We study the problem of estimating the mean reward of the best arm in a multiarmed bandit (MAB) setting. Specifically, given a target precision εand confidence level 1 δ, the goal is to return an ε-accurate estimate of the largest mean reward with probability at least 1 δ, while minimizing the number of samples. We first establish an instance-dependent lower bound on the sample complexity, which requires handling the infinitely many possible candidates of the estimated best mean. This lower bound is expressed in a non-convex optimization problem, which becomes the main difficulty of this problem, preventing the direct application of standard techniques such as Track-and-Stop to provably achieve optimality. To overcome this difficulty, we introduce several new algorithmic and analytical techniques and propose an algorithm that achieves the asymptotic lower bound with matching constants in the leading term. Our method combines a confidence ellipsoid-based stopping condition with a two-phase sampling strategy tailored to manage non-convexity proposed algorithm is simple, nearly free of hyperparameters, and achieves the instance-dependent, asymptotically optimal sample complexity. Experimental results support our theoretical guarantees and demonstrate the practical effectiveness of our method.

Diffusion-based virtual staining methods of histopathology images have demonstrated outstanding potential for stain normalization and cross-dye staining (e.g., hematoxylin-eosin to immunohistochemistry). However, achieving pathology-correct cross-dye virtual staining with versatile tone controls poses significantchallenges due to the difficulty of decoupling the given pathology and tone con-ditions.

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various signal geometries. Despite this versatility, generalizing the attention mechanism to scenarios where data is presented at different scales from potentially different modalities is not straightforward. The attempts to incorporate hierarchy and multimodality within transformers are largely based on ad hoc heuristics, which are not seamlessly generalizable to similar problems with potentially different structures. To address this problem, in this paper, we take a fundamentally different approach: we first propose a mathematical construct to represent multi-modal, multi-scale data. We then mathematically derive the neural attention mechanics for the proposed construct from the first principle of entropy minimization. We show that the derived formulation is optimal in the sense of being the closest to the standard Softmax attention while incorporating the inductive biases originating from the hierarchical/geometric information of the problem. We further propose an efficient algorithm based on dynamic programming to compute our derived attention mechanism. By incorporating it within transformers, we show that the proposed hierarchical attention mechanism not only can be employed to train transformer models in hierarchical/multi-modal settings from scratch, but it can also be used to inject hierarchical information into classical, pre-trained transformer models post training, resulting in more efficient models in zero-shot manner.

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to the number of classes and underutilize the rich prototype information available at intermediate hierarchical levels. We introduce deep taxonomic networks, a novel deep latent variable approach designed to bridge these gaps. Our method optimizes a large latent taxonomic hierarchy, specifically a complete binary tree structured mixture-of-Gaussian prior within a variational inference framework, to automatically discover taxonomic structures and associated prototype clusters directly from unlabeled data without assuming true label sizes. We analytically show that optimizing the ELBO of our method encourages the discovery of hierarchical relationships among prototypes. Empirically, our learned models demonstrate strong hierarchical clustering performance, outperforming baselines across diverse image classification datasets using our novel evaluation mechanism that leverages prototype clusters discovered at all hierarchical levels. Qualitative results further reveal that deep taxonomic networks discover rich and interpretable hierarchical taxonomies, capturing both coarse-grained semantic categories and fine-grained visual distinctions.

Selective prediction [Dru13, QV19] models the scenario where a forecaster freely decides on the prediction window that their forecast spans. Many data statistics can be predicted to a non-trivial error rate without any distributional assumptions or expert advice, yet these results rely on that the forecaster may predict at any time. We introduce a model of Prediction with Limited Selectivity (PLS) where the forecaster can start the prediction only on a subset of the time horizon. We study the optimal prediction error both on an instance-by-instance basis and via an average-case analysis. We introduce a complexity measure that gives instancedependent bounds on the optimal error. For a randomly-generated PLS instance, these bounds match with high probability.

Recent advances in reinforcement learning (RL) have strengthened the reasoning capabilities of vision-language models (VLMs). However, enhancing policy exploration to better scale test-time compute remains largely underexplored. In addition, VLMs continue to struggle with imperfect visual perception, which in turn affects the subsequent reasoning process. We introduce NoisyRollout, a simple yet effective data augmentation method that addresses these issues by mixing training trajectories from both clean and moderately distorted images. This approach injects perceptual diversity, encouraging better policy exploration and leading to more robust reasoning. A noise annealing schedule gradually reduces distortion strength, aiding exploration early in training while ensuring later stability. Crucially, our method is easy-to-adopt--requiring no additional training cost and no modifications to the RL objective. Extensive experiments on 2distinct training datasets demonstrate that NoisyRollout achieves state-of-the-art performance among opensource RL-tuned models across 5 out-of-domain reasoning and perception benchmarks.

Visual Place Recognition (VPR) enables robust localization through image retrieval based on learned descriptors. However, drastic appearance variations of images at the same place caused by viewpoint changes can lead to inconsistent supervision signals, thereby degrading descriptor learning. Existing methods either rely on manually defined cropping rules or labeled data for view differentiation, but they suffer from two major limitations: (1) reliance on labels or handcrafted rules restricts generalization capability; (2) even within the same view direction, occlusions can introduce feature ambiguity. To address these issues, we propose MutualVPR, a mutual learning framework that integrates unsupervised view self-classification and descriptor learning. We first group images by geographic coordinates, then iteratively refine the clusters using K-means to dynamically assign place categories without orientation labels. Specifically, we adopt a DINOv2-based encoder to initialize the clustering.

In this paper, we propose Tortoise and Hare Guidance (THG), a training-free strategy that accelerates diffusion sampling while maintaining high-fidelity generation. We demonstrate that the noise estimate and the additional guidance term exhibit markedly different sensitivity to numerical error by reformulating the classifier-free guidance (CFG) ODE as a multirate system of ODEs. Our error-bound analysis shows that the additional guidance branch is more robust to approximation, revealing substantial redundancy that conventional solvers fail to exploit. Building on this insight, THG significantly reduces the computation of the additional guidance: the noise estimate is integrated with the tortoise equation on the original, fine-grained timestep grid, while the additional guidance is integrated with the hare equation only on a coarse grid. We also introduce (i) an error-boundaware timestep sampler that adaptively selects step sizes and (ii) a guidance-scale scheduler that stabilizes large extrapolation spans. THG reduces the number of function evaluations (NFE) by up to 30% with virtually no loss in generation fidelity ( ImageReward 0.032) and outperforms state-of-the-art CFG-based training-free accelerators under identical computation budgets. Our findings highlight the potential of multirate formulations for diffusion solvers, paving the way for real-time high-quality image synthesis without any model retraining. The source code is available at https://github.com/yhlee-add/THG.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics--InfoBias and InfoGain--to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Large Language Model (LLM) agents are capable of task execution across various domains by autonomously interacting with environments and refining LLM responses based on feedback. However, existing model serving systems are not optimized for the unique demands of serving agents. Compared to classic model serving, agent serving has different characteristics: predictable request pattern, increasing quality requirement, and unique prompt formatting. We identify a key problem for agent serving: LLM serving systems lack session-awareness. They neither perform effective KV cache management nor precisely select the cheapest yet competent model in each round. This leads to a cost-quality tradeoff, and we identify an opportunity to surpass it in an agent serving system. To this end, we introduce AGSERVE for AGile AGent SERVing.