Papers

Health technology assessment often aims to balance evidence across multiple treatments and outcomes and assess treatment benefit-harm profiles. Multivariate network meta-analysis (mvNMA) is well suited to this task, as it synthesizes evidence across treatments and outcomes. However, the potential of mvNMA has been overlooked, leading decision-makers to rely on outcome-specific NMAs that ignore outcome correlations. Based on independent NMA models, previous work proposed methods such as multivariate P-scores or spie charts to assess treatment benefit-harm profiles by yielding across-outcomes treatment hierarchies. In this article, we propose an mvNMA-based framework for assessing treatment benefit-harm profiles. Our framework uses a hybrid-correlation mvNMA model and incorporates DuMouchel priors for treatment effects, enabling estimation of all treatment effects even when outcomes are missing for some treatments. We then extend common NMA ranking metrics, including SUCRA, the probability of being best, and median ranks, to the mvNMA setting. Based on these metrics, we adapt the VIKOR algorithm for mvNMA. This deterministic multicriteria decision method quantifies overall and worst-case treatment performance and, by balancing these aspects, produces an across-outcomes ranking while identifying treatments offering the optimal compromise between these two aspects. To facilitate use of our framework, we developed the R package mvnma. We applied our framework to two clinical datasets: one comparing eleven physical therapy treatments across two outcomes and another comparing nine antidepressants across five outcomes. Our framework provides an alternative strategy for assessing treatment benefit-harm profiles across multiple outcomes and encourages multivariate approaches in applied clinical and policy settings.

Penalized function-on-function regression, as implemented in the R package refund, treats all grid values of all curves as independent. Residual curves are smooth, so values within a curve are dependent. We study what this does to point estimates and pointwise confidence intervals, in a simulation with Gaussian, count and binary responses and in a plasmode study built on nine real datasets. Under within-curve dependence, model-based 95% intervals cover 0.63–0.82. A curve-clustered sandwich covariance with a leverage adjustment for the penalized hat matrix (CL2), computed after the usual REML fit, brings coverage close to nominal in the simulation; in the plasmode study it is a few points short on eight datasets and 0.84–0.91 for the coefficient surface on the ninth. Satterthwaite degrees of freedom recover most of the remaining shortfall except on that dataset, also with only 20 curves, at the cost of wider intervals. REML, however, undersmooths the coefficient surface: its error is two to four times that of a fit whose smoothing parameters are chosen by curve-blocked neighbourhood cross-validation (NCV), and its CL2 intervals for the surface are wide. Intervals centred at the smoother NCV estimate are narrow but undercover, the familiar tension between estimation and pointwise inference in nonparametric regression. We recommend the NCV estimate to describe the shape of the surface and REML + CL2 with Satterthwaite degrees of freedom for inference. For a surface that is zero everywhere, under dependent errors, these intervals exclude zero at about 5% of the grid points, and the NCV estimate is five to seven times closer to zero than REML's. For fitted means, intercepts and scalar effects, REML + CL2 intervals are close to nominal, except for binary intercepts and scalar effects and for misregistered counts. We state which defaults of refund the evidence supports.

We consider the computation of the network modularity, a common measure of the structure of networks or graphs that quantifies the division of a network into modules or clusters. The computation of the network modularity is an NP-hard problem, thus making its exact computation often infeasible in practice. This has resulted in the development of several heuristics in the literature. In this work, we consider the exact computation of the network modularity with the help of a branch-and-bound algorithm. Our algorithm is guaranteed to find the optimal clustering that maximizes the network modularity, however it achieves this without a full exploration of the search space. This is accomplished by bounding partial solutions and discarding them if it can be foreseen that a partial solution will not yield an improvement over an existing solution. We assess our algorithm with respect to accuracy and runtime and compare it to a brute-force approach as well as two state-of-the-art benchmarks, simulated annealing and the Louvain method.

Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

Large language models (LLMs) increasingly mediate human communication, from drafting emails to summarizing scientific reports, yet whether they faithfully preserve a speaker's position remains largely untested. We model AI-mediated communication as a two-step generation-extraction pipeline: one LLM produces an argument from a specified stance, and a second LLM extracts the stance from that argument. We represent the pipeline as a probabilistic state transition over five Likert-type stance categories and define the stance preservation rate (SPR) as the average probability that the extracted stance matches the initial stance. Across 112 debate propositions, none of the nine LLMs tested exceeded an SPR of 0.7 under the default configuration. Three drift patterns accounted for most of the drift: polarization, deviation from neutrality, and flipping. Among the mitigation strategies tested, including in-context learning, multiple extraction with shuffled options, assertion, and reflection, only adding medium reasoning effort to a reflection prompt for GPT-5.4 substantially improved the SPR, to 0.775, yet polarization remained the largest pattern, with 0.119 of the transition mass. An exploratory comparison with human extraction on a single proposition suggests that drift arises at both the generation and the extraction stage. These results point to a fidelity gap in AI-mediated communication, with implications for journalism, policy deliberation, scientific communication, and other domains where opinion-laden messages pass through language models.

We introduce a sampling approach for energy- and score-based generative models that requires no gradient evaluations of the model. Replacing the drift term that would normally contain the score $\nabla_\mathbf{x} \log p_\theta(\bf{x})$ with a high-frequency dithered cosine of the model's value, $\sqrt{\alpha\omega}\,\cos(\omega t + k \log p_\theta(\bf{x}))$, produces, in the high-frequency averaging limit, Langevin Markov chain Monte Carlo for energy-based models and the reverse-time SDE of score-based diffusion. We prove that trajectories of the dithered Itô SDE converge to those of the target SDE, driven by the same Brownian motion, uniformly on compact time intervals in probability, by an averaging argument that extends bounded extremum seeking (ES) to Itô processes, with an explicit $O(\omega^{-1/2})$ mean-square rate under global bounds. The approach is not confined to smooth targets: it extends to $C^{1,1}$ energies with discontinuous curvature (without ellipticity requirement) and to Sobolev energies whose Hessians exist only off measure zero sets; for Lipschitz energies with gradient kinks the averaged limit remains well posed; the Krylov-Röckner integrability class is the boundary of provability. The approach provides a hard a priori bound on the per-step update rate and applies to explicitly time-varying targets on finite horizons. Gradient-free pixel-space sampling is not competitive with well-tuned backpropagation-based samplers at practical evaluation budgets; the regime where the approach offers an advantage is latent-space sampling when the model is a black box and the target drifts in time. We demonstrate latent-space tracking for time-varying images on CelebA-HQ ($256{\times}256$) from limited 1D projection measurements and latent-space EBM sampling on CIFAR-10.

External causal reports can improve structure learning from limited observations, but their reliability varies across sources and variable pairs. We introduce HB-NoisyKG, a Bayesian framework that combines observational data with repeated causal reports from sources such as large language models. Each report is a noisy observation of a direct pair state implied by one DAG. A feature-conditioned Beta prior pools information about pair reliability, and a shared error matrix captures systematic mistakes. Alternating inference uses the graph posterior to refine reliability estimates, which determine how reports influence subsequent graph updates. The report likelihood uses only graph pair-state marginals, so the same observation layer supports discrete and continuous likelihoods in graph-only and joint inference. Against an 80-restart no-KG baseline, HB uses at most 80 total restarts and lowers mean SHD from 22.39 to 16.06 on five discrete benchmarks. On a physical light tunnel with random variable IDs and retained descriptions, HB lowers SHD from 39.00 for no-KG to 27.30. On continuous Sachs, graph-only BGe raises AUROC by 0.121 over no-KG Top-K. In a controlled synthetic study, continued updating also reduces mean reliability estimation error and held-out report log loss compared with one-time estimation.

