Papers

Covariate-rich time-series forecasting requires deciding how external variables enter the target forecasting path. Existing Transformer-based forecasters usually build a covariate representation and pass it to the encoder without an explicit admission stage. This paper studies pre-encoder covariate admission as an input-side interface that regulates that representation immediately before encoder processing. We implement the interface with a lightweight representation-level pre-encoder gate that assigns sigmoid scores to representation units, and we also study a usage-regularized variant that penalizes average admission. The interface is evaluated as a plug-in module for TimeXer, Inverted Transformer (iTransformer), and Patch Time Series Transformer (PatchTST) under a zero-extra-tuning protocol, where each gated model inherits the corresponding baseline configuration. Experiments on the Electricity Transformer Temperature minute-level (ETTm1 and ETTm2) datasets, Traffic, Energy, and influenza-like illness (ILI) include paired forecasting comparisons, gate-placement ablation, initialization ablation, controlled covariate-admission analysis, and a variance inflation factor (VIF)-informed permutation feature importance (PFI) diagnostic case study. In the tested settings, the gate is competitive with the corresponding baselines, and the usage penalty reduces average admission scores while keeping forecasting errors close to the unpenalized TimeXer setting.

We study $K$-regularity for complex varieties with finite quotient singularities. We prove that for such varieties, $K_1$-regularity is equivalent to smoothness whenever the singular locus is contained in an affine closed subvariety (e.g., affine varieties or those with isolated singularities). In contrast, we construct projective varieties with finite quotient singularities which are $K_m$-regular for every $m$ but are not local complete intersections. Our smoothness criterion is obtained by affirmatively answering Fogarty's 1988 question concerning differential forms on finite quotients.

Mask-based lensless imagers capture measurements using simple, compact hardware and recover images using a reconstruction algorithm. The reconstruction algorithm affects the image quality, inference speed, and computational requirements of the imaging system, often trading off image quality against computational efficiency. Advancing toward integrated lensless imagers, where encoding and reconstruction occur within a single device (e.g., a mobile phone), requires a fast, high-quality, and practical reconstruction method. We introduce the Real-Time Lensless Vision Transformer (RTLViT), a lightweight, purely data-driven reconstruction architecture for high-quality and real-time lensless reconstruction. With only 1.09 million learnable parameters, RTLViT provides higher-quality reconstructions than both real-time baselines and substantially larger attention-based architectures, including improvements of up to 3.46 dB in peak signal-to-noise ratio over architectures with $15 \times$ more learnable parameters. We demonstrate that RTLViT maintains high-quality reconstructions across a wide range of training dataset sizes and two different mask designs (lenslets and a diffuser). Finally, we implement real-time reconstruction with RTLViT on laptops and smartphones, supporting future integrated lensless imagers for real-time applications.

Freestanding thin films of quantum materials naturally develop sub-micrometer, nonuniform strain fields that strongly affect their electronic, magnetic, and structural properties in both equilibrium and nonequilibrium conditions. However, current methods to quantitatively resolve these mesoscopic features are primarily restricted to scanning probes, making it challenging for dynamical measurements such as single-shot imaging and femtosecond microscopy. Here, we present a new computational framework which we denote as bend contour electron tomography (BCET), which efficiently converts bend contours in transmission electron microscope images into quantitative two-dimensional maps of strain and topography. By iteratively minimizing a designed loss function between experimental and simulated bend contour images, BCET retrieves both surface morphology and in-plane strain tensor fields without requiring scanning or diffraction mapping. We applied BCET to freestanding SrTiO$_3$ thin films, demonstrating the successful reconstruction of the local strain distribution and curvature field with high fidelity. Our approach provides a quantitative framework for characterizing mesoscale structures in freestanding films using wide-field imaging, opening new avenues to investigate how spatial inhomogeneity governs phase transitions and nonequilibrium dynamics in two-dimensional quantum materials.

