The first reports appeared on foreign screens, beyond the reach of most Iranians. On 28 February Prime Minister Benjamin Netanyahu said there were signs that the tyrant is no more, suggesting Supreme Leader Ayatollah Ali Khamenei had been killed in a joint US-Israeli strike. Iranians watching state television, however, encountered silence. Government officials would neither confirm nor deny Khamenei's death. On one of the state broadcaster's channels, IRTV3, one news presenter urged viewers to trust him and the latest information the government had.

Offline reinforcement learning (RL) aims to learn decision policies from a fixed batch of logged transitions, without additional environment interaction. Despite remarkable empirical progress, offline RL remains fragile under distribution shifts: value-based methods can overestimate the value of unseen actions, yielding policies that exploit model errors rather than genuine long-term rewards. We propose \emph{Bayesian Conservative Policy Optimization (BCPO)}, a unified framework that converts epistemic uncertainty into \emph{provably conservative} policy improvement. BCPO maintains a hierarchical Bayesian posterior over environment/value models, constructs a \emph{credible lower bound} (LCB) on action values, and performs policy updates under explicit KL regularization toward the behavior distribution. This yields an uncertainty-calibrated analogue of conservative policy iteration in the offline regime. We provide a finite-MDP theory showing that the pessimistic fixed point lower-bounds the true value function with high probability and that KL-controlled updates improve a computable return lower bound. Empirically, we verify the methodology on a real offline replay dataset for the CartPole benchmark obtained via the \texttt{d3rlpy} ecosystem, and report diagnostics that link uncertainty growth and policy drift to offline instability, motivating principled early stopping and calibration

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.

Reinforcement learning (RL) has become a standard technique for post-training diffusion-based image synthesis models, as it enables learning from reward signals to explicitly improve desirable aspects such as image quality and prompt alignment. In this paper, we propose an online RL variant that reduces the variance in the model updates by sampling paired trajectories and pulling the flow velocity in the direction of the more favorable image. Unlike existing methods that treat each sampling step as a separate policy action, we consider the entire sampling process as a single action. We experiment with both high-quality vision language models and off-the-shelf quality metrics for rewards, and evaluate the outputs using a broad set of metrics. Our method converges faster and yields higher output quality and prompt alignment than previous approaches.

Existing convergence of distributed optimization methods in non-Euclidean geometries typically rely on kernel assumptions: (i) global Lipschitz smoothness and (ii) bi-convexity of the associated Bregman divergence function. Unfortunately, these conditions are violated by nearly all kernels used in practice, leaving a huge theory-practice gap. This work closes this gap by developing a unified analytical tool that guarantees convergence under mild conditions. Specifically, we introduce Hessian relative uniform continuity (HRUC), a regularity satisfied by nearly all standard kernels. Importantly, HRUC is closed under concatenation, positive scaling, composition, and various kernel combinations. Leveraging the geometric structure induced by HRUC, we derive convergence guarantees for mirror descent-based gradient tracking without imposing any restrictive assumptions. More broadly, our analysis techniques extend seamlessly to other decentralized optimization methods in genuinely non-Euclidean and non-Lipschitz settings.

Random sample consensus (RANSAC), which is based on a repetitive sampling from a given dataset, is one of the most popular robust estimation methods. In this study, an energy-based model (EBM) for robust estimation that has a similar scheme to RANSAC, energy-based RANSAC (EB-RANSAC), is proposed. EB-RANSAC is applicable to a wide range of estimation problems similar to RANSAC. However, unlike RANSAC, EB-RANSAC does not require a troublesome sampling procedure and has only one hyperparameter. The effectiveness of EB-RANSAC is numerically demonstrated in two applications: a linear regression and maximum likelihood estimation.

