Papers

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

Since spectroscopic measurements provide only the line-of-sight velocity, transverse motions are difficult to constrain. In the vast majority of cases, transverse velocities have been measured only for local galaxies. Radio galaxies whose jets are bent back by ram pressure into nearly parallel Narrow-Angle Tails (NATs) offer a way to extend such measurements to higher redshifts. Here, we present proprietary 15~GHz (Ku-band) and archival 6~GHz (C-band) continuum observations from the Very Large Array (VLA) of six radio galaxies in the galaxy cluster field PLCK G165.7+67.0 (G165). VLA imaging resolves two of the cluster galaxies into NATs whose tails both extend toward the Southwest, away from the cluster center of mass. Spectral index maps made at matched angular resolution resolve a steepening gradient consistent with radiative aging along the length of the tails. Physical properties of the NATs are measured and used to constrain two independent models: a Mach cone model and a nonrelativistic hydrodynamic flow model based on Euler's equation. The models returned transverse velocities of $\sim 2000 ~\rm km~ \rm s^{-1}$ for both galaxies. One NAT is the brightest cluster galaxy (BCG) and has a measured radial velocity of $-3300 ~\rm km ~\rm s^{-1}$, resulting in an even higher space velocity. The high inferred 3D velocity of the BCG may be explained if it is intercepted close to core passage.

In this paper, we consider a random walk in a non-homogeneous random environment on two types of random trees and non-negative integers. The random trees here have progeny distributions that depend on the parent's generation. We provide a sharp threshold for the type of the random walk in a random environment on the random trees and the non-negative integers, up to the critical case. Then, we find the speed of the random walk on the non-negative integers and on random spherically symmetric trees. We use the method based on the relationship between the mean exit time from a vertex and speed. Meanwhile, we discuss several special cases that could be derived from those results. We also include many limiting formulas for sequences and series in the appendix, which are helpful for this study and others.

A useful visual representation is a statistic of the observed past that retains the latent factors shared with the future and discards patch-private noise. We formalize this requirement as a conditional predictive sufficient statistic (CPSS). Under a shared-factor model of image patches, the mutual information between the past and the next patch equals the information the past carries about the shared factor, up to a remainder that the next patch itself fails to reveal. Predicting the next patch embedding with a cosine loss is maximum likelihood for a von Mises-Fisher model of that embedding's direction, and is therefore a tractable surrogate for the predictive information. The same population loss is also minimized by a constant embedding, so stop-gradient does not by itself select the sufficient statistic; it only blocks the symmetric gradient that implements the constant solution in one step. The regression target is a shallow embedding, which forces the network output back into that shallow range and leaves the sufficient statistic in intermediate blocks. Small causal Transformers on MNIST and CIFAR-10 are used as diagnostics, not as a leaderboard. On MNIST the future shift and the stop-gradient move probe accuracy by tens of points, and the CPSS readout peaks before the output. On CIFAR-10, with the same short budget and no augmentation, every objective lands near a linear classifier on pixels. What still matches the derivation is the geometry: the CPSS output is a worse readout than its best intermediate block, next-pixel regression does not pay that penalty, and removing the stop-gradient collapses the effective rank of the embedding even when the pretext loss looks perfect.

Spatial disease maps help public-health researchers identify geographic inequalities, but standard Bayesian smoothing can obscure localized disparities when neighboring communities have sharply different socioeconomic or behavioral profiles. Analysts therefore need to determine where smoothing should be interrupted and repeat that analysis as maps, adjacency structures, and outcomes change. We develop a covariate-informed Bayesian boundary model and an amortized posterior approximation trained across heterogeneous areal graphs. The model distinguishes local interruptions in smoothing from broader residual spatial dependence; the trained approximation handles maps with different numbers of regions. Simulations examine posterior calibration, boundary-probability recovery, replicated-data behavior, and MCSE-controlled agreement with prior-matched MCMC. In contrast to traditional approaches that analyze these data separately, we demonstrate the effectiveness of using a single trained deep learning network to analyze respiratory hospitalizations in Greater Glasgow; lung cancer incidence in California; and tracheal, bronchial, and lung cancer mortality in South Korea, comprising 58 to 241 regions. Selected boundary density is greatest in Glasgow and lowest in South Korea despite substantial residual spatial dependence in both, showing that local interruption and broader spatial persistence need not vary together. Across all three applications, edge-level boundary probabilities agree substantially with dataset-specific analyses, although posterior spread and thresholded boundary sets differ. These results support reusable Bayesian boundary analysis across the evaluated disease-map class and identify the validation needed before deployment to new applications.

