When considering a model selection or, more generally, an aggregation approach for adaptive statistical inference, it is often necessary to compute estimators over a wide range of model complexities including unnecessarily large models even when the true data-generating process is relatively simple, due to the lack of prior knowledge. This requirement can lead to substantial computational inefficiency. In this work, we propose a novel framework for efficient model aggregation called the early-stopped aggregation (ESA): instead of computing and aggregating estimators for all candidate models, we compute only a small number of simpler ones using an early-stopping criterion and aggregate only these for final inference. Our framework is versatile and applies to both Bayesian model selection, in particular, within the variational Bayes framework, and frequentist estimation, including a general penalized estimation setting. We investigate adaptive optimal property of the ESA approach across three learning paradigms. We first show that ESA achieves optimal adaptive contraction rates in the variational Bayes setting under mild conditions. We extend this result to variational empirical Bayes, where prior hyperparameters are chosen in a data-dependent manner. In addition, we apply the ESA approach to frequentist aggregation including both penalization-based and sample-splitting implementations, and establish corresponding theory. As we demonstrate, there is a clear unification between early-stopped Bayes and frequentist penalized aggregation, with a common "energy" functional comprising a data-fitting term and a complexity-control term that drives both procedures. We further present several applications and numerical studies that highlight the efficiency and strong performance of the proposed approach.

The Sauer-Shelah-Perles Lemma is a cornerstone of combinatorics and learning theory, bounding the size of a binary hypothesis class in terms of its Vapnik-Chervonenkis (VC) dimension. For classes of functions over a $k$-ary alphabet, namely the multiclass setting, the Natarajan dimension has long served as an analogue of VC dimension, yet the corresponding Sauer-type bounds are suboptimal for alphabet sizes $k>2$. In this work, we establish a sharp Sauer inequality for multiclass and list prediction. Our bound is expressed in terms of the Daniely--Shalev-Shwartz (DS) dimension, and more generally with its extension, the list-DS dimension -- the combinatorial parameters that characterize multiclass and list PAC learnability. Our bound is tight for every alphabet size $k$, list size $\ell$, and dimension value, replacing the exponential dependence on $\ell$ in the Natarajan-based bound by the optimal polynomial dependence, and improving the dependence on $k$ as well. Our proof uses the polynomial method. In contrast to the classical VC case, where several direct combinatorial proofs are known, we are not aware of any purely combinatorial proof in the DS setting. This motivates several directions for future research, which are discussed in the paper. As consequences, we obtain improved sample complexity upper bounds for list PAC learning and for uniform convergence of list predictors, sharpening the recent results of Charikar et al.~(STOC~2023), Hanneke et al.~(COLT~2024), and Brukhim et al.~(NeurIPS~2024).

Large language models (LLMs) can struggle to memorize factual knowledge in their parameters, often leading to hallucinations and poor performance on knowledge-intensive tasks. In this paper, we formalize fact memorization from an information-theoretic perspective and study how training data distributions affect fact accuracy. We show that fact accuracy is suboptimal (below the capacity limit) whenever the amount of information contained in the training data facts exceeds model capacity. This is further exacerbated when the fact frequency distribution is skewed (e.g. a power law). We propose data selection schemes based on the training loss alone that aim to limit the number of facts in the training data and flatten their frequency distribution. On semi-synthetic datasets containing high-entropy facts, our selection method effectively boosts fact accuracy to the capacity limit. When pretraining language models from scratch on an annotated Wikipedia corpus, our selection method enables a GPT2-Small model (110m parameters) to memorize 1.3X more entity facts compared to standard training, matching the performance of a 10X larger model (1.3B parameters) pretrained on the full dataset.

Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before changing its prediction. However, its applicability is more limited than some of its alternatives, since it requires the use of generative models and restricts the analyses either to specific model architectures or discrete features. In this work, we propose a new robustness metric applicable to any probabilistic discriminative classifier and any type of features. We demonstrate that this new metric is capable of distinguishing between reliable and unreliable predictions, and use this observation to develop new strategies for dynamic classifier selection.

This paper proposes REFUEL, a reinforcement learning method with two techniques: reward shapingand feature rebuilding, to improve the performance of online symptom checking for disease diagnosis.

The Sony World Photography Awards announced the winning and shortlisted photographers of the 2026 National and Regional Awards . Captured during a dive in the Galápagos Islands, the image reveals the predator's agility against the fluid patterns of the fish, providing a raw look at the survival instincts, and the high-energy interactions that define this unique volcanic ecosystem. Breakthroughs, discoveries, and DIY tips sent six days a week. From a solitary leopard in Botswana to a herd of buffaloes in Sri Lanka, and a church in Slovenia to a rocky landscape in Saudi Arabia, beauty exists in all corners of our humble planet. The Sony World Photography Awards celebrates photographers who capture riveting images around the world in its 2026 National and Regional Awards.

'Comatose' Mojtaba Khamenei'is UNAWARE there is a war on and has no idea he is supreme leader', report says - despite regime issuing his'first statement' FBI storms home of Lebanese-born restaurant worker who drove truck filled with explosives into synagogue and opened fire after his'family were killed in airstrike' Trump slammed after lifting oil sanctions on Russia as gas prices skyrocket: 'It's a betrayal' Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Billy Joel's daughter Alexa Ray gives health update amid his battle with rare brain disorder Concerning whispers inside Trump World that Operation Epic Fury is suddenly at risk... and the critical question that will determine how this ends: MARK HALPERIN Meghan Markle masks up to cheer young patients at Los Angeles children's hospital as she agrees deal to sign her latest documentary Beauty queen slams Trump as she's FIRED by White House: 'I stood by you for 20 years... now, I don't even recognize you' Wall Street issues stark warning that Iran oil attacks could wreck Trump's key election promises Truth behind the massacre of 110 school girls in Iran: How shameful episode sparked a deluge of conspiracy theories and lies... as JAKE WALLIS SIMONS explores what really happened Long hair over 45 is ageing and try-hard. I've finally cut mine off. NFL fans left divided as team replace historic logo with'boring' new design as part of franchise rebrand I worked with Carolyn Bessette. This is the'messy' truth about what she was REALLY like in secret. After she met JFK Jr she tried to hide it... but we all knew the nighttime gossip Trump says US is'totally destroying' Iran as he issues chilling threat of more action coming TODAY The 7 types of'hyperarousal' - so, do you get cold sweats or tingling fingers?

AML Trends in 2022: What Y ou Need to Know .

The UN estimates 2-5% of global GDP or $0.8 - $2.0 trillion dollars are laundered