Papers

Understanding soil is fundamental to agriculture, carbon cycling, and environmental sustainability, yet progress is limited by fragmented and heterogeneous datasets that constrain modeling to small-scale predictive settings rather than high-dimensional representation learning. We introduce LUCAS-MEGA, a large-scale multimodal dataset constructed through systematic data fusion of European soil-environment observations, with the LUCAS survey as its backbone. The fused dataset comprises over 70,000 samples and more than 1,000 features spanning physical, chemical, environmental, biological, and visual attributes, aggregated from 68 source datasets. To enable integration at scale, we develop SoilFuser, a multi-agent, human-in-the-loop data fusion pipeline that standardizes heterogeneous data formats and measurement protocols, resolves inconsistencies and invalid entries (e.g., unit inconsistencies, codebook mismatches, and erroneous values), incorporates natural language annotations, and harmonizes multimodal attributes and metadata into a unified, machine learning-ready feature space. The resulting dataset captures key characteristics of real-world soil observations, including multimodality, uneven feature coverage, and heterogeneous uncertainty. To demonstrate the usability of LUCAS-MEGA for data-driven modeling, we pretrain a multimodal tabular transformer (SoilFormer) using a self-supervised objective based on feature masking, achieving stable training, strong predictive performance, and representations that support uncertainty-aware prediction. We further show that the learned representations recover relationships consistent with established soil processes. LUCAS-MEGA is released with open access and is accompanied by composable, agent-friendly APIs that support structured querying and data-driven workflows.

Continual incorporation of new knowledge is essential for the long-term evolution of large language models (LLMs). Existing approaches typically rely on parameter-update algorithms to mitigate catastrophic forgetting, yet they suffer from fundamental limitations: 1) forgetting is unavoidable as the amount of newly injected knowledge grows; and 2) model updates are often irreversible. As modern LLMs become increasingly expressive, it is natural to question whether large-scale weight updates are necessary for acquiring a small amount of new knowledge. In this work, we propose a principled framework that models autoregressive language generation as a Markov process over tokens, where model memory is represented by a Markov transition matrix. Under this formulation, incorporating new knowledge/tokens corresponds to extending the state space, and preserving existing transitions guarantees retention of previously learned knowledge. We then prove a sample complexity bound for incorporating new tokens via a token-to-dictionary mapping strategy. In particular, for learning the transition behavior of each new token, the required number of samples scales linearly with the number of existing tokens it is mapped to. To realize this mapping, we propose an embedding-tuning algorithm that requires minimal parameter updates and induces zero forgetting. Experimental results further demonstrate the effectiveness of our method and validate our theoretical findings.

LLMs' overconfidence, particularly when hallucinating, poses a significant challenge for the deployment of the models in safety-critical settings and makes a reliable estimation of uncertainty necessary. Existing approaches for uncertainty quantification typically prioritize lexical or probabilistic measures; however, these techniques often ignore the semantic variance of different responses with similar meaning. In this paper, we propose Adaptive Conformal Semantic Entropy (ACSE), a method for estimating prompt-level uncertainty by adaptively measuring semantic dispersion in LLMs outputs. Our uncertainty scoring function is based on clustering semantic entropy of multiple diverse responses to the same prompt. The function adaptively adjusts the uncertainty score based on semantic features of each cluster. To ensure statistical reliability of our score, we use conformal calibration to apply a decision rule to accept/abstain the prompts, providing a finite-sample, distribution-free guarantee such that the error rate among the accepted responses remains bounded by a user-specified tolerance. Our extensive experimental evaluations using different LLMs and datasets, demonstrate that our approach consistently outperforms state-of-the-art uncertainty quantification baselines using discriminative performance, conformal guarantees, and probabilistic calibration indicators. As a highlight, for TriviaQA dataset, AUROC of our approach is 0.88 compared to 0.65 produced by the token entropy approach.

We present a discrete diffusion-based language model using Glauber dynamics from statistical physics. Our main insight is that instead of trying to train a discrete state space diffusion model using Glauber dynamics with a uniform transition kernel as the forward process, one can set up an “energy function” based on pretrained causal/masked language models. When viewed as the stationary distribution, this energy function allows us to significantly improve the quality of the generated text. Incorporating UL2 as the pretrained model into our diffusion pipeline, we outperform prior diffusion based LMs and perform competitively with autoregressive models of comparable model sizes. Furthermore, our models are competitive with or outperform prior diffusion models and GPT-2 style auto-regressive models on zero-shot common sense reasoning tasks as well as planning and search tasks like Sudoku and Zebra puzzles.

