Papers

In safe hypothesis testing with test supermartingales, Ville's inequality provides anytime-valid type-I error guarantees for every significance level $\alpha\in(0,1]$, if one rejects the null hypothesis whenever the wealth process first exceeds $1/\alpha$. Due to an inherent asymmetry, the type-II error behaves differently. We prove two things about the latter, for a simple null and alternative. First, the mean growth rate $\mathbb{E}_{P_1}[\log E]$, the e-power, that Kelly betting and growth-rate-optimal e-variables maximise, bounds nothing on its own. For every level $c>0$, every $\alpha$ and horizon $t$ we construct e-variables of conditional e-power exactly $c$ whose probability of not rejecting by $t$ is arbitrarily close to one. It forces eventual rejection, but no finite-horizon guarantee follows. Second, the quantity that does control the type-II error is the Chernoff-Stein exponent of an e-variable, $\Lambda(E)=\sup_{s\ge0}\{-\log \mathbb{E}_{P_1}[E^{-s}]\}$, whose range is exactly determined: $\sup_E \Lambda(E)=\mathrm{KL}(P_0\|P_1)$, the classical Chernoff-Stein exponent, and so the ceiling of its own per-e-variable form. One conditional application of Hoelder's inequality per step gives it, for every test supermartingale on an arbitrary filtered space, with no independence or product structure; the i.i.d. case adds that it is matched, and attained by nothing. The e-power has its own ceiling, $\mathrm{KL}(P_1\|P_0)$, and that one is attained, $P_0$-a.s. uniquely, by the likelihood ratio $R$. The two optima are the same divergence in opposite arguments, at opposite ends of the flattened family $R^{\beta}/\mathbb{E}_{P_0}[R^{\beta}]$: the ceiling as $\beta\downarrow0$, $R$ at $\beta=1$. Which $\beta$ is best is settled by the horizon, exactly: $R$ is optimal at $t=\log(1/\alpha)/\mathrm{KL}(P_1\|P_0)$ alone, beaten by sharpening $(\beta>1)$ below it and by flattening above.

Diagnostic medical tests and devices provide useful information for evaluating the potential benefits and risks of therapeutic treatments. However, unlike treatments, their impact on health outcomes is generally indirect because measuring diagnostic information typically does not itself affect patient outcomes, which complicates evaluation of their effectiveness. In this work, we develop a causal inference approach for evaluating diagnostic tests by distinguishing explanatory and pragmatic effectiveness. Explanatory effectiveness evaluates whether a diagnostic test result provides treatment-relevant information beyond baseline covariates by explaining additional treatment-effect heterogeneity, which we characterize using a variance-based treatment-effect variable importance measure. Pragmatic effectiveness evaluates whether incorporating this information into personalized treatment decisions improves expected outcomes, a question central to decision-making for patients, clinicians, and other health care stakeholders. We formalize pragmatic effectiveness as a contrast between expected outcomes under optimal personalized treatment rules defined with and without access to the diagnostic test result. We establish identification of the proposed estimand and provide Targeted Maximum Likelihood Estimation (TMLE) and cross-validated TMLE procedures for nonparametric estimation and inference. Simulation studies and a synthetic colorectal cancer application illustrate the proposed estimands and estimation performance. More broadly, this approach provides a causal inference perspective for evaluating AI-enabled devices by distinguishing their dual roles as information-enrichment and personalized decision-optimization tools, clarifying whether AI improves outcomes by expanding information for downstream decisions, improving the decision rule used to act on that information, or through both pathways.

Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate. However, the inputs a deep network sees during training can be highly anisotropic, with a few directions queried frequently while most are seen rarely. Preconditioning methods address this anisotropy by wrapping extra processing around this buffer and leave the momentum update itself unchanged. We propose Activation-Keyed Momentum (AK-Momentum), which builds direction-awareness into the momentum update rule. The gradient of a linear layer splits into an input activation that acts as a key and an output-side error that acts as a value. Keying on that activation, AK-Momentum updates the momentum buffer by the canonical delta rule, so each direction is forgotten at a rate set by how often it appears. We prove that it is a valid momentum, that it applies the input-side curvature correction without matrix inversion, and that it clears stale directions faster than EMA under both a fixed and a drifting optimum. It is a drop-in replacement for the momentum buffer of any optimizer, its coefficient transfers across widths under $\mu$P, and its extra compute stays between $22.2\%$ and $25.0\%$ of a gated-MLP block's linear cost with no persistent memory. In FineWeb-Edu pretraining, AdamW with AK-Momentum (AK-AdamW) reaches AdamW's validation loss in up to $46.39 \pm 4.32\%$ fewer steps at 67M and $22.12 \pm 0.80\%$ at 370M over three seeds, and the gain persists at 1B on a Chinchilla-optimal budget. A Muon baseline tuned under the same protocol sits above AK-AdamW at both language-model scales, and the gain holds for SGD, ResNet-18, and ViT-Tiny on CIFAR-10. Training-time diagnostics confirm the predicted mechanism, better gradient tracking and healthier input directions.

Average dose-response functions are widely used to summarize causal effects of continuous treatments, but most existing methods assume that the observed sample represents the target population. We study a covariate-shift setting in which covariates, treatment, and outcome are observed in a labelled source sample, while only covariates are observed in the target sample. We develop a two-sample local polynomial regression framework based on pseudo-outcomes that use source outcomes to address confounding and target covariates to define the population of interest. We further propose a source-to-target extension of distance covariance optimal weighting (DCOW), designed to remove treatment-covariate dependence in the source sample while aligning the weighted source covariate distribution with the target population. A central theoretical contribution is a weight-level analysis of this optimization-based procedure: we show that the population criterion identifies the oracle source-to-target weights and that approximate empirical minimizers, including exact minimizers as a special case, converge uniformly to these weights under regularity conditions. We also establish consistency and asymptotic normality of the resulting estimator. Simulations show that the proposed method improves target dose-response estimation relative to DCOW, generalized-propensity-score weighting, entropy balancing, and unweighted alternatives. We illustrate the method in a county-level analysis of PM2.5 exposure and subsequent heart-disease mortality using a source-target validation design.

Uncertainty quantification (UQ) is essential for the safe deployment of large language models (LLMs). Existing methods, from verbalized confidence to ones requiring multiple generations, are often zero-shot and produce scores quantifying uncertainty without the need for labelled data. Nonetheless, in practice one must always evaluate their performance on a dataset of interest before deployment. In this work we show that, by leveraging this dataset, we consistently outperform these existing scores. Specifically, we build simple classifiers that predict LLM response correctness by using these scores and the correctness of similar queries as features. Our method produces minimal computational overhead, making it a cheap and straightforward enhancement for UQ in LLMs for real-world applications.

Given a set of input states, we consider the task of predicting the expectation value of a Pauli observable at the output of an unknown quantum evolution, using only a limited number of measurements. Recently, quantum Gaussian process (QGP) regression was introduced for this task across various classes of unitary evolution. Here, we extend the QGP framework beyond unitary dynamics. In particular, we prove convergence of the channel's outputs to a QGP and derive the associated closed-form kernel under a uniform (Lebesgue measure) prior over quantum channels. The kernel's dimensional factor, however, dictates the required observation precision. While manageable when the channel and observable are restricted to small subsystems, exponential suppression precludes learning when the subsystem grows extensively with the system size. Since the Lebesgue prior is overly broad for many applications, we propose an empirical Bayes heuristic that replaces the dimensional factor with a learnable scale parameter while retaining the kernel's state-overlap correlation structure. In numerical simulations of up to 64 qubits, channel QGP regression with the Lebesgue kernel exhibits a strong inductive bias for local channels, enabling faithful extrapolation. For global 64-qubit channels, the rescaled kernel restores learnability, with predictions improving systematically with the shot budget. Results from a noisy quantum computer further demonstrate the robustness of QGP regression under experimental conditions. Beyond regression, we validate QGPs as Bayesian-optimization surrogates for state preparation under noisy XXZ dynamics.

