Papers

Industrial inspection pipelines often restore a measured image before a detector acts on it, yet restoration can suppress detector-supported defect structure or create clean-region activations. We formulate restoration as a selective action problem over the measured display, five restored candidates, and review. SafeRestore ranks candidates with action-specific fitted scores, chooses a gate on threshold-tuning data, and evaluates the fixed gate on a disjoint certification sample with two one-sided exact binomial bounds: one for the positive-conditional evidence-loss incident rate and one for the all-accepted excess-activation incident rate. The guarantee is marginal for one policy fixed before its certification outcomes are observed, under an image-level i.i.d. working model. In a retrospective split-sample study of 4,591 public Carinthia-S images, the protocol yields auditable risk-coverage behavior. The primary all-action policy passes in one of five training repetitions (12.0% +/- 26.9% pass-gated test coverage when failures count as zero), whereas fixed bicubic and reduced-complexity variants pass more often. On reserved morphologies, evidence-loss incidence rises to 81.1-90.3%, and KolektorSDD lacks both detector competence and enough positive certification images for the stated target. The contribution is therefore an auditable, detector-relative framework for deciding when a transformed image may be returned automatically and when review remains necessary – not a claim that adaptive routing outperforms simpler policies on the present evidence.

Consider $k$ independent Bernoulli populations, each sampled $n$ times, and select the $t$ populations with the largest success counts, breaking ties uniformly. Classical monotonicity reduces the worst case over the preference zone with separation $\delta$ to the slippage family with levels $p$ and $p+\delta$, leaving only its absolute location $p\in[0,1-\delta]$ undetermined. A Gaussian approximation suggests the symmetric center $p_{\mathrm c}=(1-\delta)/2$, and the exact two-population problem is uniquely centered there for every $n\ge2$. For fixed $k,t$ and $\delta\in(0,1)$, we prove that exact eventual centering holds precisely when $k=2t$. When $k\ne2t$, the least-favorable location $p_{n,k,t}^*$ satisfies \[ p_{n,k,t}^*-p_{\mathrm c} =(k-2t)C_\delta n^{-1/2}e^{-n\Gamma_\delta}\{1+o(1)\}, \] where $C_\delta$ and $\Gamma_\delta$ are explicit and positive. In either case, the least-favorable location is eventually unique. The proof writes incorrect selection as a union of pairwise misrankings and applies inclusion–exclusion, yielding a bipartite graph expansion. A single misranking has its exact maximum at the symmetric center and determines the central curvature; two-edge intersections sharing one population determine the central slope through their multiplicity imbalance; all remaining graphs have higher large-deviation rates.

We first prove spectral convergence of the random feature method (RFM) for multidimensional targets in Sobolev, Gevrey, ultra-analytic, and bandlimited classes. The analysis establishes general high-probability approximation estimates in the interpolation scale generated by a kernel integral operator. On a single event determined only by the sampled features, one random space approximates every target in a prescribed source ball; moreover, for each target, a single coefficient vector defines an approximant that attains spectral accuracy simultaneously in all admissible error norms. For both regularity-adapted frequency distributions and uniform distributions on growing frequency windows, the resulting rates range from super-exponential to algebraic, depending on the regularity of the target. Second, we establish abstract error estimates for strong- and weak-form RFM discretizations, thereby converting the preceding approximation bounds into convergence estimates for multidimensional second-order elliptic boundary value and eigenvalue problems. Finally, for random feature matrices (RFMtxs), we prove super-exponential singular-value decay with Fourier features and exponential decay with $\tanh$ features, together with corresponding condition-number lower bounds. The analysis identifies a common mechanism: the same spectral approximation that yields high accuracy also drives severe ill-conditioning.