Personalized federated learning can improve estimation for high-dimensional time series while preserving client-specific dynamics. However, parameter heterogeneity creates a fundamental ambiguity between shared and personalized structure. We introduce the principle of personalization diversity, under which genuinely personalized effects recur in only a limited fraction of clients. Based on this principle, we propose PerFeCT-VAR, Personalized Federated Vector Autoregression via Frequency-Capped Thresholding, which decomposes each client-specific transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures. A cross-client frequency cap yields a sharp shared–personalized separation threshold and motivates frequency-capped thresholding for federated estimation. Our theory further accounts for heterogeneous client distributions through a distributional compatibility condition and establishes joint linear convergence of the shared and personalized components. Under sufficient personalization diversity, the shared dynamics retain federated total-sample-size gains while the personalized components achieve client-level accuracy. Simulations and an application to multi-store retail revenue data demonstrate the predictive and interpretive benefits of the proposed framework.

Large language models (LLMs) are increasingly used to generate, complete, and transform information in settings where their outputs can shape consequential decisions, raising concerns about their impact on demographic disparities. In this context, causal inference provides a principled basis for assessing fairness, because it attributes observed disparities to the mechanisms that generated them, which a purely statistical approach cannot do even with infinite data. In LLM generation, a query may request several causally related variables, each of which is both an outcome of interest and a possible cause of other outputs, and the information supplied in the prompt need not follow a topological or a temporal order. This calls for methods that can analyze and selectively remove disparities from such a flexible generation process. In this paper we introduce Causally Fair Generation with LLMs (CFG, for short). CFG extracts relevant concepts, grounds generation in a reference population and causal diagram, and removes user-selected causal effects. CFG also allows pathways deemed justifiable for the task's utility to be retained, which is known in legal literature as business necessity. Further, we provide formal guarantees for our method when eliminating all discriminatory causal effects in the adapted population model, under appropriate causal assumptions. We evaluate CFG with four LLMs in three real-world settings based on population data and on a synthetic dataset with a known causal ground truth.

To mitigate the quadratic complexity bottleneck of the Transformer, sparse attention has emerged as a pivotal technology. Despite the extensive empirical success of sparse Transformers, the theoretical understanding of sparse attention remains fragmented. In particular, two fundamental questions remain unclear: (1) How does sparsification affect the information fidelity of attention mechanisms? (2) How does this information loss interact with the generalization behavior of the model? To bridge this gap, this paper proposes a systematic analysis of the Jensen-Shannon (JS) divergence and of the generalization gap of sparse attention mechanisms. Specifically, we first characterize the approximation error via the JS divergence. Through an order-statistics-based concentration analysis of the truncation mass alpha — where the attention scores are assumed to be independent and identically distributed sub-Gaussian random variables with parameter sigma — the JS divergence between the full attention distribution and the sparse attention distribution is shown to admit the closed form log 2 + ((1 - alpha)/2) log(1 - alpha) - ((2 - alpha)/2) log(2 - alpha). Subsequently, we derive a generalization bound through Rademacher complexity, quantified by O(gamma * sqrt(M/n) * (sqrt(log(3eL/M)) + sqrt(pi)/2)). Furthermore, building on a mutual-information-based generalization bound together with an entropy and covering-number analysis of the sparse hypothesis class, we obtain the sparsity-dependent generalization bound O(sqrt((M/(2n)) * (log(eL/M) + log(1 + 2/epsilon)))). Our analysis shows that sparsity reduces the complexity of the considered hypothesis class while introducing approximation error that can be quantified by the JS divergence. These findings provide a theoretical characterization of the trade-off between information fidelity and generalization in sparse Transformer architectures.

Simulation-free training of latent Stochastic Differential Equations (SDEs) relies on a variational posterior process whose one-time marginals are tractable, typically Gaussian. Such marginals, however, do not determine the underlying dynamics: many processes share the same marginals while differing in their temporal structure, and existing parameterizations fix this structure implicitly, which restricts the posterior family and biases the learned model. We introduce Gaussian flow dynamics, which construct stochastic processes directly from smoothly evolving Gaussian marginals while making the marginal-preserving, or gauge, degrees of freedom explicit and parameterizable. The construction admits state-dependent diffusion coefficients and recovers every linear SDE with additive noise and a non-degenerate Gaussian initial distribution. Building on it, we propose Gauge Matching, a simulation-free method for latent SDE learning that combines Gaussian flow dynamics with the SDE Matching objective. Gauge Matching costs at most quadratically in the latent dimension per step, like SDE Matching, but learns the temporal structure of the posterior beyond its one-time marginals. It comes within a nat of Helmholtz-SDE, which computes the gauge from the prior Jacobian at cubic cost, on the linear benchmark where the exact posterior is known, matches it on nonlinear systems, and applies where Helmholtz-SDE does not, to state-dependent noise.

