimal deletion rate is polynomial for $β<1$ and logarithmic on the boundary $β=1$, where the leading constant is exact; outside it, stability fails through two distinct mechanisms: a supercritical budget and dilution by light atoms. In both unstable regimes the limiting defect is computed exactly. The upper bounds follow from a coarsening inequality with best possible constant, which also yields an entropy-free removal theorem, a finite combinatorial consequence for moments of the representation function, and extensions to $B_h[g]$ sets. Matching constructions show that the phase boundaries and rates are sharp.

math.CO↗
arXiv2026

Budgeted Act-or-Defer Multi-Agent LLM Deliberation with Local Reliability Bounds

Multi-agent deliberation among LLMs can improve reasoning, but deployment requires deciding when the current answer is reliable enough to act on and when it should be escalated to human review. We formulate this as budgeted act-or-defer decision making. At each round, the system maps the debate prefix to a low-dimensional state, computes a $k$-nearest-neighbor lower confidence bound on state-conditional correctness using calibration data, and acts only when the bound exceeds a user-specified reliability threshold. The certificate controls wrong actions through the decomposition $β= δ+ α+ \varepsilon_{\mathrm{act}}$, separating calibration failure, residual action risk, and representation gap. The guarantee is conditional, not distribution-free: it relies on a valid local bias envelope and an action-region representation-gap bound, and each assumption is paired with falsification-style diagnostics. Because the same absolute wrong-action budget has different meanings across tasks of different difficulty, we set budgets relative to each task's final-round error using training data only, and evaluate safety by normalized budget usage $\mathrm{WA}/β$. On six benchmarks against nine baselines, the method uses 9--12% of the pre-declared budget on activated datasets, reaching up to 84% automation and 96% acted-on accuracy; on stress-test datasets, it defers rather than forcing unreliable automation. Rather than relying on per-task post-hoc threshold search, the method prospectively converts a user-declared wrong-action budget into an auditable act-or-defer operating point before deployment, under explicitly stated assumptions.

cs.AI↗
arXiv2026

Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty

Large language models can arrive at the same answer through reasoning paths that are unstable, contradictory, or difficult to rank consistently -- a failure mode especially prevalent in multi-step deductive reasoning. Existing methods assess reliability primarily through output dispersion -- measuring how much sampled answers differ -- but this discards a complementary signal: whether the model can consistently rank competing reasoning candidates. We propose structural uncertainty, a consistency-aware framework derived from the stability of self-preference-induced rankings over sampled reasoning solutions. Given a query, we generate multiple candidate solutions and ask the model to judge pairwise preferences among its own outputs. We aggregate self-preferences into ranking distributions via Bradley-Terry modeling with PageRank, and decompose the signal into two entropy-based components: across-trial ranking instability and within-trial candidate ambiguity. Across five LLMs and eight benchmarks, structural signals provide information complementary to answer dispersion: on logical and mathematical reasoning tasks, the combination improves identification of unreliable instances, while on factual retrieval the structural signal collapses toward uniformity, diagnosing a regime boundary where reasoning-level consistency evaluation is uninformative. The two components relate differently to accuracy: within-trial ambiguity correlates positively with correctness -- consistent with settings where multiple plausible solution paths remain competitive -- while across-trial instability correlates negatively, signaling unreliable reasoning. Structural uncertainty is best understood not as a universal confidence estimator, but as a regime-sensitive evaluator of logical reasoning consistency.