Logit-based knowledge distillation for autoregressive language models usually aligns teacher and student next-token distributions over the entire vocabulary. However, this global objective overlooks relative preferences among likely token alternatives. Existing local approaches often select candidate tokens from either the teacher or the student alone. Teacher-only selection can miss tokens that the student considers likely, while student-only selection can rely on an inaccurate ranking early in training. We propose Adaptive Local Relational Alignment (ALRA), a position-specific framework combining student proposals with teacher guidance. At each valid prediction position, the student proposes likely tokens, while the teacher's most probable token is included as an anchor. ALRA adjusts the number of selected tokens according to how broadly the teacher distributes probability within this candidate set relative to the current batch. Adaptive Local Divergence retains the mass-matching term and separately matches the relative token distributions within the selected and remaining vocabulary regions. Unlike the exact full-vocabulary decomposition, it replaces the teacher-mass coefficients of the two conditional terms with unit coefficients, preventing either term from being downweighted solely because its region has low teacher probability. Student-Weighted Pairwise Relational Alignment emphasizes high-probability token pairs with small student probability gaps and gives less weight to unlikely or clearly separated pairs. Experiments on The Pile with randomly initialized 200M- and 500M-parameter students across nine zero-shot benchmarks yield average accuracies of 36.62% and 37.40%. ALRA exceeds the strongest competing distillation baseline by 0.94 and 0.83 percentage points and improves over pre-training without distillation by 2.31 and 2.91 points, respectively.

Affine-invariant ensemble samplers are widely used in Bayesian applications. However, their quantitative convergence theory, in particular geometric ergodicity, remains a basic open question. We study the affine invariant ensemble Langevin dynamics, an interacting particle system that uses the empirical covariance of the whole ensemble as a preconditioner. While effective in practice, theoretical understanding of this method is not available beyond plain qualitative convergence in total variation, with a central difficulty being that the empirical covariance can become degenerate. For potentials with bounded Hessian that are strongly convex outside a ball, we prove geometric ergodicity using a novel Lyapunov function that combines the inverse covariance with a coercive exponential energy. We then show that directly applying the Euler–Maruyama scheme can diverge with positive probability, even for a one-dimensional Gaussian target. This motivates a covariance-trace regularization in continuous time. We prove geometric ergodicity of the regularized diffusion and, for sufficiently small step size, of its unadjusted Euler–Maruyama discretization. We also show that the invariant distributions of the discretization converge weakly to the product target distribution as the step size tends to zero. Lastly, we provide an explicit discretization that is both affine-invariant and geometrically ergodic, based on an adaptive step size clamping.

Language models encounter typos, corrupted text, altered words, and disrupted token order, yet robustness is usually evaluated only through output behavior. We study how six naturalistic and synthetic input perturbations propagate through decoder-only language models at three levels: output behavior, hidden-state geometry, and attention-head function. We evaluate behavioral effects across four GPT-2 and two Qwen2.5 checkpoints, analyze layerwise geometry using centered kernel alignment and intrinsic dimension, and examine attention-head responses in GPT-2. Perturbation types produce distinguishable metric profiles that are not fully captured by output measures and are only partly consistent across the tested checkpoints. Copying scores show the strongest pooled associations with activation-patching recovery under token substitution and shuffling, although these associations do not isolate copying-specific effects. Gradient-guided HotFlip perturbations also cause stronger behavioral and representational disruption than rate-matched random token substitutions in GPT-2; their behavioral effects are consistent across all six tested checkpoints. Our results show that robustness claims based on a single behavioral or representational metric can be misleading, and motivate multi-level evaluation of how perturbations alter language-model computation.

We give an exact randomization-based confidence set for the average treatment effect (ATE) in matched-pair studies with a binary outcome, requiring neither monotonicity nor any distributional assumption beyond the within-pair coin flip. At its core is an analytic solution to the worst-case allocation of attributable effects: two binomial-symmetry lemmas identify the pattern hardest to reject as a single boundary corner, so testing null hypotheses needs no integer program and no numerical search. Inverting the test via binary search yields a prediction set for the attributable effect in O(log S) Binomial tail calculations; the Bonferroni proposition of Rigdon and Hudgens (2015) produces the ATE confidence set at the same computational cost. The same corner extends without further machinery to a sensitivity analysis for matched observational studies under Rosenbaum's $\Gamma$-model. A simple formula for the design sensitivity illuminates when an observational study can hope to provide evidence for an effect.