We introduce the categories $\CM(X)$ and $\SCM(X)$ of reflexive sheaves on a minimal partial resolution $f\colon X \to \Spec R$ of a rational surface singularity $\Spec R$. The main result of this paper establishes that $\SCM(X)$ possesses a natural Frobenius structure, serving as a geometric counterpart to the algebraic Frobenius structure on special Cohen–Macaulay $R$-modules, introduced by Iyama–Wemyss and Iyama–Kalck–Wemyss–Yang. Utilizing this geometric framework, we establish an exact equivalence between $\SCM(X)$ and the category of special Cohen–Macaulay $R$-modules equipped with a specific exact structure, which induces a triangle equivalence between their stable categories. Consequently, this provides a direct, geometric proof of the Iyama–Kalck–Wemyss–Yang equivalence and yields a Buchweitz-type equivalence $\underline{\SCM}(X) \simeq D_{\sg}(X)$.

Finding globally optimal paths remains a fundamental challenge in multi-robot motion planning. Despite acceleration of almost-surely asymptotically optimal (a.s.a.o.) planners via CPU-based parallelism, achieving both probabilistic convergence guarantees and strong computational performance, these algorithms still struggle to scale to multi-robot settings. As such, we introduce MR. POP, a GPU-based a.s.a.o. multi-robot planner based on dRRT and the AO-x meta-algorithm. MR. POP uses large-scale GPU-based SIMT-parallelism to simultaneously run hundreds of roadmap construction and tree search iterations with underlying parallel nearest neighbor search and collision checking operations. We show that this enables MR. POP to become the only planner achieving a 100% solve rate while being faster than state-of-the-art a.s.a.o. planners in multi-robot systems up to 35-DOF. MR. POP also raises the success rate of downstream motion optimizers (e.g., from 4% to 72%), by creating high-quality, diverse seeds that help avoid local minima.

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

As Large Language Models (LLMs) become integrated into software development workflows, concerns regarding unintentional biases in AI-generated code. Although evidence suggests these biases exist, limited research has systematically identified, categorized, and explained them. This study investigates bias in AI-generated code and evaluates whether LLMs can reliably identify and explain it through a taxonomy-driven framework. We extended an existing dataset of biased AI-generated Python code and manually annotated snippets with bias categories and human-authored justifications to establish a ground-truth dataset. Using this dataset, we evaluated proprietary and open-source LLMs as automated bias detection and justification systems through ICL. Finally, we analyzed similarity between LLM-generated explanations and human-authored justifications using structured justification and code identification metrics. Our findings demonstrate that LLMs can effectively support code bias identification and explanation. Gemini achieved 80.14% classification accuracy, with 84.0% precision and 95.7% recall, while the best open-source alternative, Qwen3-coder, achieved 82.45% accuracy, 68.64% precision, and 80.22% recall. Additionally, the models achieved justification similarity scores of 80.4% and 80.14%, respectively, relative to human-authored reasoning, and code identification similarity scores of 86.0% and 87.82%. These results suggest that LLMs can detect biased logic in generated Python code and produce explanations that substantially align with expert interpretations.

Extreme high-frequency peaked BL Lac objects (EHBLs) have their synchrotron peak above $\sim 1$ keV and their inverse Compton peak extends up to several TeVs. Due to low luminosity of EHBLs, these objects are often undetected, and only a small number of them are thus known. As a result, they are poorly understood. Using a photohadronic model and including extragalactic background light correction we analyzed 22 very high-energy (VHE) gamma-ray spectra of 15 EHBL sources observed in different periods. We find that the photohadronic model used can adequately describe the observed VHE spectral energy distribution and furthermore, we classify them according to the value of the photon spectral index, $\delta$. The redshift of the EHBL HESS J1943+213 is also tightly constrained using the same photohadronic model. Within the sample, a plurality of flaring epochs fall in the high-emission state which is followed by the low-emission state and the very-high-emission state respectively. These fractions of flaring epochs characterize only the present sample, not the EHBL population at large. Due to the anomalous behavior of the VHE gamma-ray spectra of the EHBL H 2356-309, we suggest it to be a new subclass of EHBL having hard and very soft intrinsic spectra during different flaring epochs.

