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Deep Learning · Generative Models and Autoencoders

Roi Benita, Miki Elad, Joseph Keshet

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models practically usable. However, certain synthesis process decisions still rely on heuristics without a solid theoretical foundation. In our work, we offer a novel analysis of the DM's inference process, introducing a comprehensive frequency response perspective. Specifically, by relying on Gaussianity assumption, we present the inference process as a closed-form spectral transfer function, capturing how the generated signal evolves in response to the initial noise. We demonstrate how the proposed analysis can be leveraged to design a noise schedule that aligns effectively with the characteristics of the data. The spectral perspective also provides insights into the underlying dynamics and sheds light on the relationship between spectral properties and noise schedule structure. Our results lead to scheduling curves that are dependent on the spectral content of the data, offering a theoretical justification for some of the heuristics taken by practitioners.

Social Aspects · Accountability, Transparency and Interpretability

Thummaluru Siddartha Reddy, Vempalli Naga Sai Saketh, Mahesh Chandran

Graph Neural Networks \texttt{(GNNs)} excel at jointly modeling node features and topology, yet their \emph{black-box} nature limits their adoption in real-world applications where interpretability is desired. Inspired by the success of interpretable Neural Additive Models \texttt{(NAM)} for tabular data, Graph Neural Additive Network \texttt{(GNAN)} extends the additive modeling approach to graph data to overcome limitations of GNNs. While being interpretable, \texttt{GNAN} representation learning overlooks the importance of local aggregation and more importantly suffers from parameter complexity. To mitigate the above challenges, we introduce Graph Neural Additive Model with Random Fourier Features (\texttt{G-NAMRFF}), a lightweight, self‐interpretable graph additive architecture. \texttt{G-NAMRFF} represents each node embedding as the sum of feature‐wise contributions where contributions are modeled via a \emph{Gaussian process} \texttt{(GP)} with a graph- and feature-aware kernel. Specifically, we construct a kernel using Radial Basis Function (\texttt{RBF}) with graph structure induced by Laplacian and learnable Finite Impulse Response (\texttt{FIR}) filter. We approximate the kernel using Random Fourier Features (\texttt{RFFs}) which transforms the \texttt{GP} prior to a Bayesian formulation, which are subsequently learnt using a single layer neural network with size equal to number of \texttt{RFF} features. \texttt{G-NAMRFF} is light weight with $168\times$ fewer parameters compared to \texttt{GNAN}. Despite its compact size, \texttt{G-NAMRFF} matches or outperforms state-of-the-art \texttt{GNNs} and \texttt{GNAN} on node and graph classification tasks, delivering real-time interpretability without sacrificing accuracy.

Computer Vision · 3D Rendering & Reconstruction

Yuqi Wu, Wenzhao Zheng, Jie Zhou, Jiwen Lu

Dense 3D scene reconstruction from an ordered sequence or unordered image collections is a critical step when bringing research in computer vision into practical scenarios. Following the paradigm introduced by DUSt3R, which unifies an image pair densely into a shared coordinate system, subsequent methods maintain an implicit memory to achieve dense 3D reconstruction from more images. However, such implicit memory is limited in capacity and may suffer from information loss of earlier frames. We propose Point3R, an online framework targeting dense streaming 3D reconstruction. To be specific, we maintain an explicit spatial pointer memory directly associated with the 3D structure of the current scene. Each pointer in this memory is assigned a specific 3D position and aggregates scene information nearby in the global coordinate system into a changing spatial feature. Information extracted from the latest frame interacts explicitly with this pointer memory, enabling dense integration of the current observation into the global coordinate system. We design a 3D hierarchical position embedding to promote this interaction and design a simple yet effective fusion mechanism to ensure that our pointer memory is uniform and efficient. Our method achieves competitive or state-of-the-art performance on various tasks with low training costs. Code: https://github.com/YkiWu/Point3R.

