Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear function of observed covariates and a latent group-specific random effect. Since exact marginalization over the random effects is typically intractable, model parameters are estimated by maximizing an approximate marginal likelihood. In this paper, we replace the linear function with neural networks. The result is a more flexible model, the neural generalized mixed-effects model (NGMM), which captures complex relationships between covariates and responses. To fit NGMM to data, we introduce an efficient optimization procedure that maximizes the approximate marginal likelihood and is differentiable with respect to network parameters. We show that the approximation error of our objective decays at a Gaussian-tail rate in a user-chosen parameter. On synthetic data, NGMM improves over GLMMs when covariate-response relationships are nonlinear, and on real-world datasets it outperforms prior methods. Finally, we analyze a large dataset of student proficiency to demonstrate how NGMM can be extended to more complex latent-variable models.

Education is on the verge of becoming fully automated. William Liu is grateful that he finished high school when he did. If the latest AI tools had been around then, he told me, he might have been tempted to use them to do his homework. Liu, now a sophomore at Stanford, finished high school all the way back in 2024. "I have a younger sibling who is just graduating high school," he said.

Machine learning competitions (MLCs) play a pivotal role in advancing artificial intelligence (AI) by fostering innovation, skill development, and practical problem-solving. This study provides a comprehensive analysis of major competition platforms such as Kaggle and Zindi, examining their workflows, evaluation methodologies, and reward structures. It further assesses competition quality, participant expertise, and global reach, with particular attention to demographic trends among top-performing competitors. By exploring the motivations of competition hosts, this paper underscores the significant role of MLCs in shaping AI development, promoting collaboration, and driving impactful technological progress. Furthermore, by combining literature synthesis with platform-level data analysis and practitioner insights a comprehensive understanding of the MLC ecosystem is provided. Moreover, the paper demonstrates that MLCs function at the intersection of academic research and industrial application, fostering the exchange of knowledge, data, and practical methodologies across domains. Their strong ties to open-source communities further promote collaboration, reproducibility, and continuous innovation within the broader ML ecosystem. By shaping research priorities, informing industry standards, and enabling large-scale crowdsourced problem-solving, these competitions play a key role in the ongoing evolution of AI. The study provides insights relevant to researchers, practitioners, and competition organizers, and includes an examination of the future trajectory and sustained influence of MLCs on AI development.

Miniature people have been a staple of science fiction and fantasy going all the way back to Jonathan Swift's, and shrunken characters have taken the spotlight in everything from classic Hollywood movies like and to family-friendly blockbusters like and . References to these movies and others are strewn throughout the new Peacock limited series, but the drawn-out, 10-episode show isn't a particularly worthwhile addition to the sci-fi shrinking canon. Taking only the title and basic premise from Manuel Gonzales's 2014 short story, stars Elizabeth Banks as Lindy Littlejohn, a once-prominent author who now works as a university professor and has been overshadowed by her scientist husband Les (Matthew Macfadyen). Lindy, you see, feels metaphorically small in both her personal and professional lives, and is about to become literally small following an accident - or it? The most pressing problem for Lindy is that Les has yet to develop a stable antidote to his formula, and everything that he has attempted to return to its original size thus far has almost immediately exploded.

Dr. David Blackwell was a mathematician and statistician of the first rank, whose contributions to statistical theory, game theory, and decision theory predated many of the algorithmic breakthroughs that define modern artificial intelligence. This survey examines three of his most consequential theoretical results the Rao Blackwell theorem, the Blackwell Approachability theorem, and the Blackwell Informativeness theorem (comparison of experiments) and traces their direct influence on contemporary AI and machine learning. We show that these results, developed primarily in the 1940s and 1950s, remain technically live across modern subfields including Markov Chain Monte Carlo inference, autonomous mobile robot navigation (SLAM), generative model training, no-regret online learning, reinforcement learning from human feedback (RLHF), large language model alignment, and information design. NVIDIAs 2024 decision to name their flagship GPU architecture (Blackwell) provides vivid testament to his enduring relevance. We also document an emerging frontier: explicit Rao Blackwellized variance reduction in LLM RLHF pipelines, recently proposed but not yet standard practice. Together, Blackwell theorems form a unified framework addressing information compression, sequential decision making under uncertainty, and the comparison of information sources precisely the problems at the core of modern AI.

