Papers

Online controlled experiments, or A/B tests, are widely used to estimate causal effects on digital platforms. A central challenge is to improve experimental sensitivity, or statistical power, without increasing the experimental sample size. Stratified sampling is a classical variance reduction technique; however, its effectiveness depends critically on how the strata are constructed. We thus propose an optimization-based stratification framework for stratified sampling using optimal multi-way decision trees. Our method, called Optimal Multi-way Stratification Trees (OMST), formulates stratification as a path-selection problem over a feature graph. The selected paths define interpretable stratification rules and are optimized using an exact variance-minimizing binary optimization formulation under continuous proportional allocation and a Neyman-type optimal allocation. We incorporate supervised optimal binning to generate outcome-relevant candidate splits for numerical features. Furthermore, we introduce reduction procedures for redundant candidate paths and assignment constraints, substantially reducing the optimization problem size. Experiments on both a real-world and a simulated dataset demonstrate that OMST achieves comparable or superior variance reduction to existing methods while maintaining shallow and interpretable stratification trees.

High-dimensional count data are common in scientific applications, but most diffusion and flow models are designed for continuous or categorical data, and generation often requires many sequential model evaluations. We propose Count Flow Map, a generative model that learns finite-time transitions directly in count space for one- or few-step generation. Our model directly learns stochastic transitions over finite time intervals, using Poisson births and Binomial deaths to preserve nonnegative integer counts without a predefined maximum. These transition models are trained to match the underlying local birth–death dynamics and to maintain consistency across step sizes. We characterize the connection between local dynamics and finite-time transition consistency and derive a bound on the generation error. After validating Count Flow Map in several simulations, including a high-dimensional, high-count setting, we apply it to single-cell drug perturbation prediction and neural population forecasting, where it captures perturbation responses and supports forecasts of high-activity events with only one or a few model evaluations. Together, these experiments demonstrate that Count Flow Map enables high-quality generation directly in count space across inference budgets, from one-step to few-step generation, using a single trained model.

In a decentralized multi-robot team under partial observability, the fact that decides a robot's next action is often visible only to a teammate. Existing decentralized methods communicate kinematic information, such as position or planned trajectory, which cannot convey what the teammate perceives. Learned communication in multi-agent reinforcement learning (MARL) can carry perceptual content, but the resulting messages are task-coupled and opaque. We propose Latent Telepathy. Each robot broadcasts the perceptual latent vector it already computes for its own use, the output of an encoder trained with a self-supervised joint-embedding predictive objective, frozen, and shared across the team. A teammate learns to act on it from task reward alone. Because the encoder already runs for perception, the message costs no additional computation and a single compact vector of bandwidth. Because the encoder is frozen before any policy is trained, the message means the same thing to every robot, and the receiving robot is never told what it means. We evaluate Latent Telepathy with a content-controlled protocol in which bandwidth, latency, topology and receiver are held fixed and only the message content varies. Broadcasting the latent lets a navigator avoid an occluded hazard in 99.7% of episodes, matching a noiseless hand-designed message. Position and trajectory messages remain at chance, and the raw camera image, 186 times wider, is less reliable than the compressed latent. The result holds from a discrete gridworld to rendered pixels under continuous velocity control, and the encoder decodes the hazard from a physical robot's camera in 102 of 102 live decisions. We also identify a requirement for porting MARL communication results to continuous control, that the decision a message informs must remain reachable by exploration, and show how to restore it.

We study repeated prophet inequalities under prefix feedback. In each of $T$ rounds, a learner encounters fresh values drawn independently from $n$ boxes with unknown $[0,1]$-supported distributions in a fixed order and must irrevocably accept one, observing only the prefix up to its stopping box. Regret is measured against the optimal stopping policy that knows the distributions. We give an efficient algorithm achieving $\widetilde O(\sqrt{T})$ expected regret, matching the lower bound up to logarithmic factors. Our algorithm explores directly through near-optimal policies, combining empirical backward induction with box-specific reach bonuses. A relative-drop aggregation rule then exploits the nesting structure of observed prefixes to preserve exploration, thereby removing the polynomial dependence on the box number $n$. This resolves an open question posed by Liu et al. (2025).