We prove a Chernoff-exponent guarantee for the output of spectrally initialized batch variational EM after a prescribed iteration budget, without assuming global maximization of its variational objective. The iteration repeatedly estimates the entire block probability matrix and community proportions from the same sparse graph. We consider a fixed number of communities with proportions bounded away from zero and fixed, positive, distinct connectivity profiles; neither assortativity nor full rank is required. The algorithm uses simultaneous softmax updates without sample splitting or posterior thresholding. Its analysis must control the feedback between estimated parameters, soft labels and reused edges at an exponentially small risk scale. We establish a uniform one-step bound over data-dependent soft assignments whose random remainder has exponentially small expectation. Combined with an exponentially reliable regularized spectral initializer, this yields an unconditional expected misclassification rate bounded by $\exp\{-(1-o(1))J_n\}$ throughout the sparse, diverging-degree regime, where $J_n$ is the minimum nodewise Chernoff information. Matching lower bounds establish first-order logarithmic minimax optimality on local parameter spaces allowing unknown connectivity and varying community counts. The algorithm also attains the sharp first-order exact-recovery threshold. Numerical experiments illustrate refinement gains and sensitivity to initialization and imbalance.

Extreme winter weather has repeatedly disrupted gas-fired power generation in the United States, yet the plant-level data needed to systematically quantify outage risk remain proprietary. Using publicly available weather and electricity demand data together with anonymized generator contingency records from the North American Electric Reliability Corporation (NERC), we develop a three-stage Bayesian probabilistic framework for estimating winter-driven generator performance. Applied to New York State (2013–2022), the framework sequentially estimates: the hourly probability of a generator contingency event, the expected net available capacity conditioned on an event occurring, and the event duration. Colder conditions and higher electricity demand are associated with higher failure probability, lower retained capacity, and longer event duration. Under the most severe observed stress conditions, estimated mean hourly event probability reaches 24% , while expected mean net available capacity falls to 13% of nameplate rating. Full outage events have a median duration of 12.7 hours, while partial derating event duration increases from 2.4 to 7.1 hours with capacity loss severity. The proposed framework establishes a transferable baseline that utilities with access to plant-level records can directly extend to obtain more precise reliability estimates for operational planning and resource adequacy assessment.

Pretrained flow models are now widely used as generative priors in science and vision, where inference-time guidance enables test-time constraints without retraining. Existing methods use projection, posterior sampling, or iterative optimization of the generative trajectory. We propose LyapuFlow, an alternative based on Lyapunov feedback control. At each sampling step, LyapuFlow predicts the terminal sample towards which the current flow is evolving, and evaluates the constraint violation on this prediction. Then, we compute the minimum-norm control that satisfies a prescribed Lyapunov decrease condition. The resulting control remains inactive when the uncontrolled dynamics already reduce the constraint violation at the prescribed rate. Otherwise, it provides a corrective update within a feedback trust region that prevents the control from dominating the pretrained dynamics. We demonstrate LyapuFlow in both data and latent spaces, outperforming alternatives spanning different mechanisms for test-time constraint enforcement in scientific machine learning and image inverse problems.

