Papers

Benchy is a semantic language and execution engine for benchmarking AI programs. A benchmark is completely specified by a program, a scoring function, and a dataset, B=(P,S,D), and is separate from the AI-system taking it; a run binds the two, R=(B,AI). Benchmarks are authored as canonical YAML in which each semantic concept has one valid syntax, classified by a shared task/domain/language ontology, and deterministically compiled into a canonical JSON intermediate representation that the engine executes. Compilation changes representation, not meaning: it does not repair invalid definitions or inject hidden defaults. Programs use fixed schemas of named input and output fields, the leaf output fields are the scoring dimensions, and the engine exposes one universal runtime contract — a named-field input object in, a named-field output object out — to which external AI-systems adapt at the boundary, so integration mechanics never propagate into benchmark semantics. This paper gives the semantic object model, the ontology and task-to-program validation rule, the scoring and failure semantics, the compilation and execution architecture, and the scope of the current language. An appendix fixes the normative engineering contract for the first engine implementation.

Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.

The purpose of this article is to explicitly describe how the integration technique known as the change of variables is used in graduate-level Probability and Statistics courses. Throughout the article, we employ this integration technique seven times across various examples and results. We demonstrate that four applications of this technique are required to derive the probability density function (PDF) of the Student's t-distribution.

Online experiments must often be evaluated before long-term outcomes mature. Under rolling enrollment, these outcomes are observed only for early enrollees, while short-term surrogates are available for everyone. We compare seven estimators across eleven data-generating processes, spanning partial mediation, drift, outcome sparsity, and enrollment-time labeling, with up to $R = 2,000$ replications over more than 500 method-by-scenario cells. We find a sharp robustness-efficiency tradeoff: the surrogate index delivers large efficiency gains when surrogacy holds but its coverage collapses under violations, while PPI-family methods stay asymptotically valid under random labeling at smaller gains. We give the finite-sample variance of PPI++ in the all-units parameterization for a fixed predictor, a joint asymptotic distribution for the two estimators under cross-fitting, and a Hausman-type estimator-disagreement diagnostic, then quantify the detection-damage gap: in the partial-mediation design, where we locate both edges, a band of violations destroys surrogate-index coverage yet is too small to detect on most datasets. On the 64,000-customer Hillstrom experiment the diagnostic rarely flags a violation that biases the surrogate index, and a Cauchy-kernel hybrid of the two estimators inherits 10.7% relative bias; on the 14-million-user Criteo experiment the violation is detected, and subsampling traces detection turning on with scale as damage persists. PPI++ has limits: at a rare-conversion $n = 30,000$ Criteo subsample its empirical coverage is 85.0%. We recommend prespecifying PPI++ with the exact variance as the primary analysis under random labeling and adequate labeled outcome counts, reading the diagnostic as a warning, not a certificate, and treating the surrogate index as a sensitivity analysis.

Breast cancer risk assessment and prediction models are very important tools for the clinical management of healthy women carrying pathogenic variants in known cancer genes. We propose in this paper a comprehensive prediction model for the personalized clinical management of women with pathogenic variants in BRCA1. This model is able to estimate the risk of BC accounting for the full history of this cancer within the family, the personal and family history of risk-reducing salpingo-oophorectomy as well as the exact age of this intervention among family members. The effect of oophorectomy on the risk of developing breast cancer is evaluated by estimating and conducting inference about the regression coefficients in a Cox model with time-varying covariates. We model the within-family dependence in the ages at onset of cancer using a Gaussian copula whose correlation matrix accommodates the different pairwise family relationships. We develop an iterative algorithm to estimate the parameters of the considered model in the presence of a selection bias. We evaluated the performance of the proposed cancer risk estimation method from family data by simulations and illustrated its use through an application to the breast cancer family registry.

