Understanding the curvature evolution of the loss landscape is fundamental to analyzing the training dynamics of neural networks. The most commonly studied measure, Hessian sharpness ($λ_{\max}^H$) -- the largest eigenvalue of the loss Hessian -- determines local training stability and interacts with the learning rate throughout training. Despite its significance in analyzing training dynamics, direct measurement of Hessian sharpness remains prohibitive for Large Language Models (LLMs) due to high computational cost. We analyze $\textit{critical sharpness}$ ($λ_c$), a computationally efficient measure requiring fewer than $10$ forward passes given the update direction $Δ\mathbfθ$. Critically, this measure captures well-documented Hessian sharpness phenomena, including progressive sharpening and Edge of Stability. Using this measure, we provide the first demonstration of these sharpness phenomena at scale, up to $7$B parameters, spanning both pre-training and mid-training of OLMo-2 models. We further introduce $\textit{relative critical sharpness}$ ($λ_c^{1\to 2}$), which quantifies the curvature of one loss landscape while optimizing another, to analyze the transition from pre-training to fine-tuning and guide data mixing strategies. Critical sharpness provides practitioners with a practical tool for diagnosing curvature dynamics and informing data composition choices at scale. More broadly, our work shows that scalable curvature measures can provide actionable insights for large-scale training.

The safety probe comes after Waymo did a voluntary software recall late last year addressing the same issue. Waymo has caught the attention of the National Transportation Safety Board as the federal agency launched an official investigation into the company for its robotaxis improperly passing school buses in Austin, Texas. The NTSB said on X that it would examine the interaction between Waymo vehicles and school buses stopped for loading and unloading students. The latest federal probe stems from a preliminary evaluation by the National Highway Traffic Safety Administration that looked into how Waymo reacts to stopped school buses in the Texas city. That report led to Waymo's voluntary software recall in December.

The hermit and mystic Richard Rolles was basically a bestselling author in the Middle Ages. Richard Rolle (depicted in this medieval illustration c. 1400) was a famous hermit and Christian mystic. Breakthroughs, discoveries, and DIY tips sent six days a week. For generations, a misidentified medieval manuscript was hidden in a 474-year-old English boarding school's library. After a careful new analysis, a medieval literature researcher can confirm the manuscript is actually the oldest and only known edition of Richard Rolle's () written in its original Latin.

You may have social jetlag. When life gets in the way of your body's ideal sleep schedule, things get messy. Waking up early can be bad for you. Breakthroughs, discoveries, and DIY tips sent six days a week. Hours before sunrise, society's earliest larks begin their day.

Border czar rips Virginia's new'Bond villain' governor after she blocked ICE on day one... as he lays out plans to move forward without her Texas's largest city warned temperatures will plunge below freezing for 40 HOURS as millions brace for life-threatening storm Mysterious UFO-shaped'Dorito' aircraft spotted over Area 51 as strange military code is heard Meghan Trainor's teary photo with her new baby born via surrogate has sparked an almost unsayable thought. Most women won't admit it... but I will: CAROLINE BULLOCK Billionaire who predicted 2008 crash issues stark warning over'worrying' new US trend but there's one way to protect your savings AND make money McDonald's customers mind-blown after seeing prices on 2009 menu...'when life was worth living' Ryan Reynolds's TORCHED by fans over'cringe' email he allegedly sent to It Ends With Us author Colleen Hoover Florida, Texas and California lead America's housing crash as other Sun Belt states start to crack as values plunge 7.6 percent Canadian woman was euthanized'against her will' after husband was fed-up with caring for her Ex-cop who was beaten on Jan. 6 unleashes on election skeptic in chaotic congressional hearing Dr. Phil's son blocked from selling'life-threatening' footage of NYPD after Mamdani lawsuit Chilling video shows high school student rampaging through classroom with knife... before teacher steps in Trump orders a'massive' military fleet toward Iran with ominous warning about what could come next: 'We're watching' Trump explains how he got bruise on his hand at Davos that sparked MORE health rumours... as he teases FOURTH term Michael Douglas and Catherine Zeta Jones's liberal nepo son is'too spooked' to return to CNN after Scott Jennings eviscerated him during debut appearance Another awkward moment between Victoria Beckham and Nicola Peltz goes viral as fans claim Brooklyn's mum'is not the problem' Woke Karen, 63, lets VERY embarrassing detail slip to the Daily Mail after she mistook cops rushing to school for ICE'and tried to obstruct them' Paris Hilton recalls'abuse' she endured after leaked 2004 sex tape as she protests against AI deepfakes The cancer now killing more Americans under 50 than any other... and why it's still being caught too late Revealed: The hilarious slang used in London 300 years ago - so, do YOU know your'fuddle cups' from your'cackling farts'? From '6,7' to'vibe-coding', new slang words and phrases seem to pop up on an almost daily basis. But it's time to wind the clock back, as a 327-year-old dictionary reveals the slang used in London in the 17th century. The glossary of terms, titled the'New Dictionary of the Terms..of the Canting Crew' was published in 1699 to help stop naive visitors to London from getting mugged or even killed.