We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence of the memory of the Hawkes intensity, this problem does not fall within classical stochastic control theory outside particular Markovian kernels. We first develop a finite-dimensional Markovianization procedure and algorithm to approximate multivariate Hawkes processes with mixtures of exponential kernels. We prove the convergence of the Markovianized approximation of the Hawkes process, its intensity, and the value of the problem to the original non-Markovian processes and the value of the primal problem. We then formulate continuous-time deterministic policy gradient learning on the Markovianized approximation of the problem, called Hawkes-CT DDPG. We propose a model-free algorithm to solve the non-Markovian Hawkes-driven optimization by observing only the event times of the process, the realization of the solution to the SDE, and a chosen set of decay filters, while the Hawkes kernel coefficients remain unknown. We compare our continuous time reinforcement learning Hawkes-CT DDPG method with discrete time reinforcement learning techniques under three different types of kernels: simple exponential, Erlang, and power-law kernels.

We present a new data-driven learning of a Random Geometric Graph (RGG) of a multivariate dataset, where the graph is drawn in a probabilistic metric space. This graph learning works for generic datasets, irrespective of the type of the observables; their probability distributions; or size of the data. We identify a metric of the space that the graph is drawn in, as a probability distribution of a random variable that we introduce, namely, a variable that represents the disparity between the connectedness of two vertices of the graph, and the correlation between the two random variables that are attached to the respective vertex. It is the closed-form {\it{cdf}} of this disparity variable that we advance as the distance function of the host space of the learnt RGG, such that the edge exists between any two nodes, if this inter-nodal distance falls short of a chosen cutoff probability. Drawing the RGG in this probabilistic space leads to the graph being an Soft RGG, such that any edge - if it exists - exists with an identified probability. We forward a simple Rejection Sampling-based technique for learning the probability of any edge. The expected degree distribution of a vertex of this RGG is identified as local, and dependent on the inter-observable correlation matrix. If said correlation matrix is not known, it can be learnt given the data, using its closed-form posterior probability density function, that we forward. We illustrate our graph learning method by learning multiple RGGs of highly multivariate real datasets.

An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity—a confidence level fixes the radius of a relative-entropy ball of alternative models—but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.

This paper investigates the estimation of the regression operator in function-on-function regression models. While traditional research has predominantly focused on linear models or their immediate nonlinear extensions, we propose a neural operator approach to accommodate general regression operators under mild smoothness assumptions. Operator learning has emerged as an active area of machine learning, particularly for solving physical models governed by partial differential equations. Using this paradigm, our methodology introduces the separable neural operator, a neural-operator architecture that represents the regression operator through input-dependent coefficient functions and output-dependent basis functions. Beyond adapting this architecture to the regression operator estimation problem, we establish the consistency of the estimator under relatively mild smoothness and sampling conditions, allowing functional data to be observed on dense, possibly irregular, discrete grids. We also apply the proposed approach to the BGC Argo data and demonstrate its potential for oceanographic research.

The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising. We bring these two areas together by studying the adaptivity of diffusion models to the structured geometry of multimodal high-dimensional data that consists of multiple clusters in $\mathbb{R}^D$, each with its own low-dimensional structure, and inter-cluster separation depending on $D$. We employ $K$-mixture Gaussian distributions as a canonical framework to capture this geometry and establish two theoretical results. First, we interpret denoising as a dynamical Bayesian classifier: the mixture score is a posterior-weighted average of cluster-wise scores, and we show that, with high probability, the posterior class probabilities concentrate on a single cluster once the signal-to-noise ratio reaches the scale $\Theta (\log (KD)/D)$. Second, by separately analysing the denoising process in its mixing and cluster-commitment phases, we prove that the KL error bound depends linearly on the maximum intrinsic dimension of a cluster, up to a logarithmic factor, even when $K$ grows polynomially with $D$. This improves on ambient-dimensional bounds and extends existing low-dimensional adaptivity analyses to multimodal distributions with heterogeneous, approximately low-rank covariances.

