Papers

Post-training turns a general next-token predictor into a chat model with a persistent assistant persona. If that persona is a character the model plays only on its own turns, its preferences should govern what the assistant says, not what the model predicts other speakers will say. We test this boundary and find that it does not hold: a safety-relevant preference of the assistant—for harmless over harmful tasks—shapes the model's predictions even on the user's turn, where the assistant is not the one speaking. We find that this preference is small or near-zero in pretrained base models, that it emerges through post-training, replicated across open-weight model families, grows with scale, and can be moved by narrow finetuning that never touches user turns. We claim that this is evidence that post-training does not merely install a shallow assistant persona, but instead generalises beyond just the local assistant turn, into the model's representation of the user.

We present a two-part neural framework for forced three-dimensional incompressible Navier–Stokes flow. Part~I develops the computational forcing system. A physics-informed neural model generates structured external-force trajectories, candidates are optimized through differentiable PDE rollouts or PPO-Clip, and selected forcings are frozen and checked by independent fixed-force replay. Part~II provides the mathematical certification layer. It separates neural candidate discovery from continuum analysis, derives integrated reciprocal-vorticity criteria that imply Riccati-type growth and finite-time loss of smooth continuation, develops a validated computational-to-continuum transfer strategy, and establishes a conditional positive-probability closure for a nondegenerate neural output law. The proof is complete at the continuum level.

Complex networks balance metric wiring costs against functional routing demands, rarely conforming to idealized dichotomies of pure planar grids or unconstrained topologies. Yet, existing latent-space models remain computationally bottlenecked by stochastic sampling on small, unweighted graphs. Here, we formulate a scalable generative framework to solve the inverse problem of spatio-functional inference in weighted networks. By coupling explicit metric spaces with an unobserved latent geometry, we jointly reconstruct hidden coordinates and infer a coupling parameter $\lambda \in [0, 1]$, quantifying the connectivity propensity explained by functional affinity conditioned on metric distance decay. Our deterministic pipeline pairs a physics-informed spectral residual initialization with hybrid first- and quasi-Newton optimization. Across diverse empirical systems, the framework reveals a continuous spatio-functional spectrum. In the Drosophila melanogaster whole-brain connectome, it resolves an architectural progression from metric-constrained sensory circuits to specialized associative and chemo-affinity neuropils. In the continental European power grid, line pruning preserves a strictly metric baseline ($\hat{\lambda} \approx 0$), whereas topological rewiring drives a sharp surge in $\hat{\lambda}$, demonstrating that macroscopic component connectivity can mask spatial degradation. Finally, tracking global aviation throughout the COVID-19 pandemic captures dynamic regime shifts toward localized metric connectivity, establishing a unified diagnostic to probe structural organization and resilience in spatially embedded networks.

This paper develops a sparsity-promoting memory regressor extension (MRE) adaptation law with directional forgetting for nonlinear control-affine systems with linearly parameterized uncertainty. The objective is to use directional forgetting to selectively discount obsolete information and leverage $\ell_1$ regularization to promote sparsity of the parameter estimates. While $\ell_1$ regularization has been applied to the system identification problem in an offline setting, a contribution of this paper is to develop a recursive least squares update law to implement $\ell_1$ regularization in online adaptive control. In particular, we show that $\ell_1$-regularized recursive least squares is realized via a sliding mode update law. A nonsmooth Lyapunov-based stability analysis is then used to show that the tracking and parameter estimation errors are ultimately bounded under a subspace excitation condition. Simulation results on a Van der Pol oscillator demonstrate the ability of the developed sparsity-promoting MRE controller to recover sparse dynamics while maintaining stable tracking.