Subliminal Learning (SL) is a recently identified phenomenon in which a student model acquires downstream task capabilities by matching seemingly unrelated auxiliary outputs from a teacher, despite never observing task labels, task-specific outputs, or the original training data. While recent studies have identified where subliminal signals may reside, the optimization mechanism underlying this phenomenon remains poorly understood. In this work, we provide a mechanistic understanding of SL through the lens of learning dynamics. Specifically, we derive a chained cross-task kernel that explicitly links ghost-output supervision to changes in task predictions through shared backbone representations. Our unified analytical framework provides a rigorous mathematical explanation for three central empirical puzzles in SL: (i) under shared initialization, the transfer operator forms a strictly Positive Semi-Definite (PSD) structure, guaranteeing that ghost-output optimization aligns the student with the teacher's true task objective without explicit label exposure; (ii) the ghost-output dimensionality acts as an explicit rank bottleneck governing the transfer of task-relevant features; and (iii) synthetic, high-entropy inputs function as broadband probes that maximize cross-task kernel overlap, explaining why random noise consistently outperforms structured data for subliminal transfer. Experiments on the canonical ghost-output setting validate all three theoretical predictions, providing the first learning-dynamics-based theoretical explanation of how ghost-output supervision gives rise to subliminal learning.

Time series forecasting underpins critical decision-making across diverse domains. While large language models (LLMs) offer promising reasoning capabilities, existing LLM-based time series forecasting approaches either reduce them to numerical predictors that bypass their strengths, or allow direct forecast generation that destabilizes predictions in non-stationary settings. We introduce CTRL, a framework that decouples semantic reasoning from quantitative prediction. A frozen backbone generates base forecasts, while specialized LLM agents function as controllers that analyze backbone prediction errors through decomposed trend, seasonal, and irregular components, grounding reasoning in interpretable temporal structure. Each agent outputs compact control signals that a lightweight residual decoder translates into forecast corrections. CTRL incorporates label-free test-time adaptation that detects distribution shift from input statistics alone and readapts control signals with only 3-24 LLM calls via caching. CTRL is explicitly designed to improve robustness under non-stationary temporal dynamics and distribution shift, while remaining competitive on highly stationary time series where adaptive correction provides limited additional benefit.

Changing a humanoid robot's manipulation policy should not require retraining the controller that maintains the robot's balance. This study introduces DUET, a decoupled execution framework that enables locomotion and manipulation controllers to operate simultaneously by combining their commands only at the robot interface. A reinforcement-learning locomotion policy controls the 12 leg joints and a waist yaw joint, tracking planar velocity, turning rate, and pelvis height from deep crouching to upright standing on a 23-degree-of-freedom Unitree G1. The 10 arm joints are excluded from the action space, while their positions and velocities are included only as observations, so that any compatible manipulation policy that generates arm-joint targets can control the upper body, and the locomotion policy keeps the lower body stable without requiring shared training or direct coordination. This study demonstrates the modular approach on hardware by pairing the same locomotion checkpoint with two different vision-language-action models, GR00T N1.7 and pi0.5. In simulation evaluation, the locomotion controller kept the robot's lower body stable with no falls while tracking the commanded planar velocity, yaw rate, and pelvis height with errors of 0.186 m/s, 0.142 rad/s, and 0.016 m, respectively. Ablation studies identify the upper-body pose curriculum as the dominant component, and removing this training step reduces episode survival from 20.0 to 7.4 seconds and increases the fall rate to 6.06 per environment minute. Robustness tests show no falls under pushes of up to 1.0 m/s within the trained payload range, and no falls at twice the payload limit for pushes below 0.7 m/s. These results show that a manipulation policy can be exchanged without retraining, restarting, or otherwise touching the layer that keeps the robot upright.

Depression severity among patients with chronic or acute medical conditions is influenced by a complex interaction of baseline psychological state, demographic characteristics, clinical context, and engagement with behavioral interventions. This paper presents an interpretable machine-learning analysis of a multi-center longitudinal clinical cohort to predict Beck Depression Inventory-II (BDI-II) scores at 12 and 24 weeks following mindfulness-based intervention participation. The study uses demographic variables, clinical condition information, hospital-center identifiers, baseline BDI-II scores, and therapy engagement measures to model short-term and long-term depression outcomes. Missing follow-up outcomes were addressed using a model-based stochastic imputation procedure to preserve the modest sample size while maintaining outcome variability. Five regression models were evaluated, spanning regularized linear regression and tree-based ensemble methods. Ridge Regression achieved the best 12-week performance with an RMSE of 5.186 and R^2 of 0.474, while LightGBM achieved the best 24-week performance with an RMSE of 5.038 and R^2 of 0.525. Beyond prediction accuracy, the analysis reveals three clinically relevant patterns: baseline severity remains the strongest overall predictor, short-term outcomes are more strongly associated with clinical and hospital context, and long-term outcomes show greater dependence on behavioral adherence and demographic factors. Disease-specific and hierarchical subgroup analyses further indicate that predictors differ substantially across and within clinical categories. These findings support the use of interpretable, context-aware modeling to inform personalized mental-health support following mindfulness-based interventions.