Despite the wide variety of existing Buy-`Til-You-Die (BTYD) models, nearly all rely upon the convenient assumption of transactions following a Poisson process. As modern customer bases grow larger and more diverse, a major gap in the marketing literature is BTYD models that can account for heterogeneity in timing patterns across millions of customers. This paper addresses that gap, introducing a family of models that assume transactions follow a Weibull renewal process and developing a highly scalable scheme for parameter estimation based on an amortized variational inference procedure. The proposed model fits to a proprietary dataset of 5 million online retail customers in 8 minutes which would take the current state-of-the-art an estimated 3-4 days. We show both theoretically and empirically that this dramatic improvement in computational performance comes with no appreciable change to either model interpretation or predictive performance. Beyond scalability, gradient-based variational inference also makes it easy to extend the model to covariates, which we illustrate on a public dataset of 4 million political donors during the 2020 US General election cycle. More generally, this paper demonstrates how to blend recent advances in approximate Bayesian inference and the tools of modern machine learning to dramatically improve the efficiency and expressivity of probabilistic models for customer base analysis.

We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model. Existing GP-UCB analyses in this setting typically require the exploration parameter to grow with the horizon to maintain uniform confidence bounds. Using per-round local confidence events, we show that GP-UCB can instead be run with a constant exploration parameter and obtain an expected-regret bound whose coefficient depends on the drift rate. We also derive a sharper time-varying maximum-information-gain bound. For the squared exponential kernel, it yields $\tilde\gamma_T/T=\widetilde{\mathcal O}(\epsilon^{1/2})$ and expected average regret $\widetilde{\mathcal O}(\epsilon^{1/4})$ in the persistent-drift regime. The same constant-exploration analysis also yields realized-regret guarantees. Simulations support the predicted logarithmic dependence of the bound-suggested exploration parameter on $1/\epsilon$.

Tabular foundation models (TFMs) achieve strong performance through in-context learning, but context-dependent inference imposes substantial latency and memory costs, hindering large-scale deployment. We propose GEAR (Generative Expansion and Real Anchoring), a modular two-stage framework that distills TFMs into lightweight MLP or tree-based predictors that can be deployed on commodity CPUs. Stage 1 uses synthetic covariates solely as teacher-query locations and trains the student on soft TFM targets, expanding coverage beyond observed rows. Stage 2 re-anchors the student to the target distribution using real labels and out-of-fold teacher predictions, whitch avoids self-labeling leakage. We further derive a risk certificate characterizing the trade-off between generated-query volume and generator fidelity. Experiments on TALENT and TabArena demonstrate the broad applicability of GEAR. Two-stage MLPs outperform supervised MLPs by 1.81–2.00 AUC points on binary tasks and 1.19–1.35 points on multiclass tasks, with additional gains over real-data-only distillation of 1.76–2.19 and 2.09–2.40 points, respectively. On binary tasks, the gains also transfer to LightGBM and XGBoost, and all three student families outperform CatBoost, the strongest non-TFM baseline, in mean AUC. Ablations show gains beyond longer training or alternative warm starts, greater stability from staged than mixed optimization, and generator-dependent diminishing returns as query volume increases. Finally, GEAR reduces median inference time by 57–2866 times and peak prediction memory by 1.9–3.3 times, while retaining higher AUC than matched supervised baselines.

