Papers

Tracking angle-of-arrival (AoA) under mobility enables proactive beam alignment in multi-antenna wireless systems. However, learning this evolution directly from raw I/Q data is challenging because multipath, channel-gain variations, hardware impairments, and noise mix with angular information. This paper proposes AngularWM, a self-supervised wireless world-modeling approach that learns a predictive latent angular state from ordered multi-antenna I/Q observations. A joint-embedding predictive architecture is combined with a label-free trajectory-level geometric regularizer that encourages an approximately affine, non-collapsed latent evolution motivated by the antenna-array response. No AoA, motion, or displacement labels are used during pretraining. The resulting structured world state supports direct multi-step encoder-space extrapolation and generalizes to angular step sizes not seen during training. On large-scale over-the-air measurements, AngularWM reduces the mean predictor-free AoA error over eight steps from $29.97^\circ$ to $0.49^\circ$. After pretraining, only three or four labeled reference angles are required to calibrate the complete 225-point AoA grid, achieving $0.48^\circ$ and $0.43^\circ$ MAE, respectively. AngularWM also maintains robust beam alignment and spectral efficiency under increasing angular displacement, while reducing the deployed model size from 1.42M to 0.30M parameters and forecast latency.

Control barrier functions are an effective model-based tool to formally certify the safety of a system. However, transferring their theoretical guarantees to real-world robotics systems requires high model fidelity. For example, payloads or wind disturbances can cause significant model perturbations to an aerial vehicle, leading to safety compromises. In this work, we propose a certifiable online learning-enhanced robust adaptive control barrier function, which adapts to disturbances using a Neural ODE and quantifies its adaptation uncertainty with conformal prediction. Our approach guarantees safety at all time under unknown time-varying model disturbances. It adopts a conservative strategy when the adaptation uncertainty is high; and efficiently adapts to reduce controller conservativeness as it receives more data. Our approach provides a provable safety guarantee with a probability bound under suitable Lipschitz smoothness assumptions on the underlying model and trajectory. These results demonstrate the potential of our method as a practical safety controller for robotics system operating under model perturbations.

Mechanistic interpretability has emerged as the primary means to understand safety behavior of LLMs. However, existing tools primarily focus on the activating neurons or features of a model. The role of the remaining large set of inactive components is invisible to such methods. This work demonstrates that the inactive set contains safety-critical features that are causally relevant for refusal of harmful prompts. Suppressing such features could turn refusals into compliance, while passing undetected by prevalent interpretability tools. We introduce the Counterfactual Activation Potential (CAP), a metric that quantifies a suppressed feature's latent activation tendency as the product of its encoder alignment (how strongly the input drives it), suppression strength (how strongly active features inhibit it), and safety criticality (how much refusal depends on it). To find suppressed safety features at scale, we propose CAP-guided Safety Feature Discovery (CSFD), a two-stage filtering algorithm that identifies candidate safety features from hundreds of thousands of transcoder features without exhaustive ablation. A significant fraction of trials turn compliant with harmful prompts when a candidate feature is ablated. Under natural jailbreaks, the suppression acting on the highest-CAP features rises 2-4x, and their activation correspondingly falls by up to 80%. Amplifying a feature's suppressors pushes its activation down and raises harmful compliance with prompts related to the suppressed feature, with no such effect for random features. Our experiments span five Gemma, Qwen, and Llama models across various parameter sizes. Our findings indicate that jailbreaks could operate in part by suppressing safety-critical features rather than solely activating harmful ones, and that suppressed features are a necessary complement to activation-focused interpretability of safety behavior.

Natural language to SQL (NL-to-SQL) benchmarks are foundational to progress in data analysis research, yet recent work has shown that widely-used benchmarks contain significant annotation errors. These errors silently corrupt evaluation metrics, penalize correct model output, and distort the field's understanding of state-of-the-art performance. We present SALUS, a system that automatically detects annotation errors in NL-to-SQL benchmarks. SALUS frames benchmark auditing as a weakly supervised error detection: SQL generated by multiple LLM agents drive a suite of complementary weak-labeling functions. By passing this noisy vote matrix through a generative label model, we extract high-confidence training samples without requiring human ground truth. These samples train a decision plane that maps gold SQL query features to per-agent trustworthiness, allowing SALUS to intelligently fuse reliability estimates with raw verdicts for rigorous benchmark error detection. We evaluate on BIRD-Clean-xs, a benchmark of 298 BIRD development tasks with manually verified correctness labels. SALUS achieves F1 = 0.9194, significantly outperforming the state-of-the-art baselines. Applying SALUS to the full development sets, we estimate annotation error rates of approximately 37% on BIRD and 27% on Spider.