Dust plays a key role in galaxy evolution by influencing star formation and shaping the observed spectrum of galaxies. However, at $z\sim2$ (cosmic noon) our knowledge of the dust mass budget is limited to the most massive, metal-rich systems. Here, we probe the lower mass, subsolar metallicity regime by measuring the dust mass of 25 galaxies at $z\approx2.3$ from the ALMA Chemical Evolution (ACE) survey. The sample contains star-forming galaxies in the COSMOS field with robust strong-line metallicities down to $\sim 0.3Z_\odot$. Using the dust continuum detected at 873$\mu$m or 1.3mm we constrain the dust mass by assuming an optically thin single-temperature modified blackbody (MBB). The resulting masses of the detected galaxies have a median of $M_\mathrm{dust}=6.4\times10^{7}\,\mathrm{M}_\odot$, which is 4-9x larger than those of $z=0$ galaxies at matched metallicity and stellar mass, but more than 10x lower than IR-selected galaxies at $z\approx 2$. We find positive correlations between dust mass and stellar mass, metallicity, and star formation rate (SFR). In contrast, we find that the $M_\mathrm{dust}/M_\mathrm{stars}$ (DtS) ratio scatters around $10^{-2}$ but has no clear with metallicity unless we adopt a metallicity-dependent prescription for dust temperature. We also find a positive correlation between $M_\mathrm{dust}/\mathrm{SFR}$ and metallicity that suggests that dust buildup becomes more efficient at higher metallicities, likely due to the role of ISM grain growth or enhanced dust survival. We also recover the relation between DtS ratio and specific SFR (sSFR), without evidence of a turnover at high sSFR that would signal inefficient dust buildup. Finally, we measure a large molecular gas fraction among ACE CO(3-2)-detected galaxies ($M_\mathrm{mol}/M_\mathrm{stars}\gtrsim$1) that potentially explains both the sSFR and DtS excess over $z\approx0$ galaxies.

A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matrices are multiplied directly, with no intervening nonlinearity. Such blocks appear in LoRA adapters, low-rank compressed layers, query-key products of self-attention, and share a common pathology: the factorization is non-unique, which can destabilize training and limit usable learning rates. Despite this, factorization blocks are typically optimized with standard Euclidean methods that ignore the underlying geometry. We introduce Stiefel-AdamW, a near drop-in replacement for AdamW for use wherever such blocks appear. By constraining one factor on the Stiefel manifold while leaving the other Euclidean, Stiefel-AdamW relaxes the full $\mathrm{GL}(\mathbb{R}^r)$ gauge symmetry to a compact orthogonal symmetry, ruling out factor blow-up while retaining the coordinate-wise diagonal preconditioning that gives AdamW its practical strength. Moment estimation is performed in the ambient Euclidean space, with geometry entering only through a tangent-space projection and a manifold retraction. The implementation overhead over AdamW is minimal, and we show that the resulting optimizer inherits both the stability benefits of Riemannian methods and standard convergence guarantees. We validate Stiefel-AdamW on LoRA-style fine-tuning of GPT2, ViT, and Mistral 7B and on full pretraining of GPT2 on OpenWebText, showing consistent improvements over strong baselines at essentially no additional cost over AdamW.

Induced pluripotent stem cell (iPSC) culture increasingly relies on segmentation foundation models, yet deployment on laboratory CPUs and edge hardware requires compression schemes that are both efficient and auditable. We present a deployment-oriented evaluation of compressed Cellpose-SAM using a pre-specified retention criterion: the 95% cluster-bootstrap interval of mean change from FP32 must remain above a fixed -0.02 margin for every imaging modality. On a stratified 176-field panel spanning BBBC038 nuclei, BBBC039 U2OS fluorescence, and NIST iPSC images across density regimes, weight-only W8A16 preserves instance F1 across all modalities. A sensitivity-guided mixed W4/W8 scheme, using four INT8 exceptions, achieves a 6.76x reduction in weight storage with no observed catastrophic failures (0/176 fields), matching W8A16 at this sample size. In contrast, ternary weight-only quantization achieves 12.08x compression but fails catastrophically on 169/176 fields. These results demonstrate that compression should be evaluated by modality-stratified downstream retention rather than single-number accuracy, and establish a reproducible protocol for auditing compressed foundation models in regulated stem-cell imaging.