cs.AI↗
arXiv2026

Knowing When to Ask: Self-Gated Clarification for Hierarchical Language Agents

In hierarchical reasoning, failures often originate at intermediate decision points where the agent commits to a wrong branch without recognizing that it lacks critical information. Rather than treating clarification as an external uncertainty trigger, we propose ACTION-RATING, a formulation that places it inside the agent's action space on a shared ordinal scale with navigation, so that asking competes directly with acting at every decision point and help-seeking becomes observable at intermediate states. Two structurally distinct information-seeking modes emerge from the agent's own ratings: mandatory (no viable branch) and opportunistic (residual uncertainty despite a leading candidate). On Harmonized Tariff Schedule classification (30,000-node taxonomy, three benchmarks, 9~LLMs across 4 families), we observe a regime shift from mandatory to opportunistic clarification, with Information-Seeking Effectiveness (ISE), a local diagnostic defined as the fraction of help interactions followed by a correct next navigation step (not a final-task metric), rising from 50% to 74%. Three diagnostic contrasts fail to reproduce this structure. A separability test shows that the information-seeking pattern (mode split, ISE ranking) persists when answer quality is degraded (-18.8% accuracy), supporting an empirical separation between where an agent seeks help and the quality of the help it receives. Under the controlled answer channel, accuracy gains reach +16.2% at 10-digit; we read this as an upper bound on what better localization could unlock, not a deployment estimate.

cs.AI↗
arXiv2026

From Debate to Decision: Conformal Social Choice for Safe Multi-Agent Deliberation

Multi-agent debate improves LLM reasoning, yet agreement among agents is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus-based stopping commits that error to an automated action with no recourse. We introduce Conformal Social Choice, a post-hoc decision layer that converts debate outputs into calibrated act-versus-escalate decisions. Verbalized probability distributions from heterogeneous agents are aggregated via a linear opinion pool and calibrated with split conformal prediction, yielding prediction sets with a marginal coverage guarantee: the correct answer is included with probability ${\geq}\,1{-}α$, without assumptions on individual model calibration. A hierarchical action policy maps singleton sets to autonomous action and larger sets to human escalation. On eight MMLU-Pro domains with three agents (Claude Haiku, DeepSeek-R1, Qwen-3 32B), coverage stays within 1--2 points of the target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: 81.9% of wrong-consensus cases are intercepted at $α{=}0.05$. Because the layer refuses to act on cases where debate is confidently wrong, the remaining conformal singletons reach 90.0--96.8% accuracy (up to 22.1pp above consensus stopping) -- a selection effect, not a reasoning improvement. This safety comes at the cost of automation, but the operating point is user-adjustable via $α$.

cs.AI↗
arXiv2025

Improving Instruction Following in Language Models through Proxy-Based Uncertainty Estimation

Assessing response quality to instructions in language models is vital but challenging due to the complexity of human language across different contexts. This complexity often results in ambiguous or inconsistent interpretations, making accurate assessment difficult. To address this issue, we propose a novel Uncertainty-aware Reward Model (URM) that introduces a robust uncertainty estimation for the quality of paired responses based on Bayesian approximation. Trained with preference datasets, our uncertainty-enabled proxy not only scores rewards for responses but also evaluates their inherent uncertainty. Empirical results demonstrate significant benefits of incorporating the proposed proxy into language model training. Our method boosts the instruction following capability of language models by refining data curation for training and improving policy optimization objectives, thereby surpassing existing methods by a large margin on benchmarks such as Vicuna and MT-bench. These findings highlight that our proposed approach substantially advances language model training and paves a new way of harnessing uncertainty within language models.

cs.CL↗
arXiv2024

Bayesian Active Learning for Semantic Segmentation

Fully supervised training of semantic segmentation models is costly and challenging because each pixel within an image needs to be labeled. Therefore, the sparse pixel-level annotation methods have been introduced to train models with a subset of pixels within each image. We introduce a Bayesian active learning framework based on sparse pixel-level annotation that utilizes a pixel-level Bayesian uncertainty measure based on Balanced Entropy (BalEnt) [84]. BalEnt captures the information between the models' predicted marginalized probability distribution and the pixel labels. BalEnt has linear scalability with a closed analytical form and can be calculated independently per pixel without relational computations with other pixels. We train our proposed active learning framework for Cityscapes, Camvid, ADE20K and VOC2012 benchmark datasets and show that it reaches supervised levels of mIoU using only a fraction of labeled pixels while outperforming the previous state-of-the-art active learning models with a large margin.

