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All of arXiv

Friday 25 September

Combinatorics

A Log-Star Comparison Between Expectation Threshold and Fractional Expectation Threshold

Xuan Fang and Tianyu Wang

We proved a log-star comparison between the expectation threshold $q(\mathcal F)$ and the fractional expectation threshold $q_f(\mathcal F)$ for any nontrivial increasing family $\mathcal F$ on a finite ground set $V$ of size $|V|=N$. Specifically, we show that $$q_f(\mathcal F)\le64\log_2^*(N+2)\,q(\mathcal F),$$ where $\log_2^* x$ is the iterated logarithm of base-2. Using similiar methods, one can extend this result to the following stronger form: there exists a universal constant $C>0$ such that \[ q_f(\mathcal F)\le Cq(\mathcal F)\log_2^*(l(\mathcal F)),\quad q_f(\mathcal F)\le Cq(\mathcal F)\log_2^*(\operatorname{VC}(\min\mathcal F)), \] where $l(\mathcal F):=\max\{2,\max_{S\in\min\mathcal F}|S|\}$ and $\operatorname{VC}(\min\mathcal F)$ denotes the VC-dimension of $\min\mathcal F$. On October 7, 2026, OpenAI released a result proving the equivalence of fractional and integral thresholds, which supersedes the findings in this note. The authors are keeping this note for historical reference.
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Statistical Methodology

Design-Ignoring versus Design-Respecting World Models for Epidemiology

Xiangyu Yu and Weiyu Liu

World models for epidemiology learn from records shaped by study designs, including assignment, sampling, measurement, and related processes. A model may therefore reconstruct observed trajectories while learning an intervention contrast that depends on how records were collected. We formalize study design as constraints on a world model latent-world interface, action mechanism, observation likelihood, and target readout. This distinguishes design-respecting models, which encode these constraints, from design-ignoring models, which fit selected records without relating assignment and observation to the intended intervention question. Using a large scale cluster-randomized test-negative trial, we hold the latent structure and fitting settings fixed and compare a design-ignoring case-count model with a design-respecting test-negative observation model. Both models achieve comparable factual reconstruction. Yet across 500 paired resampling experiments at different relative sampling intensity, median contrast changes are substantial for the design-ignoring model, versus merely marginal for the design-respecting model. The same qualitative separation holds when sampling also varies across clusters. Thus, factual reconstruction alone does not establish design alignment; testing whether fitted contrasts preserve design-implied observation-process invariances provides a sharper evaluation.
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Computational Engineering

Simulation-Efficient Analog Circuit Yield Optimization via Monte Carlo Zeroth-Order Gradient Estimation

Liyan Tan, Yequan Zhao, Ben F. Jamroz et al. (+2 more)

Yield optimization under process variation is expensive because each candidate design must be evaluated across many Monte Carlo SPICE samples. The resulting finite-sample yield is also piecewise constant in the design parameters, providing little local information for optimization. We introduce zeroth-order Monte Carlo stochastic gradient descent (ZO-MC-SGD), a black-box method that converts continuous specification margins into stochastic descent directions. Each update evaluates opposite design perturbations under shared process samples, allowing a small simulation batch to estimate a local direction without differentiating SPICE or fitting a global surrogate model. A Spearman rank-correlation test checks that the margin-based loss orders designs consistently with empirical yield. We prove that the estimator is unbiased for a Gaussian-smoothed surrogate and derive variance and sample-complexity bounds with no explicit dependence on process dimension. Across five analog circuit benchmarks with up to 30 design variables and 42 process variables, ZO-MC-SGD reaches a mean yield of 0.95 on four circuits within 50–200 simulations and the empirical yield ceiling on the fifth. Relative to the best of five black-box and learning-based baselines, it reduces the required simulation budget by up to a factor of eight.
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All authors Liyan Tan, Yequan Zhao, Ben F. Jamroz, Ari Feldman, Zheng Zhang

Superconductivity

Electrochemical Growth of Full Volume Meissner Effect Superconducting BKBO

Oleksandr Foyevtsov, Kateryna Foyevtsova, Mohamed Oudah et al. (+2 more)

In this work we show the results of electrochemical synthesis of BKBO crystals using three different experimental setup configurations. The setups differ between each other by varying level of control over physical variables and progressing from a two-electrode to a three-electrode configuration using highly oriented platinum counter electrode. By systematic analysis of the temperature dependence of the magnetic susceptibility at the superconducting transition of the collected crystals we observe that an order of magnitude sharper superconducting transition is achieved for the most comprehensive three-electrode setup. In addition, the level of chemical substitution can be controlled by the value of the overpotential versus reference electrode. We demonstrate that with this technique a full volume Meissner effect can be achieved with a sharp transition temperature for the superconducting crystal.
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All authors Oleksandr Foyevtsov, Kateryna Foyevtsova, Mohamed Oudah, Dan Bizzotto, George Sawatzky