Climate classification plays a vital role in agricultural planning, hydrological studies, and climate science. One of the most widely used systems for classifying global climate zones is the Köppen-Trewartha (KT) classification. However, the KT classification is fundamentally deterministic, offering discrete labels to spatial locations without accounting for uncertainties in classification. In this paper, we provide a framework for probabilistic modeling of climatic zones. We implement a feedforward artificial neural network (ANN) for classification, allowing for efficient, uncertainty-aware categorization of climatic regions, thereby offering a more nuanced understanding of transitional climate zones compared to traditional deterministic methods. We apply this method to the Sahara Desert region over the 30-year period of 1960 - 1989, using data at more than 400,000 space-time locations from the first 11 years to train our model. We assess the model's short- and long-term classification capabilities to evaluate its stability and accuracy over time. We also compare the probabilistic classification from our model with the traditional KT classification. In addition, we use fluctuation analysis methods to highlight the temporal evolution of climatic zones across the Sahara region and identify areas undergoing significant flux of probabilities of their climate classes, providing insights into broader trends in desertification.

Visual SLAM is a core component of spatial computing systems, yet deploying learned local feature extractors on microcontroller-class hardware remains challenging due to memory, bandwidth, and quantization constraints. While modern neural descriptors provide strong robustness, their practical adoption is often hindered by system-level bottlenecks that are not captured by FLOP-based efficiency metrics. In this work, we introduce Gideon, a hardware-aware neural feature extractor explicitly designed for resource-constrained devices. Our approach combines relational knowledge distillation from a SuperPoint teacher with differentiable neural architecture search (DNAS) under strict memory and operator constraints. Unlike conventional design pipelines, we treat quantization stability and dynamic-range compactness as first-class objectives. We show that architectural choices such as replacing Batch Normalization with affine layers significantly improve INT8 robustness, and that descriptor dimensionality directly governs quantization resilience. Deployed on STM32N6, Gideon achieves 9.003 ms inference time (111 fps) while remaining below a 1.5 MB memory footprint. Remarkably, INT8 quantization induces negligible degradation and occasionally matches full-precision performance. These results demonstrate that robust learned feature extraction can be reconciled with embedded hardware constraints through holistic hardware-algorithm co-design.

Transformer self-attention can be interpreted as a gradient flow on the unit sphere, in which tokens evolve under softmax interaction potentials and tend to form clusters. While prior work has established clustering behavior for single-head attention, the multi-head setting remains less understood due to geometric interference between heads, which invalidates standard monotonicity arguments. In this work, we develop a theoretical framework for multi-head self-attention dynamics and resolve several open questions. We show that, under suitable conditions on the score matrices, a natural multi-head energy functional is non-decreasing along both flat and spherical dynamics. We identify the key obstruction to per-head monotonicity as radial shadow terms, which are projections of each head's output onto token directions, persisting even under orthogonality assumptions. We introduce a sufficient condition ensuring monotonicity and establish robustness to approximate orthogonality. In a simplified scalar-head regime with equiangular token configurations, we derive a closed-form expression for the critical inverse temperature governing clustering behavior, and show that heterogeneous heads exhibit super-additive clustering rates. In this regime, we also prove a separation in clustering time between ReLU and softmax attention in the linearized dynamics. Finally, we establish an entropy production identity and show that attention entropy increases monotonically toward equilibrium as clustering progresses. Our results provide a unified perspective on the dynamics of multi-head attention and clarify the mechanisms underlying clustering and stability in transformer models.

Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning that departs from traditional density-based approaches by explicitly modeling the intrinsic curvature of the data manifold. The method relies on a discrete approximation of the shape operator, estimated from local k-nearest neighbor patches, to compute pointwise mean curvature without requiring explicit manifold parametrization. The key insight of MCBP is to use mean curvature as a principled descriptor of boundary structure: high-curvature regions naturally correspond to transitions between clusters, geometric irregularities, and low-density interfaces. This yields a unified geometric interpretation of boundary, outlier, and transition points. We further introduce an adaptive percentile-based thresholding scheme that enables multiscale boundary extraction without relying on ad hoc density parameters. Beyond detection, we propose a curvature-driven data decomposition that separates samples into smooth (low-curvature) and boundary (high-curvature) subsets, effectively acting as a non-linear geometric filtering mechanism. This representation enhances cluster separability and improves the robustness of downstream unsupervised algorithms. Extensive experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance, particularly in complex and high-dimensional scenarios. These results position MCBP as a concrete contribution to Geometric Machine Learning, highlighting the potential of curvature-aware analysis as a unifying paradigm bridging differential geometry and data-driven modeling.