cs.CV↗
arXiv2023

Unsupervised Accuracy Estimation of Deep Visual Models using Domain-Adaptive Adversarial Perturbation without Source Samples

Deploying deep visual models can lead to performance drops due to the discrepancies between source and target distributions. Several approaches leverage labeled source data to estimate target domain accuracy, but accessing labeled source data is often prohibitively difficult due to data confidentiality or resource limitations on serving devices. Our work proposes a new framework to estimate model accuracy on unlabeled target data without access to source data. We investigate the feasibility of using pseudo-labels for accuracy estimation and evolve this idea into adopting recent advances in source-free domain adaptation algorithms. Our approach measures the disagreement rate between the source hypothesis and the target pseudo-labeling function, adapted from the source hypothesis. We mitigate the impact of erroneous pseudo-labels that may arise due to a high ideal joint hypothesis risk by employing adaptive adversarial perturbation on the input of the target model. Our proposed source-free framework effectively addresses the challenging distribution shift scenarios and outperforms existing methods requiring source data and labels for training.

cs.CV↗
arXiv2023

Active Learning in Bayesian Neural Networks with Balanced Entropy Learning Principle

Acquiring labeled data is challenging in many machine learning applications with limited budgets. Active learning gives a procedure to select the most informative data points and improve data efficiency by reducing the cost of labeling. The info-max learning principle maximizing mutual information such as BALD has been successful and widely adapted in various active learning applications. However, this pool-based specific objective inherently introduces a redundant selection and further requires a high computational cost for batch selection. In this paper, we design and propose a new uncertainty measure, Balanced Entropy Acquisition (BalEntAcq), which captures the information balance between the uncertainty of underlying softmax probability and the label variable. To do this, we approximate each marginal distribution by Beta distribution. Beta approximation enables us to formulate BalEntAcq as a ratio between an augmented entropy and the marginalized joint entropy. The closed-form expression of BalEntAcq facilitates parallelization by estimating two parameters in each marginal Beta distribution. BalEntAcq is a purely standalone measure without requiring any relational computations with other data points. Nevertheless, BalEntAcq captures a well-diversified selection near the decision boundary with a margin, unlike other existing uncertainty measures such as BALD, Entropy, or Mean Standard Deviation (MeanSD). Finally, we demonstrate that our balanced entropy learning principle with BalEntAcq consistently outperforms well-known linearly scalable active learning methods, including a recently proposed PowerBALD, a simple but diversified version of BALD, by showing experimental results obtained from MNIST, CIFAR-100, SVHN, and TinyImageNet datasets.

cs.LG↗
arXiv2022

Self-Supervised Contrastive Representation Learning for 3D Mesh Segmentation

3D deep learning is a growing field of interest due to the vast amount of information stored in 3D formats. Triangular meshes are an efficient representation for irregular, non-uniform 3D objects. However, meshes are often challenging to annotate due to their high geometrical complexity. Specifically, creating segmentation masks for meshes is tedious and time-consuming. Therefore, it is desirable to train segmentation networks with limited-labeled data. Self-supervised learning (SSL), a form of unsupervised representation learning, is a growing alternative to fully-supervised learning which can decrease the burden of supervision for training. We propose SSL-MeshCNN, a self-supervised contrastive learning method for pre-training CNNs for mesh segmentation. We take inspiration from traditional contrastive learning frameworks to design a novel contrastive learning algorithm specifically for meshes. Our preliminary experiments show promising results in reducing the heavy labeled data requirement needed for mesh segmentation by at least 33%.

cs.CV↗
arXiv2022

Highly Efficient Representation and Active Learning Framework and Its Application to Imbalanced Medical Image Classification