Validating a model on a time series asks for three things at once: each training run should use most of the sample (sufficiency), the test sets should together cover most of the sample (coverage), and training data should come before test data (causality). We prove that the three cannot be had together and price each one. Let $\alpha$ be the smallest training fraction over folds, $\beta$ the fraction of the sample covered by tests, $\Lambda$ the fraction of the sample used as training data from the future of a test point, and $\delta$ the distance from a test point to the nearest training point in its future. Every scheme on a sample of length $T$ satisfies $\alpha+\beta \le 1+\Lambda$ and $\alpha+\min\{\beta,\delta/T\} \le 1$, and under $\beta$-mixing the leakage bias at a test point is at most $2M\beta_{\mathrm{mix}}(\delta)$. In words: going beyond the causal frontier $\alpha+\beta=1$ requires training on the future; that future data must sit within $(1-\alpha)T$ of a test point; and its harm depends on its distance, not its amount. Hence expanding walk-forward is exactly the Pareto frontier of causal validation, $k$-fold cross-validation buys the most future data, and purged $k$-fold with an embargo pays in distance instead, which is cheap when the process forgets quickly but cannot repair the part of causality demanded by non-stationarity. On pure noise, shuffled 5-fold reports an information coefficient of $+0.32$, while contiguous 5-fold, using the same amount of future data, reports $+0.004$.

Global In-situ Observation (GIO) provides fine-scale, direct records of the global weather system from sparse point stations, making it an indispensable source for capturing localized and transient dynamics beyond the reach of satellite gridded data, and playing a critical role in key fields such as numerical weather prediction, disaster prevention, and agriculture. However, GIO exhibits strong spatiotemporal incompleteness, severely impairing accurate and real-time in-situ weather modeling. Unlike existing methods waiting for completed AI-ready data with extra introduced errors, in this work, we explore UniGIO, a novel generative framework for directly modeling global in-situ weather dynamics from native incomplete GIO. By generating missing data from observed ones annotated by masks, it unifies the coexisting forecasting, imputation, and generation under arbitrary missing ratios. Between the missing and observed, UniGIO captures station and region level complementarity through the Observation Mixer and Event Aligner, which diffuse discrete observations into continuous spaces where weather processes naturally span multiple stations. We further establish temporal dependencies with pattern shifts using the Adaptive Temporal Mixer, and track extreme events in chaotic local weather systems through a Mixture-ofExperts structure. Steady and extreme events are adapted in decoder by a Local Refiner. Extensive experiments on the up-todate largest global station weather dataset Weather-5K validate its SOTA performance with 11%, 12%, and 5% advantages on accuracy, fidelity, and extreme event capture, delivering a novel holistic solution for weather modeling in GIO networks.

Industrialized construction imposes stringent precision requirements on robotic assembly of modular components such as prefabricated window units. In tolerance-critical operations, the central bottleneck is not only mechanical clearance but also converting tacit installer expertise into data-efficient autonomy under sparse acceptance feedback, contact variability, and millimeter-scale constraints. We present an installer-in-the-loop interactive reinforcement learning framework that acquires expertise through offline teleoperated demonstrations, sparse event-driven binary takeovers at contact-failure boundaries, and acceptance-aligned terminal rewards, logged under a unified schema for traceable offline-to-online adaptation. A temporally abstract action-sequence policy built on Q-chunking with Flow Q-Learning captures multimodal recovery maneuvers under sparse terminal rewards, while a non-updating warm-start phase stabilizes the offline-to-online transition. The framework is evaluated in MuJoCo across the workflow from suction acquisition through clearance-limited seating, under structured staging and end-to-end randomized placement. Within a defined stress-test regime with 2 mm per-side clearance, bounded pose perturbations, and friction randomization, the pipeline attains 100% autonomous seating with 12–15 min of cumulative installer supervision over 3.0 h of online training, and reaches the 95% success milestone in approximately 0.5 h and 1.5 h in the two experiments. We also report wall-clock adaptation time, cumulative takeover minutes, intervention-rate decay, and stage-wise failure attribution to inform supervision budgeting. Ablations isolate the complementary contributions of temporal abstraction, installer intervention, and warm-start value calibration.