Applications · Health

Christopher Chiu, Silviu Pitis, Mihaela van der Schaar

Clinical reasoning in medicine is a hypothesis-driven process where physicians refine diagnoses from limited information through targeted history, physical examination, and diagnostic investigations. In contrast, current medical benchmarks for large language models (LLMs) primarily assess knowledge recall through single-turn questions, where complete clinical information is provided upfront. To address this gap, we introduce VivaBench, a multi-turn benchmark that evaluates sequential clinical reasoning in LLM agents. Our dataset consists of 1762 physician-curated clinical vignettes structured as interactive scenarios that simulate a $ \textit{viva voce}$ (oral) examination in medical training, requiring agents to actively probe for relevant findings, select appropriate investigations, and synthesize information across multiple steps to reach a diagnosis. While current LLMs demonstrate competence in diagnosing conditions from well-described clinical presentations, their performance degrades significantly when required to navigate iterative diagnostic reasoning under uncertainty in our evaluation. Our analysis identified several failure modes that mirror common cognitive errors in clinical practice, including: (1) fixation on initial hypotheses, (2) inappropriate investigation ordering, (3) premature diagnostic closure, and (4) failing to screen for critical conditions. These patterns reveal fundamental limitations in how current LLMs reason and make decisions under uncertainty. Through VivaBench, we provide a standardized benchmark for evaluating conversational medical AI systems for real-world clinical decision support. Beyond medical applications, we contribute to the larger corpus of research on agentic AI by demonstrating how sequential reasoning trajectories can diverge in complex decision-making environments.

Deep Learning · Everything Else

Xueqi Ma, Jun Wang, Yanbei Jiang, Sarah Erfani, Tongliang Liu, James Bailey

Large language models (LLMs) have achieved state-of-the-art performance in a variety of tasks, but remain largely opaque in terms of their internal mechanisms. Understanding these mechanisms is crucial to improve their reasoning abilities. Drawing inspiration from the interplay between neural processes and human cognition, we propose a novel interpretability framework to systematically analyze the roles and behaviors of attention heads, which are key components of LLMs. We introduce CogQA, a dataset that decomposes complex questions into step-by-step subquestions with a chain-of-thought design, each associated with specific cognitive functions such as retrieval or logical reasoning. By applying a multi-label probing method, we identify the attention heads responsible for these functions. Our analysis across multiple LLM families reveals that attention heads exhibit functional specialization, characterized as cognitive heads. These cognitive heads exhibit several key properties: they are universally sparse, and vary in number and distribution across different cognitive functions, and they display interactive and hierarchical structures. We further show that cognitive heads play a vital role in reasoning tasks—removing them leads to performance degradation, while augmenting them enhances reasoning accuracy. These insights offer a deeper understanding of LLM reasoning and suggest important implications for model design, training and fine-tuning strategies.

Computer Vision · Vision Models & Multimodal

Ansel Blume, Jeonghwan Kim, Hyeonjeong Ha, Elen Chatikyan, Xiaomeng Jin, Khanh Nguyen, Nanyun Peng, Kai-Wei Chang, Derek Hoiem, Heng Ji

Real-world objects are composed of distinctive, object-specific parts. Identifying these parts is key to performing fine-grained, compositional reasoning—yet, large multimodal models (LMMs) struggle to perform this seemingly straightforward task. In this work, we introduce PARTONOMY, an LMM benchmark designed for pixel-level part grounding. We construct PARTONOMY from existing part datasets and our own rigorously annotated set of images, encompassing 862 parts and 5346 objects for evaluation. Unlike existing datasets that simply ask models to identify generic parts, PARTONOMY utilizes highly technical concepts and challenges models to compare objects’ parts, consider part-whole relationships, and justify textual predictions with visual segmentations. Our experiments demonstrate significant limitations in state-of-the-art LMMs (e.g., LISA-13B achieves only 5.9% gIoU), highlighting a critical gap in their part grounding abilities. We note that existing segmentation-enabled LMMs (segmenting LMMs) have two key architectural shortcomings: they use special [SEG] tokens not seen during pretraining which induce distribution shift, and they discard predicted segmentations instead of using past predictions to guide future ones. To address these deficiencies, we train several part-centric LMMs and propose PLUM, a novel segmenting LMM that utilizes span tagging instead of segmentation tokens and that conditions on prior predictions in a feedback loop. We find that pretrained PLUM dominates existing segmenting LMMs on reasoning segmentation, VQA, and visual hallucination benchmarks. In addition, PLUM finetuned on our proposed Explanatory Part Segmentation task is competitive with segmenting LMMs trained on significantly more segmentation data. Our work opens up new avenues towards enabling fine-grained, grounded visual understanding in LMMs.