John Pendry is known for creating an invisibility cloak. John Pendry's kitchen is dominated by a huge photograph of what looks like the view through a kaleidoscope: dizzying shards of purple, green, yellow and white. Given that Pendry is famous above all else for inventing an invisibility cloak - a device that can bend light around objects - I wonder if I am looking at something related to that. But no, he tells me, the image simply shows crystals of vitamin C magnified many times. All that invisibility-cloak stuff is in the past, he says, and he has moved on to "more exciting things".

We introduce the Hiremath Early Detection (HED) Score, a principled, measure-theoretic evaluation criterion for quantifying the time-value of information in systems operating over non-stationary stochastic processes subject to abrupt regime transitions. Existing evaluation paradigms, chiefly the ROC/AUC framework and its downstream variants, are temporally agnostic: they assign identical credit to a detection at t + 1 and a detection at t + tau for arbitrarily large tau. This indifference to latency is a fundamental inadequacy in time-critical domains including cyber-physical security, algorithmic surveillance, and epidemiological monitoring. The HED Score resolves this by integrating a baseline-neutral, exponentially decaying kernel over the posterior probability stream of a target regime, beginning precisely at the onset of the regime shift. The resulting scalar simultaneously encodes detection acuity, temporal lead, and pre-transition calibration quality. We prove that the HED Score satisfies three axiomatic requirements: (A1) Temporal Monotonicity, (A2) Invariance to Pre-Attack Bias, and (A3) Sensitivity Decomposability. We further demonstrate that the HED Score admits a natural parametric family indexed by the Hiremath Decay Constant (lambda_H), whose domain-specific calibration constitutes the Hiremath Standard Table. As an empirical vehicle, we present PARD-SSM (Probabilistic Anomaly and Regime Detection via Switching State-Space Models), which couples fractional Stochastic Differential Equations (fSDEs) with a Switching Linear Dynamical System (S-LDS) inference backend. On the NSL-KDD benchmark, PARD-SSM achieves a HED Score of 0.0643, representing a 388.8 percent improvement over a Random Forest baseline (0.0132), with statistical significance confirmed via block-bootstrap resampling (p < 0.001). We propose the HED Score as the successor evaluation standard to ROC/AUC.

Despite the sustained popularity of Q-learning as a practical tool for policy determination, a majority of relevant theoretical literature deals with either constant ($η_{t}\equiv η$) or polynomially decaying ($η_{t} = ηt^{-α}$) learning schedules. However, it is well known that these choices suffer from either persistent bias or prohibitively slow convergence. In contrast, the recently proposed linear decay to zero (\texttt{LD2Z}: $η_{t,n}=η(1-t/n)$) schedule has shown appreciable empirical performance, but its theoretical and statistical properties remain largely unexplored, especially in the Q-learning setting. We address this gap in the literature by first considering a general class of power-law decay to zero (\texttt{PD2Z}-$ν$: $η_{t,n}=η(1-t/n)^ν$). Proceeding step-by-step, we present a sharp non-asymptotic error bound for Q-learning with \texttt{PD2Z}-$ν$ schedule, which then is used to derive a central limit theory for a new \textit{tail} Polyak-Ruppert averaging estimator. Finally, we also provide a novel time-uniform Gaussian approximation (also known as \textit{strong invariance principle}) for the partial sum process of Q-learning iterates, which facilitates bootstrap-based inference. All our theoretical results are complemented by extensive numerical experiments. Beyond being new theoretical and statistical contributions to the Q-learning literature, our results definitively establish that \texttt{LD2Z} and in general \texttt{PD2Z}-$ν$ achieve a best-of-both-worlds property: they inherit the rapid decay from initialization (characteristic of constant step-sizes) while retaining the asymptotic convergence guarantees (characteristic of polynomially decaying schedules). This dual advantage explains the empirical success of \texttt{LD2Z} while providing practical guidelines for inference through our results.

This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples $M$ diverge at fixed ratio $α= M/N$, and for finite hidden widths $(p,p^*)$ of the student and teacher, respectively, we study the low-dimensional ordinary differential equations that govern the evolution of the student--teacher and student--student overlap matrices. We show that overparameterization ($p>p^*$) only modestly accelerates escape from a plateau of poor generalization by modifying the prefactor of the exponential decay of the loss. We then examine how unconstrained weight norms introduce a continuous rotational symmetry that results in a nontrivial manifold of zero-loss solutions for $p>1$. From this manifold the dynamics consistently selects the closest solution to the random initialization, as enforced by a conserved quantity in the ODEs governing the evolution of the overlaps. Finally, a Hessian analysis of the population-loss landscape confirms that the plateau and the solution manifold correspond to saddles with at least one negative eigenvalue and to marginal minima in the population-loss geometry, respectively.