Papers

Tree-Adjoining Grammars (TAGs) have recently been introduced to Nonlinear System Identification (NLSI) as a means of encoding an entire model class as a finite set of grammatical rules, from which candidate models are assembled as trees. Existing TAG-based identifiers rely on evolutionary optimisation and return point estimates of the model structure. This paper instead proposes the TAG framework within a Bayesian setting. A generative prior is defined over tree structures and their parameters, and a Reversible-Jump MCMC sampler with structure-preserving tree moves is used to infer the joint posterior over model structure, parameters and predictions. Two training objectives are considered; that is, a one-step-ahead objective with conjugate parameter proposals, and a simulation-based objective handled by likelihood-free inference. The approach is validated on a simulated polynomial NARX system, the Silverbox benchmark, and wave-loading data from the Christchurch Bay Tower, where embedding Morison's equation as a fixed initial tree yields a grey-box model that outperforms the physics-driven baseline. The results demonstrate that Bayesian TAGs are well suited to quantifying uncertainty in equation discovery for dynamical systems and to fitting physics-informed models.

Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. We show that the adversary's problem can be reformulated as an optimization problem over transport maps that push empirical samples to adversarial ones, and we prove that optimal maps are cyclically monotone. We also show that standard adversarial training—based on per-sample local optimization—violates cyclical monotonicity and wastes transport costs unless the adversary is severely restricted. We propose two remedies. First, we introduce multi-start particle ascent, which alternates parallel gradient ascent with reassignment to enforce cyclical monotonicity across samples. Second, we parameterize adversarial maps as gradients of input-convex neural networks, which guarantees cyclical monotonicity by construction. Experiments on robust regression, image classification, and robust control show that our methods consistently outperform standard adversarial training and state-of-the-art baselines, achieving improved robustness and better generalization under distribution shift.

Unobserved common causes are pervasive in real-world time series and can induce spurious associations that causal discovery methods mistake for direct edges. We propose LUCID (Learning Under Confounding for Inference and Discovery, a regime-adaptive deconfounding layer that first estimates the confounding regime from data using a Marčenko–Pastur spectral router, then applies a deconfounding strategy matched to that regime. When the spectrum indicates pervasive factor confounding, LUCID attenuates factor-dominated variation and recovers contemporaneous (lag-$0$) structure from the resulting innovations, with edge selection calibrated against a data-driven edge-free null. Rather than being tied to a particular discovery algorithm, it can wrap existing discovery engines; we demonstrate consistent improvements across three such methods. On a diverse synthetic out-of-distribution benchmark spanning changes in confounder strength and sparsity, loading density, lag structure, volatility dynamics, edge heterogeneity, persistence, intermittency, and tail behavior, LUCID achieves the best family-weighted directed, lag-resolved graph $F_1$ ($0.60$), improving over the strongest baseline by $0.19$ absolute ($\approx\!46\%$ relative). Its advantage widens relative to looser lag-collapsed scoring, and remains robust under intermittent and heavy-tailed confounding. Code reproducing the method, the benchmark generators, and every reported experiment is available at https://github.com/bloomberg/causal-ts.

We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \[ Y_k=\Theta_k+\beta(\Theta_k-\Theta_{k-1}),\qquad \Theta_{k+1}=Y_k-\gamma G(Y_k,X_{k+1}). \] Under mean strong monotonicity and stochastic $L^p$ Lipschitz continuity, an explicit Perron comparison proves synchronous $L^p$ contraction when $\beta\gamma L_p<(1-\beta)(1-q_{\gamma,p})$. This direct criterion includes infinite-variance gradients for $1<p<2$, but its small-step regime requires $\beta<\mu/(\mu+L_p)$. A complementary power-Lyapunov argument establishes a positive, generally much smaller, step-size interval for every fixed $\beta<1$ and every $p>1$, using only a finite $p$th gradient moment. At $p=2$, a simpler explicit certificate gives \[ 0<\gamma<\frac{2\mu(1-\beta)^2}{L_2^2(1-\beta+2\beta^2)}. \] Its quadratic high-momentum scaling is a limitation of the chosen metric, not a sharp stability boundary. We quantify this loss, provide a general mean-only quadratic $S$-procedure, and exploit endpoint Lyapunov inequalities under stronger samplewise sector information. Verified endpoint certificates can be orders of magnitude less conservative than the explicit metric.

