Papers

We investigate line defect Coulomb and Higgs indices in 3d $\mathcal{N}\ge 4$ supersymmetric gauge theories. The normalized line defect indices defined by ratios of the decorated defect indices to the ordinary indices yield well-defined integer values, the line defect Witten indices in the unit R-charge fugacity limit. We propose general formulae for these Witten indices in both Coulomb and Higgs limits for the theories without Chern-Simons terms, and we show that both count the states invariant under the residual gauge group left unbroken at a generic point of the branch, which we read off from the vacuum equations. Furthermore, we find powerful algebraic recursion relations for Wilson line defect Coulomb indices in the 3d SCFTs describing M2-branes, including ADHM-type theories and ABJ(M) theories. These relations imply that higher rank line defect indices are recursively determined by lower rank data across $U(N)$, $USp(2N)$, $SO(2N)$ and $SO(2N+1)$ ADHM-type theories and ABJ(M) theories.

We prove an asymmetric version of the discretised ring theorem.

A small excitation gap makes a quantum dot a sensitive probe of a weak electric field, but the charge detector reading it can also excite it. We calculate how much of this enhancement survives continuous readout for two interacting electrons tuned through a confinement-driven crossover in a gate-defined dot. The probe is a few-level system read by a weakly coupled linear detector, with second-order transition rates and information from the mean detector current, for gaps up to a few hundred microelectronvolts, couplings up to 50 $\mu$eV and temperatures up to 100 mK. The outcome depends on the energy structure of the detector, not only its noise. A quantum point contact measures more strongly at higher bias but, once the bias energy exceeds the gap, also excites the probe; when this back-action dominates the relaxation of the probe, the optimised information rate grows only as the inverse of the gap. A sensor quantum dot with a narrow level instead reaches full strength at a bias below the gap, where a non-interacting detector cannot excite it at zero temperature. This energy-filtered readout keeps the inverse-square gap dependence of the quantum Fisher information down to gaps comparable to the level width of the detector or ten times the thermal energy. At the tested operating points, higher probe states change the sensitivities by up to 6% and the exponents by up to 0.06; coherence corrections to the populations and transduced signal are negligible, and any gain from the full detector record is unresolved within 1-2% numerical uncertainty. Under the same conditions the interacting pair gives about three times the information rate of a single electron with the same gap and detector, for contact and Coulomb-type interactions alike. The different gap dependences and optimal biases of the two detectors can be tested by bias and gate sweeps on charge-sensed double dots.

$\mathsf{Datalog}^\circ$ has been introduced as an extension to Datalog that increases expressiveness, yet retains simple least fixpoint semantics and admits optimization techniques such as semi-naïve evaluation and demand transformation. $\mathsf{Datalog}^\circ$ accomplishes this by generalizing the or and and operators of Datalog to addition and multiplication over a semiring. Finding a (minimal) fixpoint of a $\mathsf{Datalog}^\circ$ program is equivalent to finding a solution to a system of polynomial equations over the underlying semiring. Solving these systems of polynomial equations is not only a fundamental problem in the theory of $\mathsf{Datalog}^\circ$, but also has many applications in computer science, such as in databases, program analysis, and optimization. This paper resolves a key open problem in the theory of $\mathsf{Datalog}^\circ$: we prove a tight upper bound on the number of steps until convergence of iterative methods for solving these polynomial equation systems over a commutative $p$-stable semiring. In particular, we show that the number of steps until convergence is $O((p+1)n)$ where $n$ is the output size of the $\mathsf{Datalog}^\circ$ program. As the number of steps until convergence is only a proxy for the runtime of $\mathsf{Datalog}^\circ$ evaluation, we also consider the number of semiring operations used and show that, for a natural class of algorithms, $O((p+1)mn)$ is a tight upper bound, where $m$ is the maximum number of semiring operations per iteration.