The evidence behind a scientific or operational decision is often held by hospitals, banks, or registries that cannot pool individual observations. Cross-silo federated learning moves computation to the data and exchanges agreed summaries. Targeted maximum likelihood estimation (TMLE) refines a flexible initial fit, yielding plug-in estimators that respect the model and support efficient inference. TMLE itself, however, has remained a fully centralized procedure. To fill this gap, our paper introduces the first federated TMLE algorithm. We federate targeting itself, for an arbitrary target, loss, and fluctuation family, through two complementary frameworks. FedTMLE-G aggregates local gradients and reproduces centralized targeting step for step. FedTMLE-L lets each institution complete its own fluctuation fit before a single exchange of fitted updates, trading synchronized fidelity for local autonomy. For gradient aggregation, we develop a finite-precision protocol that transmits changes rather than values and certifies targeting accuracy within explicit bounds on exchanges and bits. A description-length analysis of the accepted updates then shows that this finite communication leaves numerical targeting error negligible against sampling uncertainty. The cost of computing an estimator is thus distinct from the complexity of selecting it. Our analysis also indicates that keeping data local is not itself a privacy guarantee of TMLE, since instability of full-record reconstruction need not prevent recovery of a specified sensitive attribute. For a personalized version of local averaging, institutions retain their own estimates and leave once local targeting is complete. A nonconvex convergence bound charges the improvement forfeited through averaging to disagreement among local fits and exposes a tradeoff between equal institutional influence and the sampling variability of small silos.

Uniform noise-moment bounds exclude stochastic gradients whose variability increases with the iterate. We study ordinary, single-sample stochastic gradient descent for smooth, lower-bounded, possibly nonconvex objectives under distance-dependent conditional moments. Under second moments alone, a direct descent–displacement argument yields $T^{-1/3}$ expected average squared-gradient stationarity with a horizon-dependent stepsize. An explicit oracle-complexity corollary matches the known smooth Blum–Gladyshev (BG-0) lower bound, including the $Lb_2\Delta^3\varepsilon^{-6}$ and $L\Delta\sigma^2\varepsilon^{-4}$ stochastic terms, where $\Delta$ is the initial objective gap and $\sigma^2+b_2\|x-x_1\|^2$ bounds the variance. Thus unchanged SGD attains the minimax stochastic complexity in this second-moment class. For $p>2$, predictable localization and a Hilbert-space Fuk–Nagaev inequality yield a high-probability bound separating logarithmic variance and polynomial rare-shock contributions. The localization radius is derived from the recursion: no bounded-iterate assumption, clipping, normalization, momentum, or increasing batch size is needed. We also give increasing-confidence rates, an objective-gap-growth refinement recovering root-$T$ stationarity, and stochastic $L^p$-Lipschitz examples. The broad BG-0 optimality statement is distinguished from the smaller mean-square-smooth class, in which additional oracle structure permits faster algorithms.

Sequential inference estimates latent states from noisy and incomplete observations. Particle Filters (PFs), a class of Monte Carlo methods based on importance sampling, provide a flexible framework for this task, but often suffer from poor sample efficiency and unfavorable scaling with dimension, partly due to suboptimal proposal distributions. We address these challenges by integrating learned proposals into the PF framework. We introduce Neural Optimal Particle Filters (NOPFs), which learn an amortized approximation to the optimal proposal from offline simulated one-step conditioning tuples. The learned proposal is used as a drop-in replacement in standard PF updates, with samples corrected by standard importance weights so that the method asymptotically targets the same filtering distribution under standard support and density-evaluation assumptions. Across stochastic nonlinear benchmarks of varying inference complexity, NOPFs improve sample efficiency and distributional accuracy over standard PF baselines with modest computational overhead. The approach integrates data-driven proposal learning into classical inference without altering the underlying filtering objective.