Four out of 10 adults aged 30 years or older in the USA are impacted by periodontal diseases which span a spectrum of inflammatory conditions. Currently, a subjective, invasive and a semi-quantitative approach, termed bleeding on probing, is employed in clinics for inflammation assessment. The long-term goal of this study is to fill the current clinical diagnostic gap in dentistry by proposing quantitative ultrasound (QUS)-based biomarkers for inflammation diagnosis and monitoring. Here, as one of the early works in this area, we investigated two QUS parameters for characterizing periodontal inflammation in gingival tissues using a longitudinal preclinical porcine study: attenuation coefficient slope (ACS) and backscatter intensity (BSI). Our study included eight pigs imaged intraorally (24 MHz) at four bi-weekly timepoints from week 0 (healthy) to week 6 (post inflammation inoculation) at their interproximal sites of the third premolars (PM3-Mes) from all quadrants. Moreover, we compared gingival tissues surrounding a tooth at lingual/palatal side versus buccal side at the second molar (M2-Dis) in healthy condition. Our results showed that gingival ACS at all inflammation timepoints were significantly lower than healthy gingival ACS (1.69 \pm 0.53 dB/cm.MHz) using a mixed effect analysis (week 6: 1.08 \pm 0.25 dB/cm.MHz). Longitudinal comparison of BSI did not demonstrate any statistical significance. Gingival ACS and BSI at lingual/palatal versus buccal sides of M2-Dis did not exhibit any statistical significance. These ACSs were linearly correlated with R-squared = 0.89 and a correlation slope of 0.87. For BSI, Bland-Altman analysis demonstrated no difference in mean BSI, although variability was high. These findings highlight the promising potential of ultrasonography paired with QUS to complement current standard of care in dentistry.

We present a framework to advance analytical theory in the area of soft matter and multiphysics using assistance from AI. The framework emphasizes (i) setting "honesty rules", (ii) focusing on a few key papers that are used to formulate a problem of interest, (iii) specifying checks a priori, (iv) using only one task per session and keeping a running log of tasks, checks, corrections, and sessions so that a mistake is not propagated through a project, and (v) ensuring all decisions are approved by humans while AI focuses primarily on execution. The framework is applied to two distinct problems to create new knowledge, including (i) diffusiophoresis of a spherical particle in the presence of an arbitrary number of electrolytes at arbitrary Debye lengths, and (ii) analytical description of I-V curves, including overlimiting current, in bipolar membranes without including the water dissociation kinetics. Both of these problems are advanced analyses and would each typically require several months to a year's worth of effort, but were solved in a matter of a few days. However, the increased efficiency should be cautiously navigated to avoid cognitive offloading and ensure that AI-assisted results are used to extract human-readable insights instead of just reporting a new mathematical formula. The usage of AI is transparently presented. Finally, we also share brief thoughts on how to integrate AI tools in theoretical research during graduate education.

We prove that a Hall $\pi$-subgroup $H$ of a finite group $G$ is normal if and only if every irreducible constituent of the permutation character $1_H^G$ has $\pi'$-degree.

Conflict scanning over synchronized robot paths requires detailed collision checking, potentially across every robot pair at every timestep, and may be repeated many times as conflicts are repaired. We present Multi-Robot SPITE (MR-SPITE), a conservative, motion-segment-based filter for accelerating these scans. MR-SPITE partitions each path into temporal intervals and assigns conservative bounds to each segment. An interval scheduler compares bounds for temporally overlapping motions: disjoint bounds certify the shared window as conflict-free, while unresolved windows are passed to the underlying collision checker. We integrate MR-SPITE into ARC and combine it with VAMP-based collision checking. For 16 Fetch robots, ARC with MR-SPITE achieves a paired median conflict scan speedup of 7.18x and reduces median planning time by 57% relative to the baseline ARC implementation with PRM+VAMP. These results demonstrate that motion-segment bounds complement configuration-level collision acceleration while preserving the behavior of the underlying discretized scanner.

This paper establishes time-uniform accuracy guarantees for deterministic square-root ensemble Kalman filters in linear–Gaussian state-space models under perfect-model dynamics. For hyperbolic, detectable systems, we prove that the ensemble means and covariances approximate their Kalman filter counterparts uniformly in time, with high probability and without inflation or resampling. The required ensemble size depends on the effective rank of the initial covariance and the dimension of the unstable subspace, rather than on the ambient state dimension. We also analyze a localized square-root ensemble Kalman filter for weakly coupled spatial systems. We show that the stabilizing Kalman covariance inherits spatial decay from the dynamics and derive accuracy bounds that separate sampling error from localization bias. For the localized filter, the required ensemble size depends on the local intrinsic dimension and only logarithmically on the number of spatial blocks, while the localization bias scales with the interaction strength. Our analysis combines stability and forgetting for possibly singular Riccati recursions, nonasymptotic covariance concentration, and perturbation estimates for localized covariance dynamics.