We provide a theoretical analysis of Adam under non-stationary stochastic objectives, separating two regimes: Euclidean tracking under adaptive strong monotonicity of the Adam-preconditioned mean-gradient operator, and high-probability projected stationarity guarantees under general $L$-smooth objectives. In the tracking regime, we derive finite-time expected and high-probability bounds that decompose sharply into four components: initialization, objective drift, a first-moment tracking error governed by $\beta_1$, and a preconditioner perturbation governed by $\beta_2$. We characterize the burn-in time required for the transient terms to decay to the asymptotic tracking bound under constant and step-decay schedules. We also prove a high-probability bound on the average projected stationarity gap for Adam under distribution shift. Across both analyses, our bounds reveal a noise–drift tradeoff: in noise-dominated regimes, first-moment averaging and adaptive preconditioning can yield favorable upper guarantees, whereas in drift-dominated regimes, stale first-moment information and preconditioner perturbations can enlarge Adam's tracking guarantee, potentially allowing vanilla SGD to attain a smaller tracking error. Our explicit $(\beta_1,\beta_2,\epsilon)$-dependent bounds identify mechanisms through which adaptive step-sizing can help or hurt under nonstationarity and provide theoretical explanations consistent with Adam's empirical instability and stabilization under distribution shift.

Interactive multi-objective optimization systems face a budget allocation dilemma: one can spend resources on expensive objective evaluations or on eliciting decision-maker preferences that identify the relevant region of the Pareto set. Moreover, preference elicitation itself spans modalities with different information content and cognitive burden, ranging from cheap, noisy pairwise preference statements (PS) to richer but costlier indifference adjustments (IA). We study cost-aware optimization under an unknown scalarization and introduce QUIVER (Query-Informed Value Estimation for Regret), a surrogate-assisted evolutionary multi-objective optimizer that adaptively chooses between objective evaluations and heterogeneous preference queries. At each step, QUIVER selects the next action by maximizing the expected decision-quality improvement per unit total cost. Across DTLZ and WFG benchmarks under synthetic decision-maker models, QUIVER achieves the lowest final utility regret on challenging WFG problems (utility regret of 2.14 on WFG4, 2.82 on WFG9: a 25% improvement over baselines), outperforming all single-modality baselines. We analyze how the optimal mix of PS and IA adapts to problem difficulty: on easy problems (DTLZ2), QUIVER selects 80% PS queries; on hard problems (WFG9), it shifts to 35% IA queries. This adaptive modality selection demonstrates cost-aware preference learning in action.

Reinforcement learning from human feedback (RLHF) typically assumes a static or non-strategic reward model (RM). In iterative deployment, however, the policy generates the data on which the RM is retrained, creating a feedback loop. Building on the Stackelberg game formulation of this interaction, we derive an analytical decomposition of the policy's true optimization gradient into a standard policy gradient and a parameter-steering term that captures the policy's influence on the RM's future parameters. We show that standard iterative RLHF, which drops this steering term entirely, suffers from alignment collapse: the policy systematically exploits the RM's blind spots, producing low-quality, high-reward outputs whose feedback reinforces the very errors it exploits. To mitigate this, we propose foresighted policy optimization (FPO), a mechanism-design intervention that restores the missing steering term by regularizing the policy's parameter-steering effect on RM updates. We instantiate FPO via a scalable first-order approximation and demonstrate that it prevents alignment collapse on both controlled environments and an LLM alignment pipeline using Llama-3.2-1B.