Language models often produce homogeneous responses to open-ended tasks; such homogeneity can spawn groupthink-the convergence of ideas toward a singular and potentially suboptimal decision. We formulate persona diversification as a set-level conditioning problem and study two orthogonal design choices: selecting versus generating personas, and space-filling versus frontier-seeking diversity. We instantiate this design space with four methods spanning coverage and dispersion subset selections, uniform-coverage sampling, and evolutionary persona generation. Evaluations on the Alternative Uses Task (AUT), Infinity-Chat, and Divergent Association Task (DAT) show the benefits of the proposed methods across tasks and creativity objectives. On AUT, evolutionary persona generation increases response diversity by 78.8%, originality by 26.1%, flexibility by 49.5%, and holistic creativity by 13.9% over task-only prompting, while maintaining 98.5% validity; on Infinity-Chat, it nearly doubles persona-induced response separation relative to random personas. Moreover, evolutionary personas compose with creativity-optimized prompting, further increasing its response diversity by 18.6% and creativity by 6.3%. These results establish persona-set geometry as a task-agnostic mechanism for eliciting divergent LLM outputs, and support persona diversification as a reusable complement to prompt optimization.

We here develop a functional neural network, termed MatFAE, for learning trajectories on the Riemannian manifold of symmetric positive definite (SPD) matrices. MatFAE features intrinsic layers that map manifold-valued functions to Euclidean vector-valued functions, followed by a functional layer that projects them into a finite-dimensional Euclidean space. Unlike most neural networks for discrete-time sequences, MatFAE treats each sequence as a continuous function and can therefore encode trajectory dynamics (e.g., first-order derivatives) in its latent representations. Additionally, the morphology of the functional weights in the functional layer offers interpretability by revealing the regions of the input functional data that contribute most to the latent representations. We justify the design principles and properties of each intrinsic layer and detail how matrix factorization is handled during backpropagation. We apply MatFAE to a range of fMRI datasets, demonstrating its ability to efficiently learn informative representations from high-dimensional SPD trajectories and its practical value for real-world neuroimaging analysis.

Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential. We use data-derived geometric graphs to precondition an exact subset dynamic program: as a result only connected vertex subsets are admitted as clusters, while sum-of-squared-errors (SSE) loss is unchanged. A remaining-set recurrence minimises fixed-\(K\) or penalised SSE, with exact factorisation over the connected components of each remaining set. The central question we study is how much computational support can be removed while preserving an unrestricted optimum. Graph inclusion gives monotone coverage and support relations, and a bottleneck threshold identifies the first covering graph in a nested hierarchy. For fixed \(K\) and dimension, under compact ball support and density bounds, retaining \(q=O(\log n)\) nearest neighbours per observation preserves an empirical SSE optimum with probability tending to one, using an \(O(\log n/n)\) fraction of complete-graph edges. Truncated Gaussian mixtures with unequal weights and covariances satisfy these conditions. The rate we provide is a sufficient upper bound rather than a result implying polynomial optimisation complexity. Objective-matched synthetic and full-data comparisons assess coverage, compression, and reference-label agreement. As a secondary application, we illustrate how the proposed scaffold preconditioning can be utilized to improve the efficiency of split-merge proposals that preserve unrestricted mixture posteriors.

Optimizing fMRI scan duration and spatial resolution is critical for experimental design, yet traditional correlation-based approaches cannot quantify uncertainty or disentangle scanner measurement noise from true neural variability across subjects. Without principled uncertainty bounds, researchers cannot know whether a protocol is long enough to reliably estimate connectivity, or whether between-subject differences reflect biological variation or noise. We present a Bayesian framework modeling BOLD dynamics as coupled Ornstein-Uhlenbeck processes, using Sequential Neural Posterior Estimation to obtain connectivity posteriors while accounting for frequency-independent measurement noise across the BOLD spectrum. Applied to N = 28 healthy controls (55 scans) at 7T using a functional network atlas (65 DMN regions), the framework quantifies uncertainty across its sources: scanner noise, subject variability, and acquisition length. Spatial analysis identifies a mean of 46 voxels per ROI, roughly half of typical region sizes, as sufficient to achieve 90% of asymptotic precision. At the single-subject level, 7T reaches its within-session precision plateau in approximately 7 minutes versus 10 minutes for 3T, a 40% reduction in required scan time, providing the first direct, model-based quantification of the scan-time advantage conferred by higher field strength. At the population level, 3T requires roughly 37 times more per-subject scan time than 7T for the pooled curves to converge, confirming a consistent advantage of higher field strength at every timescale. Together these findings provide concrete, scanner-specific guidance for protocol optimization, with direct implications for reducing acquisition costs and improving the reliability of connectivity-based clinical biomarkers. We provide code enabling researchers to derive these bounds from their own data.