Robotics

Can a Robot Read Braille? - Learning to Adapt Contact via Imitation Learning for Tactile Braille Recognition

Xi Chen, Yunlong Shan, Sihan Chen et al. (+7 more)

For people who are blind, touch provides an essen-tial channel for accessing written information through Braille. Bringing a similar capability to robots requires them not only to recognize tactile patterns, but also to actively establish physical contact that makes those patterns readable. Yet existing robotic Braille readers largely focus on recognition after contact, leaving contact establishment itself insufficiently addressed. We present an adaptive-contact framework for robotic tactile Braille reading that assesses contact quality and physically corrects unsuitable contact before recognition and reconstruc-tion. Multi-Head Policy Learning uses expert-guided contact-adjustment demonstrations to jointly learn contact acceptability and pose corrections. During deployment, the robot iteratively evaluates and re-establishes contact, retaining reliable tactile observations for pose-aware fusion and Braille reconstruction. Across 20 physical Braille plates used for learning and eval-uation, the proposed approach achieves 94.0% tactile quality and 88.6% tactile reconstruction on the ten online-evaluation plates. These results demonstrate the importance of actively establishing readable contact, rather than relying solely on recognition under imperfect tactile observations, for reliable robotic Braille reading.
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All authors Xi Chen, Yunlong Shan, Sihan Chen, Jun Hu, Zhongxuan Li, Shiyao Zhang, Sichao Liu, Zhong Zhao, Kosta Jovanovic, Peng Zhou

Computational Engineering

SkillRefine: Cross-Source Skill Induction and Execution Validation for LLM Agents in Refinery Planning Software

Dongxiao Liu, Boren Zhu, Yuwen Ding et al. (+3 more)

Operating industrial planning software such as AspenTech PIMS (Process Industry Modeling System) requires an LLM agent to combine structural knowledge, procedural knowledge from expert records, and constraints revealed only during execution. These evidence sources are heterogeneous and individually incomplete: documentation describes tables and interfaces but omits task-level coordination, expert CASE records expose multi-table modification patterns without explicit schema grounding, and execution feedback reveals latent constraints only when a plan is executed. We present SkillRefine, a framework that exploits the Documentation–Practice Gap between documented structure and expert practice to extract candidate coordination patterns, ground them against table definitions and COM specifications, and compile them into progressively disclosed skill packages with provenance. The library is then refined through label-free compliance screening, oracle-based match decomposition over table, row, column, and value dimensions, and signal-conditioned trajectory attribution for localized repair. We evaluate SkillRefine on PIMS-Bench, a benchmark built from two AspenTech PIMS demonstration models, using disjoint construction and held-out test tasks. On the held-out test set, SkillRefine achieves absolute component match F1 gains of 14%–30% across four LLM backbones, with the largest gains on complex multi-table coordination tasks.
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All authors Dongxiao Liu, Boren Zhu, Yuwen Ding, Linghui Li, Lei Li, Xiaoyong Li

Soft Condensed Matter

Realignment of ferroelectric nematic by photoinduced electric field

Sathyanarayana Paladugu, Oleksandr Kurochkin, Ruslan Kravchuk et al. (+5 more)

Liquid crystal displays (LCDs) employ thin pixels of a paraelectric nematic, confined between two glass plates with transparent indium tin oxide (ITO) electrodes. A voltage applied to the electrodes realigns the molecules, changing the optical appearance of the pixel. Here we demonstrate that a similar molecular realignment can be triggered by low-power light irradiation when the paraelectric nematic in the cell with ITO electrodes is replaced with a ferroelectric nematic (NF). Irradiation creates an intrinsic electric field that is strong enough to realign the NF but too weak to affect the paraelectric nematic. The extraordinary sensitivity of the ITO/NF pair to light irradiation creates a platform for optical control of ferroelectric polarization and applications in photonics, sensing, smart windows, and beyond.
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All authors Sathyanarayana Paladugu, Oleksandr Kurochkin, Ruslan Kravchuk, Mykola Kravets, Volodymyr Sashuk, Bijaya Basnet Vassili G. Nazarenko, Sergij V. Shiyanovskii, Oleg D. Lavrentovich