Density-Ratio Rescoring (DRR) augments a classifier trained at the original class prior with a survey-raking dual score. Raking reweights the majority sample to match minority feature moments within a tolerance. DRR marginally standardizes the dual and base scores and combines them with a fixed weight of one half, using the fitted dual directly for prediction without resampling or refitting the base classifier. Under exact population matching and a correctly specified log-linear tilt model, the dual equals the log density ratio up to an additive constant. A class-separation analysis characterizes the signal strength and correlation conditions under which fusion improves separation under common within-class covariance. On 24 tabular benchmarks, evaluated over 30 trials and five base learners, DRR at the D=128 random-feature setting improves average precision over the standardized base on every dataset, with a mean gain of 0.034. It exceeds the shared-dual raking-and-relabeling resampler on 22 of 24 datasets, with a mean gain of $0.092$, and on all eight one-versus-rest tasks of a shared gene-expression cohort. These results demonstrate the effectiveness of using raking duals as reusable scores for improving rare-class ranking while retaining classifiers trained at the original prior.

We study whether LLMs can produce executable workflow artifacts that remain consistent across graph structure, tool implementation, schema bindings, and runtime wiring. In this setting, correctness depends on cross-layer consistency: a workflow may be structurally plausible, yet still fail because tool implementations, schema bindings, or runtime execution do not align. Existing benchmarks largely evaluate these capabilities in isolation or rely on trajectory-level proxies, leaving open whether generated workflow artifacts execute end-to-end. We introduce MCPGen, an executable benchmark for Model Context Protocol (MCP) workflow development. MCPGen contains 100 self-contained MCP projects across 16 application domains and evaluates three diagnostic tasks: workflow reconstruction, tool creation, and backward-compatible workflow extension. We evaluate 11 representative LLMs in a single-turn foundation-model setting, assessing generated artifacts through static analysis, unit and integration tests, and process-isolated end-to-end execution. Models reach 88.5% on workflow reconstruction, but no model exceeds 57% end-to-end execution success. Per-tool unit-test pass rates reach 63.8%, while project-level integration success does not exceed 45%, suggesting that integration remains a major bottleneck even when isolated tool tests pass.

Pretrained EEG foundation models are increasingly proposed as general-purpose encoders for brain-computer interfaces, yet recent benchmarks disagree about when their representations transfer to downstream tasks. We audit LaBraM and CBraMod on motor imagery under a validation-locked protocol in which preprocessing, architecture, optimization, freeze depth, checkpoint, temperature, and method selection are determined using training-session data only. On four-class BCI Competition IV-2a, every supervised comparator evaluated here outperforms every foundation-model configuration, including validation-selected fine-tuning. We then examine a key confound: foundation models and task-specific decoders are normally evaluated using different input pipelines. Retraining three supervised architectures on the broadband arrays consumed by the foundation models produces matched-input accuracy differences of opposite sign across architectures: broadband input improves ATCNet by 0.078 accuracy while reducing EEG Conformer accuracy by 0.088. None of the three individual matched-input terms is significant after multiple-comparison correction at n = 9, so we treat the sign variation descriptively rather than as a formal architecture-by-pipeline interaction. These observed sign differences suggest that a single comparator may not provide an architecture-invariant decomposition of a pretrained-versus-supervised performance gap. The four-class deficit also does not reproduce uniformly across motor-imagery datasets: on two-class BNCI2014-004 we cannot detect the same separation between fine-tuned CBraMod and the supervised comparators. Finally, validation-fitted temperature scaling returns foundation-model calibration error to the supervised range despite substantially lower four-class accuracy.

Let $\lambda_k$ be the $k$th eigenvalue of the Dirichlet Laplacian on an open set $\Omega\subset\mathbb R^n$ of finite positive measure. The direct individual consequence of the Berezin–Li–Yau sum inequality has leading coefficient $n/(n+2)$ relative to the Weyl term. The main contribution of this paper is a strict improvement of this coefficient. Energy orthogonality gives a frequency-dependent cap on the Fourier density of the first $k$ eigenfunctions. Combining this cap with the standard Bessel bound and a bathtub principle for the radial capacity yields \[ \lambda_k\geq c_n(2\pi)^2\omega_n^{-2/n} |\Omega|^{-2/n}k^{2/n}, \qquad \frac{n}{n+2}<c_n<1, \] for every $k\geq1$ and every $n\geq2$, without boundary regularity. The constants are characterized by explicit scalar equations; in dimension two, $c_2=0.5383068077\ldots$, giving a $7.66\%$ improvement over the individual Li–Yau coefficient. We emphasize that this improves the leading coefficient in the individual eigenvalue bound and the new constant $c_n$ is independent of the geometry and index $k$.