Two-sample Mendelian randomization (MR) is a widely used methodology in epidemiology. In two-sample MR, summary data (typically regression coefficients and standard errors) quantifying the association between multiple genetic variants and the exposure and the outcome are used in an instrumental variable framework to estimate the causal effect of the exposure on the outcome. Most two-sample MR methods assume that the association between each genetic variant and the exposure, as well as the causal effect of the exposure on the outcome, are constant on the additive scale. These assumptions are useful because they imply that, if all genetic variants were valid instruments, they would all estimate the same causal parameter - namely, the constant causal effect. We call this condition summary-level homogeneity. In this paper, we show that summary-level homogeneity follows from the following conditions: the causal effect is linear on the additive scale within population strata, but is not necessarily constant across strata; and heterogeneity in the causal effect is uncorrelated with heterogeneity in the association between each genetic variant and the exposure. Under these conditions, typical two-sample MR methods can be interpreted as estimators of the average causal effect. These results clarify that point-identifying assumptions required for two-sample MR methods are weaker than previously anticipated, making them more plausible and clarifying the interpretation of the resulting estimates if those assumptions hold.

We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditioned method coupled with a Krylov subspace iteration is shown to be independent of the highly discontinuous (and anisotropic) jump coefficients as well as the subdomain size. To increase efficacy, various auxiliary spaces are considered to reduce the size of the coarse grid operator. We demonstrate how to modify the additive Schwarz preconditioner such that it is applicable to the nonsymmetric IPDG schemes. Several numerical experiments verify the theory and validate the robustness of the preconditioner.

Let $R$ be a commutative noetherian local ring. We extend the work of the author and Takahashi by investigating the structure of irreducible monomorphisms originating from free modules in the category of finitely generated $R$-modules. In the case where $R$ is complete, we further study the structure of irreducible monomorphisms and epimorphisms to and from injective modules in the category of artinian $R$-modules.

Aggregate lexical frequencies reflect both what speakers do and how a corpus records it. We develop a stochastic framework for lexical adoption, abandonment and reactivation on a temporal multilayer network, together with a count observation model separating speaker prevalence, use intensity and detectability, and ask what such data identify. We give a necessary and sufficient condition for the never-active and dormant states to be merged exactly, collapsing the three-state chain to two, and show that the condition constrains the exposures a given network can deliver, not the response function as a whole. No count design can distinguish use intensity from detectability, an exact invariance distinct from the merely practical loss of information in sparse series. And we prove that in a low-prevalence community approximation the rates enter only through the net growth $\beta-\mu$ and the coupling product $\beta\kappa$, so that a one-parameter family of triples has identical trajectories, the only separating information lying in a term quadratic in prevalence whose size depends on the emission scale. Simulations characterise recovery, prediction and sensitivity to misspecification. An exploratory analysis of 144 candidate forms in CREA and CORPES XXI press subcorpora illustrates the consequences: under the chosen emission scale and a symmetric contact graph, very different rate triples give nearly identical fitted trajectories, and in leave-one-country-out comparison with training-only proxies and seeds on a retrospectively selected cohort, a constant-rate count baseline beats the evaluated dynamic specifications on 84 to 94% of forms. These findings neither establish nor refute contact-driven diffusion. They delimit what this model and panel can support, and name the calibration, geographical contrast and repeated speaker observations that would make the question answerable.

In this paper, we study the algebraic properties of $\mathcal{S}_\theta$ — the class of truncated Toeplitz plus truncated Hankel operators — on the model space $\mathcal{K}_\theta$. We also give a complete characterization of the intersection class of truncated Toeplitz and truncated Hankel operators. As a by-product of our findings, we give a complete characterization for $S_\theta$, where $\theta$ is a finite Blaschke product and also obtained the commutant of $S_\theta + S_\theta^{*}$ in that case.

Artificial intelligence (AI), as a decision-support aid, provides new tools for studying history effectively using multimodal data, including text, images, and audio. We present, to our knowledge, the first digital assistant named Lighthouse–commonly called a chatbot–for exploring the Civil Rights period of the United States using data from South Carolina. From an AI perspective, the system's novelty lies in its guiding design principles of (a) focusing on trustworthiness of content and (b) by modeling and reducing potential harm to users from generated answers. It implements these with a neuro-symbolic approach that combines neural learning through a large language model (LLM) with rule-based symbolic solving, balancing risk of answers with generality of coverage. We evaluate Lighthouse with both factual objective questions that admit a single acceptable answer as well as subjective questions. For the latter, a dataset of subjective question-answer pairs (QAs) is created by discovering a "gold standard" by aggregating answers from independent experts. Lighthouse has access to over 18k primary sources from a range of collections and can be easily extended.