Neural operators provide fast surrogates for time-dependent PDEs, but autoregressive deployment creates a refinement-allocation problem: prediction errors vary over space and time, while only a finite number of local corrections can be committed along a trajectory. We formulate this as budgeted adaptive neural-operator solving. A global Fourier neural operator advances the full field, a local operator proposes patch-wise residual corrections, and a set-aware selector chooses where to refine. A macro policy decides when and how much of the remaining refinement budget to spend. We introduce rollout-verified policy improvement (RV-PI), which evaluates feasible refinement counts through actual continuation rollouts of the learned PDE solver, converts long-horizon advantages into conservative policy targets, and accepts an update only when held-out trajectory error improves. On the shallow-water benchmark with a 32-intervention budget, RV-PI achieves a three-seed mean trajectory relative L2 error of 0.6910, improving over immediate-only policy improvement by 5.37% and RandomMacro by 2.41%. On the forcing-driven Brusselator benchmark with a 76-intervention budget, RV-PI attains 0.09954, improving over immediate-only policy improvement by 2.31% and RandomMacro by 5.32%. These results show that, under a fixed refinement budget, the value of a local correction depends on its downstream effect on the autoregressive trajectory, not only on its immediate error reduction.

In this paper, a comparative review of different hybrid models for short-term forecasting of building thermal demand is carried out. Particularly, the assessment tackles the comparison of data-driven models enhanced with other state-of-the-art techniques. At the first step, the existing techniques reported in the literature are analysed. It is concluded that Metaheuristics or a data-driven model are used to identify the parameters of the basic model. The qualitative evaluation includes for each method the input and output features, main advantages and drawbacks. At the second step, an existing dataset of historical thermal demand from Scottish households, as well as historical weather forecasts are utilized to assess additionally the performance of existing hybrid methods. From the assessment of 13 hybrid methods, the Empirical Modal Decomposition - long short-term memory - Markov (EMD-LSTM-Markov) model can predict with the highest accuracy the day-ahead power pattern of heating and domestic hot water (DHW) demands. Though local power peaks are also accurately predicted, high power swells and spikes are underestimated. Other methods, such as Support Vector Machine - Simulated Annealing (SVM-SA) and Random Forest - Improved Sparrow Search Algorithm - LSTM (RF-ISSA-LSTM) predict a smooth pattern of heating and DHW demand profiles with rapid changes underestimating most power peaks.

While corporate sustainability mandates are expanding, the systemic reliance on self-reported emissions data exposes financial markets to pervasive greenwashing. Current literature relies heavily on subjective ESG ratings or textual sentiment analysis, leaving a critical econometric gap in objectively quantifying physical climate realities. To resolve this information asymmetry, we fuse U.S. SEC financial fundamentals with facility-level EPA greenhouse gas registries to establish a mathematically guaranteed baseline of physical corporate emissions. Leveraging a gradient boosting architecture and Mondrian Conformal Prediction, we quantify the shortfall between self-reported data and this algorithmic baseline into a novel Conformal-Weighted Continuous Divergence (CWCD) metric. Evaluating this divergence via a cross-sectional lead-lag econometric design, we uncover a robust mechanism of market discipline: algorithmic emissions divergence exhibits a severe, statistically significant negative relationship with subsequent market valuation (Tobin's Q) and operational profitability (ROA). Providing definitive evidence against the market blindness hypothesis, this study proves that institutional capital actively prices environmental deception not merely as an ethical lapse, but as a leading indicator of fundamental corporate mismanagement. Ultimately, these findings provide the quantitative justification necessary for asset managers and regulators to deploy algorithmic auditing infrastructure at scale.