Sparse causal discovery calls for methods that exploit graph structure without estimating high-dimensional densities. We introduce Fisher Information Completion Search (FiCS), a source-first algorithm for additive noise models that uses one local Fisher score for both ordering and parent selection. Under regularity and nonconstant-parent conditions, we prove that a node's local Fisher information equals the noise Fisher information exactly when the conditioning set contains all parents, provided that it contains no descendants. This Fisher parent completion identifies the parent set as the unique minimal Fisher completion. With a maximum conditioning set size $q$ at least the maximum indegree $d$, population FiCS queries marginals of at most $q+1$ variables and recovers the true directed acyclic graph under a positive ordering margin. Bounded conditioning also has a population advantage: reducing $q$ toward $d$ cannot decrease, and can strictly increase, the ordering margin. A growing non-Gaussian family separates local Fisher selection from conditional-variance and leaf-first Fisher ordering. For the regularized kernel Stein estimator, we establish high-dimensional DAG consistency under $q\{1+\log(p/q)\}+\log p=o(n)$, uniform Fisher separation, local approximation, and compatible ridge and parent penalty parameters. Experiments show the strongest gains when $n$ is small relative to $p$, quantify the effect of the conditioning size, and demonstrate competitive reference-graph recovery on three real-data benchmarks.

We consider the ill-posed inverse problem of recovering the drift potential of an overdamped Langevin diffusion from discrete, possibly irregular position observations. Specializing the suboptimality gap for inverse stochastic control to drift-potential recovery, we parametrize the associated value function in a finite basis. Under a basis nondegeneracy condition, the resulting Galerkin estimator is obtained from one positive-definite linear system whose entries are smooth functionals of the empirical time marginals; no transition density is required. The gap equals one half of the squared energy distance to the true potential, yielding a best-approximation identity and energy-seminorm consistency as the basis becomes complete. At a fixed basis, we separate the sample fluctuation from the time-quadrature error, thereby avoiding the Euler–Maruyama $O(\Delta t)$ drift-discretization bias. We also analyze the finite basis as regularization, give a dimension-dependent convergence rate for a concrete basis family, and bound observation-noise bias. One- and two-dimensional experiments verify the predicted sampling-interval behavior. An application to irregular animal telemetry illustrates the method on a single long trajectory.

High-dimensional mean testing is challenging under strong dependence and heavy tails, since classical Hotelling statistics are ill posed and regularized versions based on sample moments remain sensitive to outliers. This paper develops a robust regularized Hotelling framework for one-sample mean inference under elliptical distributions. The proposed HRST statistic combines a Hettmansperger-Randles spatial location estimator with the inverse of a trace-normalized shrinkage Tyler scatter matrix, and calibrates the resulting quadratic form through ridge-resolvent random-matrix theory rather than sparse covariance or precision-matrix assumptions. In the regime $p/n\to y\in(0,\infty)$, allowing a vanishing lower bulk edge and finite-rank diverging spikes, we establish feasible asymptotic normality for each shrinkage level, derive local-alternative distributions with explicit noncentrality parameters, and prove joint Gaussian limits over finite shrinkage grids. These results justify an adaptive Cauchy combination test across shrinkage levels. Simulations and a paired tumor-normal gene-expression study show that HRST maintains size and improves robustness under heavy-tailed distributions while retaining power under strong correlation.

Binary classification often requires controlling both type I and type II error rates at prespecified levels. When the class distributions overlap substantially, the two error limits may be incompatible if every observation must be classified. We study Neyman-Pearson classification with indecisions (NPI), which permits uncertain observations to remain unclassified and assesses selective type I and type II errors among definitive classifications within each class. For an independently trained score, we develop a model-free calibration procedure that combines all candidate threshold pairs passing calibration into a rule whose decision region contains that of every passing candidate. We couple the entire threshold search to a common martingale within each class and compute its finite-horizon crossing probability exactly, avoiding a multiplicity adjustment for the number of candidate pairs. The resulting classifier satisfies both population selective error limits simultaneously with user-specified high probability in finite samples, without assumptions on the accuracy of the fitted score. We bound the additional indecision due to calibration and evaluate the procedure in simulations and applications to recidivism and credit-default prediction.