Theory · Learning Theory

Vicky Kouni

Unfolding networks are interpretable networks emerging from iterative algorithms, incorporate prior knowledge of data structure, and are designed to solve inverse problems like compressed sensing, which deals with recovering data from noisy, missing observations. Compressed sensing finds applications in critical domains, from medical imaging to cryptography, where adversarial robustness is crucial to prevent catastrophic failures. However, a solid theoretical understanding of the performance of unfolding networks in the presence of adversarial attacks is still in its infancy. In this paper, we study the adversarial generalization of unfolding networks when perturbed with $l_2$-norm constrained attacks, generated by the fast gradient sign method. Particularly, we choose a family of state-of-the-art overaparameterized unfolding networks and deploy a new framework to estimate their adversarial Rademacher complexity. Given this estimate, we provide adversarial generalization error bounds for the networks under study, which are tight with respect to the attack level. To our knowledge, this is the first theoretical analysis on the adversarial generalization of unfolding networks. We further present a series of experiments on real-world data, with results corroborating our derived theory, consistently for all data. Finally, we observe that the family's overparameterization can be exploited to promote adversarial robustness, shedding light on how to efficiently robustify neural networks.

Deep Learning · Generative Models and Autoencoders

Keuntae Kim, Eunhye Jeong, Sehyeon Lee, Seohee Yoon, Yong Suk Choi

Recent advances in enhancing the reasoning ability of Large Language Models (LLMs) have been remarkably successful. LLMs trained with Reinforcement Learning (RL) for reasoning demonstrate strong performance in challenging tasks such as mathematics and coding, even with relatively small model sizes. However, despite these impressive improvements in task accuracy, the assessment of creativity in LLM generations has been largely overlooked in reasoning tasks, in contrast to writing tasks. The lack of research on creativity assessment in reasoning primarily stems from two challenges: (1) the difficulty of defining the range of creativity, and (2) the necessity of human evaluation in the assessment process. To address these challenges, we propose CLAWS, a novel method that defines and classifies mathematical solutions into Typical, Creative, and Hallucinated categories without human evaluation, by leveraging attention weights across prompt sections and output. CLAWS outperforms five existing white-box detection methods—Perplexity, Logit Entropy, Window Entropy, Hidden Score, and Attention Score—on five 7–8B math RL models (DeepSeek, Qwen, Mathstral, OpenMath2, and Oreal). We validate CLAWS on 4,545 math problems collected from 181 math contests (A(J)HSME, AMC, AIME). Our code is available at https://github.com/kkt94/CLAWS.

Applications

Zijie Lin, Yang Zhang, Xiaoyan Zhao, Fengbin ZHU, Fuli Feng, Tat-Seng Chua

Large Language Models (LLMs) have shown strong potential for recommendation by framing item prediction as a token-by-token language generation task. However, existing methods treat all item tokens equally, simply pursuing likelihood maximization during both optimization and decoding. This overlooks crucial token-level differences in decisiveness—many tokens contribute little to item discrimination yet can dominate optimization or decoding. To quantify token decisiveness, we propose a novel perspective that models item generation as a decision process, measuring token decisiveness by the Information Gain (IG) each token provides in reducing uncertainty about the generated item. Our empirical analysis reveals that most tokens have low IG but often correspond to high logits, disproportionately influencing training loss and decoding, which may impair model performance. Building on these insights, we introduce an Information Gain-based Decisiveness-aware Token handling (IGD) strategy that integrates token decisiveness into both tuning and decoding. Specifically, IGD downweights low-IG tokens during tuning and rebalances decoding to emphasize tokens with high IG. In this way, IGD moves beyond pure likelihood maximization, effectively prioritizing high-decisiveness tokens. Extensive experiments on four benchmark datasets with two LLM backbones demonstrate that IGD consistently improves recommendation accuracy, achieving significant gains on widely used ranking metrics compared to strong baselines. Our codes are available at \url{https://github.com/ZJLin2oo1/IGD}.