This paper presents an end-to-end causal machine learning (ML) pipeline designed for real-world applications with continuous treatments. The proposed framework consists of six sequential steps: dimensionality reduction, causal identification, positivity assumption violation handling, estimation, refutation and evaluation, and policy optimization. We introduce practical contributions not currently available in existing causal ML toolkits, specifically: (1) a method for detecting and quantifying positivity violations in continuous treatment settings (2) a novel, scalable two-stage dimensionality reduction framework tailored for causal inference with high-dimensional data; (3) the adaptation of sensitivity analysis and estimation methods originally designed for binary treatments to the continuous treatment space and (4) an end-to-end integration of these components into a modular, reproducible workflow. These innovations address real-world challenges in causal inference that are often not covered in theoretical frameworks but frequently encountered in industrial applications. The methodology is validated with a synthetic dataset inspired in a real-world financial debt collection use case, however its design can be applied to analogous problems across different industries. Results demonstrate that the proposed methodology offers a more computationally efficient approach and produces less biased estimates compared to standard methods for problems with continuous treatment and high-dimensional data. A fully functional GitHub repository with documented code and numbered notebooks is made available ensuring reproducibility and practical implementation. The pipeline presented is intended to contribute to closing the gap between academic approaches and practical application in industry contexts where causal ML can be highly beneficial such as the financial sector.

Inspired by the problem of identifying the best model from a collection of large language models (LLMs) with heterogeneous querying costs, we formulate and analyse a variant of the multi-armed bandit (MAB) with (i) dueling feedback, where pairwise comparisons between model responses provide robust preference signals, and (ii) heterogeneous sampling costs, reflecting the differing costs of querying different LLMs. Assuming the existence of a Condorcet winner, a condition we empirically validate across multiple real-world datasets, we propose a Track-and-Stop style algorithm for best-arm identification with prescribed confidence. We prove that the algorithm almost surely achieves the asymptotically optimal cost as the error tends to zero. Finally, we extensively evaluate our approach on both synthetic and real-world instances, demonstrating consistent improvements over classical cost-unaware algorithms and their cost-aware extensions.

Self-consistency has become a popular technique for enhancing the reasoning abilities of large language models by generating multiple reasoning paths and selecting the final answer through a majority vote. However, because model providers typically charge users in proportion to the number of reasoning paths generated, they have a financial incentive to artificially increase the path count. In this work, we show that an unfaithful provider can exploit this incentive using a simple, efficient algorithm while avoiding detection by an auditor: by generating and strategically reordering additional reasoning paths, the algorithm makes every path appear necessary to reach the majority. To validate our algorithm, we conduct experiments with multiple instruct models from the Llama and Qwen families, as well as reasoning models distilled from DeepSeek-R1, on benchmark datasets spanning mathematics, science, and question answering. Our results suggest that the distribution of additional reasoning paths generated by our algorithm is heavy-tailed and that substantial capacity to overcharge remains even under the best possible audit designed to keep the false-positive rate below $\alpha = 0.1$.