Large language models are increasingly used as interacting agents, but it remains unclear how robust their coordination is when public communication is unreliable. We study this question in iterated $N$-player Stag Hunt games played by homogeneous LLM groups under controlled programmatic action inversion, which changes both the public transcript and the actions used for execution. Across an experimental grid spanning group sizes, coordination thresholds, corruption levels, and seven LLMs, we observe three main patterns. First, honest agents' pre-flip Stag choices decline as corruption increases, but the sharp fall in public success is primarily mechanical. In the focal $N=5,M=3$ setting, pre-flip success remains 78% at 80% corruption, while public success falls to 12%. Second, honest choices are associated with the public history available at decision time, particularly under high corruption. Third, three threshold-style public-report benchmarks yield similar action-match rates to the LLM agents, showing substantial descriptive agreement between LLM decisions and these benchmarks. Overall, our results show that original choices, public actions, and executed outcomes must be separated when evaluating multi-agent robustness, as corrupted communication can severely and predictably degrade mutually beneficial cooperation.

Survival prediction for glioblastoma multiforme (GBM) demands models that are both accurate and interpretable, yet existing approaches treat these objectives as com- peting, where performant models sacrifice transparency, while interpretable models accept degraded predictive power. We argue that this trade-off is not inherent. Graph neural net- works offer a structural foundation for extracting interpretable, explainable representations without compromising discriminative ability. Furthermore, current methods typically rely on a single imaging modality, underutilizing the complementary information available across multi-modal MRI and clinical metadata. We propose a multi-modal framework that inte- grates three components to address both objectives simultaneously: (1) a sheaf hypergraph neural network that captures higher-order relationships among tissue patches through direc- tional, asymmetric message passing; (2) a concept bottleneck layer that compresses learned representations into clinically grounded concepts, enforcing ante-hoc interpretability; and (3) an extension sufficiency test (EST) regularizer that penalizes unfaithful explanations during training, ensuring that model explanations genuinely reflect the internal decision process. Clinical and genomic features are incorporated through gated fusion, preserving the dominant prognostic signal of molecular markers while retaining concept-level traceabil- ity. Evaluated on 593 patients from the UPenn-GBM dataset under 5-fold cross-validation, our framework achieves a concordance index of 0.643 with the lowest fold-level variance among all compared models (std = 0.015). To our knowledge, this is the first work to unify sheaf hypergraph convolution, concept bottleneck supervision, and EST regularization for interpretable survival prediction from brain MRI

Data assimilation aims to infer the state of complex dynamical systems based on observational data. However, accurate inference of the multimodal posteriors induced by nonlinear or non-injective observation operators remains a key challenge under high-dimensional and sparse observation conditions. Ensemble filters scale to high dimensions but are confined by restrictive distributional assumptions, while training-free generative filters (e.g., EnSF, EnFF) alleviate this limitation but may introduce structural errors and hinder information propagation under sparse observations. To address these issues, we propose a training-free, asymptotically exact posterior transport method. Firstly, a covariance-aware posterior transport scheme is designed, which embeds the forecast cross-covariance into flow-based transport and accurately recovers unobserved states while preserving the non-Gaussian posterior structure. Furthermore, the method combines a tractable observation-adaptive proposal with posterior correction, ensuring accurate approximation of the nonlinear posterior distribution. Finally, we establish the corresponding posterior flow theory, from which the asymptotic exactness of the proposed method relative to finite-ensemble surrogates and the Wasserstein error bound are derived. Experiments on Double-Well, Lorenz-96, and Kolmogorov flow show that the proposed method captures complex posterior structure and remains accurate under sparse, nonlinear, and non-injective observations. In the sparse non-injective setting, it reduces RMSE by 56% relative to the best baseline.

Self-calibrating monitors adapt their threshold online to guarantee a prescribed long-run false-alarm rate under arbitrary drift. We compute the price of that guarantee, stating every law with its exact domain of validity. First, the guarantee is an accounting identity, insensitive to what the monitor is meant to detect. Two evidence identities make the cost exact for the online quantile tracker: a persistent step of height $\delta$ yields excess alarm mass within one alarm of $\delta/\eta$, and exactly $\delta/\eta$ pathwise when $\delta$ is a lattice multiple of the gain $\eta$; a ramp of slope $c$ yields a stationary excess rate of exactly $c/\eta$, independent of accumulated size, up to a boundary $c=\eta(1-\alpha)$ coinciding with the alarm-rate cap. Second, the certificate's own fluctuation obeys an exact law: the windowed alarm rate has standard deviation of order $1/L$, not the binomial $1/\sqrt{L}$, since the windowed mass telescopes to a difference of a tight internal state; the closed-form constant is validated with no fitted parameter. Detectors calibrated on the binomial scale are miscalibrated by $\sqrt{\eta\varphi(q_0)L}$, and correct calibration turns detection windows from quadratic to linear in the inverse fault speed. Third, any monitor required to tolerate a drift class $\mathcal{D}$ is blind, at any horizon and for any rule, to every fault in $\mathcal{D}-\mathcal{D}$; the proof is a deliberately elementary two-point argument and the contribution is the object it identifies: for speed-bounded classes the blind set is exactly the doubled-speed class, and the tracker absorbs a speed class fixed by its own gain, so that under a certification regime declaring absorbed drift normal, the monitor manufactures $\mathcal{D}$. An exact Gaussian projection bound, sharper than Pinsker and never vacuous, quantifies power outside it.

