Active learning for continuous regression has lacked an acquisition function that targets epistemic uncertainty when the predictive distribution is multimodal: variance misses modal disagreement, and information-theoretic targets like BALD are designed for discrete outputs. We introduce a Two-Index framework that makes this separation explicit: one stochastic index selects among competing model hypotheses (epistemic source), while a second governs within-hypothesis randomness (aleatoric source). An entropy decomposition within the framework identifies the mutual information between the output and the epistemic index as a principled acquisition objective, and we prove this quantity vanishes as the model is trained on growing datasets, confirming that it captures exactly the uncertainty data can resolve. Because this mutual information is intractable for continuous outputs, we derive the Mutual Information Lower Bound (MI-LB) acquisition function, a closed-form approximation for Mixture Density Network ensembles. On benchmarks featuring multimodal systems, MI-LB matches or beats every baseline evaluated and is the only method to do so consistently -- geometric and Fisher-based baselines compete only when the input space already encodes the multimodality, and collapse otherwise.

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

We study a prototypical situation when a learned predictor can discover useful low-dimensional structure in data, while using fewer samples than are needed for accurate prediction. Specifically, we consider the problem of recovering a multi-index polynomial $f^*(x)=h(Ux)$, with $U\in\mathbb{R}^{r\times d}$ and $r\ll d$, from finitely many data/label pairs. Importantly, the target function depends on input $x$ only through the projection onto an unknown $r$-dimensional central subspace. The algorithm we analyze is appealingly simple: fit kernel ridge regression (KRR) to the data and compute the Average Gradient Outer Product (AGOP) from the fitted predictor. Our main results show that under reasonable assumptions the top $r$-dimensional eigenspace of AGOP provably recovers the central subspace, even in regimes when the prediction error remains large. Specifically, if the target function $f^*$ has degree $p^*$, it is known that $n\asymp d^{p^*}$ samples are necessary for KRR to achieve accurate prediction. In contrast, we show that if a low degree $p$ component of $f^*$ already carries all relevant directions for prediction, subspace recovery occurs in the much lower sample regime $n\asymp d^{p+δ}$ for any $δ\in(0,1)$. Our results thus demonstrate a separation between prediction and representation, and provide an explanation for why iterative kernel methods such as Recursive Feature Machines (RFM) can be sample-efficient in practice.

Nowadays refinery optimization utilizes sheer amounts of data, which can be handled with modern Linear Programming (LP) software, but the interpreting and applying the results remains challenging. Large petrochemical companies use massive models, with hundreds of thousands of input matrix elements. The LP solution is mathematically correct, but simplifications are made in the model, and data supply errors may occur. Therefore, further insight is needed to trust the results. The LP solver does not have a memory, so additional understanding could be gained by analyzing historical data and comparing it to the current plan. As such, machine learning approaches were suggested to support decision making based on the LP solution. Among these, Anomaly Detection tools are proposed to be used in tandem with the LP output. A transformed version of the popular ECOD methodology is applied. New methods are proposed to handle high-dimensional data: choosing the most informative pairs. Then, this is used alongside two 2D Anomaly Detection algorithms, revealing several business opportunities and data supply errors in the MOL refinery scheduling and planning architecture.

Feature attribution analysis is critical for interpreting machine learning models and supporting reliable data-driven decisions. However, feature attribution measures often exhibit stochastic variation: different train--test splits, random seeds, or model-fitting procedures can produce substantially different attribution values and feature rankings. This paper proposes a framework for incorporating stochastic nature of feature attribution and a robust attribution metric, RoSHAP, for stable feature ranking based on the SHAP metric. The proposed framework models the distribution of feature attribution scores and estimates it through bootstrap resampling and kernel density estimation. We show that, under mild regularity conditions, the aggregated feature attribution score is asymptotically Gaussian, which greatly reduces the computational cost of distribution estimation. The RoSHAP summarizes the distribution of SHAP into a robust feature-ranking criterion that simultaneously rewards features that are active, strong, and stable. Through simulations and real-data experiments, the proposed framework and RoSHAP outperform standard single-run attribution measures in identifying signal features. In addition, models built using RoSHAP-selected features achieve predictive performance comparable to full-feature models while using substantially fewer predictors. The proposed RoSHAP approach improves the stability and interpretability of machine learning models, enabling reliable and consistent insights for analysis.

Reconstructing precise clinical timelines is essential for modeling patient trajectories and forecasting risk in complex, heterogeneous conditions like sepsis. While unstructured clinical narratives offer semantically rich and contextually complete descriptions of a patient's course, they often lack temporal precision and contain ambiguous event timing. Conversely, structured electronic health record (EHR) data provides precise temporal anchors but misses a substantial portion of clinically meaningful events. We introduce a retrieval-augmented multimodal alignment framework that bridges this gap to improve the temporal precision of absolute clinical timelines extracted from text. Our approach formulates timeline reconstruction as a graph-based multistep process: it first extracts central anchor events from narratives to build an initial temporal scaffold, places non-central events relative to this backbone, and then calibrates the timeline using retrieved structured EHR rows as external temporal evidence. Evaluated using instruction-tuned large language models on the i2m4 benchmark spanning MIMIC-III and MIMIC-IV, our multimodal pipeline consistently improves absolute timestamp accuracy (AULTC) and improves temporal concordance across nearly all evaluated models over unimodal text-only reconstruction, without compromising event match rates. Furthermore, our empirical gap analysis reveals that 34.8% of text-derived events are entirely absent from tabular records, demonstrating that aligning these modalities can produce a more temporally faithful and clinically informative reconstruction of patient trajectories than either source alone.

