Papers

A vision-language model may need to combine an image with a prompt to recognize a safety risk that neither reveals alone. Where does this joint safety judgment become accessible inside the model? We introduce SSU-Bench, a dataset of matched safe and unsafe image-text combinations constructed using single-item prompt edits or image edits with annotated intended regions. Using three vision-language models, we transfer internal states between paired inputs and measure the resulting change in the safety verdict. Across models and both types of counterfactual, interventions at the changed input positions are effective in earlier decoder layers, while interventions at the final input token become effective later. Directions estimated from other examples produce similar late-layer effects. A linear readout of the final-token state also predicts the model's own verdict, including incorrect judgments, and cross-model comparisons reveal similarities in the patterns of counterfactual change. These findings identify a recurring transition in where interventions can influence a joint safety verdict and distinguish a readable model decision from a correct safety judgment.

Approximating linear operators on high-dimensional spaces using only forward operator-vector product queries is a common but challenging task in scientific computing and machine learning arising when access to the adjoint action is experimentally unavailable or difficult to construct computationally. Existing query-efficient methods with polylogarithmic query complexity in the error tolerance rely on self-adjointness or access to the adjoint operator, while existing adjoint-free methods based on global low-order regularity have polynomial query complexity. We show that a priori local row-space information can be exploited for query-efficient, adjoint-free operator approximation, and that this information can be supplied by local high-order regularity estimates. Our approach first extends the fixed-sparsity matrix approximation algorithm of (Amsel et al., SIMAX, 2026) to approximating a matrix by one whose rows lie in prescribed subspaces, providing a general template for exploiting local row-space structure from forward queries alone. We then apply this framework to Hilbert-Schmidt integral operators with asymptotically smooth kernels. We establish asymptotic smoothness for Green's functions of canonical second-order elliptic PDEs in $d\leq 3$ dimensions including Poisson's equation in balls and constant coefficient equations on tori. In $d$ spatial dimensions, our algorithm uses $\mathcal{O}\big(\log(\varepsilon^{-1})\log^{d}(\varepsilon^{-1}\delta^{-1/2})\big)$ non-adaptive randomized queries to produce an $\varepsilon$-accurate approximation in Hilbert-Schmidt norm with probability $1-\delta$. This implies the error decreases as $\mathcal{O}\big( \exp(- c q^{1/(d+1)}) \big)$ in the query count $q$, which we observe in numerical experiments using tens to hundreds of queries to approximate solution operators of one-dimensional variable-coefficient second-order elliptic equations.

We present a method to obtain the proven exact 2-component (X2C) method, normally applied to Gaussian-type fixed Hilbert bases, in an adaptative non-uniform grid basis of the Hilbert space, namely Multiwavelets. The X2C method manages to block-diagonalise the Dirac Hamiltonian restricted to the subspace of the basis, in an energy-independent manner. The method takes inspiration from the success of the atomic mean-field X2C method on the Gaussian bases to represent the coupling operator as a projector onto the small components of the eigenstates of the constituent atoms of the system.

Mobile manipulators such as humanoid robots are increasingly deployed in dynamic, unstructured environments to perform dexterous manipulation tasks. However, end-to-end manipulation policies trained to imitate demonstration data collected from a single robot pose are brittle: even centimeter-scale deviations in robot pose at deployment can drive ego-centric observations and end-effector trajectories out of the training distribution, leading to sharp drops in performance. We introduce MobileVISTA, a data generation framework that transforms demonstrations captured at canonical poses into diverse, pose-perturbed training data by jointly (1) augmenting egocentric visual observations and (2) retargeting actions to compensate for base pose changes. Unlike prior methods, which assume a camera rigidly mounted off the actuated chain or non-trivial articulated robot geometry largely out of frame, MobileVISTA targets compatibility with egocentric platforms (e.g., humanoids) where the camera is both influenced by and must observe the robot's kinematic chain as it moves. We study MobileVISTA in simulated tasks spanning humanoid and bimanual embodiments, and on a real Galaxea R1 Pro. We find policies trained on MobileVISTA-augmented data demonstrate improved robustness to previously out-of-distribution poses encountered at test time, without additional demonstration collection or a trained generative model. Additionally, we find MobileVISTA's benefit is largest on tested humanoids, where the camera rides the actuated chain and the robot fills much of the frame. Additional videos and appendix can be found on our website: https://mobilevista.github.io