Large language models (LLMs) as a judge enable scalable evaluation, but their judgments can be sensitive to response order and, even after removing such position effects, can still diverge systematically from human preferences.We introduce DIAL, a unified framework that combines abundant LLM comparisons with limited human comparisons to separate judge-specific position effects, learn shared structure in position-debiased LLM preferences, and adaptively calibrate that structure toward the human preference target. Theoretically, we study three aspects of DIAL: (i) identification of latent LLM preferences, position effects, and human calibration; (ii) adaptive estimation that balances LLM anchoring against limited human evidence; and (iii) fixed-weight uncertainty quantification for the calibrated human preference. Empirically, we evaluate position debiasing and human alignment separately in controlled simulations and on three human-preference benchmarks, showing that DIAL remains robust to unbalanced response order, achieves strong human-aligned rankings with limited labels, and adapts toward human evidence when LLM information is imperfect. Our real-data study collects over 410K judgments from 21 LLM judges in both display orders, providing a resource for future studies of LLM-judge bias, heterogeneity, and human alignment.

The flatness of the loss landscape at a minimizer is a widely used heuristic for reasoning about neural-network generalization, yet evidence for this relation is mostly empirical and controversial. We study this relation in a teacher-student tree committee machine, where both the ERM estimator and the Hessian spectrum are analytically tractable in the proportional high-dimensional limit. First, we use a zero-temperature Gibbs formulation to obtain predictions for the observables of the typical minimizers of the empirical loss. Secondly, we use Edwards-Jones formalism to derive the limiting Hessian resolvent around these typical minimizers. All predictions agree with finite-size gradient-descent simulations. Finally, we study three measures of flatness, namely the left and right edges and the spectral mean, and check if a decrease in generalization error as the dataset size is increased corresponds to an increase in flatness. We find that the answer strongly depends on the learning task and on the ratio of the number of parameters to the number of data points. In regression, the spectral mean and right edge correlate with the generalization error, while the left edge does so only in the overparametrized regime. In classification this correlation reliably holds only in the highly overparametrized phase, while for underparametrized networks it can even reverse.

Knowing where species occur is fundamental for biodiversity research and conservation. Species distribution models (SDMs) link species observations to environmental conditions to estimate their spatial distribution. However, accuracy varies with the underlying data and models, making it essential to know for which species models can be trusted. Deep-learning-based SDMs ("DeepSDMs") now jointly model thousands of species, drawing on hundreds of millions of community-science records. At this scale, averaging performance hides substantial species-level variability, particularly for rare species, often of greatest conservation concern. Records are also strongly biased, making occurrence counts misleading. Accounting for these factors is essential for a reliable and informative evaluation of multi-species SDMs. Here, we introduce a Sampling-Aware Global Evaluation (SAGE) benchmark, combining GBIF records for training with sPlotOpen vegetation plots for presence-absence evaluation across 5771 plant species. We propose an evaluation framework that groups species based on two properties, sampling effort and relative prevalence, which describe how densely a species' range is sampled and how frequently the species is recorded. Evaluating single-species SDMs and multi-species DeepSDMs, we find that Random Forests and DeepSDMs perform best overall, but neither dominates: DeepSDMs outperform single-species SDMs for infrequently recorded species while offering no consistent advantage for well-sampled ones. Crucially, this advantage emerges only when established bias-correction practices, such as spatial thinning and reweighting, are carried over to the deep-learning setting. SAGE helps identify the species and data conditions for which a given approach is beneficial, thereby supporting the development of more transparent and ecologically credible SDMs. Data and code: https://earens.github.io/sage/

