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Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

In 2020, the U.S. Census Bureau adopted differential privacy for the Decennial Census by injecting integer-valued Gaussian noise into published census tabulations. Exactly evaluating the privacy guarantees of these data releases would enable the Bureau to determine the absolute minimum noise required to satisfy a given privacy budget, preventing the injection of unnecessary excess noise and thereby substantially enhancing the statistical utility of the data for downstream applications such as federal funding allocation and political redistricting. In this paper, we introduce a computationally efficient and mathematically rigorous quadrature method to evaluate the exact privacy profile of practical, large-scale census releases under the composition of heterogeneous discrete Gaussian mechanisms. Mathematically, this problem reduces to evaluating the tail probabilities of high-dimensional convolutions of integer-valued random variables sampled from heterogeneous discrete Gaussian distributions under exceptionally stringent numerical error tolerances (e.g., $10^{-35}$). By recasting the exact privacy accounting as a numerical integration problem via the discrete Fourier transform, we explicitly exploit the exponential convergence of the trapezoidal rule for complex analytic, periodic characteristic functions. Furthermore, to overcome the computational bottleneck of evaluating highly oscillatory integrands in high dimensions, we develop a sieve algorithm that identifies and prunes negligible quadrature nodes, accelerating the computation by three orders of magnitude. Taken together, these numerical innovations enable the first exact, assumption-free privacy accounting for the 2020 Census Demographic and Housing Characteristics File, achieving a 1,824-fold speedup over prior methods while maintaining census-mandated error tolerances.

US Olympic legend Bode Miller's alleged illegal drug stash revealed after he was arrested just days before anniversary of daughter's tragic death Trump's inner circle reveal his true feeling on JD Vance... and why the succession war with Rubio is already won: MARK HALPERIN My girlfriend's cuckolding fetish is getting out of hand... Dr. Fauci is subpoenaed after refusing to testify on COVID origins Noah Presgrove's friends hire famous attorney to battle lawsuit claiming teenager was'beat to death' by someone he knew... as fight between'jealous love rivals' emerges Joe Manganiello reveals secret life-threatening health battle which resulted in'amputation' 'Frankenstein' rabbits with tentacles sprouting from their heads invade several US states AMANDA PLATELL: Why Kate must stand firm and protect her family from Sussexes' manipulation - and most of all, her children Shania Twain, 60, slammed for failing to dress age'appropriate' as she hits the stage in VERY racy look Trump's press secretary joins him on Pennsylvania campaign trip less than two months after birth of daughter Vivi Beloved grandma unmasked as killer of autistic granddaughter and second female family member in horror execution-style double murder... as haunting Mother's Day post emerges Dietitians urge caution over'nature's Ozempic' as people take desperate measures to lose weight Aching joints, exhausted, suffering from brain fog... it might not be the menopause says DR PHILIPPA KAYE READ MORE: Scientists blame mothers for Britain's decline in religiosity Religious rituals are practised all around the world - and experts may now know why they're so popular. Researchers have discovered that taking part in ceremonies like baptisms and bat mitzvahs appears to trigger the release of opioids in the brain. These chemicals have been linked to feelings of pain relief, reward and pleasure. They are also released when people take drugs like heroin, morphine and prescription painkillers, producing the'high' that many associate with the experience. The researchers said their findings support the theory that religious rituals evolved as a way for large groups of people to bond.

We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations grow longer, due to error accumulation. To calibrate the model and improve text quality, it has become standard practice to truncate the distribution, but this approach reduces output diversity, which we would like to avoid. Therefore, in this paper, we ask: does miscalibration improve automatically with scale, and if not, is it theoretically possible to calibrate without tradeoffs? To build intuition, we first study a simplified theoretical setting to characterize the scaling behavior of miscalibration with respect to dataset size. We find that the rate of scaling depends on the power law exponent of the data distribution -- in particular, for a power law exponent close to 1, the scaling exponent is close to 0, meaning that miscalibration improves very slowly with scale.

We study the problem of stabilizing an unknown partially observable linear timeinvariant (LTI) system. For fully observable systems, the state-of-the-art approaches leverage an unstable/stable subspace decomposition to achieve sample complexity that depends only on the number of unstable modes, independent of the dimension of the system state. However, it remains open whether such sample complexity can be achieved for partially observable systems because such systems do not admit a uniquely identifiable unstable subspace. In this paper, we propose LTS-P, a novel technique that leverages compressed singular value decomposition (SVD) on the "lifted" Hankel matrix to estimate the unstable subsystem up to an unknown transformation.

Recent advances in multi-modal representation learning have led to unified embedding spaces that align modalities such as images, text, audio, and vision. However, human motion sequences, a modality that is fundamental for understanding dynamic human activities, remains largely unrepresented in these frameworks. Semantic understanding of actions requires multi-modal grounding: text conveys descriptive semantics, vision provides visual context, and audio provides environmental cues. To bridge this gap, we propose MotionBind, a novel architecture that extends the LanguageBind embedding space to incorporate human motion. MotionBind has two major components. The first one is a Multi-Scale Temporal Motion Transformer (MuTMoT) that maps motion sequences to semantically meaningful embeddings. Multimodal alignment is achieved via diverse cross-modal supervision, including motion-text pairs from HumanML3D and KIT-ML, motion-video pairs rendered from AMASS, and motion-video-audio triplets from AIST++. The second component is a Retrieval-Augmented Latent diffusion Model (REALM) that can generate motion sequences conditioned on many modalities. MotionBind achieves state-of-the-art or competitive performance across motion reconstruction, cross-modal retrieval, zero-shot action recognition, and text-to-motion generation benchmarks.

Weak-to-strong generalization--where a student model trained on imperfect labels generated by a weaker teacher nonetheless surpasses that teacher--has been widely observed, but the mechanisms that enable it have remained poorly understood. In this paper, through a theoretical analysis of simple models, we uncover three core mechanisms that can drive this phenomenon. First, by analyzing ridge linear regression, we study the interplay between the teacher and student regularization parameters and prove that a student can compensate for a teacher's under-regularization and achieve lower test error. We also analyze the role of the parameterization regime of the models and show that qualitatively different phenomena can happen in different regimes. Second, by analyzing weighted ridge linear regression, we show that a student model with a regularization structure better aligned to the target function, can outperform its teacher. Third, in a nonlinear multi-index learning setting, we demonstrate that a student can learn easy, task-specific features from the teacher while leveraging its own broader pre-training to learn hard-to-learn features that the teacher cannot capture.

Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (density of states) landscape as a function of training loss and test accuracy.

We consider the problem of estimating the correlation of two random variables X and Y, where the pairs (X, Y) are not observed together, but are instead separated co-ordinate-wise at two servers: server 1 contains all the X observations, and server 2 contains the corresponding Y observations. In this vertically distributed setting, we assume that each server has its own privacy constraints, owing to which they can only share suitably privatized statistics of their own component observations. We consider differing privacy budgets (ε1, δ1) and (ε2, δ2) for the two servers and determine the minimax optimal rates for correlation estimation allowing for both noninteractive and interactive mechanisms. We also provide correlation estimators that achieve these rates and further develop inference procedures, namely, confidence intervals, for the estimated correlations. Our results are characterized by an interesting rate in terms of the sample size n, ε1, ε2, which is strictly slower than the usual central privacy estimation rates. More interestingly, we find that the interactive mechanism is always better than its non-interactive counterpart whenever the two privacy budgets are different. Results from extensive numerical experiments support our theoretical findings.