The recent emergence of large language models (LLMs) has produced research focusing on the ability of these tools to solve physics problems, evaluate student work, or otherwise impact the problem-solving process of students. However, studies exploring how physics students perceive LLMs (in terms of capabilities, educational impacts, usage, and role in problem solving) remain limited. This study evaluates the first-year physics students' perceptions toward LLMs and further explores how these perceptions change after practicing problem-solving with and without LLMs and engaging in a reflective lesson on the functioning and educational impacts of LLMs. We find that student opinions toward LLMs vary, with generally favorable perceptions of their capabilities but greater skepticism regarding their value for learning. Despite this skepticism, a majority of students self-report regularly using LLMs to obtain help, commonly reporting deadlines and convenience as motivating factors. Following the lesson, students expressed greater skepticism toward LLMs in several areas, with 88% of students believing that LLMs can leave them with a false sense of confidence about their understanding, up from 58% before the lesson.

We study intrinsic Diophantine approximation on the sphere $S^d$, measured by the quality of the best rational approximation available at a given height. We show that, for $d\geq 3$ and along sufficiently sparse sequences of heights, these quantities have a Weibull limit distribution and the associated counting functions are asymptotically Poissonian.

Every finite planar set of at least $880$ points contains four collinear points or six pairwise visible points.

Given a complex algebraic variety, we relate the product structure on its absolute Hodge cohomology with mixed Hodge formality, a notion of formality in the sense of rational homotopy, that takes into account the mixed Hodge structures present in complex algebraic geometry. Namely, we prove that mixed Hodge formality implies the splitting of absolute Hodge cohomology as a square-zero extension. We define and study certain products, akin to Massey products, which live in the absolute Hodge cohomology and obstruct its splitting. We also relate mixed Hodge formality to the existence of multiplicative Chow-Künneth decompositions.

Black holes that merge repeatedly carry a record of that history in their mass distribution. We treat hierarchical merging as a coagulation problem, in which a single kernel encodes how the merger rate depends on the masses involved and on cosmic time, and we derive the late-time spectra that such populations approach. The framework yields closed scaling laws, an exactly solvable benchmark, and a classification of merger environments by a single exponent measuring how strongly mergers favor or suppress massive participants. Applying it to primordial black holes requires care in translating published merger rates into kernel form; done correctly, three of the four standard binary-formation channels map onto superlinear kernels and are therefore candidates for runaway growth, in which the heaviest objects would dominate and no steady mass-conserving spectrum exists; establishing physical gelation, however, requires the full population-dependent kernel and its finite coagulation history, neither of which we settle here. Only the early three-body channel maps into the nongelling regime and admits slow self-similar growth. Numerical solutions across thirteen suppressive, nongelling kernels show that the shape of the spectrum is not fixed by the scaling exponent alone, and that accounting for the energy radiated at each merger measurably changes the high-mass cutoff and drains the population's total black-hole mass.

Science advances not in isolation but through collaboration, yet existing agentic systems capture little of this. Whether communicating agents help remains an open question with mixed prior results. We show that test-time communication can substantially outperform independent parallel attempts on challenging tasks, where sharing a breakthrough can push the whole group forward. We first study the effect of scaling multi-agent test-time communication, where agents have no predefined roles and communicate via a shared directory, on ARC-AGI-3, a benchmark requiring novel problem solving. We find that a team of $k$ communicating agents, team@$k$, matches the success rate of $4k$ independent agents, and this advantage grows with $k$, suggesting gains compound with scale. The effect is not merely efficiency: a task that no single agent can solve, a team of agents can solve reliably. Furthermore, these gains transfer to research-oriented tasks, given sufficient compute. On polyomino packing, communicating agents outperform best@$k$ and exceed the prior best-known score. On MNIST classifier compression, communication surpasses the best-known human solution. A team of four agents produced a 1,957-byte classifier submission achieving 99.4% test accuracy, smaller than both the best-known human solution and the best single-agent result. These gains are not unconditional. Independent agents may outperform communication when compute is limited or when a clear measure of progress is absent. However, under sufficient compute and clear feedback, multi-agent communication consistently yields stronger results.