Trimming methods for robust clusterwise regression discard a fixed fraction of the data. Too low a level breaks the fit; too generous a level can trim away a small group. We first propose a group-recovery step that can follow any trimming or flagging method: it searches the discarded units for a line, tests whether those near it form a peak rather than a band, and restores the line as a group when the likelihood of Gaussian groups plus uniform noise improves by a margin like that of the Bayesian information criterion. In simulations it repaired the failures of a generous TCLUST-REG level with unequal groups, but not with three or four groups. The second proposal, ESF (exact-subsample flagging), is a flagging procedure without a trimming level: it solves the clusterwise least-squares problem exactly on small subsamples, flags units far from the best fit, and draws later subsamples from the rest. Two constants stand in for the level: a subsample size, set from a lower bound on the smallest group proportion, and a cap on the flagged set. It is meant for data about whose contamination nothing is known: TCLUST-REG at the fixed level 0.30, followed by reweighting and the recovery step, was as accurate as ESF on average up to a fifth of outliers, and higher levels were more accurate beyond. The flagged fraction estimates the contamination only when the errors are close to Gaussian. On taxi fares with known tariffs, ESF found both in every sample.

Lexical semantic change is usually summarized by a scalar distance between independently sampled period distributions. This measures how much a word changed, but does not reveal when it changed, which mechanisms and component movements carried the change, or which usages support the attribution. We introduce Coupled Usage–Sense Processes (CUSP), which derives these answers from a single marginal preserving temporal process. A hierarchical coupling relates contextual distributions through latent usage components, while Markov composition makes adjacent and longer span correspondences compatible. Displacement operators quantify change magnitude and timing, split variation exactly between movement of component centers and reorganization within components, and attribute it to transported component pairs. Word-local modes resolve distinct directions of change and their activity over time, while representative passages from attributed components ground the analysis in text. Under a Gaussian mixture specialization, we prove parametric recovery of the operators and squared distances. Synthetic experiments support the predicted rate. CUSP remains competitive on English and German DWUG and recovers controlled Janus profiles while maintaining compositionally coherent transport. A large corpus of US court opinions demonstrates transition, mode, and passage attribution in unlabeled natural text. CUSP thus makes magnitude, timing, mechanism, movement, modes, and textual evidence compatible views of one lexical history.

Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExTRA), introduced for classification by Maity et al. (2023), to estimate structured distribution shifts. We compare using its estimated weights in conformal calibration with additionally tilting the source predictive distribution. Shared learned predictors, estimated weights, calibration samples, and test observations isolate the effect of tilting. Existing theory gives both procedures target coverage with true weights and a common coverage bound with estimated weights. Identification calculations and an analysis of how scoring interacts with weight estimation error help explain why their performance can nevertheless differ. In a synthetic regression setting where the assumed models match the data-generating process and target inputs are informative about the shift, tilting reduces mean set length by about $30\%$ relative to weighting alone, with both methods attaining coverage near nominal. Tilting can instead cause substantial coverage losses in synthetic classification and in regression when target inputs provide little information about the response shift. Real-data experiments also show no consistent benefit. Good coverage from weighted calibration alone does not ensure that adding predictive tilting will preserve coverage. Deciding when to apply this additional adjustment using only source labels and target inputs remains an open problem.

We consider stochastic nonlinear optimization problems with deterministic equality constraints. While unconstrained stochastic optimization is well understood, the interplay between optimality and feasibility in the constrained setting poses significant challenges. Moreover, existing theoretical guarantees for constrained stochastic methods predominantly rely on bounded-variance assumptions, leaving the heavy-tailed noise regime largely unexplored. To address this gap, we propose a novel trust-region method within the stochastic sequential quadratic programming framework, termed TR-SSQP. Our method employs a normal-tangential decomposition in the step computation to balance optimality and feasibility. In addition, we incorporate a normalization mechanism in the design of the trust-region radius, together with Polyak momentum for gradient estimation, ensuring stable updates without gradient clipping. When the trust-region radius and the momentum parameter decay at appropriate rates, we establish global almost-sure convergence of the method. To the best of our knowledge, this is the first asymptotic convergence result for constrained stochastic optimization under heavy-tailed noise. We demonstrate the promising performance of the proposed method through extensive numerical experiments, including comparisons among its variants and with existing constrained stochastic optimization methods.