A set $B$ in an abelian group is a $B_h$ set if every $h$-term sum has a unique representation up to permutation; for $h=2$ these are the Sidon sets. We study a weighted removal problem for this collision-free property: if the $h$-fold sum map has small Rényi entropy loss, how much probability mass must be deleted so that the remaining support is a $B_h$ set? Two Rényi orders arise: $\alpha$ is the order at which the coarsening loss is measured, whereas $\beta$ is the order of the entropy constraint. The diagonal specialization $\beta=\alpha$ ties the two roles together. We determine the resulting stability problem on the positive $(\alpha,\beta)$-quadrant. Stability holds exactly when $\beta\le1$ and $\alpha\ge\beta$. Inside this region the optimal deletion rate is polynomial for $\beta<1$ and logarithmic on the boundary $\beta=1$, where the leading constant is exact; outside it, stability fails through two distinct mechanisms: a supercritical budget and dilution by light atoms. In both unstable regimes the limiting defect is computed exactly. The upper bounds follow from a coarsening inequality with best possible constant, which also yields an entropy-free removal theorem, a finite combinatorial consequence for moments of the representation function, and extensions to $B_h[g]$ sets. Matching constructions show that the phase boundaries and rates are sharp.

We revisit Frolov and Zelnikov's electrostatic Green function for a test charge in a multi-center Majumdar–Papapetrou spacetime, correcting its horizon-charge condition and extending the result to higher dimensions. In four dimensions, we derive the exact Dirichlet-to-Neumann map for a minimally coupled spectator Maxwell field with independently prescribed horizon potentials. The horizon flux charges obey a capacitance matrix with entries $C_{AA}=M_A+\sum_{B\ne A}M_AM_B/R_{AB}$ and $C_{AB}=-M_AM_B/R_{AB}$, where $M_A$ are center masses and $R_{AB}$ their separations. This matrix is a positive diagonal term plus a weighted graph Laplacian, yielding an exact common-mode/differential-mode decomposition of the field energy. The grounded Dirichlet Green function partitions a point charge's flux among infinity and the horizons through harmonic measures. We show that the diagonal condition imposed by Frolov and Zelnikov [Eq.~(4.14)] preserves only the total horizon charge, allowing redistribution between individual horizons. A corrected symmetric Green function preserving each horizon charge instead involves the inverse capacitance matrix. For two centers, the correction produces a finite, negative-semidefinite self-energy shift and an exact self-force difference, without additional ultraviolet subtraction. Finally, we extend the capacitance matrix, flux partition, and fixed-charge Green function to $D=n+3$ dimensions, where the graph weights contain the universal factor $\pi^{n/2}/\Gamma(n/2)$.

It is an unnatural feature of the Standard Model that the difference between the baryon number $B$ and the lepton number $L$ is conserved, which implies an exact, global symmetry. We promote it to a naturally exact, local symmetry by coupling the difference $B-L$ to an Abelian gauge field. Gauge anomalies are cancelled by adding right-handed neutrinos $\nu_{R}$. They are not sterile in this case, which forbids the Majorana term, but we arrange for a $\nu_{R}$-mass by adding a Higgs-type 1-component complex scalar field. Thus we arrive at a well-motivated, modest extension of the Standard Model (SM). We investigate the field equations in the corresponding gauge-Higgs sector, involving both Higgs fields and the non-standard U(1) gauge field. This leads to a set of coupled, non-linear differential equations, which we solve numerically. We use cylindrical coordinates, thus focusing on the structures of cosmic strings. For a large variety of parameters, we identify the string profiles and energy densities. These profiles depend on the winding number of each of the Higgs fields. For our parameters, the characteristic string radii are below $10^{-3}~{\rm fm}$, and the string tension is not ruled out by observations of the Cosmic Microwave Background or gravitational waves. As an amazing peculiarity, we discover - for high winding numbers - “overshooting” and “co-axial” profile functions. In the latter case, the profile of the standard Higgs field changes its sign near the core of the cosmic string.