We establish statistical consistency for the penalized maximum-likelihood estimator underlying CPLASS, a method for detecting changes in velocity in $d$-dimensional time-series data. The signal is modeled as a continuous piecewise-linear trajectory observed with independent Gaussian noise. Unlike classical change-in-mean models, continuity across adjacent segments couples their parameters and prevents direct application of standard segmentation arguments. Under compact parameter spaces, minimum segment-length and velocity-jump conditions, and a strengthened Schwarz information criterion penalty $\rho_k(\log n)^\gamma$ with $\gamma>1$, we prove joint consistency of the estimated number of segments and all changepoint locations in the high-frequency regime $n\to\infty$. The maximum changepoint-location error is $O_{\mathbb{P}}\{(\log n/n)^{1/2}\}$. The proof first uses empirical-process theory to establish convergence of the fitted signal, variance, and likelihood for each fixed model size. It then combines overfitting and underfitting arguments with a two-stage geometric localization analysis, yielding an initial $(\log n/n)^{1/3}$ rate that is sharpened by exploiting the local two-segment continuous piecewise-linear structure.

We propose confidence intervals with near-nominal coverage of variance-covariance parameters in linear mixed models, even when interest or nuisance parameters are near the boundary, that is, when some random effects have small variances or are strongly correlated. In such settings, our simulations show standard Wald, likelihood ratio, and score intervals with nominal level 95% can have coverage as low as 45% and as high as 99%, while the proposed intervals are near nominal. The proposed intervals invert a modified profile score statistic based on the restricted likelihood, with nuisance parameters estimated on an extended parameter set. In a longitudinal study of socialization in children with autism, where the estimated correlation between the random intercept and slope is near minus one, our intervals show that children who start higher improve more slowly. In a genetic study of white blood cell count in mice, they distinguish the contributions of variant classes even though several intervals include zero. Compared to universal inference intervals, which are valid in finite samples, ours are 1.7 to 3.1 times narrower, and finite where one universal interval is not, at a forty-seventh of the computing time. We establish asymptotically correct coverage uniformly in the parameter under a condition known to hold with independent clusters and crossed random effects.

Inference-time steering combines pretrained diffusion experts or rewards without retraining by changing the dynamics that transport noise to data. Feynman-Kac correction compensates for proposal mismatch through importance-weighted sequential Monte Carlo (SMC), whose finite-particle behavior depends on the proposal. Variance-controlling guidance (VCG) improves that proposal by fitting a linear drift correction to minimize empirical log-weight-rate variance. Although its population optimum cannot worsen residual variance, finite-particle VCG can nearly eliminate its fitting residual while increasing residual risk on new states by orders of magnitude. The resulting update can degrade unweighted generation or accelerate particle collapse. We show that the centered Feynman-Kac rate is the normalized transport residual and that expected out-of-fit benefit is exactly population headroom minus coefficient-estimation penalty. Under regularity assumptions, a Wasserstein analysis bounds the unweighted proposal's terminal error using this residual. These results motivate Risk-Calibrated Proposal Transport (RCPT), which uses deletion leave-one-out residuals to calibrate the retained fraction of the VCG update, adding no model calls and only small linear-algebra overhead. Experiments on 2D checker distributions, scaffold decoration, molecular property optimization, and class-conditional CIFAR-10 generation demonstrate recovery from harmful fitted updates. Across molecular and image domains, RCPT mitigates harmful fitted updates and improves a broad range of terminal metrics relative to uncalibrated VCG.

Spatial clustering increasingly involves complex objects, including probability distributions, networks, and structured matrices, for which conventional parametric likelihoods may be difficult to specify. We construct a generalized likelihood by exponentiating a cluster-specific Bregman loss on fixed representations of the responses, avoiding the need to specify a parametric sampling model for each response class. Each cluster is associated with an unknown representative, and the generalized likelihood measures within-cluster homogeneity through the Bregman divergence between the represented observations and that representative. A prior family matched to the Bregman geometry yields conjugate generalized posterior updates and permits exact marginalization of the cluster-specific representatives. The resulting collapsed scores combine within-cluster Bregman dispersion with uncertainty in the representatives, while a spanning-tree partition prior restricts posterior partition support to spatially contiguous clusters. This collapsed representation also leads to a tractable MCMC algorithm for posterior computation. The framework accommodates multiple complex-object response classes within a common inferential construction. We establish posterior consistency for the spatial partition and cluster-specific representatives under infill-domain asymptotics. Simulation studies with different complex-object responses demonstrate accurate recovery of spatial partitions and cluster-specific representatives. We further analyze racial-composition distributions across spatial units in Houston, illustrating geographically coherent clusters with distinct demographic compositions.