Developers can build LLM agents by adapting third-party models through benign post-training. We study a supply-chain threat in which an attacker supplies a model with a backdoor: hidden behavior that produces malicious outputs when a particular input pattern appears. Focusing on software-engineering agents, we ask whether such backdoors survive the developer's supervised fine-tuning (SFT) and subsequent task-level reinforcement learning (RL). We observe that benign SFT substantially reduces attack success, but subsequent RL often preserves the residual behavior and sometimes even increases attack success. Our analysis of backdoor erosion during SFT identifies two factors that may favor survival: initial backdoor strength and gradient compatibility with benign training. These factors motivate PersistBD, which refines an already-backdoored model before release to improve its persistency through the benign post-training process. On Qwen2.5-Coder-7B, PersistBD raises attack success from 20% to 74% after SFT and from 20% to 76% after SFT-RL, while maintaining comparable benign task performance. Together, our results show that backdoors can remain active through benign post-training and that adversaries can deliberately increase their persistence. This highlights a supply-chain risk for AI developers and motivates stronger techniques for detecting and mitigating inherited backdoors when adapting third-party models into agents. Our code is available at https://github.com/uiuc-kang-lab/PersistBD.

Information elicitation is an open-ended information-seeking problem in which an interaction can unfold in many potentially valuable directions, requiring an elicitor to continually determine which information to pursue as new information emerges. In agentic elicitation, these decisions may be delegated to a foundation model, yet how model choice shapes the resulting information-seeking behavior remains understudied. We study how judgments about information value vary across LLMs and how these differences shape sequential information seeking. We first examine these judgments across 11 LLMs spanning multiple model families and parameter scales, using a shared set of information and elicitation objectives. We then develop a controlled elicitation simulation in which different models encounter the same information space and use the same selection rule, isolating these judgments from question generation and respondent behavior. Using this setting, we characterize the breadth-depth behavior that emerges from model-specific information-seeking preferences over the course of elicitation. We further examine how interaction history changes the evaluation and subsequent selection of prospective information. We test the robustness and boundaries of these findings through sensitivity analyses and ablations over the opportunities available to the elicitor, the response labels used to operationalize information-seeking preferences, the presence of interaction history, and whether redundancy is explicitly relevant to the assessment. The project code, data, and trajectory files are available at https://github.com/infosenselab/open-elicitation.

Essential dimension counts the parameters needed to define a torsor, but it can drop sharply over a field extension, and it does not say how large an extension is needed. For a $G$-torsor $\tau$ over a field $F\supseteq k$ we study the finite-degree profile $\edd d_k(\tau)=\min\{\ed_k(\tau\otimes_FF'):[F':F]\le d\}$, a variant of invariants of Farb–Kisin–Wolfson and Farb–Wolfson, and its jump degrees $d_j(\tau)$, the least degree of an extension over which $\tau$ needs only $j$ parameters. The profile is geometric over every field: $\edd d_k(\tau)\le j$ iff some generically free $G$-variety of dimension $\le j$ has a closed point of degree $\le d$ in the free locus of its twist by $\tau$. We prove a Sylow divisibility theorem for jump degrees and a valuation-theoretic rank–index theorem, $\edd d_k(\tgen)\ge\min\{\rk B:B\le A,\ [A:B]\le d\}$ for abelian $A$ of order prime to $\operatorname{char}k$, which determines the profile of every abelian group over a field with enough roots of unity, for instance $n-\lfloor\log_2d\rfloor$ for $(\Z/2)^n$. For $\Z/p$ in characteristic $0$ we show $\lceil m/2\rceil\le d_1\le[k(\zeta_p+\zeta_p^{-1}):k]$, $m=[k(\zeta_p):k]$, with equality for $m$ even. For $S_5$ in characteristic $0$ we prove $d_1=4$, so Klein's reduction of the generic quintic is optimal; the lower bound comes from Abel–Jacobi rigidity, not from cohomological invariants. For $n\ge6$, $6\mid d_1(S_n)$.