The construction of a reliable renormalization group (RG) flow for discrete gravity models that preserves their underlying symmetry group, typically $U(N)$ or $O(N)$, remains an open problem. For random matrix models, which are the focus of this paper, this symmetry is intrinsically tied to the interactions encoding the random geometry of two-dimensional quantum Euclidean spacetime. We develop a novel approach based on the introduction of a partial matrix-valued intermediate field. In the large-$N$ limit, measure concentration strongly suppresses fluctuations of its singular values, allowing it to play the role of a self-consistent background field. This provides the basis for a relational RG in which the notion of scale is dynamically induced by the effective Gaussian measure in the basis where the intermediate field is diagonal. Our construction preserves the symmetry of the original model and admits a well-defined continuum limit. We show that the resulting infrared theory is described by a three-dimensional non-local Euclidean field theory with a non-trivial Wilson-Fisher-like fixed point and a single relevant direction. Remarkably, the associated critical exponent exactly matches the standard double-scaling exponent. We finally discuss extensions of the background-field approach to other discrete gravity models, such as random tensor models, and to different symmetry groups, as well as connections with more formal RG frameworks and information geometry.

We consider $V_{g,n}(\{b_i\})$, the Weil-Petersson volumes of the moduli space of Riemann surfaces of genus $g$ with $n$ geodesic boundaries of lengths $b_i$, $(i=1,...,n)$, and various ${ N}{\geq}1$ supersymmetric generalizations of them, using a framework within which they are specializations of a larger family of quantities naturally governed by the integrable KdV hierarchy. An exact boundary-addition identity is derived that directly relates $V_{g,n+1}(\{b_1,b_2,...,b_n,b\})$, for any $b$, to the corresponding $n$-boundary KdV data underlying $V_{g,n}(\{b_1,b_2,...,b_n\})$. For ordinary Weil-Petersson volumes, expansion about the special removable-cone value $b=2\pi i$ reproduces three known results of Do and Norbury, organizing them as the first levels of a complete hierarchy. The higher levels are naturally built from additional KdV data, which we interpret geometrically in intersection theory as a tower of $\kappa$-decorated volumes. Several other recursive relations in the literature are illuminated by the identity, and various new ones are derived. The cases with ${ N}=1,2$ and (small) ${N}=4$ supersymmetry are also covered by the identity, and we exhibit some of the striking special features and results arising in each case. Among many applications presented, we use the identity to uncover the intersection theory descriptions of ${N}=2$ and small ${ N}=4$ Weil-Petersson volumes.

The notion of gap-richness was recently introduced to quantify the ability to open spectral gaps for periodic word models by arbitrarily small perturbations and is useful in the construction of almost-periodic operators having exotic spectral properties, such as Cantor spectrum of zero Hausdorff dimension. Given a subset of Euclidean space that is locally dense in the Zariski topology, we show that any image of such a set under a nonconstant polynomial is gap-rich. This generalizes the scope of previous work in several ways, including allowing local correlations into potential blocks and allowing for totally disconnected sets of realizations.

We study uniform approximation of $\exp(tz)$, $t>0$, on $(-\infty,0]$ by rational functions $P_m(z)/(q_m-z)^m$ with a prescribed repeated pole $q_m>0$. A Möbius transformation reduces the problem to polynomial approximation of $F_\lambda(x)=\exp\!\left(-\lambda\frac{1-x}{1+x}\right)$ on $[-1,1]$, where $\lambda=tq_m$. We derive a uniform two-saddle asymptotic formula for the Chebyshev coefficients, including explicit amplitude and phase and a relative remainder for each localized complex saddle contribution, covering fixed, sublinear, and linear pole scalings away from saddle coalescence. Because the two saddle contributions can cancel in a single coefficient, we pass to a growing block of neighboring coefficients and prove that the whole block cannot cancel. This transfers the coefficient asymptotics to approximation errors. For $q_m=(\alpha/t)m$, $0<\alpha<3\sqrt3/2$, the best uniform error has two-sided order $m^{-1/2}H_e(\alpha)^m$; at the optimal ratio $\alpha=1/\sqrt2$ this becomes $m^{-1/2}(\sqrt2-1)^m$. The normalized Chebyshev-weighted $L^2$ projection error has an explicit bounded oscillatory profile. These prefactor-resolved estimates yield a two-term precision-to-work law and quantify mismatch between pole-design and stopping degrees. Finally, the scalar error gives an exact worst-case matrix-action benchmark for self-adjoint negative semidefinite matrices and dimension-independent shift-and-invert Krylov bounds.