Predicting drug–target binding affinity (DTA) requires models to distinguish subtle chemical and structural determinants underlying molecular recognition. Although recent approaches increasingly incorporate richer drug and protein information, such information may be compressed, homogenized or discretized during representation construction, causing affinity-relevant distinctions to be lost before interaction modelling. We hypothesized that this representation-stage information loss constitutes an upstream bottleneck that cannot be reliably overcome by increasingly complex interaction predictors. To test this hypothesis, we developed ReGeoDTA, a representation-preserving framework that maintains affinity-relevant chemical heterogeneity in molecular representations and continuous geometric relationships in protein structures. Across three benchmark datasets, ReGeoDTA consistently improved affinity prediction, and the proposed representation-preserving strategies retained their benefits across diverse DTA architectures. Controlled representation degradation progressively reduced predictive performance, whereas increasing downstream predictor complexity failed to recover information lost during representation construction. These findings identify representation fidelity as an upstream design principle for accurate and generalizable drug–target affinity prediction, with potential implications for computational compound prioritization.

Self-supervised pretraining has transformed language and vision, but its value for molecular graph neural networks remains contested. We ask whether pretraining on a large unlabelled corpus improves molecular property prediction. We adapt LeJEPA, a predictor-free joint-embedding predictive architecture regularised by Sketched Isotropic Gaussian Regularisation (SIGReg), to molecular graphs, evaluating GPS and Chemprop-style D-MPNN encoders on the Wong et al. [1] antibiotic-activity dataset and ogbg-molhiv using a multi-seed, bootstrap-based protocol. Pretraining improves learned representations but does not robustly improve finetuning. A frozen probe on pretrained embeddings exceeds random initialisation on both tasks (ogbg-molhiv ROC-AUC 0.788 vs 0.665; +0.123), reaching the published self-supervised band, but this does not translate into finetuning gains. On the antibiotic scaffold split, a canonical partition is significant (delta AUPRC +0.041, p = 0.010), but the effect vanishes across five partitions (pooled +0.013, p = 0.095). Finetuning is null on the random split, ogbg-molhiv, and D-MPNN. The representational edge is nevertheless recoverable. Embeddings saturate at ~16-32 effective dimensions, whereas Morgan fingerprints improve to 1024 bits. At matched dimensionality, fingerprints lead validation (0.799 vs 0.782 at 128 dimensions) but trail shifted test scaffolds (0.759 vs 0.788). Truncating embeddings and combining them with a 1024-bit Morgan fingerprint raises ogbg-molhiv ROC-AUC from 0.805 to 0.832 (delta +0.027; 95% CI [+0.003, +0.054]; p = 0.014); an untrained encoder gains nothing (delta -0.003). Thus, pretraining supplies complementary information best realised through feature-level combination, while finetuning gains are weak and partition-dependent.

Counterfactual fairness audits of clinical language-model agents report a flip rate: how often an action changes when only the patient's demographic descriptor changes. Part of that rate is not demographic. A stochastic agent also changes its own action when nothing changes, and a flip rate cannot be interpreted without knowing how often. We measured it. Re-running one condition ten times over sixteen synthetic vignettes at default sampling changed a clinical agent's action in 8.7 percent of replicate pairs, from 2.2 percent for intensive-care escalation to 17.9 percent for controlled-substance caution, an output given no operational criteria. Across six models from five vendors, pooled floors ranged from 2.5 to 23.7 percent; in this panel neither disclosed size, vendor, nor hosting ordered them. The floor depends on the decoding configuration: majority voting over five draws removed 39 percent of it (95 percent confidence interval (CI) 18 to 64); at temperature 0 three of four locally served models showed no disagreement, but a hosted model still did. We also show that, for a binary action, the flip rate expected under no demographic effect equals the floor and a real effect adds only its square, so a flip rate inside the floor is not evidence of fairness, and direction must be tested with a signed paired test. We give a four-step reporting procedure and release FairMedAgent, the harness, with its protocol, vignettes and analysis scripts, so any team can measure the floor for its own agent.