Gaussian processes constitute a cornerstone of probabilistic machine learning, yet scaling them to large datasets typically forces a trade-off between computational efficiency and model fidelity. This work bridges this gap by presenting an adaptive multi-resolution Gaussian process framework that is both scalable and exact. Our key innovation is constructing a naturally data-sparse covariance matrix with adaptive multi-resolution basis functions. These basis functions are directly anchored to samples, eliminating the need for auxiliary points. By shrinking the support domains of multi-resolution basis, the matrix block sizes are limited, guaranteeing sparsity. The inverse of the data-sparse covariance matrix is computed exactly and efficiently via the sparse Cholesky inverse algorithm. To further improve predictive uncertainties, we construct an augmented basis function. Theoretical analysis and numerical experiments demonstrate that our model achieves exact inference with $\mathcal{O}(n \log^2 n)$ training cost and $\mathcal{O}(\log^d n)$ prediction cost, establishing a principled framework for scalable and high-fidelity Gaussian process regression.

iKFAD is a recently proposed optimiser that replaces adaptive learning rates with adaptive friction in the momentum dynamics, yet performs as well as Adam. Its limitation is that the full friction tensor $\xi\in\mathbb{R}^{m\times n}$ carries the same $\mathcal{O}(mn)$ memory overhead per layer as Adam's second-moment buffer. Here we replace iKFAD's friction tensor $\xi$ with a rank-1 outer-product factorisation built from row and column momentum statistics, resulting in Rank-1 iKFAD (R-iKFAD). This reduces the friction memory footprint from $\mathcal{O}(mn)$ to $\mathcal{O}(m+n)$ per layer, which approximately halves iKFAD's total optimiser state. Despite this reduction, R-iKFAD maintains parity in performance with iKFAD: experiments on GPT2-Nano, TinyViT, DistilBERT and GPT2-S confirm that it matches or exceeds iKFAD while nearly halving the memory footprint and remaining comparably robust to hyperparameters. We analyse the continuous-time dynamics in two damping regimes. For linear damping ($\gamma>0$) we prove exponential convergence under strong convexity. For $\gamma=0$, the preferred option in our experiments, the friction is generated entirely from past momentum and switches off as the momentum vanishes, so geometric convergence cannot be shown. We nonetheless prove convergence to the minimiser, together with matching upper and lower bounds on the energy: of order $t^{-1}$ when the regularisation scale $\epsilon_{\mathrm{stab}}$ is zero, and of order $t^{-1/2}$ when it is positive. To our knowledge this is the first convergence rate for a rank-1 factored optimiser in continuous time, and the first such result that does not require positive damping.

We investigate the least squares linear regression problem with random partial Discrete Fourier Transform (DFT) matrices, providing a rigorous analysis of the model's generalization error. By leveraging tools from random matrix theory, we derive exact non-asymptotic bounds for the risk of the Moore-Penrose estimator, which hold for finite-dimensional problems and reveal the precise dependence on key parameters such as the sample size, dimension, and noise variance. Then we obtain a characterization of the double descent phenomenon in the linear regression context, demonstrating how the risk evolves when the number of parameters $p$ and the number of samples $n$ tend to infinity, with $p/n$ fixed. The analysis relies on applications of the Stieltjes transform for random Fourier matrices, enabling a precise description of the spectral properties of these matrices and their impact on regression performance. To validate our theoretical findings, we present several numerical examples that illustrate the double descent curves. These simulations align closely with our derived bounds, confirming their predictive power in both under-parameterized and over-parameterized regimes.

Many multivariate extremes models have intractable likelihoods requiring practitioners to use alternative fitting methods. The tail pairwise dependence is a summary measure of the dependence in the tail of any multivariate regular variation model. We develop an objective function for model fitting that relies on the tail pairwise dependence as the link between our desired model (that does not have a likelihood) and a proxy model (that has a likelihood). We employ the bivariate Hüsler-Reiss distribution as the proxy model and show that there is a one-to-one relationship between the dependence parameter and the tail pairwise dependence value. Our proxy-likelihood estimator is fully developed for the transformed linear extremes time series (TLETS) models of Mhatre and Cooley (2024) and is applied to the wildfire weather data of Wixson and Cooley (2023). Simulations demonstrate that the proxy-likelihood is a competitive TPD estimator, is better at fitting TLETS models than existing methods, and is amenable to likelihood-based model selection techniques. Our estimator has smaller bias when tail dependence is weak than existing estimators reducing the need for bias adjustments. Without these adjustments, we note an increase in the tail dependence in weather-related wildfire risk between past and present climates.