Free-floating planets (FFPs) may retain dynamical signatures of the mechanisms that eject them from their host systems. We integrate $10^6$ collisionless FFP test particles for $10^8$~yr in a static, phenomenological Galactic potential, comparing a mass-independent kick model with a mass-coupled prescription ($\sigma_{\rm CB}\propto M^{-0.15}$, $v_{\rm PL}\propto M^{-0.5}$) against a matched no-kick control. The imposed mass dependence is recovered at injection, with the combined-channel median coupled kick decreasing from $10.716$ to $0.708~{\rm km\,s^{-1}}$ across five mass bins—a factor of $\sim15.1$. A mass-dependent trend remains visible after $100$~Myr of Galactic propagation in the matched kicked-versus-control displacement, whose median decreases from $0.7001$ to $0.0539$~kpc across the same bins. The remaining numerical distinction is concentrated in this mass-resolved differential displacement rather than in the bulk phase-space moments: the final velocity dispersions of the null and coupled kicked populations are nearly identical, only a few percent of particles leave the adopted disk region, and the fraction of particles satisfying the formal Galactic-unbound criterion ($E_i>0$) remains negligible in every diagnostic we report. Comparing each kicked population against its matched no-kick control shows that much of the overall kinematic heating arises from the evolution of the initially warm, nonequilibrium disk rather than from the ejection kick itself, isolating the kick's smaller contribution.

Localizing a radio-frequency (RF) transmitter from received signals often requires a model of the environment to predict how obstacles block and reflect the signal. In many robotic applications, however, only a partial map is available, particularly when a robot localizes the source while exploring with simultaneous localization and mapping (SLAM). We study single-snapshot transmitter localization on such partially explored maps and compare two approaches that output a posterior over transmitter locations. The first extends a digital-twin method, which ray-traces every candidate location, to partial maps by treating unexplored space as free and training on mixed map coverage. The second, MAPLE-RF, encodes estimated path angles of arrival and signal-to-noise ratios as grid channels aligned with map knownness, occupancy, and line-of-sight visibility, and a U-Net scores all candidate positions in one pass without simulating propagation at inference. Ray-tracing simulations of indoor environments indicate that training on mixed map coverage is essential for both approaches. The digital-twin approach is more accurate on most single-snapshot metrics, while MAPLE-RF comes close at a query cost that does not depend on the propagation model and is more than two orders of magnitude below a fresh full-grid query with general-purpose ray tracing. Both outperform Gaussian and Gaussian-mixture baselines, and on exploration routes guided by its own estimates, fused MAPLE-RF posteriors place more probability near the source than the compared methods. Code and data will be released.

We study interacting relativistic charged bosons at finite temperature and isospin density in a thermodynamically consistent mean-field approach with repulsive phi-4 and phi-6 interactions. The thermodynamics is formulated in an Extended Canonical Ensemble, in which the conserved isospin density, not the chemical potential, is the independent variable. This is essential in the condensed phase, where mu_I is fixed by condensation. With one constant fitted to the lattice pressure at T=120 MeV, the model reproduces the lattice isospin density, energy density, and trace anomaly, phi-6 being more accurate.

This paper extends an existing algorithm for the first-order derivatives of rigid-body dynamics to the case of closed-chain kinematic systems modeled using constraint embed- ding. Many standard dynamics algorithms apply to both open- chain and constraint-embedded models, but existing efficient derivative methods assume joint velocity effects are locally config- uration invariant. We remove this assumption and derive adapted algorithms that extend dynamics derivatives to more general joint types, including those arising in constraint-embedded closed- chain models. Our results compare conventional pin-joint robot models with more complete actuation models that capture local closed chains. We show that the additional terms introduced by these generalizations have low computational impact when mod- eling actuation kinematics alone, but can incur higher cost when additional rigid bodies, such as motor rotors, are included in the actuation chain, or when considering non-local loops. Overall, these results enable more accurate dynamics computations for constraint-embedded actuation submechanisms to be adopted in model-predictive control and differentiable simulation.