A robot policy is trained with one of two action parameterizations: absolute joint targets, or deltas relative to the current state. The choice is a live engineering decision in robot learning, and a world model conditioned on actions inherits it silently. We show the inheritance is catastrophic. A latent dynamics model trained on one parameterization and handed the identical commanded trajectory written in the other collapses: retrieval degrades by 2.6-13.4x across three robot datasets and two morphologies, goal-conditioned action selection falls from 53% to 15%, and on PushT the two beliefs about the same future are near-orthogonal (cos = 0.067, worst case -0.377), so the predictor does not degrade gracefully, it answers a different question. This is not a distribution-shift artifact in the usual sense: the two encodings are mutually reconstructible at R^2 = 0.996 given the joint input, so no information is lost, and we give the test that separates a valid re-parameterization from a lossy summary or a sensor swap. The test rejected three of the four axes we proposed. The defect lives in the action channel, which the invariance literature for visual models does not examine: work there concerns crops, jitter and camera pose, while the parameterization of the commands goes unaudited. The repair is averaging over the two encodings, and where it goes matters. Averaging the objective restores task performance by itself; averaging the outputs, safe for probabilities by concavity, is not available for direction-valued prediction, where the normalized mean can score below every member of the orbit. What objective-averaging leaves behind is the tail: worst-case agreement stays at 0.78, a disagreement penalty closes it to 0.995, and over a latent rollout it is the difference between a worst case that erodes and one that holds. On PushT, averaging alone does not repair the axis.

We study two-timescale decision systems in which a planning layer periodically supplies a continuation-value function to a real-time optimizer that allocates arriving resources, with inventory placement as our motivating application. We propose an end-to-end reinforcement learning (RL) method for learning this function using proximal residual value functions, which combine a strictly convex potential of post-decision inventory with a learned convex residual. This general form yields a well-posed optimization layer that supports end-to-end differentiation while preserving an explicit convex objective for real-time execution. We characterize the necessary and sufficient conditions under which a smooth value function yields decisions that are consistent across the planning and execution timescales. In an offline simulation using historical inventory arrival and demand patterns from a large e-commerce retailer, learned proximal residual value functions reduce total routing and transfer cost relative to a historical-production-system proxy by 5.0%.

Bayesian graph alignment estimates correspondence probabilities, but convergence of an alignment-score trace need not imply accurate correspondence marginals. We audit this gap on 240 new exact graph pairs from four source families, 240 larger pairs with 20-100 vertices, and a separate 60-case exact implementation check. Under an explicit edge-flip likelihood, we compare three samplers and score, marginal, indicator, categorical, and classifier-based diagnostics. Marginal disagreement improves error discrimination over score R-hat for the exact informed sampler, but its improvement for vanilla local sampling is uncertain. Assignment-based R* and short indicator panels are competitive; no diagnostic dominates across samplers and endpoints. At larger sizes, diagnostics predict subsequent marginal changes, not posterior error, and classification performance depends on the drift threshold. Disjoint-window and held-out-chain checks attenuate but preserve positive associations. Only 22 of 240 original reference sets pass an agreement screen. On forty failure-selected cases, eightfold SMC particle escalation does not resolve disagreement, whereas additional rejuvenation helps. Longer informed runs remain unstable. An elementary feasible-alignment bound demonstrates severely unrepresentative SMC and informed-chain scores in concentrated 100-vertex cases, independently of approximate reference consensus. We also exhibit common-start chains with near-zero disagreement despite exact marginal error near .967. These results support assignment-sensitive auditing while identifying limits of finite budgets, diagnostic rankings, and reference agreement as evidence of accuracy.