Automated brain tumor segmentation supports diagnosis, treatment planning, and monitoring of disease progression, but building models that generalize across heterogeneous tumors and limited annotated data remains difficult. We present VGG16-MCA UNet, a hybrid architecture pairing an ImageNet-pretrained VGG16 encoder with a decoder in which a Multi-Channel Attention (MCA) module recalibrates features after each skip-connection fusion, trained with the Focal Tversky loss to counter severe foreground-background imbalance. We evaluate the model as a 2D, FLAIR-only, whole-tumor segmenter on tumor-positive slices from two public datasets: the BraTS 2020 benchmark and the LGG MRI Segmentation dataset. Using 5-fold cross-validation and a single network formed by averaging the weights of the five fold models, the method attains an aggregate pixel-level Dice (F1) of 95.10% on our held-out BraTS 2020 split and 88.32% on LGG. These scores are computed over all test pixels pooled into a single confusion matrix rather than averaged per case, and are therefore not directly comparable to the per-case mean Dice used in the BraTS challenge protocol. All partitions were drawn over individual slices rather than over patients, so every patient contributes slices to both training and test; the figures above therefore measure interpolation within known patients and should be read as an upper bound rather than as generalization to new ones. The model segments a 256x256 slice in 66.32 ms on a single 6 GB NVIDIA RTX 2060, approximately 8 ms more than an equivalent VGG16-UNet without MCA. We release the split records and report the protocol in full, with the aim of providing a precisely specified and reproducible 2D FLAIR baseline.

This paper presents a nonlinear control law for a quadrotor unmanned aerial vehicle (UAV) under single-rotor failure that guarantees set stabilization via quasi-static feedback (QSF). Given a geometric curve in three-dimensional space, we characterize and stabilize the zero-dynamics manifold, also known as the path-following manifold, which represents all feasible motions along the path. Stabilizing this manifold ensures path-invariance: a UAV with a failed rotor initialized on the path with an appropriate orientation remains on the path for all future time. Furthermore, local exponential convergence to the manifold is guaranteed under certain conditions, implying that, under the stated assumptions, rotor failure during flight does not cause transverse deviation from the path. The proposed controller thus provides theoretical safety guarantees, which are validated through numerical experiments in the Drake physics-based simulation engine. The code is publicly available at https://gradslab.github.io/quasistatic-ftc/.

Chess involves complex reasoning in a deterministic environment, which makes it a useful setting for studying the mechanisms of computation inside transformers. The Maia-3 chess transformer takes Elo, a measure of competitive chess skill, as an input to the pre-trained network, so we can vary the skill the network is conditioned on with no change to its weights. Here we investigate how turning this skill dial affects self-attention. Ablating every attention head at every Elo from 700 to 2500, we find 1) increasing skill pushes the causal center of mass of the computation deeper, monotonically, for every chess piece and move type we measured; 2) the depth migration is much greater for specific tactics, especially knight forks, than for other move types; 3) the migration consists of deeper heads getting recruited for more specialized computations while one shared shallow head keeps a roughly constant contribution. These results may shed light on how conditioning inputs redistribute computation in larger transformers.

Large language models (LLMs) drift out of date the moment their pretraining ends, yet retraining from scratch is prohibitively expensive. Continued pretraining (CPT) is the natural remedy, but it is typically evaluated through a continual learning lens that assumes disjoint data streams. This is a poor fit for time-incremental updates on web-scale crawls, where successive snapshots share substantial URL overlap by design. We study time-incremental CPT in this realistic regime: continued pretraining on FineWeb-Edu dumps drawn strictly from after each model's knowledge cutoff, evaluated across six open-weight models spanning three families (OLMo2, Llama-3.1/3.2, Gemma-3-1B) and four parameter scales (1B-3B-7B-8B). We organize our findings around four practical questions. (i) Is knowledge acquired? Yes, but heterogeneously, and without catastrophic forgetting: five of six models also improve on pre-cutoff factual recall, and the gains track pretraining saturation (driven primarily by token budget per parameter). (ii) What does it cost? Almost nothing: the macro-average across a thirteen-task suite stays within 0.01 of the base for every model. (iii) What is the recipe? Data quality dominates quantity (a curated 6B-token slice matches a broader 40B one); the optima for knowledge acquisition and general capability are separated by roughly an order of magnitude in learning rate; and LoRA at sufficient rank matches full CPT. (iv) Does it survive deployment? CPT gains transfer through SFT, while DPO's effect is family-dependent. Together, these results paint a more optimistic picture of time-incremental CPT than the prior continual learning literature suggests.