Standard radiation spectra modeling of active galactic nuclei like Seyfert galaxies typically involves tuning the relative contributions from an optically thick disc, optically thin corona, dust torus, and outflow by hand to match observations. The physics that quantifies this relative partitioning is not precisely understood. Here we make progress toward improving this understanding by testing the implications of a conceptual paradigm that the corona is supplied from below only by magnetic fields whose scales are large enough to escape turbulent shredding on their buoyant rise time. We use a generalized mean field accretion disc theory that includes both local radial angular momentum transport and angular momentum transport into a corona. We then use previous numerical simulations of magnetized turbulent accretion disc energy spectra to connect the fraction of disc magnetic energy that would escape to the fraction of coronal to total luminosity. Without explicitly calculating detailed particle acceleration and radiative processes, we assume that the disc radiation spectrum is thermal and the coronal radiation spectrum is a power law. We then show that the aforementioned paradigm for corona formation constrains the allowed x-ray power law index to a narrow range which agrees with observations. For the three AGNs studied here the predicted mean photon index is $\overline{\Gamma}=1.76$, consistent with the mean observed value of $\overline{\Gamma}_{\rm obs}=1.73$, bolstering confidence in the paradigm.

Synthetic gene expression data is increasingly proposed as a privacy-preserving substitute for controlled-access genomic repositories, but its safety depends on empirical auditing. Membership inference attacks (MIAs) provide that audit by testing whether a patient's gene expression profile was used to train a generative model. We report a red-team study on synthetic gene expression data derived from bulk RNA-seq profiles in The Cancer Genome Atlas, released by the ELSA Health 2026 Challenge. We unify five no-box attacks under a single weighted-distance framework in which each variant differs only in how it weights genes: uniformly (baseline), by variance, by synthetic-versus-reference KL divergence, by spectral residualization removing dominant principal components, and by curated pathway membership. Against a conditional variational autoencoder, spectral residualization raises AUC from 0.8251 to 0.8951 and TPR at 1% FPR from 0.3842 to 0.5970 on pan-cancer TCGA. Biological pathway priors did not transfer across targets.

We present ab initio calculations of atomic ionization by bare ions and antiprotons within the continuum distorted-wave eikonal initial-state (CDW-EIS) model. The dataset covers atomic targets from H to Kr, impacted by bare ions over a broad range of projectile charges and by antiprotons. Particular attention is given to elements in periods 3 and 4 of the periodic table, which are relevant to pigment analysis and technologically important materials. The resulting subshell-resolved total ionization cross sections are made openly available through an online repository covering a broad range of projectile–target systems, occupied initial subshells, and projectile velocities. We analyze systematic trends in the cross sections, including their dependence on projectile charge and velocity, binding-energy scaling, and charge-sign effects in proton and antiproton impact. To extend the practical coverage of the database, we also develop a neural-network surrogate, CDWEIS-NN, trained on the subset of the database with projectile charge $|Z_\mathrm{P}|\leq 8$. The network interpolates the CDW-EIS results to additional projectile–target systems and impact energies, reproducing both held-out CDW-EIS calculations and the experimental benchmarks considered in this work with satisfactory accuracy.

In this paper we use machine learning methods to predict radiation damage in the lead tungstate crystals of the CMS electromagnetic calorimeter at the Large Hadron Collider. We analyze LHC Open Data collected from 2016 to 2018 and study the time evolution of the crystal optical transparency. We apply deep neural network models to predict its behavior over different future time intervals, and find that encoder-decoder sequence-to-sequence architectures can effectively describe crystal aging.