Graph neural networks (GNNs) are widely used, but how parameter sparsity affects the expressivity of relational (RGNNs) and temporal (TGNNs) variants is poorly understood. The Strong Expressive Lottery Ticket Hypothesis (SELTH) posits the existence of sparse GNNs that preserve Weisfeiler-Leman (WL) expressivity on static graphs. We generalize this existence result to a probabilistic statement for multi-relational and temporal domains via the relational WL (RWL). We prove that sufficiently parameterized RGNNs contain sparse subnetworks that maintain 1-RWL expressivity and derive a lower bound on the probability that a random pruning yields such a subnetwork. We show that common TGNNs and cross-graph message passing schemes admit RGNN reformulations such that they inherit these guarantees and, moreover, that the expressivity of a sparse RGNN is connected to its optimization behavior under common update regimes. Experiments instantiate the bound, compare it to empirical probabilities on synthetic data, and study how pre-training expressivity relates to optimization and prediction quality metrics on temporal and molecular benchmarks.

Researchers often choose a proxy dataset from many releases, transformations, or seeds. Search can make an invalid release appear adequate, while one adequate release does not establish that its generator is reliable. ProxyGuard controls both errors using prespecified bounded risks and a sealed target set. Named-release mode corrects for multiplicity and certifies specific releases. Direct shared-target mode evaluates independent mechanism draws on a common target, lower-bounds their favorable-score rate, and subtracts a bound on favorable scores contributed by invalid releases. Conditional on the target, release scores are independent, yielding a finite-sample mechanism-reliability guarantee without independent target batches or assumptions on release-level $p$-value dependence. We show that the mean-only penalty is sharp and derive a smooth-score certificate with additive target concentration. In a registered three-requirement study, direct mode raises power from 5.6% to 64.2% at reliability 0.95, while named mode remains stronger under high-signal evidence. Prospective audits span full-pipeline Rice–TVAE, which retrains on every draw, and a non-tabular text mechanism.

This paper proposes a multi-level Bayesian calibration approach that fuses information from heterogeneous sources and accounts for uncertainties in modeling and measurements for time-dependent multi-component systems. The developed methodology has two elements: quantifying the uncertainty at component and system levels, by fusing all available information, and corrected model prediction. A multi-level Bayesian calibration approach is developed to estimate component-level and system-level parameters using measurement data that are obtained at different time instances for different system components. Such heterogeneous data are consumed in a sequential manner, and an iterative strategy is developed to calibrate the parameters at the two levels. This calibration strategy is implemented for two scenarios: offline and online. The offline calibration uses data that is collected over all the time-steps, whereas online calibration is performed in real-time as new measurements are obtained at each time-step. Analysis models and observation data for the thermo-mechanical behavior of gas turbine engine rotor blades are used to analyze the effectiveness of the proposed approach.

We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, either assume bounded data or leave non-vanishing remainder terms that prevent adaptation to a polynomially vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lower bound, up to logarithmic factors, across both dense-tail and sparse-tail regimes under a mild nondegeneracy condition. The analysis yields a linearization of Oja's iterates, which in turn enables a high-dimensional Gaussian approximation for the general-rank subspace estimation error with an explicit limiting covariance. We also establish a row-wise Gaussian approximation over convex sets for the aligned difference, recovering prior rank-one results as special cases. For practical inference, we develop an online multiplier bootstrap algorithm and prove its consistency. Beyond streaming PCA, our techniques contribute to Gaussian approximation and bootstrap inference for nonconvex stochastic approximation.