Estimation of parameter of probabilistic models is an important task in the field of machine learning.For models of discrete variables, calculation of the normalization constant of model is sometimes difficult and a lot of researches have been done to avoid the calculation of the normalization constant. In this paper, we tackle with the difficulty by combining a technique of empirical localization and a deformed Bregman divergence.The technique of empirical localization makes it possible to drastically reduce computational cost of the calculation of the normalization constant, and in addition, appropriate choice of the deformation for the Bregman divergence can invest the proposed estimator with various kinds of favorable statistical properties, such as efficiency or robustness against outlier noise.

World models for epidemiology learn from records shaped by study designs, including assignment, sampling, measurement, and related processes. A model may therefore reconstruct observed trajectories while learning an intervention contrast that depends on how records were collected. We formalize study design as constraints on a world model latent-world interface, action mechanism, observation likelihood, and target readout. This distinguishes design-respecting models, which encode these constraints, from design-ignoring models, which fit selected records without relating assignment and observation to the intended intervention question. Using a large scale cluster-randomized test-negative trial, we hold the latent structure and fitting settings fixed and compare a design-ignoring case-count model with a design-respecting test-negative observation model. Both models achieve comparable factual reconstruction. Yet across 500 paired resampling experiments at different relative sampling intensity, median contrast changes are substantial for the design-ignoring model, versus merely marginal for the design-respecting model. The same qualitative separation holds when sampling also varies across clusters. Thus, factual reconstruction alone does not establish design alignment; testing whether fitted contrasts preserve design-implied observation-process invariances provides a sharper evaluation.

Task performance need not determine which intervention mechanism an agent retains. We study causal retention: whether a frozen learned state answers a mechanism-probe map fixed independently of training, including action, context, direct target, value, and delay. For finite structural causal model classes, the optimal probe error is a Bayes decision risk. It vanishes exactly when every learning-interface fiber lies within one probe-answer fiber; any state obtained by post-processing that interface inherits the same lower bound. A posterior-coverage theorem characterizes budgeted retesting, while an exact edit decomposition shows that the shifted set is the unique support of an error-free target update. Causal Core implements these conditions through evidence-gated writing, readout filtering, temporal credit, hidden-context setup, and local diagnostic updates. Experiments cover finite causal systems, continuous simulators, an official TD-MPC2 world model, and Qwen2.5-7B-Instruct. A frozen Qwen last-layer probe reaches 0.958 balanced accuracy on source mechanisms but 0.583 on changed delays; the gated mechanism state reaches 1.000 and accepts only 0.056 of synchronized-readout candidates. In TD-MPC2, five target states per actuator recover effect-sign accuracy from 0.057 to 0.948 without degrading stable responses. Causal retention is therefore distinct from task sufficiency and source-domain decodability.

We consider the problem of learning the underlying causal directed acyclic graph (DAG) structure corresponding to a structural equation model (SEM) with non-Gaussian errors. Motivated by an intentionally misspecified non-Gaussian SEM with all Laplace errors, we first introduce the mean absolute residual risk, defined over the space of all real matrices, and show that, asymptotically, the risk of the true weighted causal DAG matrix is strictly smaller than that of any other matrix. Nevertheless, to enhance generality and account for high-dimensional and finite-sample settings, we further incorporate row-specific sparsity penalties along with a soft DAG constraint to derive a continuous score function over the space of real matrices. Accordingly, we propose a score-based DAG learning method, named MARCEDES, formulated as an unconstrained score minimization problem, which can be efficiently solved using gradient-based optimization techniques, thereby circumventing the challenges associated with constrained optimization. Furthermore, we develop a computational algorithm to handle the non-smoothness of the score objective and to enable optimal tuning of row-specific sparsity penalties under a generalized Bayes framework. Finally, we demonstrate the efficiency and improved performance of the proposed method over existing approaches through an extensive simulation study.