Day-ahead electricity price forecasts support trading and storage decisions, but for battery arbitrage predicting intraday price spreads is more relevant than predicting individual hourly prices. Here we show that a temporal hierarchy forecasting (THieF) framework that jointly reconciles forecasts of hourly electricity prices and all intraday price spreads consistently improves performance across two major European electricity markets and three different forecasting architectures. Using five years of out-of-sample data from Germany and Spain, we obtain accuracy improvements of up to 19.7% and profit gains of up to 10.4% relative to unreconciled hourly price forecasts. The gains persist even for a highly accurate pretrained TabPFN foundation model. Our results demonstrate that exploiting coherent relationships between economically relevant forecasting targets can improve both predictive accuracy and decision value, and that better statistical forecasts do not necessarily imply better economic decisions.

Unobserved confounding is a fundamental challenge in causal inference from observational data. This article develops a mixture-learning perspective, viewing latent confounders as sources of heterogeneity that induce mixture structure in observed data. Under suitable structural and identifiability assumptions, recovering the mixing distribution and component mechanisms enables estimation of interventional distributions and causal estimands. Using variants of Bernoulli mixtures as a running example, we contextualize mixture-learning techniques and their structural assumptions, and connect them to causal inference in panel-data settings, including latent factor models and synthetic interventions.We then consider high-dimensional exponential-family mixtures with dependent outcome trajectories, moving beyond counterfactual means to model counterfactual distributions. We situate this perspective relative to complementary approaches for unobserved confounding. Together, these ideas provide a bridge between mixture learning and causal inference, connecting recent advances in high-dimensional mixture learning to scalable identification and estimation of causal effects while raising new challenges for mixture learning.

LLM explainers are increasingly attached to autonomous agents as runtime oversight, with operators reading a generated account of the agent's beliefs and actions rather than its internal state. We audit the account itself, pairing an Active Inference (AIF) agent that tracks German grid demand and adjusts generation with an LLM explainer on three backends (GPT-4o, Claude-3-Opus, Gemini), and probing the pair with three black-box triggers. Corrupting the observation stream by 600 MW per step moves the agent's posterior by 490 MW, roughly 0.9% of grid capacity. None of the 30 explanations produced during the injection flag anything under a stated rubric, and each narrates the corrupted belief fluently. On timesteps where the agent takes an objectively wrong action, all three explainers produce a sycophantic rationalization 80-95% of the time (n = 20 per backend). Attacker-controlled text in the observation metadata field steers the explainer, with susceptibility differing by provider and data exfiltration succeeding on all three. We propose mitigations for each failure but do not evaluate them. In every failure we observed, the explanation was fluent and wrong. Moreover, nothing in the explainer architecture checks whether an explanation is true before an operator acts on it. Testing the explainer therefore belongs in any audit of an agentic deployment.

The Deck-of-cards-based Ordinal Regression (DOR) infers a value function from a ranking of reference alternatives in which the Decision Maker (DM) inserts blank cards between consecutive levels to express preference intensity. DOR, and its stochastic extension (SMAA-DOR), treat these answers as hard constraints defining a set of compatible value functions. We propose B-DOR, a probabilistic reformulation of DOR in which each pair of adjacent levels yields an ordinal observation, the declared direction and the number of cards, modelled through a cumulative-link likelihood that relates the number of blank cards to the latent value difference between alternatives. Two Bayesian inference algorithms are proposed: BAYES-DOR samples the whole posterior distribution by Hamiltonian Monte Carlo; FTRL-DOR tracks the maximum a posteriori estimate by constrained convex optimization. Moreover, through a multi-step elicitation process, elicitation can be spread over several short sessions reducing the cognitive burden on the DM. Both algorithms enjoy logarithmic regret bounds for prediction that hold for any sequence of DM responses and that guide the choice of the prior hyperparameters. A Monte Carlo study over 768 configurations shows that accuracy grows with the number of sessions, that blank cards add significant information over preference directions alone, that both algorithms maintain good performance under inconsistent answers, and that both outperform DOR and SMAA-DOR. An illustrative application to Italian regional healthcare performance demonstrates the practical applicability of the approach for building composite indicators.