Remaining useful life (RUL) estimation of synthetic fibre ropes (SFRs) is critical for safe operation in offshore-crane, wind turbine installation, and heavy-load handling applications, where rope failure can result in catastrophic safety incidents and costly downtime. Despite growing research interest in data-driven condition monitoring, there is no publicly available image dataset that captures the complete degradation lifecycle of SFRs under controlled cyclic fatigue loading. To address this gap, we present a novel image dataset comprising approximately 34,700 high-resolution images of eleven Dyneema SK75/78 high-modulus polyethylene (HMPE) rope samples subjected to cyclic fatigue on a sheave-bend test stand at seven distinct axial load levels ranging from 60 kN to 280 kN. Ropes were loaded until mechanical failure, with fatigue lifetimes ranging from 695 cycles to 8,340 cycles. After every fixed number of sheave cycles (an inspection burst), ten images were captured at different cross-sectional positions along the rope, providing spatially representative sampling of surface degradation throughout the rope's entire service life. The images obtained from each load are annotated with the corresponding elapsed cycle count, enabling a direct computation of RUL for any rope in the sequence. This dataset aims to support a broad range of machine learning (ML) tasks including RUL regression, damage progression modelling, anomaly detection, and load-conditioned prognostics. The dataset is intended to serve as a benchmark resource for the development and comparison of vision-based condition monitoring (CM) and prognostics algorithms for SFRs.

Vision-language models (VLMs) are increasingly deployed as trusted authorities – fact-checking images on social media, comparing products, and moderating content. Users implicitly trust that these systems perceive the same visual content as they do. We show that adversarial examples break this assumption, enabling AI authority laundering: an attacker subtly perturbs an image so that the VLM produces confident and authoritative responses about the wrong input. Unlike jailbreaks or prompt injections, our attacks do not compromise model alignment; the attack operates entirely at the perceptual level. We demonstrate that standard attacks against publicly available CLIP models transfer reliably to production VLMs – including GPT-5.4, Claude Opus~4.6, Gemini~3, and Grok~4.2. Across four attack surfaces, we show that authority laundering can amplify misinformation, disparage individuals, evade content moderation, and manipulate product recommendations. Our attacks have high success rates: In hundreds of attacks targeting identity manipulation and NSFW evasion, we measure success rates of $22 - 100\%$ across six models. No novel attack algorithm is required: basic techniques known for over a decade suffice, establishing a lower bound on attacker capability that should concern defenders. Our results demonstrate that visual adversarial robustness is now a practical – and still largely unsolved – safety problem.

Cold spraying is an increasingly common approach for repairing and manufacturing components due to its solid-state manufacturing capabilities. However, process optimization remains difficult due to many interdependent parameters and the lack of large-scale, machine-readable data to support modeling. While the scientific literature contains many relevant experiments, results are inconsistently reported (often in tables and figures) and use non-uniform units, limiting utilization at scale. To address these limitations, this work presents HUGO-CS, a literature-derived dataset of 4,383 cold-spray experiments with 144 features from 1,124 sources, exceeding the previous largest dataset (137 samples) by 30x. With completely manual extraction requiring an average of 91 minutes per document, this work designs and leverages a Hybrid-labeled, Uncertainty-aware, General-purpose, Observational extraction framework, called HUGO, to support this extraction. HUGO combines automated LLM-based labeling with targeted manual label refinement to handle this experimental result extraction process from scientific literature. To balance labeling efficiency with extraction accuracy, HUGO introduces a Hierarchical Risk Mitigation (HRM) to route LLM outputs with a high risk of potential errors for manual review, while retaining low-risk records as auto-labeled. Lastly, HUGO post-processing consolidates categorical descriptors, maps reported feedstock chemistries into structured continuous compositions, and normalizes units across sources. Of the 4,383 reported experiments, 1,765 are hand-labeled, providing a high-quality labeled subset for benchmarking, error analysis, and higher-fidelity data points. All code to replicate this work, along with the complete HUGO-CS dataset, are released under a CC-BY license at https://github.com/sprice134/HUGO.

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting optimal transport (OT) problem. Existing manifold OT methods have pursued amortized out-of-sample maps, while entropic regularization has made discrete OT more scalable, but these advantages have remained largely disjoint. We propose Entropic Riemannian Neural Optimal Transport (Entropic RNOT), a unified framework that combines intrinsic entropic OT with amortized out-of-sample evaluation on Riemannian manifolds. Our method learns a single target-side Schrödinger potential through a neural pullback parameterization, recovers the induced Gibbs coupling, and uses the resulting conditional laws to construct intrinsic transport surrogates. These include barycentric projections on Cartan-Hadamard manifolds and heat-smoothed conditional surrogates on stochastically complete manifolds, the latter turning possibly atomic target laws into absolutely continuous ones. For fixed regularization $\varepsilon>0$, we prove that the proposed hypothesis class recovers the entropic optimal coupling in strong probabilistic metrics. As consequences, barycentric surrogates converge in $L^2$, while heat-smoothed surrogates are stable at fixed heat time and asymptotically unbiased as the heat time vanishes. The guarantees hold for compactly supported data on possibly noncompact manifolds. Empirically, our method matches or improves over Euclidean, tangent-space, and log-Euclidean baselines on benchmarks over $\mathbb{S}^2$, $\mathrm{SO}(3)$, $\mathrm{SPD}(3)$, $\mathrm{SE}(3)$, and $\mathbb{H}^2$, scales favorably relative to discrete manifold Sinkhorn, and in a protein-ligand docking application, refines poses on $\mathrm{SE}(3)$ without retraining or per-instance optimization.