Social Aspects · Fairness, Equity, Justice and Safety

Jiaxin Song, Yixu Wang, Jie Li, Xuan Tong, rui yu, Yan Teng, Xingjun Ma, Yingchun Wang

Vision-Language Models (VLMs) exhibit impressive performance, yet the integration of powerful vision encoders has significantly broadened their attack surface, rendering them increasingly susceptible to jailbreak attacks. However, lacking well-defined attack objectives, existing jailbreak methods often struggle with gradient-based strategies prone to local optima and lacking precise directional guidance, and typically decouple visual and textual modalities, thereby limiting their effectiveness by neglecting crucial cross-modal interactions. Inspired by the Eliciting Latent Knowledge (ELK) framework, we posit that VLMs encode safety-relevant information within their internal fusion-layer representations, revealing an implicit safety decision boundary in the latent space. This motivates exploiting boundary to steer model behavior. Accordingly, we propose \textbf{JailBound}, a novel latent space jailbreak framework comprising two stages: (1) \textbf{Safety Boundary Probing}, which addresses the guidance issue by approximating decision boundary within fusion layer's latent space, thereby identifying optimal perturbation directions towards the target region; and (2) \textbf{Safety Boundary Crossing}, which overcomes the limitations of decoupled approaches by jointly optimizing adversarial perturbations across both image and text inputs. This latter stage employs an innovative mechanism to steer the model's internal state towards policy-violating outputs while maintaining cross-modal semantic consistency. Extensive experiments on six diverse VLMs demonstrate JailBound's efficacy, achieves 94.32\% white-box and 67.28\% black-box attack success averagely, which are 6.17\% and 21.13\% higher than SOTA methods, respectively. Our findings expose a overlooked safety risk in VLMs and highlight the urgent need for more robust defenses. \textcolor{red}{Warning: This paper contains potentially sensitive, harmful and offensive content.}

Computer Vision · Image and Video Generation

Kaibo Wang, Jianda Mao, Tong Wu, Yang Xiang

Classifier-Free Guidance (CFG) is an essential component of text-to-image diffusion models, and understanding and advancing its operational mechanisms remains a central focus of research. Existing approaches stem from divergent theoretical interpretations, thereby limiting the design space and obscuring key design choices. To address this, we propose a unified perspective that reframes conditional guidance as fixed point iterations, seeking to identify a golden path where latents produce consistent outputs under both conditional and unconditional generation. We demonstrate that CFG and its variants constitute a special case of single-step short-interval iteration, which is theoretically proven to exhibit inefficiency. To this end, we introduce Foresight Guidance (FSG), which prioritizes solving longer-interval subproblems in early diffusion stages with increased iterations. Extensive experiments across diverse datasets and model architectures validate the superiority of FSG over state-of-the-art methods in both image quality and computational efficiency. Our work offers novel perspectives for conditional guidance and unlocks the potential of adaptive design.

Deep Learning · Algorithms

Jörg Franke, Urs Spiegelhalter, Marianna Nezhurina, Jenia Jitsev, Frank Hutter, Michael Hefenbrock

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization and normalization techniques that usually require tuning additional hyperparameters. An alternative is to force all parameters and representations to lie on a hypersphere. This removes the need for regularization and increases convergence speed, but comes with additional costs. In this work, we propose a more holistic, approximate normalization via simple scalar multiplications motivated by the tight concentration of the norms of high-dimensional random vectors. Additionally, instead of applying strict normalization for the parameters, we constrain their norms. These modifications remove the need for weight decay and learning rate warm-up as well, but do not increase the total number of normalization layers. Our experiments with transformer architectures show up to 40% faster convergence compared to GPT models with QK normalization, with only 3% additional runtime cost. When deriving scaling laws, we found that our method enables training with larger batch sizes while preserving the favorable scaling characteristics of classic GPT architectures.