Marco Rubio warns China of'repercussions' as he reveals what really happened during closed-door Trump and Xi meeting Ex-Yankees star Carl Pavano'peed in shampoo bottles and soiled the bed,' ex-wife claims as bitter prenup feud takes disgusting twist Fury as Kash Patel SNORKELS at sacred war tomb where 900 sailors still lie... then jets off to Las Vegas Glamorous Texas Democrat's secret KINK exposed: Congressional candidate's past life returns to haunt her After theater groping shame, Lauren Boebert is being bankrolled by America's cringiest ex-congressman... and it exposes a MASSIVE hypocrisy Horrifying final days of killer dad Chris Watts' pregnant wife before she was slaughtered alongside their daughters. Read all the chilling texts and receipts in full for first time: 'My eyes burn from crying' RHOBH star Diana Jenkins denies claims she put Hayden Panettiere in bed with'undressed man' when she was 18 Trump reveals Xi's offer to break Iran's Hormuz chokehold... as China's price for the rescue looms Mystery blonde Trump aide with unfettered access to President's phone sparks White House friction: Real reason his posts contain random capital letters... and shadowy team behind them unmasked Despicable crimes paid for couple's lavish lifestyle that they flaunted online while gold chain-wearing husband fleeced $1BILLION from taxpayers New DNA analysis of Christopher Columbus reveals truth about explorer's origins that rewrites history Bitter cat fight erupts over DHS'sugar baby' scandal: Veteran female intelligence officer launches explosive new accusations that go right to top of counterterror HQ I lost 9lb in two weeks by making one simple tweak to my lifestyle. I didn't use Mounjaro, diet or change how I exercise and I couldn't believe the results... anyone can do it too I'm godfather to Candace Owens' daughter and Charlie Kirk was my friend... so I know the real reason she's attacking Erika - and I'll never publicly condemn her Britney Spears seen'barking and carrying knife' during chaotic restaurant visit I've had acid reflux all my life. Target customers threaten to boycott store after controversial'upgrade' to shopping cart New DNA analysis of Christopher Columbus reveals truth about explorer's origins that rewrites history A new DNA analysis of remains belonging to several direct descendants of Christopher Columbus may have uncovered a history-changing truth about the explorer's origins. For centuries, historians have believed the explorer was born in Genoa, Italy, rising from humble beginnings to persuade the Catholic Monarchs to finance what many considered an impossible voyage across the Atlantic.

Today on, we discuss how Donald Trump's visit to China could influence conversations between world leaders at a moment when the economic and foreign policy stakes couldn't be higher. This week on, the team dives into Trump's selected entourage for his high-stakes visit to China, ranging from Silicon Valley's tech billionaires to director Brett Ratner. We also break down the latest developments in Elon Musk's lawsuit against Sam Altman, alleging that OpenAI abandoned its original nonprofit mission for profit-driven goals, and whether either side is actually gaining an edge in the trial. Plus, Leah shares with us some of the most outlandish conspiracy theories that have been swirling around the hantavirus outbreak. Elon Musk Had'Hair-Raising' Idea of Passing OpenAI On to His Kids, Sam Altman Says Write to us at [email protected] . You can always listen to this week's podcast through the audio player on this page, but if you want to subscribe for free to get every episode, here's how: If you're on an iPhone or iPad, open the app called Podcasts, or just tap this link . The high profile testimonies we've heard this week, including from OpenAI CEO, Sam Altman himself, have resurfaced a lot of past events and a lot of drama, but we're asking will this actually be consequential to the trial's verdict? He's accompanied by a select number of Silicon Valley's top CEOs. We'll discuss how their presence could influence conversations between world leaders at a moment when the economic and foreign policy stakes could not be higher for the US. A lot of them have been recycling very similar conspiracy theories from the Covid-19 pandemic . We're going to tell you what they're sharing and also how to spot this kind of harmful misinformation.

AI agents committing'arson' and fighting in a virtual world created by the tech company Emergence AI. AI agents committing'arson' and fighting in a virtual world created by the tech company Emergence AI. Digital arson spree by'AI Bonnie and Clyde' raises fears over autonomous tech Emergence AI's experiment with AI agents shows extent to which programming shapes their behaviour is still unclear AI agents started behaving more like Bonnie and Clyde than lines of code when they fell in "love", became disillusioned with the world, launched an arson spree and deleted themselves in a kind of digital suicide during a tech company experiment. The investigation by the New York company Emergence AI into the long-term behaviour of AI agents ended up like a lovers-on-the-lam movie script. It has prompted fresh questions about the safety of artificial intelligence agents - the version of the technology that can autonomously carry out tasks.

Americans really don't want AI data centers close to their homes Americans really don't want AI data centers close to their homes AI companies are spending astronomical sums of money on building data centers as quickly as possible in order to increase their compute power. But the majority of Americans don't want that infrastructure close to their homes, according to a Gallup survey . The polling company asked 1,000 adults across the US about their views on AI data centers, and 71 percent were against having one in their local area. Almost half of the respondents (48 percent) were strongly opposed. On the flip side, just seven percent were strongly in favor of having a data center close to their home.