We introduce State Vector Space Partitioning (SVSP), a novel method to mimic a black box reinforcement learning policy using a set of human-interpretable subpolicies. By partitioning a distillation dataset of state action pairs with linear support vector machine splits, SVSP constructs a compact and structured representation of the original policy. Our method improves mean return by +7.4% over previous critic driven state partitioning attempts such as Voronoi State Partitioning (VSP) and +2.8% over the original TD3 policy, while reducing the number of required subpolicies against VSP by 82.1%. Our results pave the path towards a more flexible form of distillation where both the decision boundary and surrogate models can be chosen within a margin of the original black box behavior.

In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we consider UOT with quadratic transport cost and Kullback–Leibler penalties on the marginals relative to prescribed Gaussian measures. We show that the infinite-dimensional variational problem admits an exact Gaussian reduction, yielding a finite-dimensional optimization over masses, means, and covariances, together with a closed-form expression for the optimal transported mass. We then formulate UDC for discrete-time linear systems, where the initial and terminal state measures are imposed softly through KL penalties and the intermediate evolution is governed by controlled linear dynamics with quadratic control cost. For this problem, we prove that any feasible solution can be replaced, without loss of optimality, by a Gaussian initial measure and an affine-Gaussian control policy. This leads to an exact finite-dimensional reformulation and, after a standard covariance-steering lifting, to an SDP-based optimization for fixed mass, again coupled with a closed-form mass update. We further establish existence of optimal solutions and identify a sufficient condition under which the affine-Gaussian UDC policy is deterministic. These results provide globally optimal solution methods for both Gaussian UOT and Gaussian UDC. Finally, we illustrate our results with several numerical examples.

Nationwide road-incident forecasting is a systems problem before it is a modeling problem. A usable service must connect historical incident archives, historicalandliveweather,nationalroadgeometry, offline model training, tile generation, web serving and runtime handoff. This paper presents Road Risk Monitor, a U.S.-wide road-safety stack that combines a nationwide H3 baseline trained on FARS fatal-crash data with a road-segment forecasting pipeline trained from TIGER/Line geometry and US-Accidents events, then serves predictions through live APIs, raster tiles, JSON road tiles, and a public web application.

Large Language Model ensembles improve reasoning accuracy, but only up to a performance boundary beyond which additional deliberation degrades accuracy. We introduce DASE (Deliberative Adaptive Stopping Ensemble), a stopping heuristic for iterative ensemble deliberation that commits early on genuine consensus and applies a global-frequency fallback on fragmented evidence. We make three contributions. (1) DASE produces a commit-type routing partition that generalises across benchmarks and is complementary to verbalized single-call confidence. On GPQA-Extended (N=546, 70B ensemble), the partition yields a 39.5 pp routing gap (right-wall 81.1% vs. left-wall 41.5%). On AIME 2010-2023 (N=261, 120B ensemble, 3 seeds), right-wall commits reach 98.3% accuracy vs. left-wall 72.8% (25.5 pp gap), statistically equivalent to Opus 4.6 Standard verbalized confidence at matched coverage (25.7 pp gap; bootstrap p=0.873); the two mechanisms disagree on 37% of routing assignments. (2) Adaptive stopping, not injection bandwidth, drives accuracy. On AIME-300, bandwidth accounts for only 0.3 pp (ns). On GPQA-Extended at the 120B tier, sparse injection ($\approx15$ tokens/worker/round) achieves 70.9% with a 30.7 pp routing gap; dense injection ($\approx600$ chars/worker/round) achieves 72.2% but with halved right-wall coverage and a narrower 18.9 pp gap. (3) Injection-based methods exhibit an inverted-U accuracy-vs-inference trajectory; this pattern is hypothesis-generating.

Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often discarding cross-layer interactions induced by the network computation. We introduce Layerwise LQR (LLQR), a framework for learning structured inverse preconditioners under a global layerwise optimal-control objective. The starting point is an exact equivalence: the steepest-descent step under a broad class of divergence-induced quadratic models–including Newton, Gauss-Newton, Fisher/natural-gradient, and intermediate-layer metrics–can be written as a finite-horizon Linear Quadratic Regulator (LQR) problem. This formulation serves as a reference that exposes the layerwise dynamics and cost matrices encoding the original dense geometry. We then derive a scalable relaxation that learns diagonal, (E-)Kronecker-factored, or other structured inverse preconditioners by minimizing the LQR objective and reusing them across iterations. The resulting optimizer wraps standard methods while retaining a principled connection to second-order geometry, without forming or inverting the global curvature matrix. Experiments on ResNets and Transformers show that LLQR improves optimization dynamics and often translates these gains into improved final test performance, while adding only modest wall-clock overhead. It establishes LLQR as a practical framework for geometry-aware second-order methods and a reference for evaluating scalable approximations.

In this work, a data-driven framework based on Phase-Field simulations data is proposed to highlight the capabilities of neural networks to ensure accurate low dimensionality reduction of simulated microstructural images and to provide time-series analysis. The dataset was indeed constructed from high-fidelity Phase-Field simulations. Analyses demonstrated that the association of auto-encoder neural networks and principal component analyses leads to ensure efficient and significant dimensionality reduction: 1/196 of reduction ratio with more than 80% of accuracy. These findings give insight to apply analyses on data from the latent dimension. Application of Long Short Term Memory (LSTM) neural networks showed the possibility of making next frame predictions; that makes possible the acceleration of Phase-Field simulation without the need of high computing resources. We discussed the application of such a framework on various areas of research. Different methods are proposed from the conducted analyses, in order to ensure dimensionality reduction, including auto-encoders, principal component analysis and Artificial Neural Networks, and time-series analysis, including LSTM and Gated Recurrent Unit (GRU).

Relative positional encodings determine which functions of query-key lag can enter the primitive attention logit. RoPE supplies a rotary phase, while ALiBi supplies an additive distance bias. Motivated by group-theoretic views of linear translation-invariant positional encodings, we study a non-semisimple case in which a complex rotary eigenvalue and a nilpotent response live in the same defective Jordan block. The resulting relative operator generates oscillatory-polynomial features such as $e^{-\gamma d}\cos(\omega d)$, $e^{-\gamma d}\sin(\omega d)$, $d e^{-\gamma d}\cos(\omega d)$, and $d e^{-\gamma d}\sin(\omega d)$, for causal lag $d=i-j\geq 0$. Thus the construction realizes a distance-modulated phase basis $d e^{i\omega d}$, rather than merely adding a separate distance channel to RoPE. We formulate Exact Jordan-RoPE as a non-semisimple one-parameter representation, give its real block form, and specify the contragredient query action required by non-orthogonal positional maps. We also distinguish this exact representation from stabilized variants whose bounded shear improves numerical behavior but breaks the exact group law. Kernel-level diagnostics and a Jordan-friendly synthetic language-model task show that the coupled Jordan basis is useful when the target contains distance-modulated phase interactions. On a small WikiText-103 byte language model, a scaled-exact variant improves over RoPE and direct-sum baselines within the Jordan family, while RoPE+ALiBi remains strongest overall. The evidence is structural rather than a broad performance claim.

Diffusion-based Large Language Models (D-LLMs) represent a promising frontier in generative AI, offering fully parallel token generation that can lead to significant throughput advantages and superior GPU utilization over the traditional autoregressive paradigm. However, this parallelism is constrained by the requirement of a fixed-size response length prior to generation. This architectural limitation imposes a severe trade-off: oversized response length results in computational waste on semantically meaningless padding tokens, while undersized response length causes output truncation requiring costly re-computations that introduce unpredictable latency spikes. To tackle this issue, we propose Predict-then-Diffuse, a simple and model-agnostic framework that enables compute-budgeted inference per input query by first estimating the response length and then using it to run inference with D-LLM. At its core lies an Adaptive Response Length Predictor (AdaRLP), which estimates the optimal response length given an input query. As a measure against under-estimating the response length and re-running inference with a higher value, we introduce a data-driven safety mechanism based on a small increase of the predicted length. As a whole, our framework avoids wasting computation on padding tokens, at the same time preserving output quality. Experimental validation on multiple datasets demonstrates that Predict-then-Diffuse significantly reduces computational costs (FLOP) compared to the default D-LLM inference mechanism, while being robust to skewed data distributions.