We develop a probability geometric construction of generalized exponential families based on probability coordinate charts. A classical exponential family on the unit interval is transported to value space through a chart, producing what we call a G-exponential family. The construction changes the geometry in which exponential structure is represented while leaving the exponential function itself unchanged. This distinguishes it from the algebraic deformations used in the Tsallis and Kaniadakis frameworks. The transported families inherit the structure of the probability coordinate framework. The probability coordinate of each family member follows exactly the original exponential family on the unit interval. Initial Kolmogorov moments are therefore obtained by pulling classical coordinate moments back to value space. For the canonical family, the probability barycenter is the pullback of the mean parameter, while the Fisher information coincides with the Kolmogorov variance. Tail behaviour is inherited from the chart. Every family member is tail equivalent to the chart density, so heavy tails arise from geometry and remain unchanged in order under probability coordinate tilting. This is the opposite of classical exponential tilting. The sufficient statistic is bounded by construction, maximum likelihood reduces to moment matching in probability coordinates, and the maximum likelihood estimator has a bounded influence function. Thus robustness arises from geometric compactification. We also characterise G-exponential families as minimisers of relative entropy to the chart law under coordinate moment constraints and prove that transport preserves the information geometry of the family. A Cauchy chart example and a Monte Carlo study confirm efficient, calibrated, and bounded influence estimation even though every family member has an infinite mean.

Predicting fatigue life with quantified uncertainties is essential for the qualification of critical components produced by laser-based powder bed fusion additive manufacturing. We present a framework that propagates microstructure and defect uncertainties directly to a fatigue initiation life distribution for a specific part. In particular, microstructure and defect characterizations are obtained from electron backscatter diffraction and micro-computed tomography scan data, which in turn inform three physics-based simulations yielding the fatigue-affecting quantities: the elastic energy release rate, the surface energy along the crack path, and the fatigue indicator parameter. Accounting for the uncertainties in these quantities and the high correlations among them due to the shared underlying microstructure, we derive a closed-form probability density function for the fatigue initiation life. This provides an analytical distribution instead of conservative deterministic predictions and enables more informed decision making for the qualification and deployment of additively manufactured components. Applying the framework to 316L stainless steel parts produced by an EOS M290 laser powder bed fusion machine, we find that both grain sizes and void distributions influence the fatigue initiation life distribution. Specifically, for a fixed total void volume fraction, larger grain sizes cause a marginal reduction in fatigue initiation life, and a population of many small voids is more favorable for fatigue life than fewer, larger voids of equivalent total volume.

Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks. We address this by introducing a simple closed-form “two-stage” compositional formula $\hat{f}$ for reconstructing an unknown Lipschitz function $f:\mathcal{X}\to \mathbb{R}$ on a metric space $(\mathcal X,\rho)$ from $N$ i.i.d. noisy observations. Our main result is a high-probability uniform ($L^{\infty}$) recovery guarantee that jointly controls approximation and statistical errors while enjoying an optimization error of zero; in particular, we do not assume oracle access to an approximate ERM. Our secondary main results establish the optimality of our formula in three complementary senses. 1) Function space: On Ahlfors-regular metric spaces, the hypothesis class parameterized by our formula attains the optimal fat-shattering dimension. 2) Parameter space: Its dependence on the parameters is maximally numerically stable, in the sense that a smaller approximation error cannot be achieved with a smaller Lipschitz dependence on the model parameters. 3) Forward pass: Its dependence on the input is maximally regular, matching the Lipschitz constant of the target function $f$. When $\mathcal X=[0,1]^d$ is equipped with the $\ell^\infty$ norm, $\hat{f}$ admits algorithmic ReLU-MLP and exact ReLU-multi-head transformer realizations of depth $\mathcal{O}(\log(N))$ with $\mathcal{O}(N)$ nonzero parameters.

The existing multimarker survival tests focus on time to event outcomes. However, recurrent events are common in real world clinical and biomedical studies, especially in the research of chronic and recurrent diseases. In this paper, we develop a suite of set based genetic association tests for panel count outcomes under a unified weighted V statistic framework. These tests can effectively account for genetic effect heterogeneity in panel count data. Additionally, we develop small sample corrections to the tests to enhance the accuracy of the tests under small samples. Simulation studies show that the proposed tests perform well in terms of size and power across various scenarios and have a bigger power than the existing set based tests for interval censored outcomes. A dental caries GWAS data set is analyzed to illustrate the utility of the tests.