An increasing number of scholars use AI to measure variables they subsequently include in downstream analyses. Although AI-measured variables are often analyzed as if observed without error, ignoring prediction errors in automated measurement leads to substantial bias and invalid confidence intervals in downstream analyses, even if AI measurement accuracy is high, e.g., above 90%. Existing solutions, such as design-based supervised learning and prediction-powered inference, combine error-prone AI-based measurements with gold-standard labels, which may be costly and difficult to obtain in some application areas. In this paper, we propose debiased inference with multiple imperfect measurements (DMM), a framework that combines multiple error-prone AI measurements to enable valid downstream inference without gold-standard labels. Building on the established results on CP decomposition, DMM assumes that these measurements are independent conditional on the latent true label and observed unit-level features, such as text features represented by embeddings. This framework allows for unknown misclassification rates to vary across annotation methods (e.g., large language models) and across units of annotation (e.g., texts). Under this assumption, we use semiparametric inference theory to prove that the DMM estimator is consistent and asymptotically normal, enabling valid inference for a wide range of downstream statistical analyses common in the social sciences. Our simulation results show that DMM yields valid inference and that adding accurate, though imperfect, measurements can improve efficiency. Focusing on common applications of large language model annotations, we also develop diagnostics to assess the conditional independence assumption.

Traffic signal control is a challenging sequential decision-making problem requiring a balance between throughput, vehicle delay fairness, signal stability, predictable switching, and emergency vehicle prioritisation. Existing reinforcement learning (RL) approaches often rely on predefined objectives and offer limited adaptability to changing operational priorities. They may also generalise poorly across geometrically equivalent intersections. To address these limitations, SIGMA (Symmetry-aware, Intelligent, Geometric, Multi-faced Adaptive traffic control) is proposed as a multi-faced RL framework augmented with a large language model (LLM) for dynamic objective adaptation and orientation-invariant policy learning. Natural language emergency instructions are translated into priority vectors that guide a multi-faced actor-critic controller. Symmetry-aware rotational augmentation supports transfer across homogeneous four-way intersections, while an offline-to-online learning strategy enables stable initialisation and adaptation to evolving traffic conditions. Structural properties concerning emergency service levels, graceful degradation under LLM failure, and sensitivity to traffic demand perturbations are established, alongside bootstrap-based statistical validation. Experiments in SUMO across four urban intersections modelled on Kolkata traffic scenarios compare SIGMA with fixed-time, actuated, and Deep Q-Network controllers. Reductions in average waiting times, emergency waiting times, and queue lengths are observed, alongside improved traffic throughput. Empirical reliability and ablation analyses further assess robustness to component failures and geometric orientation. SIGMA integrates language-guided objective adaptation, multi-faced policy learning, and statistical reliability assessment into an adaptive framework for intelligent traffic control.

Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $O(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tilde{\Omega}(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.

Selecting a small, diverse subset from a large candidate pool often means balancing several incompatible notions of diversity. In trademark curation, for instance, a subset should cover both the language used to describe marks and the visual space of their logos. A single determinantal point process (\DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation by an ordinary single-kernel spectral problem. We formulate fair multi-view determinant selection: maximize the weakest per-view log determinant of a size-$k$ subset. We smooth this nonsmooth objective and relax it to the Stiefel manifold. The relaxation embeds every discrete subset exactly, but unlike its single-view counterpart it has no closed-form spectral solution in general. Its stationarity condition is a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights. We derive an adaptive self-consistent-field (\SCF) solver with damping and level shifting, and round the resulting subspace by leverage-score screening followed by fair local refinement. The solver needs only feature-map products for each view. We report conflicting-view synthetic experiments and specify a multimodal USPTO protocol; the real-data multimodal results require aligned logo embeddings and are not claimed in this version.

Categorising invoices into the correct General Ledger (GL) code underpins financial reporting and tax compliance. This is a skilled accounting judgement rather than a routine task: the correct category depends subtly on the nature of the purchasing business, the vendor and the invoice text. Whilst AI is increasingly being adopted across industries to automate tasks, including invoice categorisation, implementations built on in-house small language models (SLMs) can simultaneously reduce cost and improve data security, confidentiality, and interpretability. We investigate this approach by first analysing the pre-trained embedding geometry of a small sentence transformer (SBERT) and classic SLM (DeBERTa). The sentence-embedding space of this financial corpus is globally anisotropic but composed of locally isotropic clusters, extending prior token-level findings to sentence embeddings in a financial setting, and these clusters are strongly correlated with the vendor identity. SBERT fine-tuned on a single GPU reaches 0.96 accuracy on invoice classification, above both a zero-shot LLM and a vendor identity baseline, increasing performance for smaller, challenging categories and new clients. For this important generalisation problem, SBERT reaches 0.9 F1 with roughly 100 client-specific invoices, showing that an in-house SLM implementation is promising. Combining these results with geometric analysis shows that pre-trained embedding geometry is associated with classification performance and reveals a counterintuitive finding that a structured input that would help a human reader does not improve the SLM performance.