Victor Lamme's Recurrent Processing Theory (RPT) proposes that the feedforward sweep (FFS) can extract and categorize visual features unconsciously, while conscious vision emerges through recurrent processing and feedback interactions across representational levels. The Motivated Emotional Mind (MEM) model, developed by Wiesław L. Galus and Janusz A. Starzyk, retains this core principle but embeds it in an embodied architecture integrating multilayer networks, semi-hierarchical semblions, receptors, effectors, allostasis, emotional valuation, and memory-based sensory reconstruction. This article examines the substantive but limited relationship between RPT and MEM. While RPT explains the role of recurrence in perceptual organization and the transition to conscious vision, MEM addresses the content of recurrent processing, its grounding in receptor activity and bodily states, its interaction with memory and action, and the possible role of reconstructed sensory representations in phenomenal experience. Particular emphasis is placed on secondary perception: the top-down reconstruction of sensory and interoceptive maps through which memories, mental imagery, dreams, hallucinations, feelings, and observed scenarios acquire experiential form. MEM thus associates phenomenality not merely with recurrent activity or reportability, but with the reconstruction of modality-specific, receptor-grounded sensory and bodily content. The article also presents the mathematical model of MEM, formalizing re-entrant processing, representational competition, allostasis, affect, curiosity, procedural gaps, and action selection. We conclude that MEM can be viewed as an embodied and motivational extension of RPT. However, its distinctive claims, particularly the sufficiency of secondary perception for phenomenality and the proposed microstructure of semblions, remain hypotheses requiring causal testing.

Synthesizing realistic graphs at scale is vital when the graphs of interest are large and real-world samples are limited or access-sensitive. Diffusion-based generators have recently driven much of the progress, offering high modeling capacity, but most such methods have quadratic computational complexity and are hence restricted to small-scale networks, currently up to 3k nodes. Existing non-quadratic methods remain limited by memorization issues and a trade-off between scalability and generation quality. Our goal is to generate large graphs whose structural statistics — e.g., degree distribution, clustering, and path length — faithfully reflect those of real-world sparse graphs, without resorting to memorizing the training data. We introduce a discrete graph diffusion model that restricts training to a structurally motivated subset of node pairs — observed edges and their wedge non-edges — reducing training complexity below quadratic in the number of nodes. To keep the noisy graph informative throughout both the forward and reverse trajectories, we design a three-class absorbing forward process governed by a degree-aware, floored cosine noise schedule: unlike a structure-blind schedule that adds noise to every pair identically, ours adapts to each node's degree and never fully erases the graph's structure, keeping the noisy graph informative at every step. Experiments across diverse datasets show that our model consistently ranks among the top methods for structural fidelity against existing discrete diffusion baselines in large graph generation.

We consider steady-state optimization of nonlinear dynamical systems under time-varying stochastic operating conditions, where the objective is an expected-value function over the current operating-condition distribution, so that changes in the distribution induce a moving stochastic optimum. To address this problem, we propose stochastic sequential feedback optimization (S2FO), which combines projected feedback-gradient updates with sequential sensitivity estimates obtained by linearizing the plant at realized stochastic operating conditions. We analyze the closed-loop performance of S2FO through expected dynamic regret, instantaneous tracking in expectation, and almost-sure convergence under diminishing step sizes. We then apply the method to wind farm power maximization under time-varying stochastic inflow. Simulations on a benchmark layout and on a realistic offshore wind farm show that S2FO improves average power generation when persistent wake interactions are present, and that its advantage decreases as wind-direction variability increases.

Recent advances in robot learning have enabled generalist control policies capable of completing a wide range of tasks. However, their performance degrades when deployed in unseen environments, making it critical to detect failures and teach recovery behaviors. Existing runtime monitoring methods often require task- and policy-specific training or hyperparameter tuning, limiting cross-task deployment and introducing additional overhead during iterative policy updates. We present Reward-DAgger, a robot-gated interactive imitation learning framework that uses dense progress signals from a general-purpose reward model to determine when human intervention is needed. Our approach is agnostic to the underlying policy architecture, requires no access to policy internals, and can be applied across tasks without retuning the gating mechanism. Our results show that Reward-DAgger achieves a better failure-detection accuracy-latency tradeoff than existing runtime monitoring baselines. Across eight simulated and real-world tasks, Reward-DAgger consistently improves the downstream policy's autonomous success rate throughout interactive learning and achieves strong return on human effort, outperforming the baselines in most settings. Importantly, the same gating configuration is used across tasks without task-specific hyperparameter tuning, demonstrating transfer across tasks, environments, and policy architectures. Code and videos are available at https://liralab.usc.edu/reward-dagger.