Due to their low accuracy, industrial robots commonly require online teaching after the offline development of a robot program in simulation. The accuracy is limited by compliance and transmission errors in the robot joints. Transmission errors are defined as errors between the load-side angles of the gearboxes and the motor encoder angles. An approach to identify the transmission errors based on laser tracker measurements is presented. The developed velocity-dependent Fourier series model is integrated in a virtual commissioning software as a co-simulated functional mock-up unit. Additionally, it is used to compensate the transmission errors by correcting the setpoint from the computerized numerical control (CNC). The model identification and the compensation are experimentally evaluated with a Stäubli TX2-40 industrial robot. The model has a mean absolute error of 0.114 mrad, and the compensation improves the accuracy by 83.26 % for axis 2 and 49.21 % for axis 3.

The position and path accuracy of industrial robots is strongly affected by temperature. In particular, temperature-dependent friction and altered hysteresis and transmission errors in the gearboxes are the main causes of these deviations. Since standard industrial robots lack temperature sensors, it is proposed to estimate the gearbox lubricant temperature using observer structures. It is planned to apply the proposed lubricant temperature observer to provide the input for temperature-dependent error compensation for gearboxes in industrial robots. First, a two-state heat transfer model describing the heat transfer from the lubricant through the gearbox housing to the environment is described and identified. It is integrated into a Luenberger observer and a Kalman filter with a correction of the lubricant temperature estimation based on measurements from a housing temperature sensor. Temperature measurements were performed in an experimental setup with a cycloidal gear filled with grease, which is common for industrial robots. Due to its changing viscosity and changing thermal conductivity at different shear rates, it shows a less uniform thermal behavior than gear-oil. For the validation measurements, the developed observers showed a mean absolute error of 1.3 K.

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

Personalizing text-to-image diffusion models from a few reference images requires preserving subject identity while following prompts that describe new contexts. Full-model fine-tuning is parameter-intensive, whereas low-rank adaptation (LoRA) reduces the number of trainable parameters but leaves open how adaptation capacity should be distributed across layers. We introduce Diffu-LoRA, a parameter-efficient method that learns this allocation through gated low-rank adaptation. Diffu-LoRA inserts trainable low-rank components into the linear layers of Transformer blocks and assigns a learnable gate to each component. Bilevel optimization updates the adaptation weights and gate parameters on separate data splits, while progressive pruning removes components with the lowest gate values to meet a prescribed rank budget. This procedure allocates adaptation capacity nonuniformly across layers while keeping the pretrained backbone frozen. Experiments with Stable Diffusion on subjects from DreamBooth and additional collected datasets show improved overall subject fidelity and prompt alignment relative to the evaluated fine-tuning baselines. Ablation studies examine the contributions of bilevel optimization, progressive pruning, and adapter placement. These results support learned rank allocation as a practical approach to parameter-efficient diffusion model personalization.

Tool-calling agents have become central to enterprise AI, yet training and evaluating them at scale remains severely constrained due to business and legal restrictions on enterprise systems, data, and database schemas. Tabular data synthesis offers a natural alternative, but its effectiveness is fundamentally limited by structural validity and schema availability, while procedure-based approaches yield the opposite weakness, typically lacking distributional fidelity without per-domain authoring. We introduce **Synthesis Through Simulation** (STS), a **schema–free** data synthesis paradigm in which an LLM agent generates data by executing operations against policy-enforcing APIs within simulated enterprise environments. Because data is generated through the same environment that defines what is valid, STS guarantees structural validity by construction while decoupling validity enforcement from distribution modeling, allowing each to be addressed independently. The **Generalist Populator** (GP), STS's domain-agnostic agent, addresses the remaining challenges of distributional fidelity and synthesis scalability: GP achieves **0.88** average marginal fidelity and **100% constraint satisfaction** across all ten environments *without access to DB schemas*, while statistical synthesizers are inapplicable to seven due to necessary seed data requirements, and schema-privileged agents fail 82% of trajectories on airline environment's tightly coupled workflows due to brittle task composition. We open-source the full framework, all ten environments, and generated datasets at https://github.com/SAP/synthesis-through-simulation.