This short work describes an extension of the permanental process model which includes fixed effects. By starting with a prior on the fixed effects coefficients we show that, in the diffuse prior limit, the intensity function of the permanental process can be found using the representer theorem and naturally decomposed into a fixed effects term and a function which is an element of a Reproducing Kernel Hilbert Space (RKHS). We show that the limiting equivalent kernel defines an RKHS whose squared norm is exactly the limiting penalty. This allows for straightforward scientific interpretation of permanental process models and the easy incorporation of domain knowledge into the estimation process.

Multi-armed bandit algorithms are evaluated by regret, yet comparable regret can coexist with different allocations across independent runs. We study the trade-off between worst-case regret $\mathcal{R}_{K,T}$ and instability $\mathcal S_{K,T}$, defined as the largest standard deviation of a terminal pull count, for $K$ arms and $T$ rounds. We prove the finite-time lower bound $\mathcal R_{K,T}\mathcal S_{K,T}\ge C T^{3/2}$, where $C$ is independent of $K$ and $T$, under a finite-time regret condition and without the regularity assumptions imposed in the prior asymptotic analysis. We also introduce Stabilized Lower-Envelope UCB (\textup{SLE-UCB}), a new tunable algorithm combining a running lower-envelope index with a decreasing pull-count stabilizer. \textup{SLE-UCB} satisfies $\mathcal R_{K,T}\mathcal S_{K,T}=O(T^{3/2}\log K)$, with an implicit constant independent of $K$ and $T$, matching the lower bound exactly in $T$ and within a logarithmic factor in $K$. To prove the instability bound, we develop a new offline top-prefix representation that removes path dependence from online decisions. Together with single-reward perturbations and the Efron–Stein inequality, this representation controls pull-count variance. Thus, regret and instability depend reciprocally on $K$, while their product has no polynomial dependence on $K$. These results resolve the open question raised in the literature concerning the sharp arm-dependent regret–instability frontier.

Accurate building height information at the individual footprint scale is essential for material stock accounting and post-disaster damage assessments yet remains difficult to obtain at city scale in the Global South where airborne LiDAR coverage is rare and commercial very high-resolution imagery is cost-prohibitive or unavailable. While recent works have demonstrated building height estimation using freely available Sentinel imagery, the resolution ceiling of resulting products is still coarse for material stock analysis. This study incorporates products derived from data freely accessible under scientific research licenses, TerraSAR-X StripMap and PlanetScope, alongside Sentinel-1 to predict building heights in a large city in Brazil. To account for the spatial autocorrelation in the training set, features from all sources are integrated in a geographically weighted random forest model, returning an RMSE of 5.34 m and R2 of 0.756 against a LiDAR reference dataset. Local feature importance showed predictor dominance to vary consistently across intra-urban contexts, with footprint geometry dominating for low-rise buildings, shadow-derived height for taller and more isolated structures, and spectral reflectance for the tallest buildings in the set. Sentinel-1 backscatter and InSAR occupy complementary spatial niches, with no single sensor uniformly preferable across the set. Results provide optioneering guidance and insight over satellite-derived products predictive relevance in distinct contexts, which global machine learning or neural network models cannot offer.