An important result due to Radjabalipour asserts that if ${A\in\BB(\H)}$ is an invertible positive operator and ${T\in\BB(\H)}$ is arbitrary, then the operator sequence $\{A^{-n}TA^n\}_{n\in\ZZ}$ is norm-bounded if and only if ${TA=AT}.$ Using the concept of spectral gaps, we show that if $A$ possesses a spectral gap and the sequence $\{A^{-n}TA^n\}_{n\in\ZZ}$ is norm-bounded, then $T$ must be block diagonal with respect to a certain orthogonal decomposition of $\H$. We also provide an alternative proof of Radjabalipour's theorem. We also extend the theorem to some rich classes of operators, including invertible normal operators and invertible weighted sums of projections. Moreover, we provide simple proofs for the fact that a positive definite matrix ${A\in\MM_N}$ is a positive multiple of the identity if and only if the sequence $\{A^{-n}TA^n\}_{n\in\ZZ}$ is norm-bounded for every~${T\in\MM_N}.$

Vision-Language-Action (VLA) models have shown strong generalization in robotic manipulation by combining semantic knowledge from pretrained vision-language models with expressive action-generation policies. Diffusion-based action generators are particularly effective for modeling temporally coherent action chunks, but these chunks are typically executed open-loop after inference. This limits responsiveness when objects move, contacts change, or the scene evolves during execution. We propose VLA-Feedback, a two-timescale architecture that combines low-frequency diffusion planning with high-frequency visual feedback. Rather than fully denoising an action chunk before execution, VLA-Feedback retains its final denoising step as a lightweight feedback interface, allowing each action to be corrected using the latest observation before it is executed. This design preserves the expressiveness of the diffusion planner while enabling real-time action correction without rerunning the full vision-language diffusion model. VLA-Feedback matched GR00T on static LIBERO tasks while improving average success on dynamic simulation tasks from 27.5% to 85.0%. On real-robot tasks, it improved average success from 51% to 73%. Additional materials can be found on our project page: https://vla-feedback.github.io.

From interstitial space to luminal cavities, fluid pressure and flow can remodel, reshape and even redefine a biological tissue. Fluids can either govern or react to mechanical interactions between cells. However, measuring flows at cellular scales is difficult, which makes it challenging to understand tissue hydraulics. Here, we develop a theoretical approach that captures cellular mechanics and fluid flow in one framework. We find that hydraulics can drastically influence tissue behavior. Hydraulic coupling between cell shape and size governs a tissue's response to osmotic shock, while tuning a tissue's permeabilities can channel fluid either between or across cell membranes. In active tissues, hydraulics can suppress cell mobility to the point of fracture, where we discover a hydraulic ratchet that drives fluid out of cells to generate small luminal spaces. We find experimental evidence that hydraulics can suppress cell motion in early stage zebrafish embryos injected with a thickening agent, which indicates that hydraulics may generally govern the behaviors of many multicellular systems.

AI coding assistants are rapidly transforming software development, but are known to produce insecure code. Prior work has measured whether AI-assisted developers produce secure code, but less is known about how they evaluate AI-generated code: whether they can identify vulnerabilities, what cues they use, and how trust shapes their decisions. This evaluation step is foundational to secure development with AI, whether using auto-complete, chat tools, or AI agents. As a first step, we conducted a remote observational study with 100 participants isolating this evaluation stage. Participants were tasked with producing secure and functional code for four C linked-list tasks. For each, participants were able to cycle through five AI-generated suggestions varying in security and functionality, select one, and edit their choice into a final submission. Participants also completed a post-study survey about their decision-making and perception of AI-generated code's security and 23 completed a more in-depth interview.

Generative AI (GenAI) can support open-ended learning through generation, personalization, and learner modeling, yet educators need ways to shape these capabilities around educational goals. Through interviews and design activities with 15 U.S. educators, we examined educator configuration of GenAI using K-12 career exploration as an exploratory context. Educators configured not only AI-generated experiences, but also when student activity became an inference, whether learner information persisted, who could access it, and how it informed subsequent human action. They also faced challenges translating teaching needs into configurations: recognizing possibilities for control beyond familiar uses of GenAI, decomposing general-purpose AI into understandable functions and responsibilities, and identifying useful information through intended teaching actions. We discuss how GenAI systems can support educators in expressing and testing configurations, while establishing boundaries around personalization, inference, persistence, disclosure, and action to keep AI-supported learning aligned with evolving learner needs.