This paper presents an end-to-end framework for reconstructing overhead power utility network topology and extracting span-level physical metadata from large-scale aerial LiDAR. The pipeline begins with semantic segmentation of the input point cloud using an improved KPConv-based model, in which data sampling and loss functions are adapted to emphasize pole and conductor (wire) classes. Network topology inference then proceeds in two stages: (i) pole instances are obtained by clustering pole-class points and validating candidates using geometric criteria, including height and verticality estimated via PCA, and (ii) candidate pole pairs are evaluated using a heuristic method and a lightweight ResNet-based classifier on 2D top-view projections of pole and wire point distributions to determine whether a physical conductor span exists. By explicitly classifying candidate spans, the approach mitigates common failure modes of heuristic connectivity rules in dense or cluttered scenes and under partial wire observation. For each validated wire, attributes regarding utility infrastructure geometry are computed, including endpoint conductor heights, ground elevation, sag-related lowest-point features, conductor arrangement, and wire width. Evaluation on multiple real-world aerial LiDAR datasets demonstrates decimeter-level endpoint height accuracy and approximately 9% relative improvement in recall for topology reconstruction compared to heuristic nearest-neighbor baselines, with larger gains in complex layouts.

Bell-CHSH measurements with polarization-entangled photons are commonly used as nonlocality witnesses. Here we show that the same coincidence data can also provide a quantitative metrological certificate for optical retardance sensing. For a local birefringent phase encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators and obtain a lower bound expressed in terms of the measured correlations and the phase derivative of the CHSH parameter. In the unbiased-marginal two-qubit regime, the canonical CHSH analyzer settings are shown to be simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation in the ideal case. We further analyze reduced visibility, phase noise, analyzer misalignment, and finite coincidence counts, and construct conservative lower confidence bounds that can be evaluated without quantum-state tomography. The results also clarify that Bell violation and metrological usefulness are distinct resources: nonzero Fisher information can persist below the CHSH-violation threshold. The protocol therefore enables a standard Bell-test data set to provide both a nonlocality benchmark and a statistically controlled sensitivity certificate for quantum polarimetry.

We show that the fractional illumination number of every convex body in $\mathbb{R}^d$ is at most $2^d$, with equality exactly for parallelotopes. We also prove that every such body can be covered by at most $2^d(d\log d+d\log\log d+O(d))$ smaller positive homothetic copies as $d\to\infty$, establishing the optimal exponential rate in Hadwiger's covering conjecture. The proofs use a covering measure obtained by minimizing an overlap energy and a greedy covering argument on a finite net.

A self-consistent treatment of strong-field laser - plasma interactions suggests a heuristically valuable extension of the notion of nonlinear-optical susceptibility to perturbative regimes of stimulated light scattering in plasmas, offering powerful insights into stimulated-scattering-induced cross-beam energy transfer processes. These findings lay grounds for a unified treatment of stimulated light scattering across a vast area of optical physics, spanning from fiber optics and neutral gases to laser - plasma physics.

We present preliminary results of a study of galaxy sizes at redshift $z \gtrsim 5$ using the high-resolution, zoom-in FirstLight simulations. We obtain a redshift-independent, chevron-shaped stellar mass–size relation with a peak at $M^{\star} \approx 10^{8.5}~\mathrm{M}_\odot$. This relation is shaped by the individual evolution of galaxies, which undergo a phase of contraction at this mass scale triggered by a strong central starburst.