Let $X$ be a curve of genus $g\ge2$ over an algebraically closed field of odd characteristic $p$, and let $G=\mathrm{Aut}(X)$. A theorem of Giulietti and Korchmaros shows that if $G$ fixes no point and a $p$-subgroup $S\le G_P$ satisfies $|S|>\frac{p}{p-1}g$, then $X$ is one of the classical hyperelliptic, Hermitian, or Ree curves. We determine the sharp boundary and the first gap below it. At equality, besides the classical curves, exactly three types occur: the ordinary curves $y^p-y=x+c/x$, the zero-$p$-rank curves $y^3=x^p-x$ for $p\equiv2\pmod3$, and, in characteristic $3$, the ordinary genus-six family $y^3-y=c\left(x+\frac1{x^3-x}\right)$. As a key ingredient, we classify zero-$p$-rank curves whose full automorphism group fixes no point and which admit a $p$-subgroup of order larger than the genus. We then prove that, when $|S|>p$, the boundary classification already follows from the weaker inequality $|S|>p(g-p+1)/(p-1)$. For $|S|\ge p^3$, the forbidden interval above $m=(p-1)|S|/p$ has width at least $p(p-1)/2$, and below $m+(p^2-1)/2$ at most one further genus can occur, with a rigid ramification structure. Finally, we classify the first admissible layer: it occurs only for $|S|=p^2$, and the resulting ordinary curves admit a complete description in terms of two-dimensional Artin–Schreier spaces.

We introduce Loop Flow Transformers (LiFT), a family of looped generative models that scales computation by repeatedly applying a shared Diffusion Transformer (DiT) core, with only light changes to the standard architecture. Rather than asking every recurrent step for the final prediction, LiFT trains each step with a single regression target: a point on a straight path from the model's initial estimate to the flow-matching target. Because we index these targets by a continuous depth coordinate, a trained model can loop far beyond its training depth with no retraining, early exits, or other modifications. In our experiments, these longer rollouts improve generation, so inference computation can grow without adding parameters. On ImageNet at 256x256, LiFT-L/2 achieves an FID 3.34 points lower than our dense DiT-XL/2 baseline while using approximately 60% fewer parameters, 32% fewer training FLOPs, and 52% fewer inference FLOPs.

We study relatively minimal Lefschetz fibrations over closed oriented surfaces whose monodromy extends over a fixed 3–dimensional handlebody. If $X$ is the total space and $\ell$ is the number of critical points, we prove that $\sigma(X)=-\ell$. Such fibrations with $\ell>0$ exist precisely for fiber genus $g\geq3$ and base genus $h\geq2$, and one can take $\ell=1$ for every such pair. We also show that hyperelliptic handlebody monodromy forces the fibration to be a surface bundle and that every meridian twist, separating or nonseparating, has commutator length two in the handlebody group for $g\geq3$.

Non-reciprocal transport underpins key functionalities in signal processing and logic; however, conventional semiconductor diodes exhibit reduced performance at sub-Kelvin temperatures. As cryogenic electronics continue to scale, there is increasing demand for diode operation compatible with low-temperature and low-dissipation conditions. This need has driven the development of alternatives to p-n junctions that rely on non-reciprocal electron transport mechanisms efficient in the deep-cryogenic regime. Superconducting devices constitute a natural low-loss platform, yet most existing superconducting diodes are restricted to either Cooper-pair or quasiparticle transport, often requiring complex material stacks, asymmetric geometries, or external magnetic fields. No single, geometrically symmetric junction has yet integrated rectification across both transport channels to achieve vanishing resistance under forward bias and strongly suppressed conduction under reverse bias. Here, we demonstrate a dynamically reconfigurable dual-function superconducting diode based on a conventional Al/AlOx/Al tunnel junction. Via microwave biharmonic driving, we exploit multi-tone photon-assisted tunneling to independently control dissipationless and dissipative transport channels within the same device. Varying the microwave drive amplitude induces a transition from a supercurrent diode to an ideal quasiparticle diode, achieving rectification efficiencies exceeding those of conventional Schottky diodes and contemporary superconducting diodes. We further demonstrate AC signal rectification under both current-bias and voltage-bias configurations. Finally, we implement a proof-of-concept "absolute diode" that combines zero forward resistance with strongly suppressed reverse conduction. This tunable approach provides a versatile building block for low-power cryogenic electronic architectures.

Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators.

Human–LLM interaction datasets shape our understanding of AI use and provide a foundation for downstream research, including training and evaluation of user models. In recent years, a growing number of datasets have sought to capture a representative picture of human–LLM interactions. But how different are the pictures these datasets provide, and what do those differences mean for research built on them? We study these questions across seven conversation datasets, spanning in-the-wild chat logs and human preference data. We begin by revisiting the dataset classification experiment of Torralba & Efros and find that neural network classifiers identify the source of a conversation from user messages alone well above chance, indicating distinctive dataset signatures. This separability persists after matching datasets on the dimensions of human-designed taxonomies, implying subtle differences that these taxonomies do not capture. We then examine the implications for user modeling: how dataset signatures propagate to the outputs of user models trained on these datasets; how dataset choice influences evaluations of user model quality and subsequent evaluations of LLM assistants paired with these user models; and how dataset classifiers can guide data selection for training user models. While each dataset is meant to capture a slice of 'real-world' interactions, our findings reveal the extent to which these slices diverge, and the consequences of those differences for research built on these foundations.

A harness search around a frozen longevity-tuned 1.7B model reported a rescue. An audit found that the gain came from rows the start left unparsed, that the caller sent each row's reference answer as an assistant turn, and that replication through the same pipeline missed it. Is a harness's gain more than a constant answer would give? We preregistered three studies and report every endpoint. In the first two, thinking off raised test accuracy over a capped thinking setting in 7 of 12 cells, mostly on rows the cap left unparsed. It was not meaningfully worse than a rescue in 7 of 9 small-model test cells or than four GEPA harnesses at 1.7B. Replication reproduced an injected defect's distortion in 9 of 20 evaluable cases (7 fixed by design). At 14B, two GEPA harnesses beat thinking off by 34 points on test but were not detectably above the strongest constant label, and answered "Yes" in 94.6% and 98.2% of parsed mortality answers on test. In the third study (SmolLM3-3B, base Qwen3-1.7B), GEPA beat the constant on FPB (confirmatory, both partitions); thinking off was not meaningfully worse than any BoolQ harness, and 3 of 4 MMLU-Pro searches kept their seed (the fourth inconclusive on test). On Autocast (exploratory), the harnesses were within 0.7 points of the constant and gave one label in 93.1% to 96.8% of parsed answers, both on test. On questions about the input or about knowledge (FPB, BoolQ, MMLU-Pro), GEPA beat the constant or found no clear gain over thinking off; on questions that ask for a prediction (14B mortality, descriptive; Autocast, exploratory), the harness ended near the constant and gave one label almost throughout while its gain over thinking off looked large. The constant label told the two apart wherever the gain was large. This rests on few tasks that also differ in label skew, number of labels and task type, so it is not shown to depend on the kind of question.

AI agents that send emails, edit files, and make purchases must decide when to act on their own and when to check with the user first. This decision is usually evaluated by showing a model a proposed action, asking whether it should proceed, and scoring agreement with human labels. We introduce DelegationBench to test whether such scores can be trusted. It has 156 scenarios with four possible responses (act, ask for permission, ask for missing information, refuse), and most scenarios come in matched pairs that change a single feature: whether the action was requested, what is at stake, whether it can be undone, or who will see it. Across ten models from five families, agreement scores mislead in three ways. A simple keyword rule, which we wrote after seeing the benchmark, agrees with our annotators more often than eight of the models, yet its decision changes in only 9 of 48 matched pairs. Equivalent ways of asking the same question change how often a model acts by up to 52.5 percentage points. And every model stops to ask the user less often when it must carry out the task with tools than when it judges a proposed action. When rules are stated explicitly, the same models follow them almost perfectly, so the gaps are not explained by a general inability to follow rules. We release the benchmark and evaluation tools and recommend reporting these properties separately rather than as one score.

