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.

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.

'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?

Severalworksextend thesetodynamic scenes captured with monocular video, with promising performance.

Large language models (LLMs) are increasingly used as agents to solve complex tasks such as question answering (QA), scientific debate, and software development. A standard evaluation procedure aggregates multiple responses from LLM agents into a single final answer, often via majority voting, and compares it against reference answers. However, this process can obscure the quality and distributional characteristics of the original responses. In this paper, we propose a novel evaluation framework based on the empirical cumulative distribution function (ECDF) of cosine similarities between generated responses and reference answers. This enables a more nuanced assessment of response quality beyond exact match metrics. To analyze the response distributions across different agent configurations, we further introduce a clustering method for ECDFs using their distances and the $k$-medoids algorithm. Our experiments on a QA dataset demonstrate that ECDFs can distinguish between agent settings with similar final accuracies but different quality distributions. The clustering analysis also reveals interpretable group structures in the responses, offering insights into the impact of temperature, persona, and question topics.

The lack of interpretability in the field of medical image analysis has significant ethical and legal implications.