Take three frontier mixture-of-experts models (Alibaba, OpenAI, NVIDIA; 3.6-4.0B active parameters each) and fine-tune them to reason in a low-resource language. On accuracy benchmarks almost nothing happens, and the benchmark itself is noise at this scale: changing only the random seed moves the score by 7.7 points, more than every data and recipe effect we measured. That null is our first result. The real changes live where accuracy cannot see. Base models never think in Greek: 0 of 1,000 reasoning traces, even when the question is Greek, so the model answers correctly while reasoning in a form its user cannot read, audit, or correct. After supervised fine-tuning (SFT), every released checkpoint reasons in the language of the question on ~98% of items, one family at 3x fewer tokens, with judged grammaticality improving on all four models and general ability within a few points of each base: nothing was forgotten, and fluency was gained. We propose six behavioural dimensions that make such changes measurable, each gated to reject any metric that correlates with output length, and we report how our own instruments lied: six failures, each caught by a control. What SFT cannot do is fix its own defects: a quarter of answers skip the requested format, answers leak into the reasoning channel, and an explicit "think in English" is obeyed under half the time. Reinforcement learning with verifiable rewards, pre-registered before training, fixes the first two outright (fallback 24% to 2.5%, leak 3.5% to 0.0%, both against a flat random-reward control) and moves the third (+9.1pp), while the Greek reasoning habit survives an accuracy-only gradient untouched. We release five checkpoints. The instruments, the controls and the pre-registration travel to any low-resource language; Greek is the case that let us measure them.

Modern machine learning is leading to substantial gains in precision, flexibility, and computational efficiency in fundamental physics. Statistical validation, uncertainty quantification, and robustness assessment are less systematically addressed. The VERaiPHY initiative (Validation & Evaluation for Robust AI in PHYsics) is a series of articles developed within the PHYSTAT programme, aimed at establishing statistical standards for the development, evaluation, and deployment of ML techniques. Each article focuses on a specific methodological domain from a statistics perspective and clarifies statistical questions, tests, and the interpretation of results. This opening article establishes the probabilistic, statistical, and machine learning foundations that the later contributions assume, together with the notation used throughout.

One-dimensional Gaussian processes with stationary, integrable kernel functions admit exact or arbitrarily accurate state-space representations, enabling linear-time inference through Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing. However, the RTS smoother requires inversion of predicted state covariance matrices, which can become ill-conditioned and may therefore lead to numerical instabilities. In this work, we revisit the modified Bryson-Frazier (MBF) smoother as an alternative to the RTS smoother for Gaussian process regression in its state-space representation. In addition to reducing computational cost and memory requirements, the MBF smoother computes the same posterior distributions as the RTS smoother while avoiding the problematic covariance matrix inversion and the associated numerical instabilities. Furthermore, we demonstrate that the intermediate quantities computed by the MBF smoother can be reused to compute gradients of the negative log marginal likelihood, enabling kernel hyperparameter learning with minimal additional cost. Together, these results establish the MBF smoother as a unified and numerically robust approach to inference and kernel hyperparameter learning for one-dimensional Gaussian process regression.

In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore–Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insufficient weight to the truly predictive coordinate. An exact target-mass identity and a two-sign argument convert this obstruction into clipped prediction loss. Hadamard constructions yield $\Omega(\min\{T,\sqrt d\})$ clipped regret for each of the three unit-power rules against a zero-loss one-sparse comparator. For every fixed power $\alpha\ge1$, one shared paired construction further yields linear regret simultaneously for all three powered rules and selectors among them in sufficiently high dimension. A rank upper bound is tight for powered univariate priming, even with Euclidean-unit inputs, and for unit-power Pearson priming with coordinatewise bounded inputs and target-preserving totalization. A separate algebraic construction gives $\Omega(\min\{T,d^{1/4}\})$ regret for unit-power multivariate priming under Euclidean-unit inputs. The univariate lower bound persists under any nonnegative second-stage ridge schedule, while a paired ridge construction yields linear lower bounds for all three powered rules. Exploratory diagnostics on frozen language-model activations are consistent with the same qualitative mechanism. The exact multivariate frontier remains open.