Virtual reality (VR) relaxation environments are increasingly proposed as accessible tools for stress management, yet the physiological correlates of self-reported stress during VR exposure remain unclear, particularly for blood pressure (BP). We conducted a within-subjects study (N = 18) in which participants viewed relaxing 360-degree videos, grouped into four sound-design categories, such as videos with rhythmic (RHYT), aperiodic (APRD), continuous (CONT), and low-ambient (LOWE) sound through an HTC Vive Focus Vision headset. Systolic (SYS) and diastolic (DIA) BP were recorded after each category using an Omron 3 Series monitor, and self-reported stress was collected via a 0-100 Visual Analogue Scale (VAS) with fixed intervals. While overall BP did not differ significantly across sound categories, self-reported stress did (Friedman chi-square(4) = 12.07, p = .017), with rhythmic sound eliciting significantly lower stress than aperiodic and continuous sound. Critically, DIA, but not SYS, correlated significantly with self-reported stress across conditions (r = .31, p = .003). This suggests that DIA may be a more sensitive physiological indicator of subjective stress than SYS in short VR exposures. We discuss implications for designing and evaluating VR mental health interventions and the value of low-cost physiological sensing alongside self-report.

Speech agents are reactive and dyadic: they speak when spoken to, and to one person at a time. We ask what it takes for a speech agent to instead take part in a conversation among several people and speak up only when it can help. We introduce Jarvis, a real-time proactive speech agent that audibly participates in multi-party human conversations. Grounded in a document shared beforehand, Jarvis follows the discussion and intervenes when the group misses or misstates a fact and does not correct itself within a few turns. We make three contributions: a problem setting based on epistemic breakdowns that makes proactive intervention measurable, realized as CHI-180-proactive, a synthetic multi-party dataset seeded with known gaps, errors, and self-corrections; a proactive backbone that harnesses a small, open-weight model with deterministic checks and grounds every claim in a source sentence; and interaction techniques for taking the floor in live speech and showing the cited evidence on screen. On CHI-180-proactive, Jarvis is correct on most events it addresses and stays silent 97% of the time when the group resolves an issue itself. A live study with 23 participants confirms these trends with real-time interventions.

Long-history recommenders often compress each user's history into a compact, candidate-independent memory that is cached and reused to score large candidate pools. We show that real user histories exhibit multi-scale semantic structure, with short-lived intent, medium-term interests, and long-term preferences coexisting in one sequence, and that monolithic cached memories preserve these scales unevenly: linear probes recover recent and mid-range content far worse than long-range content. We call this failure mode temporal aliasing. We propose MARS, a multi-resolution user memory that writes the full history into recurrent state tracks anchored to different half-lives, and a sparse routing reader that materializes compact seed memories by selecting the relevant temporal resolutions for each seed, preserving fixed-size candidate scoring. MARS outperforms strong baselines on three public datasets, with gains that grow with history length. Component-matched ablations with paired tests show that temporal diversity and selective routing each contribute beyond what hard-window memories or added capacity provide. The advantage of MARS over its interface-matched baseline also widens after within-user behavioral shifts, at about $1.02\times$ that baseline's warm-cache serving latency for $1{,}000$ candidates per user.

GPUs are increasingly in demand for AI workloads, yet often remain substantially underutilized, motivating workload colocation. However, colocation introduces interference that can degrade latency-critical workloads. Existing approaches mitigate interference using either heuristic-based scheduling or interference predictors. Heuristics rely on coarse-grained metrics that overlook important interference sources, while predictors often depend on simulator-specific or similarly coarse metrics. However, GPU interference is complex and arises from multiple mechanisms, including thread-block placement, memory hierarchy contention, and intra-SM resource contention. We present Mosaic, a kernel-level interference predictor that explicitly models these mechanisms using a combination of analytical and lightweight learned models. Across four GPU architectures, Mosaic reduces prediction error by up to an order of magnitude compared to prior predictors. We integrate Mosaic into a scheduler, MosaicSched, that performs online kernel admission control and selects between full-GPU colocation and SM partitioning to maximize best-effort throughput while satisfying latency SLOs. Across all workloads, MosaicSched keeps the p99 latency below or very close to the target SLO.