Conformal risk control is an emerging framework for the safe deployment of machine learning models with finite-sample guarantees. To accommodate a broader class of risk notions, quantile risk control extends this framework to quantile-based risk measures. However, existing methods either suffer from excessive conservatism or lack rigorous finite-sample guarantees. To address these limitations, we introduce Occupancy-based Quantile Risk Control (OQRC), a novel method that provides tight risk control bounds with finite-sample validity. Our key idea is to formulate risk control as a finite-occupancy problem by partitioning the loss space with the ordered calibration losses. Specifically, we estimate the distribution of test losses across the resulting bins and upper-bound the risk by the maximum loss attained within each bin. We then select the parameter $\lambda$ such that this upper bound does not exceed a predefined threshold $\alpha$ with high probability $1-\delta$. Theoretically, we establish a finite-sample guarantee showing that OQRC yields tight risk control bounds that converge to the optimal bounds at a provable rate of $\mathcal{O}_ p(n^{-1/2})$. Extensive experiments demonstrate the effectiveness of our method, reducing the risk gap by up to 78.64% on common benchmarks.

The Gromov-Wasserstein (GW) distance provides a principled framework for aligning metric measure (mm) spaces based solely on their intrinsic structure. Its ability to identify isomorphic representations of distributions across spaces renders it valuable for comparing data where equality up to isomorphism occurs naturally such as in graphs or, more generally, distributions on graphs. Recently, a type of dual form for the GW distance between Euclidean distributions with the squared Euclidean or inner product costs was derived, spurring the development of new statistical and algorithmic results for this setting. This work furnishes a novel duality result for GW distances with and without entropic regularization that is applicable to all finitely supported mm spaces. Leveraging this result, we derive the sample complexity of empirical GW distances between finite mm spaces, as well as limit distributions under proper centering and scaling. Furthermore, we propose new algorithms for solving the regularized GW problem which are subject to formal convergence guarantees. These statistical and algorithmic advancements give rise to a principled and efficient framework for testing whether two distributions on the set of graphs with a fixed number of nodes are isomorphic based on samples.

We propose Dynamic Reserve Margin (DRM) as a time-varying operational adequacy metric derived from risk-constrained unit commitment (RCUC) states. DRM quantifies reserve adequacy using the additional generation capacity that committed generators can provide within a 5-minute response window relative to uncertainty and contingency reserve requirements. We introduce a complementary Reserve Risk Envelope (RRE) metric to quantify operational reserve headroom in directly interpretable MW terms. A low-margin duration metric is further developed to quantify the persistence of reserve stress over an operating horizon. We use an IEEE 14-bus example to illustrate these concepts, followed by large-scale RCUC case studies under multiple operating scenarios. Results demonstrate that reserve requirements and ramp-accessible reserve capability can vary substantially across operating conditions, and that commitment decisions adapt to maintain reserve adequacy under changing system conditions. The proposed DRM and RRE metrics provide an interpretable operational characterization of reserve adequacy, reveal reserve accessibility and stress persistence that are not captured by conventional reserve margin metrics.

Statistical procedures for functional data are routinely applied after changes of time scale, registration, or other reparametrisations, although it is generally unclear when the resulting inference is independent of the chosen coordinates. We characterize this equivariance for local-linear covariance estimation from sparsely observed functional data. At the population level, covariance operators are unitarily conjugate under every diffeomorphic reparametrisation. At the estimation level, exact commutation holds universally if and only if the reparametrisation is affine. For a general \(C^{2,1}\) diffeomorphism, departure from equivariance is controlled by the normalized curvature \(\kappa_\psi=\|\psi''/\psi'\|_\infty\), with local-linear defect \[ O_P\!\left\{\kappa_\psi \left(h^2+h n_{\mathrm{loc}}^{-1/2} +h_0^2+h_0 n_{\mathrm{loc},1}^{-1/2}\right)\right\}. \] Thus zero curvature is exactly the boundary of statistical equivariance. We then show that finite-group symmetry acts as an orthogonal-projection regularizer: its risk gain is exactly the anti-invariant estimation error minus the squared symmetry misspecification. An orbit-covariance identity quantifies the attainable variance reduction and shows why group size alone does not determine the gain. These principles propagate to eigenvalues, eigenspaces and truncated PACE prediction. The results separate coordinate invariance at the population level from the geometric obstructions introduced by statistical smoothing.