Deep Learning · Algorithms

Ahmed Rashwan, Keith Briggs, Chris Budd, Lisa Kreusser

Many machine learning applications require outputs that satisfy complex, dynamic constraints. This task is particularly challenging in Graph Neural Network models due to the variable output sizes of graph-structured data. In this paper, we introduce ProjNet, a Graph Neural Network framework which satisfies input-dependant constraints. ProjNet combines a sparse vector clipping method with the Component-Averaged Dykstra (CAD) algorithm, an iterative scheme for solving the best-approximation problem. We establish a convergence result for CAD and develop a GPU-accelerated implementation capable of handling large-scale inputs efficiently. To enable end-to-end training, we introduce a surrogate gradient for CAD that is both computationally efficient and better suited for optimization than the exact gradient. We validate ProjNet on four classes of constrained optimisation problems: linear programming, two classes of non-convex quadratic programs, and radio transmit power optimization, demonstrating its effectiveness across diverse problem settings.

Optimization · Optimization and Learning under Uncertainty

Lingxiao Huang, Zhize Li, Nisheeth K. Vishnoi, Runkai Yang, Haoyu Zhao

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging, as the true underlying dataset is unobserved. To address this, we investigate coreset construction using surrogate error metrics that are tractable and provably related to the true clustering cost. We analyze a traditional metric from prior work and introduce a new error metric that more closely aligns with the true cost. Although our metric is defined independent of the noise distribution, it enables approximation guarantees that scale with the noise level. We design a coreset construction algorithm based on this metric and show that, under mild assumptions on the data and noise, enforcing an $\varepsilon$-bound under our metric yields smaller coresets and tighter guarantees on the true clustering cost than those obtained via classical metrics. In particular, we prove that the coreset size can improve by a factor of up to $\mathrm{poly}(k)$, where $n$ is the dataset size. Experiments on real-world datasets support our theoretical findings and demonstrate the practical advantages of our approach.

Applications · Language, Speech and Dialog

Jiawei Zhou, Lei Chen

As retrieval-augmented generation (RAG) becomes increasingly widespread, the role of information retrieval (IR) is shifting from retrieving information for human users to retrieving contextual knowledge for artificial intelligence (AI) systems, where relevance becomes difficult to define or annotate beforehand. To address this challenge, we propose R3, a Retrieval framework optimized for RAG through trial-and-feedback Reinforced contrastive learning. Unlike prior approaches that rely on annotated or synthetic data for supervised fine-tuning, R3 enables the retriever to dynamically explore and optimize relevance within the RAG environment. During training, the retrieved results interact with the environment to produce contrastive signals that automatically guide the retriever’s self-improvement. Extensive experiments across diverse tasks demonstrate that R3 improves RAG performance by 5.2% over the original retriever and surpasses state-of-the-art retrievers by 4.9%, while achieving comparable results to LLM-augmented retrieval and RAG systems built on post-trained or instruction-tuned LLMs. It is both efficient and practical, requiring only 4 GPUs and completing training within a single day.

Computer Vision · Classification and Understanding

Hongyang He, Xinyuan Song, Yangfan He, Zeyu Zhang, Yanshu Li, Haochen You, Lifan Sun, Wenqiao Zhang

We introduce TRiCo, a novel triadic game-theoretic co-training framework that rethinks the structure of semi-supervised learning by incorporating a teacher, two students, and an adversarial generator into a unified training paradigm. Unlike existing co-training or teacher-student approaches, TRiCo formulates SSL as a structured interaction among three roles: (i) two student classifiers trained on frozen, complementary representations, (ii) a meta-learned teacher that adaptively regulates pseudo-label selection and loss balancing via validation-based feedback, and (iii) a non-parametric generator that perturbs embeddings to uncover decision boundary weaknesses. Pseudo-labels are selected based on mutual information rather than confidence, providing a more robust measure of epistemic uncertainty. This triadic interaction is formalized as a Stackelberg game, where the teacher leads strategy optimization and students follow under adversarial perturbations. By addressing key limitations in existing SSL frameworks—such as static view interactions, unreliable pseudo-labels, and lack of hard sample modeling—TRiCo provides a principled and generalizable solution. Extensive experiments on CIFAR-10, SVHN, STL-10, and ImageNet demonstrate that TRiCo consistently achieves state-of-the-art performance in low-label regimes, while remaining architecture-agnostic and compatible with frozen vision backbones.