Two populations of graphs often have to be compared without any correspondence between their vertices, for instance when networks come from different communities, or when a graph generative model is evaluated against held-out graphs. We study how many graphs such an unaligned two-sample test needs, and which graph statistics can detect which differences. For an Erdős–Rényi null and a planted two-block difference that leaves every expected degree unchanged, we show that $m\asymp t^{-3}$ graphs per group are necessary and sufficient when the per-graph signal-to-noise ratio is $t<1$. Signed triangle counts attain this rate, and the lower bound holds for every graph size. With aligned vertices $m\asymp t^{-1}$ graphs suffice, so misalignment costs a factor of order $t^{-2}$. When the triangle signal cancels, the rate becomes $t^{-4}$ and $4$-cycles are needed. Statistics built from trees have exactly the same expectation under both hypotheses, and tests based on finitely many of them have asymptotically no power. In the graphon limit, this class includes degree distributions and message-passing graph neural network features. For a non-constant null, a generic difference is visible at first order, and a simple motif test attains the aligned order of sample size, suggesting that misalignment is costly mainly for differences that are invisible at low orders. We also give an exactly valid test for one or two graphs per group, at a cost in power. In our simulations, the fitted exponents are close to the predicted ones, and degree-based and random-GNN evaluation metrics stay at their level in a setting where signed triangles need about $65$ graphs.

Provider queries are clarifying requests sent by clinical documentation specialists to physicians to close gaps in the clinical note and ensure accurate billing. Prior work automates note drafting, ICD-10 coding, and order extraction assuming a complete transcript, leaving these gaps unaddressed. We study whether an LLM can automate the query loop, termed DAU (Draft, Ask, Update), across those three tasks. An audit of 3,000 real visits identifies the sources of missing documentation, from which we build five transcript-degradation benchmarks on public data. Analyzing 21k clarification turns on real conversations, we find useful-question predictors are task-specific: oracle confidence dominates, but note completeness needs only simple recall questions while ICD-10 coding needs harder, multi-option ones. About 9% of turns hurt performance, driven by redundant questions and non-answers that still trigger a rewrite. Deployment depends on learning "when not" as much as "what to" ask.

Probe-and-drogue refueling (PDR) requires accurate terminal alignment of a receiver probe with an uninstrumented, dynamically moving drogue despite uncertainty in both relative-state estimation and closed-loop motion. Existing vision-based docking approaches provide relative-state estimates, but generally do not quantify estimation and operational uncertainty in a way that informs the control authority required for robust docking performance. We present an uncertainty-aware vision-based PDR docking architecture that fuses keypoint-based drogue measurements, differential GPS, and avionics in an extended Kalman filter. Split conformal calibration characterizes near-contact error in the fused probe-to-drogue displacement estimate, while a covariance-based operational uncertainty quantification designs position-dispersion limits along with corrective-command variance budgets under modeled handoff variability and disturbances. The resulting uncertainty statistics define geometric and command margins for a range-conditioned deterministic predictive controller. In high-fidelity FlightGear/JSBSim simulations with four controller variants and 50 runs per variant, the combined-margin controller achieved 45/50 centered basket-plane crossings versus 34/50 for nominal MPC. Median planar crossing error decreased from 0.231 to 0.175~$\mathrm{m}$ and the empirical 90th percentile from 0.403 to 0.286~$\mathrm{m}$, while the roll-command RMS increased from 0.22$^\circ$ to 0.48$^\circ$.

We develop a novel debiased machine learning (DML) estimator to analyze count data, which are common in clinical or biomedical studies. Specifically, we estimate the effect of a binary treatment on count outcomes using a partially linear Poisson model. A key advantage of this model is that it represents the complex covariate structure through a nuisance function, which is estimated flexibly using neural networks. We use a Neyman-orthogonal score function to construct the estimator, reducing its sensitivity to errors in estimating the nuisance function. Cross-fitting is used to mitigate overfitting bias in neural networks. Under mild regularity conditions, this DML estimator is asymptotically normal with root-$n$ convergence. We derive a closed-form variance estimator and construct a Wald confidence interval for the treatment effect. Extensive simulations demonstrate that the proposed estimator reduces bias and root mean square error compared with the generalized linear model and the augmented inverse probability weighting (AIPW) estimator in most settings, while achieving a coverage probability near the nominal level. The proposed procedure is implemented in the R package $\texttt{PoissonDML}$. We apply our approach to a synthetic HIV cohort data to investigate the effect of treatment on AIDS-defining event counts of 7,141 analyzed patients. Our approach provides practical and valid estimation and inference for treatment effects under the partially linear Poisson model while combining modern machine learning methods to estimate complex covariate structures.

