Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on Gaussian processes, kernel machines, linear models, or linearized neural approximations, leaving a gap between theory and the nonlinear models used in practice. We develop a kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data. Our approach uses kernels over the parameter space to induce reproducing-kernel Hilbert space structures over the corresponding model class, yielding confidence bounds for models trained with broad classes of regularized convex losses. We show how these bounds can support convergence guarantees for nonlinear acquisition and surrogate models, including randomized regularized policies that select points by maximizing a trained random model. These results provide a unified route to analyzing nonlinear parametric models in Bayesian optimization and related adaptive optimization settings.

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic $R^2$ gap up to 0.057). We further introduce a black-box diagnostic $ρ_R(α)$ that estimates the proportion of baseline uncertainty resolved by context level $α$, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

We study multiple change point localization under bandit feedback. An unknown piecewise-constant function on a compact interval can be queried sequentially at adaptively chosen inputs, and each query returns a noisy evaluation of the function. The goal is to identify a prescribed number of discontinuities, known as change points, within a target precision $η$ and confidence level $1-δ$, while using as few samples as possible. We propose an adaptive algorithm that first detects intervals likely to contain change points and then refines their locations to precision $η$. We establish non-asymptotic upper bounds on its sample budget, together with corresponding lower bounds. Prior work shows that jump magnitudes alone determine the asymptotic sample complexity as $δ\to 0$. We reveal that this picture is incomplete beyond this regime. We demonstrate, both empirically and theoretically, that for general $δ$ and $η$, the complexity is jointly governed by the jumps and the relative positions of the change points.

Training large language models (LLMs) such as GPT-5 and Qwen-3 (Singh et al., 2025; Yang et al., 2025) on massive text corpora aims at capturing the underlying distribution of natural language. Yet, it remains challenging for the trained model to extrapolate to out-of-distribution or out-of-domain settings beyond the support of its training data. The literature has seen the development of various data perturbation techniques, such as synonym replacement, random insertion, deletion, and swap, that modify training instances into semantically similar variants to effectively expose LLMs to a broader range of inputs and improve their ability to generalize beyond the training data (Feng et al., 2019, 2020; Li et al., 2024; Cen et al., 2026). However, their approach remains grounded in the discrete, word-level augmentation procedures mentioned previously, which may restrict its adaptivity across diverse domains. While discrete perturbations are simple to use, they could be too coarse and hard to refine due to the complexity of natural language (Park et al., 2022; Li et al., 2023). Meanwhile, fixed perturbations apply the same transformations to the data regardless of the contexts, thus failing to generalize appropriately (Ismailov and Asanova, 2025).

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in Ωpe|β|Hq where H is the horizon of the MDP, while the state-of-the-art upper bound achieves at best Ope2|β|Hq (Mortensen and Talebi, 2025) using a generative model. We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. To close this open gap, we revisit the analysis of this problem through a forward-model based algorithm building on KL-based exploration bonuses that we adapt to the entropic criterion. The improvement we get is due to two main novel technical innovations. We leverage the smoothness properties of the exponential utility to derive sharper concentration bounds, and we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.

Some of the world's biggest and most powerful brands are attempting to be more cute and cuddly. Tech giants Microsoft and Apple are among a wave of businesses who have recently introduced new cartoon character mascots, a tactic experts say is often used to make a brand seem more human and friendly, and to build a stronger connection with customers. Apple's character, a blue and white figure with an outsized head, has become unofficially known as Little Finder Guy. Introduced in March in social media videos to promote a new laptop, it has gained some positive coverage. Microsoft, which years ago shelved its widely-disliked Clippy paperclip virtual assistant, has also unveiled a new cartoon character for its AI assistant Copilot.

For animals, certain colors scream poison. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Although largely safe, turbines still pose a danger to some migratory birds. Breakthroughs, discoveries, and DIY tips sent six days a week. Wind turbines are a net positive for a sustainable society, but that doesn't mean they don't have an environmental impact.

The Metropolitan Police has warned that it is preparing for potential violence and hate speech crimes across two protests in London this Saturday. More than 4,000 officers will be drafted in to police the rival events - possibly one of the largest protest deployment in decades - amid fears that far-right demonstrators could clash with pro-Palestine marchers if the two groups are not kept apart. In addition, tens of thousands of football fans are also expected at Wembley Stadium for the FA Cup Final, adding further pressures on the capital's police. Scotland Yard said the risks meant it had to impose the highest degree of control. Measures the Met is planning include the first authorisation of live facial recognition cameras at a demonstration.

Neanderthal'dentists' treated cavities 59,000 years ago A molar points to some sophisticated dental work performed by our extinct cousins. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The molar tooth found in Chagyrskaya Cave and its macro-features. Breakthroughs, discoveries, and DIY tips sent six days a week. Neanderthals () were once considered to have been extremely primitive and unsophisticated compared to us humans ().