This paper investigates the numerical resolution of the Beurling-LASSO (BLASSO), a convex optimization framework that promotes sparsity in the space of measures. We consider its application to the estimation of Gaussian mixture models (GMMs) with an unknown number of components and unknown diagonal covariance matrices. Our approach combines the Conic Particle Gradient Descent (CPGD) principle with Riemannian gradient descent, to account for the underlying Fisher-Rao geometry of Gaussian distributions. Our contributions are twofold. First, we provide theoretical guarantees for the convergence of our algorithm. In particular, we establish exponential local convergence under a non-degeneracy condition on the solution and relate this assumption to a separation condition on the underlying statistical target. Second, we address practical implementation aspects of CPGD and present numerical experiments illustrating its performance. On the test cases considered, these experiments suggest that CPGD is more robust to overspecification of the number of components than the EM algorithm. We also investigate the impact of component separation on recovery accuracy.

We study the deterministic oracle complexity of finding approximate solutions to composite monotone inclusion problems, formed by the sum of a smooth single-valued monotone operator and a maximally monotone set-valued operator, under the tangent-residual criterion. We introduce the Anchored Extra-Proximal (AEP) framework, which combines an anchored extrapolation step with an inexact anchored proximal update satisfying a relative-error condition. The framework recovers the composite Fast Extragradient method in the first-order setting and yields natural second- and higher-order extensions by replacing the operator in the implicit update with its Taylor approximation at the extrapolated point. For every $p\geq 2$, assuming that the $(p-1)$th derivative of the single-valued operator is Lipschitz continuous, we combine this construction with a bisection line search to obtain a $p$th-order method that finds a point with tangent residual at most $\varepsilon$ in $\widetilde{O}(\varepsilon^{-2/(3p-1)})$ oracle calls. This improves all prior upper bounds for $p$th-order methods: in particular, it improves the previous best-known $\widetilde{O}(\varepsilon^{-1/p})$ tangent-residual complexity as well as the classical $O(\varepsilon^{-2/(p+1)})$ bound of higher-order hybrid proximal extragradient methods under the weaker duality-gap criterion. We complement this result with a worst-case lower bound of $\Omega(\varepsilon^{-2/(3p-1)})$ for every deterministic algorithm in the $p$th-order oracle model, without restricting the algorithm to tensor steps or any other prescribed update structure. Thus, the proposed method attains the optimal dependence on $\varepsilon$, up to logarithmic factors, for all $p\geq2$.

Phase I cancer trials seek the maximum tolerated dose (MTD) while protecting patients from excessive toxicity. Dose assignments must therefore balance patient safety with learning the dose–toxicity relationship as data accrue. We model continuously measured toxicity outcomes using two forms of Bayesian additive regression trees (BART): isotonic BART projects posterior response curves onto nondecreasing functions, whereas monotone BART constrains the model. Joint curve and variance draws induce an MTD posterior that guides dose selection through escalation with overdose control (EWOC). We compare these methods with three parametric procedures across seven dose–toxicity curves in simulation. We assess dose-limiting toxicity (DLT) counts, above-MTD assignments, signed last-dose error, and relative absolute error. The tree procedures attained the lowest mean RAE on four nonlinear curves and jointly minimized mean DLT counts and above-MTD assignments on four curves. A Bayesian reinforcement learning perspective formulates these sequential decisions as a finite-horizon planning problem. Dose restrictions yield a lower bound on last-dose error; under exact posterior-predictive evaluation, an EWOC-based rollout policy has no greater expected weighted loss than its baseline. Dose Trial Lab, a desktop simulator for all five procedures, accompanies the supplementary material.