We study a two-regime summary of a real-valued loss distribution. The two representative levels and the boundary between them are chosen by minimizing a convex residual loss. When the distribution has an atom at the boundary, assigning that atom to the lower or upper regime can give different optimized costs. Taking the better whole-atom assignment yields the lower-semicontinuous cutoff profile. We prove epi-convergence of this profile under a loss-adapted \(\psi\)-weak topology and obtain convergence of minimum values and outer stability of optimal cutoff sets. Under a unique finite atom-free limiting cutoff, positive regime masses, and unique conditional centers, the two fitted levels and a canonical one-jump representation converge as well. We also examine the resulting summary from the viewpoint of monetary risk axioms, establish explicit failures of external monotonicity and subadditivity, and give finite-support algorithms with conditional error control. A four-scenario model illustrates the cutoff geometry and the role of ties and atoms.

Large language model-based multi-agent systems improve complex problem solving through collaboration, while latent communication directly transmits model internal states to avoid the high inference costs of natural language. However, existing KV-based latent communication methods prioritize sender-side state fidelity, leading to substantial communication and computation overhead and potentially introducing redundant information. To address these limitations, we revisit latent communication from a task-oriented perspective, shifting its objective from sender-side state fidelity to receiver-side task sufficiency. Under this formulation, we propose KITE, a training-free framework for task-oriented key-layer KV communication. KITE identifies a task-effective key layer using a receiver trajectory distortion criterion, transmits only the latent working memory associated with the key layer, and further uses the same layer as the entry point for autoregressive latent reasoning. Experiments on seven benchmarks across two model families and three model scales show that, compared with full-layer KV communication, KITE reduces communication volume by 28-36$\times$, achieves up to 3$\times$ end-to-end inference speedup, and improves accuracy by up to 23.3 percentage points.

Rapid industrialization and urban growth are increasing pressure on water quality and wastewater treatment systems, while conventional treatment plants often rely on static monitoring and control strategies that cannot easily adapt to changing pollutant conditions. This paper presents HydroSphere, a governed, data-driven framework for real-time water quality monitoring, forecasting, treatment optimization, and fault recovery. HydroSphere is evaluated using 2.82 million water-quality measurements collected between 1940 and 2023. The framework integrates three main components. First, a hybrid TCN-LSTM model performs multi-step forecasting across seven water-quality parameters, achieving an RMSE of 0.1417, MAE of 0.1047, and R2 of 0.3596. Second, the Adaptive Dosage Optimization Module uses PPO reinforcement learning to adjust chemical dosing, achieving a mean step reward of 1.059 compared with 1.017 for a fixed-dose baseline. The results also show that unconstrained reward optimization can lead to excessive dosing, demonstrating the need for explicit operational safeguards. Third, the SHADE anomaly detection module uses a deep autoencoder to identify sensor and process anomalies, achieving an F1 score of 0.651 under controlled fault injection. HydroSphere combines these capabilities with tiered governance, deterministic safety bounds, and human oversight to support safer and more adaptive water infrastructure. The framework provides a scalable foundation for intelligent wastewater management and supports the objectives of UN Sustainable Development Goals 6 and 13.

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

Electroencephalography (EEG)-based brain-computer interfaces (BCIs), particularly steady-state visual evoked potential (SSVEP) systems, are highly vulnerable to noise and artifacts, which severely degrade decoding accuracy. Although recent denoising approaches have shown promise, they are fitted without paired ground truth, can settle on reproducing their input, and are optimized on waveform distance alone, which says nothing about whether the output stays decodable. To address these issues, we propose DenoFlow, which casts SSVEP denoising as transport: instead of learning a direct map from a contaminated trial to a clean one, a field network regresses the velocity of the straight path between them, following the rectified-flow formulation, and denoising integrates that field forward from the observation. The field network is an encoder-decoder that sees the contaminated trial at every layer and the path position at its bottleneck, and a classifier trained alongside it supervises the integrated output. Because the observation itself is both the conditioning input and the starting point of the integration, the model never generates a trial from noise, and training reduces to regression, removing the adversarial min-max game. To obtain paired data on datasets with no ground truth, we injected physiological artifacts of the recorded electromyography (EMG) and electrooculography (EOG) signals under a controlled signal-to-noise target. Experiments on two public SSVEP datasets with five popular SSVEP decoders showed that DenoFlow outperformed seven baseline denoising models on both signal fidelity and downstream decoding accuracy. Code is available at https://github.com/wzwvv/DenoFlow.