Embodied systems need geometric perception that exploits available observations beyond images alone. Recent feed-forward 3D models incorporate geometric priors, including camera poses, intrinsics, and depth. However, handling noisy poses, preserving accurate priors, and recovering physical scale require more than simply accepting these inputs. We introduce Vision-Prior Geometry Grounded Transformer (VPGGT), a VGGT-based framework that extends OmniVGGT for prior-aware embodied perception. We formulate sensor-motivated pose corruptions from ground-truth trajectories for training and introduce a parameter-free prior residual connection (PRC) to mitigate prior dilution, where predictions are less accurate than their supplied pose priors. Our noise formulation targets camera poses; supplied intrinsics and depth receive no additional corruption. We further introduce Metric Global Attention, which conditions a global scale token on available pose and depth scales and predicts a shared metric scaling factor for the geometric outputs. Experiments across four datasets show that PRC improves translation-direction accuracy and joint pose AUC over a matched training baseline when camera priors are provided for all views, under both exact and corrupted poses. These results support explicit prior access during refinement as a useful addition to feature-level conditioning.

We formulate a novel optimal control problem for data-driven dynamic resource allocation in multicore real-time systems. The proposed formulation accounts for hard deadline constraints and resource bounds. Under mild assumptions, we prove several results on the feasibility and existence of optimal solution for the proposed formulation. Building on these analyses, we design an algorithm to solve the multi-core dynamic resource allocation problem. We demonstrate the practical use of this new algorithm by experimentally evaluating it on a real multicore platform using four benchmarks from the literature.

We present DynaMesh, a dynamic texture generation method for 3D meshes. Given a textureless shape and a text prompt describing an effect, our method produces an appearance that evolves while the object's geometry remains unchanged. Previous works on dynamic 3D content generation have focused on motion, where an object's geometry and position change while keeping its appearance the same. Methods on texture generation sit on the other side of the problem, painting appearance onto a shape as a fixed surface property and not as an evolving process. Neither addresses a visual effect that propagates on a 3D object. A natural route consists of two generators: a video model that shows the effect from a single view, and an image-to-3D generator that lifts each frame to 3D. However, the latter has no notion of time, so running it per video frame produces a sequence that flickers, loses effect details, and yields a different mesh at every video frame. Our method addresses these failures by conditioning a video model on a render of the mesh and the prompt to obtain a reference video, then running a frozen image-to-3D generator on the video with two changes. The conditioning of each frame is blended over a temporal window, and low-rank adapters are fit per shape to restore the lost details. The mesh is encoded once for the whole sequence, so geometry is constant by construction, and the output is a single mesh with a texture per frame. Applied to various objects and effects, DynaMesh substantially improves over recent video-to-4D and texturing methods, and can generalize its temporal effect to different shapes never seen during training. Our project page is at https://threedle.github.io/dynamesh/.

We study spectral zeta densities associated with complex powers of principally scalar Laplace-type operators on pseudo-Riemannian scattering spaces of mixed signature and arbitrary dimension. The construction extends, beyond the even-dimensional Lorentzian case, the local analysis of Feynman complex powers developed by Dang and Wrochna. Namely, for $\varepsilon > 0$, we consider complex powers $(P\pm i\varepsilon)^{-\alpha}$ and prove that the diagonal trace densities admit meromorphic continuation. We relate their poles to local geometric invariants, in particular to the pseudo-Riemannian scalar curvature. Our proof combines uniform Feynman resolvent estimates with a direct analysis of the Hadamard parametrix in pseudo-Riemannian signature. Beyond the Lorentzian case, the use of causal convexity is replaced by a geometric no-return argument.

We investigate the problem of data payload uncertainty (DPU) in bistatic integrated sensing and communication (ISAC) systems, which refers to imperfect knowledge of transmit data symbols at the sensing receiver. DPU may result from limited fronthaul capacity in base station (BS)-to-BS bistatic sensing or data demodulation errors in BS-to-user equipment (UE) bistatic sensing, and can impair target detection through elevated sidelobe levels in the delay-Doppler domain. To characterize this effect, we derive closed-form expressions for the peak-to-sidelobe level ratio (PSLR) of two common OFDM receivers, namely reciprocal filtering (RF) and matched filtering (MF), under DPU. The analysis shows that the DPU-induced sidelobe degradation of RF depends on the inverse second-, fourth-, and sixth-order constellation moments, whereas that of MF depends only on the direct fourth-order moment, making RF considerably more vulnerable to DPU. To mitigate the resulting sidelobes, we further propose a novel, DPU-aware minimum mean-squared-error (MMSE) receiver. Simulation results validate the PSLR analysis and demonstrate superior detection performance of MMSE over RF and MF while revealing the extent to which it can recover DPU-induced performance loss relative to a genie-aided receiver with perfect knowledge of data payload.