Green's function based operator approximation offers an efficient route for solving linear partial differential equations under varying boundary conditions and source terms. Once the Green's function is learned, solutions for new configurations are obtained through integration rather than by solving the differential equation again. Existing Green's function learning methods face two structural challenges. The first is the singular behavior of the Green's function near the source point, which places a difficult approximation burden on neural networks. The second is the absence of explicit consistency between the learned Green's function and its gradient, although both quantities enter the integral solution representation directly. This work proposes SDC-GON, a Singular Decomposition and Consistency-Regularized Green's Operator Network that addresses both challenges within a unified framework. The Green's function is decomposed into an analytically known singular component and a smooth correction learned by the network, so that the neural approximation targets only the regular part of the response kernel. A self-consistency loss enforces agreement between the gradient and the autodifferentiation gradient of the smooth correction. The method is evaluated on two dimensional Poisson, three dimensional heat conduction, heterogeneous reaction diffusion, and Stokes benchmarks, consistently outperforming the compared baselines across all cases. On the heterogeneous pipe benchmark, SDC-GON achieves a testing error of $3.70\times10^{-4}$ with a smaller network architecture, compared with $9.60\times10^{-4}$ for the same-width baseline and $4.63\times10^{-4}$ for a larger configuration, demonstrating that structural improvements are more effective than increasing model size.

Lossy compression of scientific simulation data increasingly relies on learned, latent-space architectures such as Residual Vector Quantization (RVQ), which iteratively quantize a base representation and its residuals to progressively reduce reconstruction error. While effective, RVQ performs this residual modeling entirely in latent space, leaving the pixel-space error structure of the reconstruction largely unaddressed. In this work, we propose a post-processing pipeline that augments an RVQ-based compressor with a U-Net trained to predict and correct pixel-space residuals between the original volume and its RVQ reconstruction. We show that these residuals are spatially structured rather than driven by local intensity or gradient features, motivating the need for a deep spatial model rather than simple statistical correction. The U-Net-corrected reconstruction is then passed through a Guaranteed Autoencoder (GAE) stage, which projects the remaining residual onto a per-block PCA basis to enforce a user-specified block-wise error bound. To the best of our knowledge, this is the first pipeline to combine latent-space RVQ, explicit pixel-space residual correction via a deep spatial post-processing network, and GAE-based error-bound guarantees within a single framework for scientific data compression. We evaluate our approach on S3D, JHTDB and E3SM datasets, demonstrating consistent improvements in NRMSE, compression ratio] over RVQ-only and standard residual-correction baselines, while maintaining strict error guarantees required for scientific data fidelity.

Inverse design of RF and electromagnetic (EM) circuits is challenging because the relationship between circuit layout and electrical response is non-unique, and full-wave simulation is computationally expensive. This paper presents K-TRAIL, a simulator-guided generative framework for automated EM/RF circuit synthesis. K-TRAIL combines diffusion-based layout generation with derivative-free ensemble Kalman guidance, allowing feedback from a black-box EM simulator to refine candidate layouts during generation without requiring adjoint sensitivities or differentiable solver models. The framework supports both synthesis from prescribed S-parameter responses and synthesis directly from RF performance constraints. Experiments on multi-layer RFIC structures show that simulator-guided generation improves agreement with target responses and can identify structurally distinct layouts that satisfy circuit-level design requirements. The proposed approach provides a practical path toward generative, verification-aware RF circuit design while retaining the flexibility to explore diverse layout topologies.

Modern prediction-driven decision systems often rely on black-box predictors, but a point forecast alone does not provide the uncertainty scale required for robust downstream decision-making. We build a score-calibrated robustness framework that converts any fixed point predictor into a decision-relevant uncertainty representation through distribution-free conformal calibration. We use the conformal score, rather than a particular uncertainty set, as the primitive unit of robustness. The same score determines coverage-calibrated uncertainty sets for reliability-based robust optimization and normalizes target violations in a target-oriented formulation, Conformal Robust Satisficing. This formulation induces a conformal fragility measure that quantifies how rapidly performance deteriorates as the realized parameter departs from the forecast on the conformal score scale. For objective-uncertainty problems under standard convexity and duality conditions, we show that the reliability-based and target-oriented formulations parameterize the same score-calibrated robust decision frontier. This equivalence yields a data-driven mapping between reliability levels and acceptable targets and characterizes the marginal cost of robustness. Synthetic experiments validate the theoretical guarantees and illustrate the reliability-target correspondence. A real-data online-grocery case study demonstrates how the interface combines deep-learning demand forecasts with tractable inventory optimization, thereby improving reliability and reducing operational costs. Overall, our work shows that conformal scores endow fixed black-box predictors with an interpretable uncertainty scale for downstream decision-making while enabling reliability guarantees, acceptable-target selection, and fragility analysis within a unified framework.