We propose a highly data-efficient active learning framework for image classification. Our novel framework combines: (1) unsupervised representation learning of a Convolutional Neural Network and (2) the Gaussian Process (GP) method, in sequence to achieve highly data and label efficient classifications. Moreover, both elements are less sensitive to the prevalent and challenging class imbalance issue, thanks to the (1) feature learned without labels and (2) the Bayesian nature of GP. The GP-provided uncertainty estimates enable active learning by ranking samples based on the uncertainty and selectively labeling samples showing higher uncertainty. We apply this novel combination to the severely imbalanced case of COVID-19 chest X-ray classification and the Nerthus colonoscopy classification. We demonstrate that only . 10% of the labeled data is needed to reach the accuracy from training all available labels. We also applied our model architecture and proposed framework to a broader class of datasets with expected success.

cs.CV↗
arXiv2022

Analytic Mutual Information in Bayesian Neural Networks

Bayesian neural networks have successfully designed and optimized a robust neural network model in many application problems, including uncertainty quantification. However, with its recent success, information-theoretic understanding about the Bayesian neural network is still at an early stage. Mutual information is an example of an uncertainty measure in a Bayesian neural network to quantify epistemic uncertainty. Still, no analytic formula is known to describe it, one of the fundamental information measures to understand the Bayesian deep learning framework. In this paper, we derive the analytical formula of the mutual information between model parameters and the predictive output by leveraging the notion of the point process entropy. Then, as an application, we discuss the parameter estimation of the Dirichlet distribution and show its practical application in the active learning uncertainty measures by demonstrating that our analytical formula can improve the performance of active learning further in practice.

cs.IT↗
arXiv2021

PatchNet: Unsupervised Object Discovery based on Patch Embedding

We demonstrate that frequently appearing objects can be discovered by training randomly sampled patches from a small number of images (100 to 200) by self-supervision. Key to this approach is the pattern space, a latent space of patterns that represents all possible sub-images of the given image data. The distance structure in the pattern space captures the co-occurrence of patterns due to the frequent objects. The pattern space embedding is learned by minimizing the contrastive loss between randomly generated adjacent patches. To prevent the embedding from learning the background, we modulate the contrastive loss by color-based object saliency and background dissimilarity. The learned distance structure serves as object memory, and the frequent objects are simply discovered by clustering the pattern vectors from the random patches sampled for inference. Our image representation based on image patches naturally handles the position and scale invariance property that is crucial to multi-object discovery. The method has been proven surprisingly effective, and successfully applied to finding multiple human faces and bodies from natural images.

cs.CV↗
arXiv2020

On the Steady State of Continuous Time Stochastic Opinion Dynamics with Power Law Confidence

This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power of opinion distances. We establish a non-local partial differential equation for the distribution of opinion distances and use Mellin transforms to provide an explicit formula for the stationary solution of the latter, when it exists. Our approach leads to new qualitative and quantitative results on this type of dynamics. To the best of our knowledge these Mellin transform results are the first quantitative results on the equilibria of opinion dynamics with distance-dependent interaction rates. The closed form expressions for this class of dynamics are obtained for the two agent case. However the results can be used in mean-field models featuring several agents whose interaction rates depend on the empirical average of their opinions. The technique also applies to linear dynamics, namely with a constant interaction rate, on an interaction graph.

math.PR↗
arXiv2020

Entropy Inequalities for Sums in Prime Cyclic Groups

Lower bounds for the Rényi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in prime cyclic groups building on Lev (2001), and notions of stochastic ordering. Several applications are developed, including to discrete entropy power inequalities, the Littlewood-Offord problem, and counting solutions of certain linear systems.

math.CO↗
arXiv2017

An Analytical Framework for Modeling a Spatially Repulsive Cellular Network

We propose a new cellular network model that captures both deterministic and random aspects of base station deployments. Namely, the base station locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity $λ_g$ and a Poisson point process (PPP) with intensity $λ_p$. Grid and PPP deployments are special cases with $λ_p \to 0$ and $λ_g \to 0$, with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the base station that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP base station. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio $ρ_λ= λ_p/λ_g$. Second, the user association is biased towards the base stations located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.

cs.IT↗
arXiv2014

Redundancy of Exchangeable Estimators

Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson-Dirichlet priors (or "Chinese restaurant processes") and the Pitman-Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators.

cs.IT↗