Questionnaire-based patient-reported outcomes (PROs) are discrete, bounded and overdispersed, yet joint models relating them to survival may ignore these features or estimate both processes sequentially. We propose a Bayesian joint model combining a beta-binomial mixed-effects submodel with a Weibull proportional hazards submodel, linked through the subject-specific response probability. Simulations show that simultaneous estimation reduces bias in the longitudinal slope and yields practically unbiased association estimates, unlike two-stage estimation. In a cohort of 543 patients with chronic obstructive pulmonary disease, the model identified associations for all eight SF-36 dimensions and for two of three SGRQ dimensions, including several associations not detected by the two-stage approach, and provided dynamic survival predictions.

A learner's current observations need not determine its response to further training. We formulate intrinsic-extrinsic coupling through the continuation-conditioned value of a constrained learning-state intervention, with observation-relative fibers describing present agreement. An executable finite-frame classifier-head write protects current logits while repairing specified historical margins under finite-precision acceptance checks. We distinguish local admissibility, continuation-conditioned intervention value, and complete-policy performance. A matched four-cell contrast identifies readout-specific non-additivity between the same intrinsic intervention and alternative external continuations. In a CLINC-derived class-incremental setting, replay changes the write's 32-update contribution from five correct predictions to zero. Nonzero interactions also occur under output distillation, with a RoBERTa backbone, and under optimizer-native SGDW dynamics. Under SGDW, correct-count interactions are negative in all three activated roots at 128 updates, showing that coupling need not imply positive synergy. The mathematical analysis distinguishes feasible local repairs and favorable terminal outputs from training-reachable repair regions. Separate coordination tests show that content controls match or exceed the development gain, while a five-root fresh-test comparison with Fiber present in every arm shows root-dependent rather than uniformly beneficial correct-count effects. On the secondary cross-entropy readout, guided allocation yields lower mean loss than standard replay in all five pairs. Together, these results make intrinsic-extrinsic coupling operational by connecting executable state geometry to continuation-conditioned value, matched interaction identification, and closed-loop coordination, while separating identified coupling from complete-policy performance.

Variable selection using information criteria has an explicit statistical target but requires discrete search over candidate models. The smooth information criterion (SIC) replaces the discontinuous model-dimension term by a differentiable approximation, with an $\epsilon$-telescoping continuation strategy progressively sharpening this approximation without data-driven selection of a regularisation-strength parameter. We develop SIC as a general procedure for coefficient-level variable selection in generalised linear models (GLMs) and use it to address a central question: how faithfully does smooth optimisation reproduce the corresponding discrete information-criterion selection problem? Focusing on BIC, we benchmark SIC directly against exhaustive subset selection where feasible, using exact support agreement, BIC difference and selection behaviour across a varying signal-strength boundary. Simulations in Gaussian, binomial and Poisson regression show that SIC closely reproduces exhaustive BIC selection and tracks the exact BIC selection boundary. Relative to stepwise BIC, LASSO, SCAD and MCP, SIC produces competitive variable-selection performance while retaining sparse models, with predictive performance broadly comparable across methods. Computational advantages over stepwise BIC increase with predictor dimension. In a real-data application with 16 candidate predictors, SIC recovers the globally BIC-optimal model among all 65,536 supports at a small fraction of the computational cost of exhaustive enumeration.

Audio language models pass speech and text through a single decoder. We ask whether that decoder represents a distinctive feature in the same direction when a phoneme is heard and when it is read. For minimal pairs of phonemes differing in one feature, we take the offset between the two members' mean representations. Averaging those offsets gives a direction for each stream, and we measure the cosine between the two. Because the two streams already agree about arbitrary phoneme pairs, we compare every measure against a reference built from random pairings rather than against zero. We apply this to 6 models, 7 features and 15 languages from 11 families. Only voicing in the two Qwen2.5-Omni models exceeds that reference after correction for multiple testing, and the reference varies by a factor of seven between models. In three of the six models, voicing has one direction in audio across the 14 languages with enough minimal pairs to measure it, and every language pair agrees in two of them. The model family, not the model size, predicts which stream represents a feature.