Fully homomorphic encryption allows arithmetic to be carried out on encrypted values, so that a party performing a computation need not see the data it operates on. This is useful wherever collaborating parties or sites cannot share data records or computed summaries yet need to do a joint analysis. We demonstrate the protocols needed to perform such analyses reproducibly via two packages in R, a platform widely used for applied statistics. The first, openfhe.R, is an interface to the OpenFHE C++ library, which exposes exact integer arithmetic (BFV, BGV), approximate real-valued arithmetic (CKKS), Boolean circuits, and multiparty key generation. The second is homomorpheR, which builds a small set of master/worker primitives for multi-party protocols on top of the first. Together, the two let an ordinary R statistical routine compose with an encrypted-arithmetic layer at the function-value boundary, provided the quantity crossing that boundary decomposes as a sum over sites. Two validation studies are presented: distributed stratified Cox regression, where stats4::mle() converges through an encrypted channel, and federated Cox-lasso via convex optimization using consensus ADMM, where the cross-site update is the only encrypted step. We also discuss federated similarity retrieval and two-party prediction. Throughout, the parties are assumed honest-but-curious, and threshold key generation removes the assumption that any single party holds a usable secret key.

Recent studies on reinforcement learning (RL) report seemingly conflicting evidence about large language model (LLM) reasoning. Training on mathematics can improve performance in other domains, yet gains in Pass@1 can coincide with lower Pass@$N$ than the base model. This raises a fundamental question: does RL expand an LLM's reasoning boundary, or merely reweight its existing reasoning space? We revisit these phenomena across Qwen and Gemma model families, showing both cross-domain gains and forgetting, while coverage at large sampling budgets increases on some tasks and decreases on others. Detailed analysis of solution traces before and after RL indicates a shift in the reasoning strategies the model employs, motivating a two-stage autoregressive policy model that separates strategy selection from problem-specific execution. Within this framework, we prove how RL's implicit bias reshapes strategy preferences, allowing gains on some tasks while suppressing strategies required by others. This mechanism can also broaden or narrow coverage at a given sampling budget even without expanding strategy support. We further provide theoretical justifications for log-sigmoid and log-linear scaling laws in RL compute, and evaluate their predictive power. Together, these results connect changes in strategy selection to cross-domain transfer, reasoning coverage, and compute scaling.

Graph Neural Networks (GNNs) often struggle to capture long-range dependencies due to over-squashing – a phenomenon in which the repeated compression of node embeddings into finite-size messages causes representations to collapse. Over-squashing is most often diagnosed as a property of the graph topology, with effective resistance serving as a principled measure of the bottleneck. We provide a complementary view on the matter: building on cellular sheaves, we introduce sheaf effective resistance, a generalization of effective resistance that depends on the sheaf attached to the graph, and we prove that for flat vector bundles, the over-squashing sensitivity in the Jacobian sense is upper bounded by a quantity related to the sheaf effective resistance between the nodes. The bottleneck thus need not lie in the graph itself: it can be relocated, and reduced, by adjusting the sheaf. We instantiate this idea in FlatNSD, a simple message-passing variant of Neural Sheaf Diffusion, and show that it implicitly learns to modulate total sheaf effective resistance, performing well on benchmarks designed to stress over-squashing without altering the original graph topology.

This paper concerns how semantic context determines geometry in learned vector representations. Similarity is typically measured using cosine similarity, which provides a single fixed geometry. Semantic similarity, however, is inherently context dependent: two images may be similar because they depict the same object, share a visual style, or are relevant to the same clinical finding. We show that contrastive representations naturally encompass a family of geometries that can be specialized to particular semantic structure. The key idea is to use an interplay between contrastive learning, exponential families, and information geometry to establish a correspondence between probability distributions over "anchors" and Bregman geometries on the representation space. We use this correspondence to define "Anchor Divergences", a method for specifying context-specific semantic geometries on fixed representations. Under this correspondence, modeling the anchor distribution models the geometry itself. Experiments on retrieval show that anchor divergences provide an effective and efficient way to specify context-specific semantic similarity.