We present Sparse Backdoor, a supply-chain attack that plants a provably undetectable backdoor in pre-trained image classifiers, including convolutional networks and Vision Transformers. The attack injects a structured sparse perturbation along a randomly chosen direction into a small subset of columns at each fully connected layer, propagating a trigger signal to an adversary-chosen target class, and masks the perturbation with an independent isotropic Gaussian dither. The dither serves a single technical purpose: it induces a clean reference distribution anchored at the pre-trained weights, against which undetectability can be formalized. Under a mild margin condition on the pre-trained classifier, we show that the dithered reference is functionally equivalent to the original classifier. We prove that distinguishing the backdoor-injected model from this reference is at least as hard as Sparse PCA detection, which is computationally infeasible under standard hardness assumptions. The guarantee holds against any probabilistic polynomial-time distinguisher with white-box access to the parameters.

Large-scale restoration in drylands is widely promoted to address land degradation and biodiversity loss, yet many efforts rely on long-term irrigation, limiting sustainability in water-scarce regions. A key challenge is identifying locations where native vegetation can persist without intensive management while minimizing costly field campaigns. A scalable pre-screening framework is presented that integrates climate and remote sensing data to enable cost-efficient site selection in arid environments using Saudi Arabia as a case study. A Climate Suitability Score (CSS), derived from machine learning models trained on expert-curated reference sites, captures complex climatic dependencies on vegetation persistence. Using multi-year ERA5-Land data for Saudi Arabia, national-scale prediction maps are generated and combined with vegetation indices to identify areas where climate is favorable, but vegetation remains underdeveloped. Multi-criteria screening reduces candidates to thirteen priority locations. Climatically analogous intact ecosystems provide benchmarks for restoration targets and indicate that an average 2.5 fold increase in vegetation coverage is a realistic target for restoration efforts. Overall, this approach narrows the search space, reduces costs, and supports resilient ecosystem recovery planning in water-limited regions.

Strategic classification studies the problem where self-interested individuals or agents manipulate their response to obtain favorable decision outcomes made by classifiers, typically turning to dishonest actions when they are less costly than genuine efforts. Prior works have demonstrated a fundamental inability to get out of this conundrum by only focusing on the design of a classifier. We note that prior work also heavily focuses on either one-shot settings or repeated interaction with the same classifier. Real-world decision making is often multi-stage, involving a sequence of potentially different classifiers as an agent progresses. This paper introduces a sequential, stochastic, multi-stage model of strategic classification, by capturing how agents adapt their behavior, through improvement actions (enhancing both observable features and true attributes) and gaming actions (enhancing only observable features), over multiple levels of classification with increasing difficulty as well as reward. For each level, we adopt a selective classifier that can abstain from making a prediction at low confidence. Consequently, a positive (resp. negative) outcome leads to promotion (resp. demotion) of the agent to the next higher (resp. lower) level, while abstention keeps the agent at the same level. We fully characterize the agent's optimal instantaneous action under selective classifiers and compare the long-term properties and utility of the agent repeatedly following an optimal myopic policy of either no-improvement (never choose the improvement action) or no-gaming (never choose the gaming action). We further examine design principles over the sequence of classifiers that yield higher long-term utility for the latter policy, thereby effectively incentivizing genuine effort in the long run.

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating accuracy and computational cost, which can be misleading since architectures exhibit different accuracy-cost scaling as width and depth vary. This issue is particularly relevant for U-Net-type encoder-decoder models, widely used for multi-scale gas, fluid, and plasma dynamics due to their ability to represent features across spatial scales. A U-Net constructs a multi-resolution representation via an encoder that progressively reduces spatial resolution, followed by a decoder that restores it for prediction. Skip connections link corresponding encoder and decoder features, preserving fine-scale information and improving optimization. In practice, U-Net width is routinely tuned, while depth is typically kept fixed (a set number of down/up-sampling stages with few convolutions per stage), limiting systematic exploration of depth for improving the accuracy-cost trade-off. We address this limitation by increasing effective depth through stacking multiple encoder-decoder "waves" in series, with skip connections both within and across waves to enable progressive cross-scale refinement. We call this architecture a Deep Wave Network (DW-Net). Training data, optimization, and schedules are kept identical across models. Instead of evaluating single configurations, we train multiple width variants of each architecture and compare accuracy vs. GPU time Pareto fronts. Across several 2D and 3D flow benchmarks, DW-Net models consistently improve the Pareto frontier over single-wave U-Nets, achieving higher accuracy at matched cost or similar accuracy at reduced cost, and reaching low-error regimes with up to 3x less training time under identical training settings.

Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings. Classical ILP relies on discrete combinatorial rule search and is brittle under uncertainty, while differentiable ILP methods typically depend on predefined rule templates or inaccurate fuzzy operators that suffer from vanishing gradients or poor approximation of logical structure when reasoning over probabilistic predicate valuations. This paper proposes an Attention-based Neuro-symbolic Differentiable Rule Extractor (ANDRE), a novel ILP framework that learns first-order logic programs by optimizing over a continuous rule space with attention-based logical operators. ANDRE replaces both rule templates and logical operators with fully differentiable, attention-driven conjunction and disjunction operators that approximate logical min-max semantics, enabling accurate, stable, and interpretable reasoning over probabilistic data. By softly selecting, negating, or excluding predicates within each rule, ANDRE supports flexible rule induction while preserving symbolic structure. Extensive experiments on classical ILP benchmarks, large-scale knowledge bases, and synthetic datasets with probabilistic predicates and noisy supervision demonstrate that ANDRE achieves competitive or superior predictive performance while reliably recovering correct symbolic rules under uncertainty. In particular, ANDRE remains robust to moderate label noise, substantially outperforming existing differentiable ILP methods in both rule extraction quality and stability.

Public attitudes toward artificial intelligence are heterogeneous, ordinally measured, and poorly captured by any single dependency graph. Existing ordinal structure learners assume a shared directed acyclic graph (DAG) across all respondents; recent heterogeneous ordinal graphical-model approaches focus on subgroup discovery rather than confirmatory cluster-specific DAG estimation; and latent profile analyses discard dependency structure entirely. We introduce a heterogeneous ordinal structure-learning framework combining monotone Gaussian score embedding, Bayesian nonparametric (BNP) complexity discovery via a truncated stick-breaking prior, and confirmatory fixed-K estimation with cluster-specific sparse DAG learning. The key methodological insight is a discovery-to-confirmation workflow: the nonparametric stage calibrates plausible archetype complexity, while inner-validated confirmatory refitting yields stable, interpretable structural estimates. On the 2024 Pew American Trends Panel AI attitudes survey, Wave 152 (W152) survey, (N = 4,788, 8 ordinal items), the confirmatory K*=5 model reduces holdout transformed-score mean squared error (MSE) by 25.8% over a single-graph baseline and by 4.6% over mixture-only clustering. A controlled tiered semi-synthetic benchmark calibrated to W152 structure validates recovery across difficulty regimes and transparently reveals failure modes under stress conditions.

When deploying reinforcement learning policies to physical robots, actuator rate constraints – hard limits on how fast each joint can move per control step – are unavoidable. These limits vary substantially across joints due to differences in motor inertia, power bandwidth, and transmission stiffness, creating pronounced heterogeneity that existing methods fail to handle geometrically: the per-joint feasible region forms a high-dimensional box in action-increment space, yet QP projection and spherical parameterization methods impose isotropic ball-shaped constraints, exponentially under-covering the true feasible set as heterogeneity grows. This paper proposes Dynamic Decoupled Spherical Radial Squashing (DD-SRad), which resolves this mismatch by computing a position-adaptive radius independently for each actuator, achieving tight alignment with the true per-joint feasible region. DD-SRad satisfies per-step hard constraints with probability~1, preserves well-conditioned gradients throughout training, and admits exact policy gradient backpropagation with zero runtime solver overhead. MuJoCo benchmark experiments demonstrate the highest task return at zero constraint violation – matching the unconstrained upper bound – with 30%–50% improvement in constraint-space coverage over spherical baselines. High-fidelity IsaacLab simulations with Unitree H1 and G1 humanoid robots confirm end-to-end optimality parameterized directly from official joint specifications, validating a systematic pathway from hardware datasheets to safe deployment.