Autonomous agents built on Large Language Models (LLMs) need standardized protocols to interoperate across systems. Several now exist (A2A, MCP, ACP, ANP, NLIP), but the Natural Language Interaction Protocol (NLIP) has not appeared in any controlled performance study, and no work has measured where an agent protocol's latency is spent. We compare NLIP and the Agent-to-Agent (A2A) protocol empirically, decomposing latency into message creation, connection, and send phases across three independent hardware environments. For lightweight coordination, NLIP is 8.4-9.6x faster than the baseline A2A SDK implementation on two environments and about 4x on a third; the direction of the advantage is consistent, its magnitude depends on the hardware. The advantage is stage-specific: for the end-to-end pipeline, where LLM inference dominates, the protocols are near parity. The difference comes almost entirely from connection setup. To test A2A at its best, we also ran A2A SDK with connection caching enabled; caching narrows its gap with NLIP by a hardware-dependent amount, from 2.75x on one machine to near-parity on faster hardware, where at scale a cache-optimized A2A-SDK matches NLIP. We report these as measured conditions without a single causal account of the residual send-phase cost. Against the more optimized Python-A2A, NLIP leads by about 4x on the same stage. We close with a protocol-selection guide keyed to workload characteristics.

Shape from shading using a single image of a Lam- bertian surface is inherently ambiguous. When the light source direction is known, the surface normal estimation has a cone- ambiguity, which worsens when the source is unknown. Recently, shape from heat conduction has emerged as an approach that leverages heat transport equations to estimate the Shape Lapla- cian operator, an intrinsic measure of shape. However, deriving surface normals from the Laplacian operator encounters a local binary convex/concave ambiguity. Our contribution introduces a novel theory to resolve these local shape ambiguities (excluding a few degeneracies) without relying on priors like smoothness, by combining the cues from shading and heat conduction. Our method ensures the mathematical constraints of both shading and the Laplacian are satisfied simultaneously, even with an unknown light source. We validate our theory through simulations of complex shapes and analyze its performance in the presence of noise, as well as on a noisy single thermal video of real-world objects with complex shapes and material properties, including varying albedo.

Accurate early screening for Autism Spectrum Disorder (ASD) is a precursor to timely intervention, which is critical for improving cognitive and behavioral outcomes. We present ASD-FEAT (ASD - Feature Extraction And Tracking), a multimodal dataset derived from video recordings of infant-adult interaction sessions. The key contribution of ASD-FEAT is the combination of longitudinal coverage from infancy through 36 months, repeated interaction sessions, clinically validated developmental outcomes, expert frame-level behavioral annotations, and privacy-conscious multimodal feature representations. To the best of our knowledge, existing ASD behavioral datasets do not jointly provide these characteristics at comparable scale. To demonstrate the utility of ASD-FEAT, we use it to evaluate a computer-vision-based end-to-end pipeline relying on machine learning techniques to automatically identify ASD risk. ASD-FEAT integrates both expert-defined and deep-learned features, including face and eye landmarks, facial action units, gaze direction, head position, mel-spectrogram audio representations, and optical flow, to identify behavioral markers of social interaction. Our automated pipeline achieves an ASD classification accuracy of 76.2% and an Area Under the Receiver Operating Characteristic (AUROC) of 0.82, compared to classifiers trained on manually labeled behaviors, which yielded 81.3% accuracy and an AUROC of 0.88. We further introduce a within-visit partner contrast: a per-visit signal contrasting examiner-directed and parent-directed social behavior which, when added to the classifier, lifts the fully automated Look Face + Smile and Look Face + Vocal configurations to Matthews correlations of 0.49 and 0.45 respectively, exceeding the human-coded single-partner baseline of 0.42.