Scientific discovery increasingly relies on AI systems to select candidates for expensive experimental validation, yet no principled, budget-aware evaluation framework exists for comparing selection strategies -- a gap intensified by large language models (LLMs), which generate plausible scientific proposals without reliable downstream evaluation. We introduce the Budget-Sensitive Discovery Score (BSDS), a formally verified metric -- 20 theorems machine-checked by the Lean 4 proof assistant -- that jointly penalizes false discoveries (lambda-weighted FDR) and excessive abstention (gamma-weighted coverage gap) at each budget level. Its budget-averaged form, the Discovery Quality Score (DQS), provides a single summary statistic that no proposer can inflate by performing well at a cherry-picked budget. As a case study, we apply BSDS/DQS to: do LLMs add marginal value to an existing ML pipeline for drug discovery candidate selection? We evaluate 39 proposers -- 11 mechanistic variants, 14 zero-shot LLM configurations, and 14 few-shot LLM configurations -- using SMILES representations on MoleculeNet HIV (41,127 compounds, 3.5% active, 1,000 bootstrap replicates) under both random and scaffold splits. Three findings emerge. First, the simple RF-based Greedy-ML proposer achieves the best DQS (-0.046), outperforming all MLP variants and LLM configurations. Second, no LLM surpasses the Greedy-ML baseline under zero-shot or few-shot evaluation on HIV or Tox21, establishing that LLMs provide no marginal value over an existing trained classifier. Third, the proposer hierarchy generalizes across five MoleculeNet benchmarks spanning 0.18%-46.2% prevalence, a non-drug AV safety domain, and a 9x7 grid of penalty parameters (tau >= 0.636, mean tau = 0.863). The framework applies to any setting where candidates are selected under budget constraints and asymmetric error costs.

Cyberbullying on social media is inherently multilingual and multi-faceted, where abusive behaviors often overlap across multiple categories. Existing methods are commonly limited by monolingual assumptions or single-task formulations, which restrict their effectiveness in realistic multilingual and multi-label scenarios. In this paper, we propose HMS-BERT, a hybrid multi-task self-training framework for multilingual and multi-label cyberbullying detection. Built upon a pretrained multilingual BERT backbone, HMS-BERT integrates contextual representations with handcrafted linguistic features and jointly optimizes a fine-grained multi-label abuse classification task and a three-class main classification task. To address labeled data scarcity in low-resource languages, an iterative self-training strategy with confidence-based pseudo-labeling is introduced to facilitate cross-lingual knowledge transfer. Experiments on four public datasets demonstrate that HMS-BERT achieves strong performance, attaining a macro F1-score of up to 0.9847 on the multi-label task and an accuracy of 0.6775 on the main classification task. Ablation studies further verify the effectiveness of the proposed components.

The InfoNCE loss in contrastive learning depends critically on a temperature parameter, yet its dynamics under fixed versus annealed schedules remain poorly understood. We provide a theoretical analysis by modeling embedding evolution under Langevin dynamics on a compact Riemannian manifold. Under mild smoothness and energy-barrier assumptions, we show that classical simulated annealing guarantees extend to this setting: slow logarithmic inverse-temperature schedules ensure convergence in probability to a set of globally optimal representations, while faster schedules risk becoming trapped in suboptimal minima. Our results establish a link between contrastive learning and simulated annealing, providing a principled basis for understanding and tuning temperature schedules.

In this paper, we consider the problem of black-box optimization with noisy feedback revealed in batches, where the unknown function to optimize has a bounded norm in some Reproducing Kernel Hilbert Space (RKHS). We refer to this as the Batched Kernelized Bandits problem, and refine and extend existing results on regret bounds. For algorithmic upper bounds, (Li and Scarlett, 2022) shows that $B=O(\log\log T)$ batches suffice to attain near-optimal regret, where $T$ is the time horizon and $B$ is the number of batches. We further refine this by (i) finding the optimal number of batches including constant factors (to within $1+o(1)$), and (ii) removing a factor of $B$ in the regret bound. For algorithm-independent lower bounds, noticing that existing results only apply when the batch sizes are fixed in advance, we present novel lower bounds when the batch sizes are chosen adaptively, and show that adaptive batches have essentially same minimax regret scaling as fixed batches. Furthermore, we consider a robust setting where the goal is to choose points for which the function value remains high even after an adversarial perturbation. We present the robust-BPE algorithm, and show that a suitably-defined cumulative regret notion incurs the same bound as the non-robust setting, and derive a simple regret bound significantly below that of previous work.