Multimodal wearable systems must remain reliable when sensor streams become noisy or unavailable. Existing multimodal test-time adaptation (TTA) methods often assess reliability online, but cross-modal agreement can be misleading when sensors measure different physical processes, and evaluating alternative modality configurations adds inference cost. We propose CARAT, which decouples model reliance from runtime corruption detection to guide omission or attenuation, amortizing reliance estimation through source training. An asymmetric modality-dropout curriculum prepares a missingness-resilient backbone for omission and derives a frozen, backbone-specific reliance proxy from windowed input-projection gradient norms. At deployment, a lightweight one-class detector flags suspect streams, and the proxy guides a joint choice between replacing the suspect set with the backbone's trained missingness symbol and attenuating its representations before fusion, without candidate-subset evaluation. Across four wearable datasets, five corruption types, three backbones, and eight TTA baselines, CARAT achieves the highest overall macro-F1 and best mean rank (2.42), exceeding EATA, the strongest baseline, by 1.58 F1 points across 12 equally weighted dataset-backbone settings. Across five profiled configurations, CARAT uses 9.49% fewer GFLOPs and updates 47.82% fewer parameters than EATA. A pattern also emerges across sensing regimes: multimodal TTA methods such as PTA are competitive on IMU-dominated homogeneous datasets, whereas unimodal TTA methods like TENT and EATA match or exceed it on heterogeneous datasets. These results position CARAT as a practical default to wearable TTA, offering competitive robustness with modest computational requirements and benefits that vary across backbones and dataset regimes.

We study Maxwell theory near a nonextremal bifurcate Killing horizon in a general static, spherically symmetric spacetime of dimension $D>3$. We impose near-horizon boundary conditions in a regular Eddington–Finkelstein chart that retain both radiative and Coulombic data, and construct the associated horizon phase space and large-$U(1)$ charge. At null infinity, the radiative falloff depends on the spacetime dimension and involves half-integer powers in odd $D$, whereas a nonextremal horizon at finite radius supports radiative data with an ordinary integer-power expansion. Expanding the horizon fields in Killing frequency and spherical harmonics, we derive the associated soft-photon relation from the large-$U(1)$ Ward identity. For comparison, we express the flat-space leading soft-photon theorem using the same spherical harmonics and commutator normalization as the horizon modes. In $D=4$, the two relations have the same soft-frequency dependence and the same angular dependence of the hard-charge terms, whereas for $D>4$ the flat-space relation contains additional dimension-dependent frequency and angular factors.

Muon combines current and past gradients into matrix momentum. For $M=U\Sigma V^\top$, the idealized polar update $Q=UV^\top$ gives every singular direction the same weight. We refer to this as the flat profile. Several recent optimizers replace this flat profile with fine-grained spectral maps that give each direction its own gain. We ask how much of this spectral detail a Muon update needs. Our spectral diagnostics show that approximately $94$–$97\%$ of measured singular modes lie below an estimated noise edge, yet collectively align positively with a reference gradient. We introduce BulkBoost, a two-band spectral reweighting framework with fixed-rank and noise-calibrated variants. The latter uses split-minibatch gradient differences to calibrate a Marchenko–Pastur reference edge for Muon's Nesterov input, separating the bulk below the edge from the spikes above it. Both variants increase the bulk's relative weight through one shared gain while preserving the Frobenius norm of each matrix's unreweighted direction. For a fixed partition, our theory gives the first-order condition under which moving weight toward the bulk lowers the loss. It also quantifies the fraction of the maximal first-order improvement rate, over all per-mode reallocations, that two bands can capture. Across 30 continued-pretraining settings spanning Pythia-14M to 410M and six corpora, two-band reweighting is competitive with the fine-grained power-law profile of Freon and outperforms Spectra. Measured against Muon's flat profile, Freon reduces final loss by $0.022\%$ of the pre-adaptation loss on average, whereas the two-band variants achieve reductions of $0.073$–$0.147\%$. These observations suggest that useful departures from the flat profile are surprisingly low-dimensional: a single bulk-to-spike gain captures at least as much benefit as the fine-grained spectral profiles.

Data assimilation (DA) is the process of combining forecasts from a model with observations in order to optimally estimate the state of a system. This is critical for chaotic systems, such as the atmosphere, since if observations are not continually assimilated the model will quickly lose skill. DA is routinely performed (usually every 6 hours) at operational forecasting centres around the world. In this article we discuss the interface of machine learning (ML) and DA. This is still an emerging and quickly developing field, and this article tries to give an overview of some of the main topics and methods.