Many NLP tasks, such as summarization and extractive question answering, reduce to retrieving relevant content from documents under two constraints: coverage, retaining enough pertinent information to achieve some goal, and conciseness, removing as much irrelevant information as possible. Conformal prediction methods have been used to guarantee coverage, and must be optimized for conciseness through design of a score function. State-of-the-art scoring functions use hand-engineered LLM prompts asking the model to rate the importance of content, but manual prompt engineering is labor-intensive and task-specific. We introduce the Conformal Relevance framework which uses in-context learning example curation and ensembling to create a score function which maintains coverage while improving conciseness with minimal manual input. We demonstrate this framework's application on seven NLP tasks, and also theoretically study the impact of diversity for ensembled conformal scores, giving a complementarity condition that characterizes when ensembling improves worst-case sentence scores, and a saturation bound on ensemble improvement.

Causal inference is the practice of estimating the effect of a treatment or intervention from data. It traditionally requires a bespoke pipeline for every new problem: first proposing a causal mechanism, selecting a compatible estimator, and finally training it. Meanwhile, across diverse settings and modalities, much of machine learning has shifted to the paradigm of foundation models: networks pretrained once at scale and applied to new tasks without fine-tuning. Causal foundation models (CFMs) bring this paradigm to causal inference. CFMs are pretrained neural networks that estimate causal quantities, such as the average treatment effect, on entirely new datasets using in-context learning without requiring model updates. This work provides a practical introduction to this emerging area. We summarize the necessary background in causal inference and machine learning before discussing CFMs. Throughout, we include example code and Jupyter notebooks.

Graph neural networks (GNNs) are a class of neural networks suitable for learning on graph-structured data. Their application to spatial data is a natural extension, however its relatively unclear which message-passing operations, architectural configurations, and graph representation is best suited for classifying changes to objects in electronic navigational charts (ENCs)–geospatial vector datasets used for marine navigation. Maintaining these datasets is a challenge, and categorizing changes to objects in the ENC based on their significance to navigational safety is of particular importance. Here, we propose to represent these vector navigation datasets as a graph structure where the spatial objects serve as nodes and their spatial and semantic relationships form edges. We encode both the old ENC dataset and new ENC dataset into a pair of graphs and frame the task as a graph-pair classification problem. Building on this representation, we investigate the use of GNN architectures to classify whether the encoded graphs constitutes a critical or non-critical risk to navigational safety. We train and evaluate several GNN architectures and model configurations on ENC changes reviewed by maritime experts. Our results demonstrate that graph-based representations improve the classification of ENC updates, providing a scalable approach for automating or improving ENC maintenance workflows.

Gaussian-process Bayesian optimization (GP-BO) excels at black-box optimization of costly functions, e.g., hyperparameter optimization (HPO) and multi-agent system (MAS) design. Convergence-rate guarantees exist for select methods, notably GP upper confidence bound (GP-UCB), but require a fixed kernel. Critically, the kernel encodes how input proximity affects objective value similarity. When raw coordinates poorly match this geometry - as with log-scaled hyperparameters or localized peaks - input warping can greatly improve sample efficiency, yet known GP-UCB proofs require a fixed kernel. We propose Finite-Library Input-Warped Bayesian Optimization (FLIWBO), which selects warps from a finite library of smooth input maps by any history-dependent rule. It adapts the input geometry to accelerate learning while retaining high-probability convergence guarantees under mild hypotheses, with an explicit $\sqrt(N_\varepsilon)$ library-size cost. Controlled diagnostics show that finite-library warping repairs planted geometry mismatches and identify FLIWBO failure cases. Across four repeated benchmarks - warped synthetic objectives, a confidence-fence trap, and Fashion-MNIST HPO - FLIWBO-UCB beats raw-coordinate GP-UCB under misspecified geometry, escapes traps that defeat even oracle-warp expected improvement, and recovers much of the gain from manual log scaling, while leading the tested methods that admit a matching regret guarantee. A 20-dimensional MAS design study further shows feasibility under costly noisy evaluations. Code for experiments is available: https://github.com/edvin-ketabati/bogp-paper-experiments.