Measuring the age and composition of interstellar objects is necessary to understand their origins. However, existing methods for measuring the age are either imprecise or require an unusually bright target, while the composition is confounded by the effects of Galactic cosmic rays, which drive chemical reactions in the cometary matrix. As the Vera C. Rubin Observatory expands the census of interstellar objects, measuring these properties will be critical to understanding the overall population. In this work, I derive a new methodology for simultaneously estimating the age and initial composition of an interstellar object from time-series observations of the coma. Measurements of both the composition and its gradient versus depth into the nucleus are shown to fully constrain both properties in most circumstances. A simple model using only CO and CO$_2$ is discussed and used to demonstrate the properties of this inference process. When applied to 3I/ATLAS, this simple model indicates that this object is at least 0.6 Gyr old and has an initial CO/CO$_2$ ratio of 1.5, supporting a formation outside the CO ice line. Further refinement of the chemical network and improved observational strategies will improve the precision and accuracy of these measurements, enabling a deeper understanding of the interstellar object population and extrasolar planet formation.

We study the maximization of a nonnegative $k$-submodular function, not assumed monotone, in which each of $n$ elements receives one of $k\ge2$ labels or stays unselected and the selected elements must satisfy a constraint. For a compact convex down-closed region $P\subseteq[0,1]^n$ of fractional selection vectors, the diagonal level $\zeta(P)=\max\{t\in[0,1]:t(1,\ldots,1)\in P\}$ is the largest selection probability that can be given to all elements at once; it equals $r/n$ for a uniform matroid of rank $r$, and $\zeta(P)=1$ means that the constraint is vacuous. We give approximation coefficients that increase continuously with $\zeta$. They come from one inequality for the multilinear extension of the objective: the algorithm computes an action without querying the objective, and objective feedback gives a comparator-independent update direction. For $k\ge3$, feasibility of the action reduces to three polynomial inequalities in one variable; for $k=2$ the profile is closed form. At $\zeta=0$ the coefficients are $0.4456\ldots$ for $k=2$ and $0.4541\ldots$ for every $k\ge3$. For every finite $k\ge3$ they reach $1/2$ above an explicit level, which is $0.4026\ldots$ for $k=3,4,5$, and at $\zeta=1$ they reach $1/2$ for $k=2$, $(\sqrt{17}-3)/2$ for $k=3,4$, and $k/(2k-1)$ for $k\ge5$. Online linear optimization gives $O(\sqrt T)$ approximate regret, with gradient feedback or with value queries made after each action. The coefficients carry over to matroids, with expected and high-probability guarantees, and to any fixed number of knapsacks: the zero-level coefficients hold on every instance, and the larger ones when items are small or when prefix enumeration keeps the diagonal level on one branch. For one budget the enumeration exponent is $O(1/\varepsilon)$.

We test the hypothesis that Newton's gravitational constant underwent a rapid transition approximately $73$-$130\,{\rm Myr}$ ago, as proposed in some resolutions of the Hubble tension. Fully convective red dwarf stars with masses below $\sim0.35\,M_\odot$ have thermal timescales comparable to the proposed transition look-back times, so an appreciable present-day memory can remain. We show that a rapid step in $G$ induces measurable changes in their radii and confront these predictions with mass-radius measurements of eight red dwarfs in detached eclipsing binaries. We find that the $G$-step models proposed to resolve the Hubble tension, corresponding to a $4\%$ change in $G$ at a look-back time of $73\,{\rm Myr}$ and an $11\%$ change at $130\,{\rm Myr}$, are excluded at significances of $3.1\sigma$ and $4.0\sigma$, respectively.