Productivity has long been recognized as a central concern in high-performance computing (HPC), yet it still lacks a workable formal definition and a broadly accepted metric for quantified assessment. Recent attempts to incorporate productivity into performance-portability analysis have introduced code-divergence, convergence, and semantic measures, but have not established a convincing formal relationship between productivity and performance portability. More recent language and compiler systems, including JACC, Mojo, JLIR, and Accl++, pursue productive performance portability through higher-level abstractions, multi-level intermediate representations, automatic kernel generation, and runtime compilation. These systems demonstrate substantial engineering progress, while productivity is still commonly represented through programmability, ecosystem reuse, code size, or reduced implementation burden rather than direct measurement of human effort. This paper presents a critical review of HPC productivity measurement, tracing its development from source lines of code (SLOC), static complexity, and empirical usability studies to development-time models and semantic approaches. We also examine how automated migration and artificial-intelligence(AI)-assisted programming weaken the correspondence between code transformation and human effort, shifting effort toward verification, correction, and performance tuning. The reviewed methods are compared in terms of what they measure, directness, objectivity, reproducibility, practicality, and their relationship to performance and portability. We conclude by identifying the principal limitations and open challenges for quantified HPC productivity assessment.

The magnetic ground state of rutile RuO2 remains disputed, raising a central question: under what structural and chemical conditions can this material support altermagnetism? We address this question by combining a critical assessment of experimental and theoretical studies with first-principles calculations of epitaxial strain, point defects, doping, and interfaces. Bulk-sensitive measurements reported in the literature are consistent with a nonmagnetic ground state, while magnetic signatures in thin films depend strongly on their structural environment and do not necessarily establish homogeneous altermagnetic order. Our calculations identify substrate-imposed epitaxial strain as the leading factor favoring altermagnetism among the conditions examined and predict several substrate-orientation combinations that stabilize an altermagnetic ground state. Carrier doping and chemical substitution modify this strain-induced magnetism in distinct ways. Uniform hole doping strengthens the magnetic tendency, whereas Ru vacancies provide little benefit and can weaken the magnetic state through local structural distortions. Cr or Mn substitution, by contrast, enhances Ru magnetic moments and further stabilizes the strained altermagnetic phase. These results distinguish the effects of carrier doping from those of local structural and chemical changes and identify concrete routes to realizing altermagnetism in RuO2 films.

Continuum Schwinger function methods\linebreak (CSM) are used to provide estimates of pseudoscalar meson pole contributions - $\mathsf P = \pi^0$, $\eta$, $\eta^\prime$, $\eta_c$, $\eta_b$ - to the muon anomalous magnetic moment. The analysis framework is benchmarked via successful applications to an array of other meson and nucleon properties. It uses the leading order CSM truncation, augmented by a parametrisation of non-Abelian anomaly effects, to deliver an internally consistent treatment of all the pseudoscalar–two-photon transition form factors required to complete such a calculation. Employing those form factor predictions, the following results are obtained (units $10^{-11}$): $a_\mu^{\pi^0} + a_\mu^{\eta} + a_\mu^{\eta^\prime} = 84.3(0.8)$ - a value lower than some other contemporary estimates; $a_\mu^{\eta_c} = 0.82(0.04)$; and a value of $a_\mu^{\eta_b}$ that is negligible. The total contribution is $\sum _{\mathsf P} a_\mu^{\mathsf P} = 85.1(0.8) / 10^{11}$. Our analysis suggests that this pole contribution to $a_\mu$ is still not known with precision better than 5%.

We determine how wide a randomly initialized ReLU layer must be to distinguish every pair of inputs. For independent Gaussian weights and zero bias, as the dimensions grow at a fixed output-to-input ratio, the probability of global injectivity tends to zero below a sharp threshold and to one above it. We characterize this threshold exactly through a variational formula for the limiting minimum number of active neurons per input coordinate. The formula accounts for correlations among input directions at arbitrarily many levels. We prove this formula rigorously, establishing a prediction from the statistical physics of the spherical perceptron. The proof compares systems of nearby dimensions and controls a Gaussian interpolation by calibrating responses to auxiliary fields. A uniform volume estimate connects the soft minimum to the worst input direction. An exact-arithmetic calculation places the threshold below seven output neurons per input coordinate. Numerical evaluations suggest a value near 6.698.