Recent visual document retrieval (VDR) systems such as ColPali use multi-vector page embeddings, in which patch-level vectors enable fine-grained evidence matching but incur substantial index storage and MaxSim scoring overhead. Post-hoc merging offers a practical route to efficient VDR by reducing this cost without retraining the retriever, but its uniform reconstruction objectives are poorly aligned with the sparse, non-uniform patch usage induced by late-interaction retrieval. Under aggressive compression, this misalignment can preserve rarely used patches while concentrating retrieval activity on too few retained representatives. To address this misalignment, we propose Marginal-Guided Compression with Optimal Transport (MAGIC), a training-free post-hoc compressor for efficient retrieval with frozen multi-vector embeddings. MAGIC derives a MaxSim-induced compression surrogate and optimizes it through a two-marginal entropic optimal-transport formulation, where a retrieval-demand source marginal prioritizes high-use patches and a balanced target marginal regularizes retained-facet usage. Across ViDoRe benchmarks, keep ratios, and retrieval backbones, MAGIC consistently outperforms strong post-hoc compressors, with particularly large gains in the aggressive-compression regime; component ablations verify the complementary effects of its two marginals. We release the code at: https://github.com/xandery-geek/MAGIC.

We study data-driven early stopping for spectral regularisation methods in the classical non-parametric regression setting. Building on the discrepancy principle, we propose a multi-scale stopping rule that applies to general kernel estimators and show that, unlike previous approaches, it achieves full adaptivity over all smoothness levels in the well-specified case. A key contribution of our work is an extension based on random feature approximations, which reduces computational cost on large datasets while preserving minimax-optimal statistical guarantees. Our procedure not only selects an optimal stopping time but also provides a fully data-driven choice of the number of random features needed to achieve optimal rates. Through the established connection between random features and neural networks in the neural tangent kernel regime, our method further yields a principled, data-driven recommendation for the network width. We prove that the resulting simultaneously chosen width and stopping time allow neural networks to attain minimax-optimal learning rates without prior knowledge of smoothness or capacity parameters.

Let $F$ be a field and let $L$ be a loop. We call $L$ just-infinite if it is infinite and every nontrivial normal subloop has finite index, and we call the possibly nonassociative loop algebra $F[L]$ just-infinite if it is infinite-dimensional and every nonzero two-sided ideal has finite codimension. We first prove that just-infiniteness of $F[L]$ always implies just-infiniteness of $L$. Next, using the Chein construction, we show for every infinite group $G$ that $M(G,2)$ is just-infinite if and only if $G$ is just-infinite, and that $F[M(G,2)]$ is just-infinite if and only if $F[G]$ is just-infinite. We extend the algebraic equivalence to the generalized Moufang doubles $M(G,*,g_0)$ whenever $G$ is infinite and nonabelian. Finally, we construct a single locally finite, residually finite, nonassociative Moufang loop $L$ for which $F[L]$ is residually finite-dimensional, locally finite-dimensional, and just-infinite over every field, and we explain why infinite nonassociative RA loops cannot be just-infinite.

Improvements to Visual-Inertial Simultaneous Localization and Mapping (VI-SLAM) for low-cost autonomous underwater vehicles (AUVs) are critical for transitioning advanced marine robotics from specialized labs to broader research and hobbyist applications. While high-end AUVs typically rely on expensive sensor suites - such as Doppler Velocity Logs (DVLs) and Ultra-Short Baseline (USBL) systems - this work demonstrates that robust, high-quality navigation is achievable using a sub-$10, 000(USD) platform equipped only with inexpensive consumer-grade sensors. By leveraging a similarly priced, open-source AUV, we evaluate the performance of stereo cameras, Micro-electromechanical System (MEMS)-based IMUs, and depth sensors in a fully unconstrained 6-degree-of-freedom (6-DOF) underwater environment. We analyze the efficacy of off-the-shelf SLAM packages and propose optimizations for sensor fusion to mitigate the visual and physical challenges of untethered underwater operation. Our results prove that a usable SLAM solution can be accessible to the masses, providing a benchmark for expectations in demanding, real-time maritime missions without the financial barrier of industrial-grade hardware.