Egocentric assistants must connect what users say with what they see across long interaction histories. We formalize this challenge as Spatially grounded Conversational Reasoning (SpaCR): cross-scene, recall-oriented, and counterfactual spatial queries that combine user-stated facts with geometric evidence. Direct vision-language models incur high inference costs and context limits as histories grow, while keyframe selection and retrieval can omit objects or evidence needed for complete recall. We propose Spatially grounded Conversational Memory (SpaC-MEM), an object-centric working memory that uses 3D reconstruction and segmentation to ground conversational information in persistent physical objects. It compresses multimodal histories while preserving spatial evidence and allowing object-specific facts to be updated through dialogue. We also introduce Ego-SpaCR, a benchmark comprising 620 ScanNet video sessions augmented with 95 task-oriented conversations and 3,100 evaluation queries. SpaC-MEM achieves the highest overall answer accuracy among the evaluated methods and improves object recall while requiring substantially fewer reference input tokens than native-video baselines. Removing 3D spatial information substantially degrades performance, highlighting the importance of preserving spatial and conversational evidence together.

We establish sharp mean value estimates for various exponential sums lacking translation-dilation invariance properties. For example, suppose that $k\ge 1$ and $s>0$. Then, for each $\varepsilon>0$, one has \[ \int_{[0,1)^k}\biggl| \sum_{1\le h\le X}\sum_{1\le z\le X}e(hz\alpha_1+\ldots +hz^k\alpha_k)\biggr|^{2s}\,{\rm d}\boldsymbol \alpha \ll X^\varepsilon\bigl( X^s+X^{2s-k(k+3)/2}\bigr), \] confirming the main conjecture for a new family of exponential sums. Our methods are based on the application of very recent work of the author employing the nested efficient congruencing method.

Variational quantum algorithms turn choices of Hamiltonian, ansatz, and parameterization into a classical nonconvex optimization problem. We study how this objective function can be visualized and characterized in ways that help explain optimizer behavior. We distinguish two properties of the objective: the number of local minima encountered along sampled directions and the differences in quality among local-search endpoints. We then ask how a local optimizer, represented by BFGS, compares with adaptive differential evolution, represented by jSO. Rather than comparing jSO with a single local run, we allow BFGS multiple starts within the same function-evaluation budget. This gives local search repeated opportunities to explore different basins and provides a stronger baseline for asking when a global evolutionary solver is useful. We study these questions using VQE and QAOA, focusing on how frustra- tion, circuit depth, parameter tying, mixed locality, and nonlinear repa- rameterization change the Hamiltonian expectation-value objective seen by the classical optimizer. Increasing independent circuit depth raises the sampled local-minimum count without making global search more effective. Parameter tying, by contrast, produces both more repeated local structure and much larger differences in quality among local-search endpoints, and in this regime adaptive differential evolution outperforms function-evaluation-matched multistart BFGS. The comparison shows that the number of local minima alone does not determine whether global search is advantageous: the important distinction is whether different basins lead to similarly good solutions or to substantially different objective values. These results provide a practical workflow for connecting model construction, objective- function geometry, empirical diagnostics, and optimizer choice.

Wide-field localization of transient sources such as gamma-ray bursts (GRBs) places new demands on the grid design of modulation collimators, whose usable field of view (FOV) is normally limited by self-vignetting. A grid slat thick enough to be opaque at the energies of interest also clips off-axis rays, shrinking the effective slit width and ultimately defining the FOV itself. Historical bigrid or rotating-modulation-collimator (RMC) designs have been designed with this trade-off as an unavoidable consequence of geometric optics. We explore whether the cross-sectional shape of the grid slats can be optimized for wide FOV applications. We derive a general transmission-function framework for a bigrid pair in terms of an effective slit width that depends on slat geometry and use it to compare four slat cross sections: the conventional rectangular slat, an idealized diamond profile, a hexagonal profile that approximates photochemical etching, and the circular wire grids of early X-ray astronomy. We show that for the same bigrid pitch and thickness, a diamond profile extends the FOV and eliminates clipping throughout most of the field. We also demonstrate that a hexagonal profile achievable with standard tungsten etching factors captures many of the benefits of the idealized diamond profile. Extending the analysis to the four-phase demodulation, we show that slat shape directly sets the extent of the resulting phase-space blind spots, and that the diamond profile removes them entirely across a target FOV where the rectangular baseline cannot. We further show that finite grid opacity is a largely separable effect. Leakage through the grid leaves the geometric blind-spot boundaries unchanged. These results identify slat cross-sectional shape as a design parameter that can substantially increase throughput and widen the blind-spot-free field of view of a wide-field modulation collimator.