When multiple agents share a cost budget, a common Lagrange multiplier can enforce the aggregate constraint but does not determine how its penalty should be allocated across agents. Uniform penalties ignore heterogeneity in the rewards agents sacrifice, while agent-specific multipliers may still rely on the same aggregate cost signal. We introduce Lagrangian Responsibility Allocation (LiRA), which learns each agent's share of a common multiplier by optimizing social welfare over a finite training horizon. The multiplier enforces the aggregate budget, while responsibility shares redistribute its influence without modifying the original rewards or constraints. For convex games under standard regularity conditions, varying these shares induces a smooth family of normalized generalized Nash equilibria in which active constraints remain at their budgets while welfare varies. To optimize responsibility before convergence, we derive a welfare gradient that accounts for both learning updates and the induced change in data distribution. Across CityLearn, MABIM, Harvest, and MetaDrive, spanning 3 to 400 agents, LiRA improves average social welfare by up to 29% over uniform and agent-specific multiplier baselines. Grid and driving costs remain within budget, inventory violations decrease, and Harvest makes more effective use of available budget.

Let $m,n\geq2$ be integers. We study the least exponent $t_{m,n}$ such that the $m$-fold additive energy of any subset $A$ of the discrete cube $\{0,1,\cdots,n-1\}^d$ in any dimension $d$ satisfies $E_m(A)\leq |A|^{t_{m,n}}$. For every fixed $m$, we obtain the asymptotic formula $$ t_{m,n}=2m-1-(1+o(1))\log_n \frac{(2m-1)^{m-1/2}}{(2m)^{m-1}} \qquad(n\to\infty). $$ For $m=2$, this gives $$ t_{2,n} = 3 - (1+o(1)) \log_n\frac{3\sqrt{3}}{4}, $$ proving a conjecture of the first author.

Increasing connectivity to the outside world and the lack of inbuilt security mechanisms have made legacy intra-vehicular networks vulnerable to cyberattacks. Initial research focused on maximising detection accuracy for known and unknown attacks, often using large, full-precision machine learning models. However, embedding IDSs into vehicular electronic systems also requires low detection latency, energy efficiency and minimal electronic control unit (ECU) resource overhead to process about 2,000 CAN frames/s. Lightweight models must balance accuracy with these deployment constraints. We propose a dual IDS framework comprising supervised and unsupervised learning-based solutions, each optimised for real-time, resource-constrained automotive platforms. A quantised LSTM-based IDS (QLSTM-IDS) achieves over 99.9% detection accuracy for DoS/Flooding, Fuzzing and Spoofing/Malfunction attacks using a single model architecture evaluated on two widely used datasets. The model is trained using the Brevitas quantisation-aware training library, transformed into a dataflow accelerator with custom blocks compatible with AMD's FINN toolchain, and synthesised using Vitis HLS. Complementing this, an 8-bit quantised convolutional autoencoder-based IDS (QCAE-IDS), quantised using AMD's Vitis-AI toolchain, detects previously unseen anomalies that alter CAN-ID sequence patterns with over 99% accuracy. An integration architecture enables both models to operate on a single FPGA, bridging the network interface IP and processing system to minimise software overhead. QLSTM-IDS achieves 0.25 ms inference latency and 0.8 mJ energy consumption per message, while QCAE-IDS achieves 0.42 ms and 1.1 mJ per block. Both solutions are deployed and evaluated on the ZCU104 SoC (XCZU7EV FPGA), demonstrating a flexible hardware/software co-design for real-time detection of known and unknown attacks on high-speed CAN buses.

A family of paths in a graph $G$ strongly separates the edges of $G$ if for every ordered pair of distinct edges $(e,f)$ some path in the family contains $e$ and avoids $f$; the minimum size of such a family is denoted by $\operatorname{ssp}(G)$. Bonamy, Botler, Dross, Naia, and Skokan proved, for every $n$-vertex graph $G$, that $\operatorname{ssp}(G)\le 19n$; Liu, Xu, and Yang recently improved this to $\operatorname{ssp}(G)\le 10n-o(n)$. We prove, for every $n$-vertex graph $G$, that $\operatorname{ssp}(G)\le 7.75n$.