Explainable Artificial Intelligence (XAI) tools have often been presented as methods to increase trust in machine learning models by making aspects of their algorithms more human-understandable. However, evidence accumulated over the last decade points to an overall failure of this objective, instead promoting overreliance on incorrect predictions, which can subsequently lead to algorithmic aversion. Rather, XAI appears to function primarily as a debugging tool, useful for obtaining anecdotal insights into, for example, features learned by the model. One of the main issues underlying this limitation is that XAI methods often oversimplify the inner workings of the model, resulting in misalignment between the explanation and the model itself - a behavior referred to as unfaithfulness or infidelity. Faithfulness can be interpreted as the degree of approximation between an explanation and the model. Computing faithfulness in a rigorous manner would thus make it possible to quantify one of the various elements of trustworthiness of an explanation. However, existing metrics present significant limitations, making this quantification either infeasible or computationally expensive. In this position paper, we outline five major shortcomings of current faithfulness metrics and propose four possible avenues for research to bolster their reliability.

Spatio-temporal forecasting is a cornerstone of logistics, urban planning, and intelligent transportation systems. However, constrained by deployment costs and maintenance resources, sensor networks often lack comprehensive spatial coverage, rendering Forecast Unobserved Node States (FUNS) a critical yet formidable challenge. Conventional models rely on historical observations and typically falter when encountering nodes without prior records. To address this, we redefine the problem as a conditional generation task on spatio-temporal graphs and propose GenST, a framework that introduces Large Language Models (LLMs) as a semantic bridge, leveraging a pre-trained LLM fine-tuned to extract rich semantic features from node descriptions, such as functional zones and road network structures, to compensate for missing spatio-temporal signals. Specifically, we design a two-stage generative architecture: a Spatio-Temporal VAE first compresses spatio-temporal dynamics into a latent space, followed by a Generative Transformer (GenT) that reconstructs the future states of unobserved nodes from noise, guided by multi-modal conditions including semantics, geographic coordinates, and neighborhood contexts. Experiments on six traffic and two non-traffic datasets show GenST significantly outperforms existing baselines in zero-shot prediction tasks, demonstrating the practical potential of semantic-guided generation for mitigating spatio-temporal data sparsity.

Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.

Large language models are often post-trained on expert demonstrations using cross-entropy (CE), even when the downstream objective is not to imitate the demonstrated solution but to produce any output accepted by a verifier. This mismatch is seen in verifiable domains with multiple correct solutions, such as mathematical reasoning and code generation, where training data may contain only one expert solution per problem. We show that minimizing cross-entropy can be misaligned with minimizing verifier risk; two policies can assign identical likelihood to the observed demonstrations while placing different probability mass on incorrect outputs. This is formalized through a learning-theoretic counterexample in which CE minimization selects a suboptimal policy. We identify that controlling the support of the learned policy can solve this problem by preventing probability mass from spreading to unsupported outputs. Since support size is non-differentiable and computationally intractable, we propose entropy-regularized cross-entropy (ER-CE), using token-level Shannon entropy as a tractable proxy. Finally, across mathematical reasoning and code-generation benchmarks, we find that entropy-regularized training consistently improves verifier accuracy over standard cross-entropy. Our results identify a simple failure mode of imitation-based post-training in verifiable tasks and provide a practical objective that is better aligned with producing correct outputs.

CryoEM map interpretation requires features that are spatially localized, consistent across samples, and informative across spatial scales. Most deep learning methods for map annotation extract features from fixed voxel grids. However, implicit neural representations (INRs) are able to model volumetric data as scale-agnostic, coordinate-conditioned functions. INRs are therefore attractive for cryoEM, but fitting a separate INR for each map is too expensive for large-scale feature extraction and produces representations that are not aligned across samples. We introduce Atelier, a self-supervised framework that amortizes INR fitting for reconstructed cryoEM maps. Pretrained on 5,439 Electron Microscopy Data Bank maps, Atelier is a transformer-based hypernetwork that generates high-fidelity reconstructions across a wide range of protein structures, including large multi-subunit assemblies. Beyond reconstruction, the INR generated by the pretrained transformer exposes a continuous, local feature field through its intermediate activations at any spatial query point, a property that voxel grid and patch-tokenizer architectures do not naturally provide. Used as auxiliary channels to a 3D nested U-Net annotation head trained from scratch, these coordinate-conditioned features improve performance on eight voxel-level property prediction tasks over a volume-only baseline. Our results demonstrate that amortized implicit neural representations are an effective primitive for geometry-aware analysis of cryoEM data.

Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry–Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.

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.

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.

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 $\alpha = 0.1$.