In precision medicine, treatment decisions often depend more on identifying which patients are most likely to benefit from treatment than on accurately estimating benefit for every patient. However, existing methods estimate patient-specific treatment effects and derive patient rankings as a secondary step. We propose a direct ranking approach for conditional RMST treatment benefit in randomized trials with right-censored outcomes. We first construct a censoring-adjusted orthogonal RMST pseudo-outcome whose conditional expectation equals the true conditional RMST difference. Then, we compare patients pairwise and optimize a smooth ranking loss that directly targets treatment-benefit ordering. The pairwise criterion incorporates orthogonal corrections for estimation of the event and censoring distributions. We show that the population minimizer of the proposed loss induces the same ordering as the true conditional RMST treatment benefit and that the resulting estimating equation is Neyman-orthogonal to nuisance survival and censoring models. In simulation studies with nonlinear treatment-effect heterogeneity and moderate to heavy censoring, the proposed approach improved rank correlation and treatment-benefit enrichment relative to both plug-in RMST estimation and regression of the same RMST pseudo-outcome. Application to a randomized breast cancer trial demonstrated improved identification of patients with greater treatment benefit. In conclusion, the proposed framework combines orthogonal survival learning with pairwise ranking and may be particularly useful in precision medicine settings where treatment prioritization and patient selection are the primary goals.

We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin $s$, based on a variational product-state ansatz that includes both pure and mixed local states. By construction, intersite entanglement – expected to remain negligible even on very short time scales in many real materials – is excluded, while local quantum effects are retained through the nonclassical structure of $s\geq 1$ density operators. Nonlinear dynamics arise from both the mean-field interdependence of the local states and the state-dependent dissipative terms. The framework recovers classical spin dynamics for $s=\frac{1}{2}$ while allowing genuinely quantum local dynamics for higher spins. It clarifies the variational and geometric origin of the inequivalence between quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics, provides a criterion for their equivalence under a common time rescaling, establishes connections with the classical theory through two qualitatively distinct limits ($s\to\infty$ and a large number of quantum spins $N$), and allows realistic $\mathcal{O}(N)$ simulations of quantum spin dynamics in materials.

This letter develops a physics-informed one-shot beam tracking method for stacked intelligent metasurface (SIM)-enabled low-Earth-orbit (LEO) links with $K$ users and an $L$-layer SIM with $N$ meta-atoms per layer. The predictable orbital motion is propagated through the line-of-sight (LoS) geometry to forecast the finite-interval variation of the user signal-to-noise ratio (SNR) profile, and an analytical multilayer Jacobian relates this variation to the $LN$ SIM phase coefficients. Beam tracking is formulated as normalized SNR-profile preservation and solved through a single regularized Gauss–Newton correction that requires one Jacobian evaluation and a $K\times K$ linear solve, thereby avoiding iterative reoptimization. A tracking-error bound separates the regularization residual from the nonlinear Taylor remainder and establishes a second-order local error under a full-row-rank Jacobian. Numerical results show that the proposed method retains approximately $94\%$ and $92\%$ of the iterative-reoptimization rate for $L=2$ and $L=4$, respectively, while running about $350\times$ and $260\times$ faster at $N=225$, and confirm the predicted second-order residual error behavior.

Let $G$ be a connected graph with minimum degree at least two, positive Lin-Lu-Yau Ricci curvature, and no $K_{2,t}$ minor, where $t\ge 3$ is an integer. We first establish tight upper bounds on the maximum degree of $G$ by showing that $\Delta(G)\le 2t+3$ for $t=4$, $\Delta(G)\le 2t+4$ for $t\in\{5,6\}$, and $\Delta(G)\le 2t+2$ for all $t\ge7$. We then prove that $G$ has at most $10$ vertices for $t=3$, and at most $(t+1)\left(\Delta(G)^2(\Delta(G)-1)/2+1\right)$ vertices for all $t\ge 4$.