A language model reads long text in one quadratic forward pass, stops at the context window, and loses accuracy with length before reaching it. We ask whether the read can be factorized when deciding over a finite set: which document is relevant, which option is supported, which passage is the evidence. Periscope, a training-free inference method, arranges the $N$ chunks of a text on a $K{\times}K$ grid with $K{=}\lceil\sqrt{N}\rceil$ and asks a frozen model the same question about $K$ local spans of consecutive chunks and $K$ strided spans that sample the whole text, reading the log-odds of every answer at one token. Each answer takes its best local and strided score, and scoring every chunk by its two spans gives an evidence map at no further cost, whose peak is the chunk behind the answer. Every probe is about $\sqrt{sc}$ tokens for a text of $s$ tokens and chunk size $c$, so a window of $W$ tokens reaches $W^{2}/c$ tokens at $s^{1.5}$ cost. The map replaces the long read. On LongBench v2, reading only the $K$ chunks the map ranks highest, 9k tokens, matches the same model's best window read across windows from 32k to 1M tokens, and on InfiniteBench, where the median context is 150k tokens, it leads the best window read by 5 points. The same map ranks BRIGHT's long-document corpora with the best NDCG@10 of six methods. Each call caches only one probe, so a 27B model reads 4.5M-token contexts on one 80GB GPU, where a single pass would need 296GB of cache. A long read then needs a GPU that holds the model, not one that holds the text.

In this paper we demonstrate that Hopf algebras and Frobenius algebras provide an appropriate setting for an analogue of the classical Lie correspondence. We introduce a compatibility structure between Hopf and Frobenius algebras called Hopf-Frobenius modules, and give constructions that can be applied to any such module, which produce corresponding Lie groups and Lie algebras. Further, we show that classical Lie algebras and Lie groups give rise to Hopf-Frobenius modules for which the corresponding Lie groups and Lie algebras produced by our construction are those of the ordinary Lie correspondence.

Let $n \geq 3$. We improve the large sieve inequality for $n$-th order Hecke characters over any number field containing the $n$-th roots of unity. Our bound is expected to be optimal in all ranges of parameters. Several applications are deduced, including a tight upper bound for the second moment of cubic characters ordered by conductor, asymptotics with lower order terms for the cubic second moment over squarefree moduli, and improved moment and zero density estimates for every $n \geq 3$.

The quadratic attention cost of Vision Transformers (ViTs) forces a trade-off between spatial resolution and rollout horizon, particularly for fine-scale PDEs where shocks, reaction fronts, and material interfaces occupy small, evolving regions of the domain. Conventional neural surrogates also lack mechanisms to adapt resolution dynamically. We propose WAMRViT, a ViT that tokenizes inputs as balanced quadtrees using a wavelet-inspired refinement criterion, jointly encodes position and refinement level with 3D rotary positional embeddings, and regrids in cell space during inference for stable long-horizon rollouts. A multi-scale variant retains each leaf at its native source resolution and lets the model learn across resolution levels. Unlike fixed-budget adaptive-tokenization methods, WAMRViT imposes no predetermined token count and supports fully adaptive topology throughout autoregressive rollout. To our knowledge, it is the first machine-learning surrogate to natively tokenize multi-level Adaptive Mesh Refinement (AMR) data. On uniform-grid benchmarks, uniform-patch WAMRViT improves finest-level region-of-interest VRMSE over a finest-patch uniform ViT while using substantially fewer tokens. The multi-scale variant achieves the lowest first-step full-field RMSE and VRMSE on both benchmarks and improves rollout-averaged full-field and refined-region accuracy at long horizons. With parallelized regridding, its end-to-end rollout cost lies between finest-patch and approximately token-matched coarser-patch ViTs. On a complex AMR combustion problem whose finest features cannot be represented natively by the evaluated uniform-grid baselines, WAMRViT operates on adaptive cells built from the simulator hierarchy and substantially reduces finest-level error at matched transformer capacity. Code: https://github.com/tonyzyl/wamrvit

We develop a quantum input-output theory for open photonic systems based on macroscopic quantum electrodynamics using the first-order electromagnetic Green's function. Quantum fields enter and leave the photonic system through waveguide ports, while the electromagnetic Green's function propagates the fields through the arbitrary interior of the photonic system, which may be dispersive and absorbing. The resulting relation contains a port-to-port scattering matrix and a Langevin-noise contribution from material absorption that together preserve the bosonic output commutation relations. For embedded emitters, the low-saturation and single-excitation scattering response is determined by Green's functions connecting the ports and emitters while retaining the non-Markovianity of the photonic environment. Using finite-difference time-domain simulation, we calculate the emitter-modified transmission for a nanophotonic cavity and inverse-designed coupler, providing a direct route from computed electromagnetic response to a quantum input-output model.