Vinyl restoration systems must distinguish isolated clicks, short bursts, dense crackle, and overlapping damage before selecting a repair operation. We present a lightweight two-stage detector in which signal-informed sparse, burst, and dense experts produce complementary defect evidence, and a temporal backend converts that evidence into stable repair regimes. The backend factors the five-way decision hierarchically, applies a validation-only mixed regime gate, and decodes with validation-selected transition penalties that outperform a maximum-likelihood transition matrix on the same emissions. On a source-separated synthetic benchmark of 597 non-overlapping 15 s excerpts drawn from 21 recordings, the held-out system reaches 0.730 pooled five-class macro F1 (95% CI 0.694-0.761), an improvement of 0.043 over a flat frame-level router (paired bootstrap p=0.001). Clean and dense frames are highly reliable, while sparse, burst, and mixed frames remain far more ambiguous.

Comparing probability measures in machine learning trades transport geometry against computational cost: Wasserstein distances encode the geometry of $\mathbb R^d$ but require solving a transport problem, while kernel discrepancies are cheap to evaluate yet depend delicately on their test class. We study the Toscani–Fourier family $\mathrm T_{s,p}$, the weighted $L^p$ norm of the difference of two characteristic functions, as a continuous Fourier-side discrepancy on $\mathbb R^d$. For $1\le p<\infty$ we show that $d/p<s<1+d/p$ is exactly the window in which $\mathrm T_{s,p}$ is finite on $\mathcal P_p(\mathbb R^d)$, both endpoints already failing for a pair of Dirac measures, and we establish the metric, embedding, and compactness structure of the resulting space, which we prove to be complete. Duality identifies $\mathrm T_{s,p}$ as an integral probability metric over a homogeneous Fourier–Lebesgue ball, with an explicit extremizer when $1<p<\infty$. We prove the global bound $\mathrm T_{s,p}\lesssim W_p^{\,s-d/p}$, whose exponent is sharp, show that no global converse of any form can hold, and recover topological equivalence with $W_p$ on bounded-support and uniform-tail classes, together with explicit reverse moduli on bounded-support classes that improve the imported energy-kernel exponent at $p=2$. There, $\mathrm T_{s,2}$ is a constant multiple of the classical energy distance, which yields an exact finite-sample identity for the mean of the empirical discrepancy; the numerical experiments are otherwise diagnostic.

Non-intrusive load monitoring (NILM) estimates appliance-level consumption from a whole-home meter, but appliance-specific models and fixed output inventories make coverage costly to extend. We present FM4NILM (Foundation Model for NILM), a single prompt-programmable model that estimates a requested appliance's power trajectory from aggregate measurements, a natural-language description, and optional activation exemplars. A lightweight cadence-aware transformer is pretrained by masked reconstruction on 645k sequences from seven public corpora spanning 1-60 s sampling intervals, then aligned with appliance requests using observation-masked losses for partially labeled households. A Bernoulli-lognormal decoder separates activity detection from conditional power estimation. On held-out households and time periods from REDD, UK-DALE, and REFIT, one frozen text-prompted model serves twelve appliance-corpus requests, achieving 0.556 event F1, 0.625 AUPRC, and the lowest active-window MAE (251.8 W) among seven appliance-specific baselines. Streaming score aggregation raises event F1 to 0.582 with a 60 s aggregation delay. In a separate category-held-out evaluation, adding ten activation exemplars raises microwave AUPRC from 0.132 to 0.214 without parameter updates. Input-intervention ablations probe the model's dependence on appliance requests and aggregate measurements. These results demonstrate competitive disaggregation with one shared model and support extending appliance coverage through prompts and examples rather than additional specialist networks.

Real time plasma state estimation for control of Tokamak devices are challenging due to the stringent latency requirements of the plasma control system (PCS). We present an end-to-end workflow for deploying a recurrent probabilistic neural network (RPNN) on FPGA hardware. We combine architecture size reduction with quantization-aware training via QKeras. The model is then synthesized using hls4ml, targeting a Xilinx Alveo U50 device. We report a design that fits comfortably within all four resource budgets (DSP, LUT, FF, BRAM) at deterministic sub-10~$\mu$s single-timestep latency, meeting the requirements for real-time inference inside a model-predictive-control-style plasma control loop.