The Fréchet distance is a de facto standard for evaluating generative models across domains, appearing as FID for images and FVD for videos. It summarizes the discrepancy between generated and reference distributions in a single scalar, with lower values typically interpreted as better generation quality. However, this scalar view can obscure what drives the comparison. For example, in COCO dataset, increasing the number of diffusion sampling steps improves ImageReward scores yet worsens (increases) FID. Motivated by this mismatch, we seek to make the Fréchet distance more interpretable by uncovering where the discrepancy lies. To this end, we introduce directional Fréchet distance, the expected squared projection of the optimal transport displacement onto a given direction. Across our image, video, and protein case studies, we find that a small number of interpretable directions account for much of the distance. We use these directions to explain the FID increase in terms of semantic concepts represented by CLIP embeddings, quantify FVD's bias toward per-frame appearance, and revisit the interpretation of Protein FID. We open-source our codebase at https://github.com/yhlee-add/directional-fd.

We study zeroth-order optimization of convex and strongly convex functions with Hölder smoothness of order $\beta>2$ from values corrupted by random noise with bias independent of the method's random directions, a Lipschitz systematic error and a bounded adversarial error. We measure the number of function evaluations (calls), of sequential rounds of parallel calls, and the largest tolerable systematic and adversarial errors. For strongly convex functions with a bounded Hessian, we prove a lower bound of order $d^2\varepsilon^{-\beta/(\beta-1)}$ on the number of calls, where $d$ is the dimension and $\varepsilon$ the accuracy, and find the sharp power of $d$ under the stronger Hilbert–Schmidt smoothness for all $\beta>2$. An accelerated finite-difference method attains them in $O(\sqrt{\kappa}\log(1/\varepsilon))$ rounds for condition number $\kappa$, like Nesterov's method with exact gradients, and tolerates the optimal systematic and, up to logarithms, adversarial errors; rate-optimal methods need $\Omega(\log d)$ rounds. The same number of calls is attained when the Hessian grows at most linearly with the gradient and, for centered noise, without an upper bound on the Hessian, also in logarithmically many rounds. For convex functions, our lower bound improves the known one polynomially in $d$ and is tight at the curvature of the hard instances; the systematic level is again optimal. These bounds extend to general norms and constraints; on the $\ell_1$ ball, mirror descent needs calls nearly linear in $d$. Experiments confirm the theory.

We study the problem of computing the tightest \(\alpha\)-potential approximation of a general-sum game over continuous action spaces, within a prescribed class of potential functions and when each player has access only to its own utility function. The difficulty is twofold: the approximation error involves a worst-case search over an infinite set of unilateral deviations, and the required utility information is distributed across players. For a linear-in-parameters potential class, we use an exact finite-tuple reformulation that separates the problem into a global outer search over deviation tuples and distributed convex inner problems. We develop a primal–dual inner oracle tailored to this structure and establish a uniform one-sided accuracy guarantee. This oracle can be combined with global outer search to obtain an end-to-end guarantee on the outer optimization error. We also develop a projected zeroth-order outer method as a computationally lighter alternative for higher-dimensional problems. Numerical experiments illustrate the accuracy–computation tradeoff between the two outer-search methods and show that the proposed optimization framework can improve upon analytical \(\alpha\)-potential constructions.

When $k\ge 2$ and $s>0$, we establish that for each $\varepsilon>0$, one has \[ \int_{[0,1)^{k-1}}\biggl| \sum_{1\le x\le X}e(\alpha_2x^2+\ldots +\alpha_k x^k)\biggr|^{2s}\,{\rm d}\boldsymbol \alpha \ll X^{s+\varepsilon}+X^{2s-(k^2+k-2)/2}, \] confirming the main conjecture for a new family of exponential sums beyond those of Vinogradov (translation-dilation invariant) type. Our methods are based on very recent work of the author employing the nested efficient congruencing method. Consequently, analogues of our results hold also in the setting of number fields and function fields.

The theory of finite translation planes is intimately tied to the theory of spreads of PG(3,q), where a spread is a partition of PG(3,q) into $q^2+1$ pairwise disjoint lines. A traditional method of generating spreads begins with the regular spread and identifies sets of lines therein that can be replaced with other lines to create a new spread, such as reguli, Bruen chains, and nests. This work provides computational algorithms to enumerate all possible replaceable sets consisting of reguli, chains and nests in the regular spreads of PG(3,q) for $q \le 11$. Additional results include a refinement to Baker and Ebert's (q-1)-nests which expands that infinite family, and counterexamples to the long-standing conjecture that a t-nest of reguli in PG(3,q) must be replaceable if $t \le q$.