Imperfect measurements allow different underlying distributions to generate the same observations. Restrictions linking unobserved components can make it difficult to characterize all compatible distributions and compute the resulting range of parameter values. We ask how to construct computable parameter bounds and tighten them without additional data or stronger assumptions. We develop a general framework for partial identification under imperfect measurement based on distributionally robust optimization. We use measurement restrictions to construct a neighborhood around a benchmark distribution, ensuring that every compatible distribution lies within it. Optimizing over this neighborhood gives parameter bounds through a common procedure that can be adapted to different measurement problems. The choice of benchmark affects how informative these bounds are. We establish conditions under which changing it can tighten the bounds while preserving every parameter value consistent with the same data and assumptions. Applications to networks, missing outcomes, and regression illustrate how the framework tightens bounds and can recover the full range of compatible values.

Most feature-based choice models, classical and deep, score items and apply a single softmax. We introduce consideration circuits (CC), feature-based models of multi-stage choice defined by directed acyclic graphs of multinomial logit (MNL) units. Source units assign probabilities to menu items, and internal units combine predecessor distributions using MNL weights computed from their probability-weighted feature summaries. On a three-item compromise task with fixed non-collinear features, menu-independent random-utility models (RUM), including a single MNL unit, suffer an error bounded away from zero. For CC, in contrast, we establish a sharp depth–norm separation: increasing depth from $2$ to $3$ reduces the optimal maximum taste-vector norm for error $\epsilon$ from $\Theta(\log(1/\epsilon)/\epsilon)$ to $\Theta(\log(1/\epsilon))$. The depth-$2$ lower bound holds for arbitrary width and menu-independent routing biases, while a five-node depth-$3$ circuit with zero routing biases attains the logarithmic rate. More generally, we characterize two geometric conditions that are necessary and sufficient for approximating arbitrary deterministic choice tables on finite menu families. Under these conditions, depth $3$ suffices, while depth $4$ achieves optimal logarithmic norm scaling whenever the family contains a non-singleton menu. In experiments, standalone tree circuits with fewer than $600$ parameters attain the lowest mean test negative log-likelihood (NLL) among the evaluated models on four fixed-pool benchmarks and the Expedia temporal split. As output heads, CC generalize the linear MNL readout and lower mean test NLL for every tested encoder on Expedia and Trivago.

We study pointwise estimation of a smooth binomial mixing density and characterize its minimax rates. Assuming that the mixing density is $s$-Hölder smooth, we first consider the homogeneous setting with a common number of binomial trials $t$. We derive matching lower and upper bounds that reveal three regimes depending on the relative sizes of the sample size $n$ and the number of trials $t$. When $t$ is small, the finite number of trials creates an identification barrier that persists regardless of sample size; at intermediate $t$, more data reduce sampling uncertainty, while the number of trials limits how finely the mixing density can be recovered; and when $t$ is sufficiently large, the usual nonparametric density estimation rate is recovered. Our lower bounds exploit the polynomial structure of the binomial mixture model, while attainability is achieved by a suitably regularized orthogonal series estimator. We then extend the analysis to heterogeneous trial parameters, where the minimax rate depends on the full trial profile through the effective sample size available at each polynomial degree. These results characterize the fundamental statistical limits of learning smooth populations of binomial probabilities under both homogeneous and heterogeneous trials.

Per-target labeled random-finite-set filters, such as the state of the art $\delta$-generalized labeled multi-Bernoulli filter, cannot represent cooperating, swarm-like, motion between targets. In this work, we present a new filter that can. The new particle filter couples the joint particle filter with ensemble Gaussian mixture filter such that a measurement updates the density at every particle instead of merely reweighting. We prove that the new particle filter converges to the joint particle filter in the limit of particle number and thus to the true Bayesian posterior, under certain assumptions. Experimental results on two coupled systems, the Vicsek model and coupled Brownian motion provide evidence on the efficacy of the filter.