Long-range temporal dependence poses a resource question for sequence models: for a specified predictive-memory law, how much state, context, or dynamical criticality is required in order to forecast accurately? We study this question directly in forecasting risk. For algebraically decaying predictive memory, we prove matching upper and lower approximation bounds for exponential and finite-state modes. The best $r$-mode forecast error decays as $e^{-\Theta(\sqrt r)}$, so reaching forecast error $\tau$ needs $r=\Theta(\log^2(1/\tau))$ states or modes. Earlier curse-of-memory results establish broad limitations of stable recurrent models under different approximation notions; here both sides match for one canonical predictive target in forecast risk, which fixes the optimal resource exponent for that target. We then show that genuine fractional long memory changes the geometry itself. In particular, forecast error is measured after fractional integration, prediction from a finite context of length $L$ has an exact $1/L$ leading order, and a fixed fractional strength $d$ keeps the square-log state-complexity law. Near the short-memory boundary, we identify the relevant $d^2$ and $d^4$ scales and give a uniform constructive law in the intermediate regime. For nonlinear contextual recurrences with uniformly contractive state dynamics, we derive an exponential first-chaos envelope and an explicit necessary condition that relates forecast accuracy to the contraction margin. Vanishing forecasting error on an algebraic target forces the recurrence quantitatively toward criticality, a condition that is necessary and not by itself sufficient. Finite-sample Kullback–Leibler calculations further connect the predictive geometry to statistical information. Theorem-matched experiments with contractive state-space, gated recurrent, and attention models reproduce the state and stability predictions.

Agentic AI-enabled automation cannot be safely deployed in high-stakes environments on probabilistic reasoning alone. A recurring risk is epistemic drift: as reasoning deepens, system behavior may move away from subject-matter-expert constraints for safe operation. This paper presents BRaVeS, a bounded reasoning and safety-governance framework termed the Defensible Next-Gen Reasoning System (DNRS). BRaVeS encodes SME-defined constraints as invariant anchors, proposes MoDA-Style (Mixture of Depths Attention) depth-aware access as a candidate mechanism for keeping these anchors visible during inference, and uses a state hierarchy (SMARtAutonomy) to reduce autonomy as epistemic risk increases. To formalize bounded recovery, we introduce the Lyapunov-Bounded Consensus Framework (LBCF), which maps continuous epistemic-risk signals into a finite K-bag abstraction and applies shielded state transitions that enforce Lyapunov-style energy descent or route the system to a human-mediated terminal state. The formal convergence result applies to the finite LBCF abstraction under fixed thresholds and feasible-shield assumptions; it does not prove safety of the full continuous neural activation space. We evaluate the framework through a discrete event Monte Carlo simulation using HAI 22.04 industrial-control-system time-series data with synthetic noise and sensor-degradation regimes. Across the tested parameter-grouping strategies and thresholds, the LBCF process achieved finite-step convergence and no safety-guard violations. These results provide simulation-based evidence that bounded governance behavior can be enforced under the stated abstraction, while motivating future work on deployed transformer implementations, live human-in-the-loop validation, and broader adversarial settings.

A tournament is $k$-universal if it contains every tournament on $k$ vertices as a subtournament. We give a 7-universal tournament on 14 vertices, improving the upper bound of 15 due to Zhang and Szeider. Together with their lower bound, it follows that the smallest 7-universal tournament has 13 or 14 vertices.

We present an industry experience report on three years of operating an event-driven cloud infrastructure for continuous machine learning training in automotive manufacturing. Our system orchestrates GPU-accelerated training of product-specialized model pairs, a physics prediction model and a reinforcement-learning control policy, across multiple plants, coordinating long-running GPU workloads triggered by manufacturing events. The architecture combines Amazon ECS with EC2 GPU capacity providers, SQS-based messaging with dead-letter queues, and an admission-controlled Lambda dispatcher that enforces cluster concurrency limits. A Conductor orchestrator on ECS Fargate initiates dependency-aware retraining chains on a weekly schedule. The entire infrastructure is codified in modular Terraform with multi-account separation. From 40000+ production training jobs we report a 72-78% cost reduction versus always-on GPU infrastructure. A discrete-event simulation confirms that admission control is necessary (naive dispatch loses 65% of jobs) and that queue-draining matches AWS Step Functions latency while eliminating per-job startup overhead. We provide lessons learned and release the simulator and Terraform module skeletons as open-source artifacts.