Bipolar disorder is strongly associated with financial instability. We examine how different interventions motivate individuals with bipolar disorder to share financial data with others. This approach can inform the development of tools for digital monitoring and intervention designed to promote financial stability in this population. 500 individuals with BD completed a pre-registered factorial vignette survey to examine level of comfort with hypothetical scenarios involving third-party financial interventions during symptomatic and euthymic periods. Scenario components were systematically varied between third-party actors, mood states, and intervention types. Participants rated sharing comfort on a 0-10 point scale. Multilevel models tested differences alongside clinical and financial histories, relational trust, and personality. Participants were most comfortable involving care partners in financial planning. They were more comfortable with temporary spending restrictions during symptomatic states than euthymic periods, underscoring the importance of accurate mood detection for intervention delivery. Prior financial help-seeking behavior and higher relational trust predicted greater comfort. Bankruptcy experience — declared by 11.4% and considered by 31.7% — was associated with increased comfort with spending restrictions. Individuals with psychiatric advance directives (8%) were significantly more comfortable sharing spending behaviors than those without. Comfort with financial interventions was higher among those with prior financial challenges or help-seeking histories. Participants distinguished between symptomatic and euthymic periods, favoring targeted, time-limited restrictions over general monitoring. These findings extend prior work on financial data sharing for illness self-management.

Continuous-discrete filtering is a classical problem in signal processing and control theory, whereby the state driving a stochastic differential equation (SDE) must be inferred from noisy, partial discrete-time observations. Corresponding filtering algorithms are often formed as discrete-time methods and applied to a discretization of the SDE, an approach limited by the incurred discretization error, or model a type of Gaussian moment ordinary differential equation (ODE) flow, which is approximate for nonlinear dynamics. We introduce a new method, the Wiener-space cubature Kalman filter (WSC-KF), for Gaussian filtering in this continuous-discrete setting. The WSC-KF combines spatial sigma-point representations with Wiener space cubature integration, effectively approximating iterated integral terms of the driving Brownian motion to higher-order than standard discretization (e.g., Ito-Taylor expansions), or approximate moment-ODE flows (e.g., as in the unscented Kalman filter). Theoretically, we characterize the path-law approximation degree of WSC-KF through a tunable model order parameter. We prove that, depending on the model order chosen, WSC-KF provides weak order bounds comparable to or dominating that of a cubature Kalman filter using a first-order Ito predict step. Numerically, we confirm that rate on a globally Lipschitz Levy-area diffusion. Degree-5 Wiener cubature matches mixed iterated integrals that existing continuous-discrete Kalman predictors omit, while remaining efficiently computable; this is the mechanism enabling higher-order weak path-law approximation.

Financial LLM agents are often evaluated by comparing their end-to-end returns with those of a baseline and testing the paired difference against zero. This measures whether deploying the agent changes realized performance, but it does not isolate event-selection skill. An agent that frequently changes positions from flat to long can earn a positive paired return from an upward-drifting event pool even when it selects events at random. We propose the Agent Policy-Value Audit, which holds fixed the observed count of each ordered action-change type and randomly reassigns them across eligible events. The average payoff from these reassignments is the composition benchmark; the difference between observed deployment value and this benchmark is selection value. In semi-synthetic benchmarks based on real earnings-event returns, a zero-centered paired test falsely attributes passive exposure to selection skill in $11.6\%$ of no-skill replications, while the transition-matched audit reduces this rate to $5.3\%$. Applied retrospectively to 723 earnings events at 44 U.S. consumer-facing firms, the audit decomposes the agent's gross deployment value of $+15.2$ bps/event into a $+25.8$ composition benchmark and a $-10.6$ selection value. The agent does not detectably outperform matched random assignments. Financial-agent evaluations should report deployment value separately from event-selection value.

Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of "Optimistic Optimization" algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-\beta / d})$ regret, where $\beta = 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. We use our approach to improve the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving $\sim10\%$ improvement in performance relative to the best possible unquantized model.

Synthetic data are increasingly used as an alternative to sharing sensitive records. However, synthetic data generation does not guarantee privacy, as diffusion models trained or adapted on sensitive data remain susceptible to reconstruction attacks. Moreover, while approaches that use differential privacy (DP), such as DP-SGD, achieve provably private diffusion model training, the repeated gradient clipping and noise injection they require result in significant utility loss. An important limitation of DP-based privacy is that, although it has a provable relationship to reconstruction privacy (RP), that relationship is indirect. RP is defined in terms of limiting how much an adversary's posterior distribution over sensitive data differs from the prior, whereas DP provides guarantees by bounding the sensitivity of outputs to changes in individual records. This indirection is an important source of the utility loss. To address this, we propose a PAC-private diffusion model adaptation to achieve reconstruction privacy. Since PAC-privacy is defined directly with respect to posterior advantage over the prior, it directly implicates RP. To obtain scalable PAC privatization in high dimensions, we first learn a compact data-dependent diffusion model component using LoRA or Textual Inversion, and then calibrate anisotropic Gaussian noise from the covariance of repeated mechanism outputs. Unlike DP-SGD, our method perturbs the learned component only once after optimization, thereby avoiding privacy composition across gradient updates. We evaluate the framework on few-shot concept personalization and full-dataset image synthesis, and show that the proposed approach better preserves subject identity, generation quality, and downstream classification accuracy than DP while achieving the same reconstruction privacy.

Modern GPU-based HPC systems rely on heterogeneous vendor stacks, yet resilience studies are largely limited to single architectures, leaving it unclear how faults behave across different GPU backends. We present BitIR, a cross-architecture fault injection framework that injects deterministic single-bit faults at the LLVM IR level, ensuring semantically equivalent perturbations prior to backend lowering and enabling direct cross-vendor comparison across NVIDIA, Intel, and AMD GPUs. We evaluate BitIR on three production supercomputers – Polaris (ALCF, NVIDIA A100), Aurora (ALCF, Intel GPU Max 1550), and Frontier (OLCF, AMD Instinct MI250X) – representing the full spectrum of current leadership-class GPU architectures. Using representative heterogeneous benchmarks, we conduct large-scale injection campaigns across all three systems and classify outcomes into masked results, silent data corruptions (SDCs), and failures. Our results show that identical faults produce markedly different behaviors across vendors: Intel most often masks faults but exhibits more hangs when faults escape masking, NVIDIA exposes more detectable hard failures, and AMD alternates between SDC-dominant and failure-dominant behavior depending on the benchmark and fault site. These findings demonstrate that resilience is not backend-invariant, underscoring the need for backend-aware and workload-aware fault mitigation.

Vision Transformers (ViTs) have shown strong performance in volumetric segmentation, but their effectiveness on clinical CT is limited by an isotropic Euclidean lattice assumption. This conflicts with anisotropic CT acquisition, leading to two key issues: (1) a metric mismatch between voxel indices and physical anatomy, and (2) accuracy degradation from isotropic resampling. To address this, we propose MAGEFormer, a geometry-calibrated framework that embeds physical metric constraints directly into representation learning. Our method introduces Metric-Adaptive Spatial Embedding (MASE) to calibrate positional frequencies using voxel spacing, Geometry-Constrained Attention (GCA) to suppress physically implausible feature correlations, and Geometric View Voting (GVV) to reduce discretization bias during inference. We evaluate MAGEFormer on two multi-organ abdominal CT benchmarks, BTCV and FLARE 22, under a unified protocol against strong CNN and Transformer-based baselines. MAGEFormer achieves the strongest boundary accuracy among the compared methods, with 10.58 mm HD95 on BTCV and 3.40 mm HD95 on FLARE 22, and shows consistent gains in Dice under the same protocol. These results show that geometry-aware internal calibration is more effective than relying on conventional isotropic preprocessing alone for anisotropic CT segmentation.