Deep Learning · Everything Else

Chenrui Cao, Liangcheng Song, Zenan Li, Xinyi Le, Xian Zhang, HUI XUE, Fan Yang

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7%, 32.8%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo_2019_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Computer Vision · 3D Rendering & Reconstruction

Chuandong Liu, Huijiao Wang, Lei YU, Gui-Song Xia

Recent advances in 3D Gaussian Splatting have shown remarkable potential for novel view synthesis. However, most existing large-scale scene reconstruction methods rely on the divide-and-conquer paradigm, which often leads to the loss of global scene information and requires complex parameter tuning due to scene partitioning and local optimization. To address these limitations, we propose MixGS, a novel holistic optimization framework for large-scale 3D scene reconstruction. MixGS models the entire scene holistically by integrating camera pose and Gaussian attributes into a view-aware representation, which is decoded into fine-detailed Gaussians. Furthermore, a novel mixing operation combines decoded and original Gaussians to jointly preserve global coherence and local fidelity. Extensive experiments on large-scale scenes demonstrate that MixGS achieves state-of-the-art rendering quality and competitive speed, while significantly reducing computational requirements, enabling large-scale scene reconstruction training on a single 24GB VRAM GPU.

Applications · Language, Speech and Dialog

Boaz Lavon, Shahar Katz, Lior Wolf

We present a novel approach to neural code generation that incorporates real-time execution signals into the language model generation process. While large language models (LLMs) have demonstrated impressive code generation capabilities, they typically do not utilize execution feedback during inference, a critical signal that human programmers regularly leverage. Our method, Execution-Guided Classifier-Free Guidance EG-CFG, dynamically incorporates execution signals as the model generates code, providing line-by-line feedback that guides the generation process toward executable solutions. EG-CFG employs a multi-stage process: first, we conduct beam search to sample candidate program completions for each line; second, we extract execution signals by executing these candidates against test cases; and finally, we incorporate these signals into the prompt during generation. By maintaining consistent signals across tokens within the same line and refreshing signals at line boundaries, our approach provides coherent guidance while preserving syntactic structure. Moreover, the method naturally supports native parallelism at the task level in which multiple agents operate in parallel, exploring diverse reasoning paths and collectively generating a broad set of candidate solutions. Our experiments across diverse coding tasks demonstrate that EG-CFG significantly improves code generation performance compared to standard approaches, achieving state-of-the-art results across various levels of complexity, from foundational problems to challenging competitive programming and data science tasks.

Theory · Reinforcement Learning and Planning

Ofir Schlisselberg, Tal Lancewicki, Peter Auer, Yishay Mansour

We study the multi-armed bandit problem with adversarially chosen delays in the Best-of-Both-Worlds (BoBW) framework, which aims to achieve near-optimal performance in both stochastic and adversarial environments. While prior work has made progress toward this goal, existing algorithms suffer from significant gaps to the known lower bounds, especially in the stochastic settings. Our main contribution is a new algorithm that, up to logarithmic factors, matches the known lower bounds in each setting individually. In the adversarial case, our algorithm achieves regret of $\widetilde{O}(\sqrt{KT} + \sqrt{D})$, which is optimal up to logarithmic terms, where $T$ is the number of rounds, $K$ is the number of arms, and $D$ is the cumulative delay. In the stochastic case, we provide a regret bound which scale as $\sum_{i:\Delta_i>0}(\log T/\Delta_i) + \frac{1}{K}\sum \Delta_i \sigma_{max}$, where $\Delta_i$ is the suboptimality gap of arm $i$ and $\sigma_{\max}$ is the maximum number of missing observations. To the best of our knowledge, this is the first BoBW algorithm to simultaneously match the lower bounds in both stochastic and adversarial regimes. Moreover, even beyond the BoBW setting, our stochastic regret bound is the first to match the known lower bound under adversarial delays, improving the second term over the best known result by a factor of $K$.