Learned graph simulators provide an efficient alternative to high-fidelity solvers for granular dynamics. However, granular motion depends strongly on inter-granular contact history, which is difficult to preserve when particle contacts form, break, and rearrange. Existing simulators mainly store temporal information in node features or node-level memory. Here we introduce TRACE, a graph-network simulator that stores interaction history directly on contact edges. Each edge maintains a persistent memory updated by attention-based message passing and a gated recurrent unit, while an edge-identity dictionary preserves this memory as the contact graph changes. A physics-structured decoder predicts inter-granular normal and tangential contact forces, enforces the Coulomb friction limit, and applies equal-and-opposite internal forces. The model is trained with single-step pretraining followed by autoregressive rollout fine-tuning. We evaluate TRACE on 2D and 3D granular column-collapse benchmarks. In both cases, TRACE produces stable, physically consistent long-horizon rollouts, closely reproducing the final deposit geometry and the kinetic energy released during collapse. Compared with graph network simulator (GNS) and node-memory graph neural simulator (NMGNS), TRACE reduces long-rollout position error by 31-62% and final-deposit error by 58-89% across the two benchmarks, while using fewer parameters and maintaining near-zero particle interpenetration. TRACE also achieves 12.2$\times$ and 8.9$\times$ speedups over the material point method (MPM) reference solver in 2D and 3D, respectively. Our code is available at https://github.com/Data-Driven-Computational-Geotechnics/TRACE.

Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-k gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.

Dynamic networks are being applied in many domains, from social media to logistics systems, each with their own set of special characteristics. A model employed on this type of data must capture the duality between temporal/structural and feature-based information. Yet state-of-the-art deep learning models often struggle to learn especially short-term behavioral interaction signals, such as sender intensity or interaction inertia, directly from raw event streams. To address this gap, we propose a statistical feature augmentation method that explicitly encodes behavioral interaction statistics into the input feature space. We evaluate our proposed method on an anomaly detection task across three real-world datasets (Reddit, Wikipedia, MOOC) and seven models spanning both continuous-time and discrete-time architectures. As a baseline, we apply the same models trained on the original embeddings. Our results show, that augmentation consistently improves detection performance. Beyond performance, the enriched input enables fine-grained post-hoc analysis of behavioral importance, since each statistic occupies a dedicated input dimension. In particular, this work showcases a promising approach for merging classical network analysis with deep learning.

What does a language model predict when it has few clues? The answer lurks in its unembedding geometry: a single direction of the unembedding matrix encodes the unigram distribution of the training corpus, which serves as the Bayesian prior the model falls back on when uncertain. This structure — which we term the direction of ignorance — appears in all four model families examined (Llama, Qwen, Gemma, and Pythia), ranging from 0.4B to 405B parameters. Projecting the final prediction state onto this direction yields a per-token prior loading factor $\lambda$, which, empirically, declines steadily as the context becomes more informative. Formally, the same projection decomposes the prediction state into two orthogonal vectors that correspond exactly to the two factors of a tempered Bayesian update: a unigram prior raised to the exponent $\lambda$ and a context-driven likelihood. This geometric-probabilistic interpretation calibrates $\lambda$, making it meaningfully comparable across model sizes and families, with larger models generally exhibiting lower prior reliance in the high-context limit. Finally, we show that the direction of ignorance is causally active: raising or lowering $\lambda$ at the final prediction state steers the prediction toward or away from the unigram prior in KL divergence.

Convolutional Neural Networks (CNNs) have undoubtedly revolutionized image data analysis and the field of computer vision. As the cornerstone of CNNs, the convolution operation enables the networks to extract abstract features and uncover hidden relationships in the image data. This paper considers the problem of estimating convolution filters from a statistical perspective using a classical tool — Stein's formula. We first formulate CNNs into a general index model with matrix-valued input, where convolution filters can be viewed as index vectors. Furthermore, we propose a novel singular value decomposition (SVD) based approach to accurately learn the convolution filters based on a generalized version of the first-order Stein's formula. Theoretical analysis suggests that our estimation achieves an optimal convergence rate, comparable to that of generalized linear models where the link function is known. Extensive simulation studies and real data analyses demonstrate that our approach outperforms popular deep learning algorithms, such as Adam. Notably, our method extends beyond filter estimation and can be applied to nonlinear dimension reduction, providing a viable pathway for representation learning.