Neutron-capture element abundances encode the time-dependent interplay between slow (s-) and rapid (r-) nucleosynthetic processes and provide critical constraints on Galactic chemical evolution. In particular, barium and europium provide important tracers of s-process and r-process nucleosynthetic enrichment, respectively. Large spectroscopic surveys enable robust statistical studies of these elements; however, determining reliable elemental abundances at intermediate spectral resolution remains challenging. Our aim was to derive homogeneous and statistically well-characterised stellar parameters and chemical abundances of Ba and Eu (hereafter collectively referred to as stellar labels) for the Gaia-ESO Survey HR15N dataset. We applied The Cannon to 36,263 FLAMES/GIRAFFE HR15N spectra (R~19,200), using a model trained on 782 stars with high-quality reference stellar labels drawn from the Gaia-ESO DR5 homogenised catalogue. The model infers Teff, log g, [Fe/H], v sin i, A(Ba), and A(Eu); its reliability was quantified through multi-dimensional quality flags and detection strength of the Ba and Eu features. Our final catalogue contains stellar parameters for 36,263 spectra, with ~21,000 and ~400 reliable Ba and Eu abundances, respectively, satisfying multiple flagging criteria. We obtained median uncertainties of ~38 K in Teff, ~0.08 dex in log g, ~0.04 dex in [Fe/H], ~0.06 dex in A(Ba), and ~0.02 dex in A(Eu). External validation against the Gaia Benchmark Stars, GALAH DR4, and multiple open clusters shows good agreement across independent reference datasets. The resulting catalogue includes newly determined Ba and Eu abundances that complement those available from previous analyses, thereby enabling investigations of neutron-capture enrichment patterns in open clusters. The model framework can readily be adapted to upcoming wide-field spectroscopic surveys such as 4MOST, WEAVE, and WST.

We report a small-data case study in adapting a pretrained latent audio diffusion model to the guqin, the seven-string Chinese zither, aiming at an "AI radio" that plays guqin-style music without end. From a library of historical recordings we curate 412 solo performances (42.5 h, 61 performers) and split them by composition. We fine-tune a rank-16 DoRA adapter on Stable Audio 3 Medium using its continuous latents, masking weighted towards continuation, captions that combine researched notes on each piece with mood tags and an automatically estimated pentatonic mode, and random-length crops, stopping when held-out loss stops improving. Seven blind listening studies by one expert listener guided every decision. The final adapter was rated highest for continuing unseen pieces (3.9/5, against 3.4 for the best earlier adapter) and 4.6/5 for generating from free-written scene descriptions. Negative results are equally informative: a from-scratch autoregressive model over the same latents produced no recognisable timbre, a signal-level friction-noise measure correlated with the listener's complaints in the wrong direction, and a pentatonic-fit measure tracked ratings overall but barely within a group of candidates. Chaining continuations for long playback exposed a silent tail on every generated clip and a loudness feedback loop, both with simple fixes. With one listener and at most ten clips per condition, no paired difference is statistically significant; we present an exploratory record of what helped, what did not, and why.

We study estimating rare-event probabilities $I = \mathbb{P}(g(\mathbf{X}) > \gamma)$ with $\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$ and general $g : \mathbb{R}^d \to \mathbb{R}$. We address this problem through importance sampling, and propose a framework that substantially improves efficiency and robustness over baselines such as crude Monte Carlo, adaptive cross-entropy, variational-inference-based methods (including reverse- and forward-KL approaches), as well as Safe-ICE, Subset Simulation, and Sequential Monte Carlo, drawing on ideas from both rare-event estimation and cross-entropy optimization. The key contribution has two parts: first, we separate the problem into coverage, to overcome the cold-start barrier, and fitting, to refine proposals once a meaningful signal is available; second, we constrain the final GMM proposal so that it has finite importance-sampling variance (since coverage alone is not sufficient – without safeguards, importance sampling may still suffer from infinite variance). Together, these ingredients yield expressive proposals; finite variance does not by itself guarantee practical stability at a fixed sampling budget. Extensive experiments demonstrate substantial variance reduction, strong robustness across diverse benchmarks, and favorable cost–efficiency trade-offs, with the proposed approach often outperforming these baselines, particularly in high-dimensional and multimodal settings where competing methods frequently become unstable or fail. Our code is available at https://github.com/lorek/robust-cfi-is.