Simulation-based evaluation provides a scalable and repeatable alternative to real-world evaluation of vision-language-action (VLA) policies. However, reconstruction errors can cause simulated policy performance to diverge from real-world performance, motivating the need to assess reconstructed environments for downstream VLA policy evaluation. We present ReVeal, a real-to-sim assessment framework combining workspace reconstruction, reconstruction-level assessment, and matched closed-loop policy evaluation. Novel-View Mesh Fidelity (NVMF) and Annotated Planar Geometry Fidelity (APGF) assess observation and planar geometric fidelity, respectively. We also develop PGSR-D, a reconstruction pipeline incorporating monocular depth supervision to improve geometry where multi-view visual cues are limited. Across 8 assessment scenes, NVMF and APGF consistently distinguish the fidelity of 2DGS, PGSR, and PGSR-D. Matched evaluations of GR00T, SmolVLA, and pi0.5 across 8 humanoid manipulation tasks show consistent ordering between reconstruction fidelity and real-sim performance agreement across pipelines. Further analysis of the evaluation workspaces shows that higher fidelity is associated with stronger real-sim agreement.

Let $p_n$ be a random polynomial of degree $n$ whose roots are independent and identically distributed according to a rotationally invariant probability measure $\mu_0$ on the complex plane with finite logarithmic moment. If $k_n/n\to t\in(0,1)$, we prove that, as $n \to \infty$, the empirical zero measure of the $k_n$-th derivative of $p_n$ converges weakly in probability to a deterministic rotationally invariant probability measure. We describe the limiting measure explicitly in terms of the radial quantile function of $\mu_0$. This proves a conjecture of Hoskins and Kabluchko [Exp. Math. 32 (2023), no. 4].

The Vlasov-Maxwell system with Newtonian particle transport is linearised about the Poisson equilibrium on $\mathbb{R}^3$, with the speed of light $c$ treated as a large parameter. For uniformly controlled initial data, with transverse fields that may remain of order one, the difference between the Vlasov-Maxwell perturbation and its linearised Vlasov-Poisson counterpart is bounded uniformly in time by their initial discrepancy plus a term of order $c^{-1}$. The same estimate holds for their scattering states, and the rate in $c$ is sharp. The longitudinal dynamics are governed by the same Volterra equation as in linearised Vlasov-Poisson and undergo Landau damping. The transverse fields exhibit Klein-Gordon-type dispersion, and control of their accumulated effect along free transport yields the uniform comparison.

Generative models of neural activity could help characterize tissue dynamics, compare experimental conditions, and simulate population activity for applications ranging from disease and drug-response studies to closed-loop experimentation. Existing approaches, however, typically assume a fixed set of sorted neurons, whereas high-density microelectrode arrays produce extremely sparse, array-wide binary spike volumes in which the observed subset of electrodes varies across assays. We introduce a discrete generative model that represents this activity using a shared vocabulary of spatiotemporal motifs. A residual vector-quantized autoencoder learns the motif vocabulary, while a factorized masked transformer predicts where activity occurs and which motif appears at each active location. We evaluate the model on 31 assays spanning human brain organoids and acute ex vivo human hippocampal tissue. The learned motifs are broadly reused: assay identity explains only $9%$ of the entropy in motif use, and motif overlap across tissue types is comparable to overlap within them. When representation quality is evaluated independently of the generative prior, our approach achieves $5.2\times$ the voxel-level reconstruction average precision of a matched flat tokenizer. For masked completion and free generation, the full model achieves $1.4$–$2.6\times$ the site-level average precision of the matched generative baseline and outperforms it across all four families of generation metrics. These results establish a compact, reusable representation for array-wide spiking activity without learned assay-specific parameters, providing a scalable foundation for generative modeling across diverse neural preparations.

This paper introduces a novel algorithm for predicting conditional joint distributions of vector-valued targets in stochastic systems whose randomness is intrinsic rather than arising from observation errors or additive noise. Multivariate quantile regression also involves modeling conditional joint distributions but represents a less challenging task. It predicts the probability that vector-valued targets fall within predefined regions, identifies regions corresponding to predefined probability levels, or performs both tasks simultaneously. The proposed identification technique employs ensembles of Kolmogorov-Arnold networks (KANs) as flexible function approximators. Although the suggested technique is not theoretically restricted to KANs, KANs are particularly well suited to the proposed construction and are therefore used throughout this study. In addition to the training procedure, this work introduces a new discrepancy measure for joint distributions and a goodness-of-fit (GoF) test based on it. This GoF test was initially developed to validate and calibrate the proposed identification technique and is used here in an ad hoc manner. Although the test could be tabulated for broader use, such a tabulation is not pursued in this work. The test is also applicable more generally.