A new survey finds 95% of faculty worry artificial intelligence makes students overly reliant on AI, with 90% saying it decreases critical thinking.

Trump orders a massive armada toward Iran with ominous warning about what could come next: 'We're watching' Mysterious UFO-shaped'Dorito' aircraft spotted over Area 51 as strange military code is heard Florida, Texas and California lead America's housing crash as other Sun Belt states start to crack as values plunge 7.6 percent Meghan Trainor's teary photo with her new baby born via surrogate has sparked an almost unsayable thought. Most women won't admit it... but I will: CAROLINE BULLOCK Billionaire who predicted 2008 crash issues stark warning over'worrying' new US trend but there's one way to protect your savings AND make money Canadian woman was euthanized'against her will' after husband was fed-up with caring for her Another awkward moment between Victoria Beckham and Nicola Peltz goes viral as fans claim Brooklyn's mum'is not the problem' Chilling video shows high school student rampaging through classroom with knife... before teacher steps in Trump describes excruciating ...

The first generation of LLMs were largely trained on human-generated data. However, the success of LLMs and their increased adoption has had an unexpected consequence of AI-generated content appearing in places where there was previously none. Thus machine learning practitioners should be aware that there is an increased chance that their training data is contaminated by LLM-generated content. Previous work has looked into the value of synthetic (i.e., AI-generated) data, and showed that while naively adding this data to the training mix may lead to model collapse, being more diligent about which data is added, the amount of curation it undergoes, and the specifics of the training process may mitigate that risk, or reverse it, leading to improved performance. These works almost uniquely focus on the LLM setting, trying to improve state of the art performance on a set of benchmarks. In contrast, in this work we take a traditional learning theory view on this problem. We begin by formalizing the setting and developing a framework that captures the invariants of having natural training data contaminated by synthetic additions. Specifically, we see three salient points: Groundtruth. There exists a (potentially small) set of natural data, coming from the true data generation distribution.

Reinforcement learning (RL) has achieved remarkable success in real-world decision-making across diverse domains, including gaming, robotics, online advertising, public health, and natural language processing. Despite these advances, a substantial gap remains between RL research and its deployment in many practical settings. Two recurring challenges often underlie this gap. First, many settings offer limited opportunity for the agent to interact extensively with the target environment due to practical constraints. Second, many target environments often undergo substantial changes, requiring redesign and redeployment of RL systems (e.g., advancements in science and technology that change the landscape of healthcare delivery). Addressing these challenges and bridging the gap between basic research and application requires theory and methodology that directly inform the design, implementation, and continual improvement of RL systems in real-world settings. In this paper, we frame the application of RL in practice as a three-component process: (i) online learning and optimization during deployment, (ii) post- or between-deployment offline analyses, and (iii) repeated cycles of deployment and redeployment to continually improve the RL system. We provide a narrative review of recent advances in statistical RL that address these components, including methods for maximizing data utility for between-deployment inference, enhancing sample efficiency for online learning within-deployment, and designing sequences of deployments for continual improvement. We also outline future research directions in statistical RL that are use-inspired -- aiming for impactful application of RL in practice.

Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.