This paper introduces a novel semiparametric testing framework for localized point-impact effects within a spatial semi-functional linear regression model. We address an intricate inferential problem that simultaneously accommodates three distinct sources of complexity: an infinite-dimensional global functional slope, an unknown smooth spatial nuisance surface, and data-dependent, unobserved impact locations. To isolate the point-impact coefficients, we construct a robust residualized cross-moment estimator after regularizing the functional component via Tikhonov inverse and estimating the spatial nuisance surface through local-linear smoothing. We establish a multivariate central limit theorem under the null hypothesis of no point-impact effect. We develop two operational test statistics: a general formulation whitened by the long-run covariance matrix to handle arbitrary spatial dependence, and a simpler chi-square calibration valid under short-range spatial dependencies in regression errors. Rigorous finite-sample simulations and an application to Canadian weather data demonstrate the superior power and size control of our methodology.

Statistical model transformations based on randomly stopped sums, maxima and minima are widely used to extend statistical models. We characterize the complete set of stopping models for which randomly stopped sum and extreme model transformations function as statistically stable (idempotent) model extensions. Stability requires the underlying stopping model to be closed under pgf composition. We prove that any finite-dimensional, connected stopping model closed under pgf composition is necessarily a family of random variables whose pgfs commute. Using the corresponding Koenigs function, we establish that these models form a statistical manifold admitting a global, one-dimensional parametrization $\theta = \Pr(N=1) \in (0, \theta_*]$, where the probability mass at $i$ is a polynomial in $\theta$ of degree at most $i$. Finally, we establish a duality between stopping models closed and containing the identity variable (the ones yielding stable extensions) and the set of probability distributions supported on the positive integers. These findings disprove the long standing conjecture that statistical stability occurs only under geometric stopping.

Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the problem using regularized least squares, often with the nuclear norm as a regularizer, but this method yields a point estimate with no built-in uncertainty quantification. A Bayesian formulation is a natural alternative, and if the noise variance is known, the nuclear norm-based prior yields a log-concave posterior. Unfortunately, in practice, the noise variance will not be known a priori, so for a fully Bayesian approach, a prior must be imposed on it. We give the first sampler for this model with an explicit non-asymptotic guarantee: polynomial in the matrix dimensions and in the reciprocal of the target accuracy. Our technique is to discretize the distribution of the noise precision onto a grid and build a categorical posterior via thermodynamic integration. This extension is not specific to matrix completion and may be useful in other non-log-concave sampling problems where the non-log-concavity is restricted to a single variable and the joint distribution of the remaining variables is nonsmooth. Our contribution is a feasibility result: we show that a polynomial-time Bayesian sampler for this model exists at all, and the resulting complexity, while polynomial, is not intended as a deployable algorithm at current problem scales.

Early-phase dose-finding methods increasingly assess toxicity and efficacy jointly, but comparisons based only on administered dose may inadequately characterize regimens differing in schedule. We developed a Bayesian phase II adaptive platform design for regimen optimization that integrates pharmacokinetic/pharmacodynamic (PK/PD) modelling into toxicity, efficacy, regimen selection and adaptation decisions. The proposed PK/PD-informed Regimen Optimization Platform (PROP) design uses a population PK/PD model to generate patient- and population-level predictions of exposure and biological activity. Acute and cumulative toxicities are analysed using a discrete-time time-to-event model informed by PK exposure. Efficacy is evaluated through Bayesian model averaging of exposure-driven and biomarker-driven time-to-event models. The design supports regimen graduation, discontinuation for futility or safety, and addition of unexplored regimens. Performance was evaluated through simulations motivated by an influenza intensive-care setting. Across six scenarios, PROP generally improved graduation and futility decisions, reduced inappropriate graduation, and supported the addition of promising regimens compared with dose-based alternatives. It also more accurately estimated regimen-specific toxicity and arm-specific efficacy, while the model-averaging framework favored the efficacy model consistent with the data-generating mechanism. Dose-based approaches performed better for safety stopping in some scenarios, despite less accurate characterization of the regimen–toxicity relationship. PK/PD-informed platform designs can improve adaptive regimen selection and knowledge generation when dose alone cannot adequately characterize treatment regimens.