Emerging Technologies

Highly Scalable Selectorless Cryogenic Memory Array Using Ferroelectric Josephson Field-Effect Transistors

Saheeb Ahmad and Shamiul Alam

Scalable memory systems that satisfy the temperature, speed, and energy requirements of cryogenic environments are essential for the development of large-scale quantum computers. They may also benefit high-performance computing and space applications. However, existing cryogenic memory technologies often suffer from limited scalability, low operating speed, and/or high power consumption, restricting the scalability of target applications. Ferroelectric Josephson field-effect transistors (Fe-JoFETs), which combine ferroelectric polarization with the superconducting properties of Josephson junctions, offer a promising solution. The ferroelectric layer enables nonvolatile storage capability, while the Josephson junction supports high-speed, energy-efficient operations. In this work, we leverage Fe-JoFETs to develop a highly scalable, ultra-low-power, nonvolatile cryogenic memory array that does not need additional selector devices for random access. Moreover, the superconducting component of Fe-JoFET provides a binary decision during read, eliminating the need for sensing peripheral circuitry. We first develop a physics-based Verilog-A compact model for Fe-JoFETs and use it to verify the functionality of the proposed memory array. By eliminating both selector and sensing circuitry, the proposed memory architecture offers higher scalability than existing technologies. The ultra-low-power operation of this memory also makes it compatible with strict power budgets of cryogenic applications.
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Signal Processing

A Vehicle-Integrated Approach to Digital Twin Deployment for Bridges

Mehri Alamdari, Zihao Liu, Jiaji Wang et al. (+2 more)

The project A Vehicle Integrated Approach to Digital Twin Deployment for Bridges is developing a scalable framework for bridge condition assessment using vibration measurements from a sensorised inspection vehicle. It combines vehicle bridge interaction modelling, state estimation, machine learning and surrogate modelling to reduce reliance on permanent sensor networks. The Old Ada Bridge in Japan is the principal case study because it provides direct and vehicle-based field measurements across multiple experimentally introduced damage states. Progress has been made across three streams. First, forward and inverse Fourier Neural Operator (FNO) models have been demonstrated on a benchmark beam, enabling rapid response prediction and identification of damage location and severity. Second, an inspection vehicle optimisation framework has been developed to select vehicle mass and tyre suspension stiffness that maximise separation between healthy and damaged responses, integrating contact-point reconstruction, damage assessment, Kriging and particle swarm optimisation. Third, an Augmented Kalman Filter-based virtual sensing framework has been developed to estimate moving loads and reconstruct displacement, velocity and acceleration at unmeasured locations from sparse sensors. The next phase will extend and integrate these methods using the Old Ada Bridge model and field data. FNO models will be transferred to the truss structure and evaluated using intact and damaged measurements. Vehicle optimisation will be tested for transferability, while virtual sensing will be extended to the coupled vehicle bridge system to estimate road roughness, vehicle parameters, moving forces and structural responses. Ultimately, these components will form an integrated vehicle-driven digital twin for rapid simulation, response reconstruction and damage assessment under realistic conditions.
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All authors Mehri Alamdari, Zihao Liu, Jiaji Wang, Kawabe Daigo, Chul Woo Kim

Computation and Language

TRACE: Temporal Audit and Condition-aware Evaluation of Streaming Video Understanding

Yibo Ma, Qianqian Zhang, Peng Liu et al. (+1 more)

Streaming video understanding requires models to interpret evidence as it arrives, yet current evaluations often report task scores without specifying when evidence becomes valid, how visual history is maintained, or how responses are triggered. As a result, similar scores may correspond to different workloads, failure modes, and operational behavior. We introduce TRACE (Temporal Audit and Condition-aware Evaluation), a condition-aware benchmark and evaluation framework that makes these factors explicit. TRACE combines temporally audited visual tasks with evidence timing and instruction-dependent trigger annotations, a unified causal Core–Adapter protocol that controls information availability while recording actual history processing and response events, and multidimensional reporting of answer quality, timeliness, response-selection behavior, workload, completion, and reliability. On 1,240 records from 517 videos, we evaluate eight publicly available models or systems in eight configurations. We find that nearly identical QA accuracy can mask substantial differences in completion, answer validity, and generation workload, while proactive performance separates into response quality, response delay, false alarms (responses emitted while no target window is currently valid and a later one remains), and missed target windows. These results show that streaming-video performance should be interpreted as execution-conditioned system behavior rather than a single score. Our benchmark and code can be accessed at \href{https://github.com/om-ai-lab/trace-bench}{https://github.com/om-ai-lab/trace-bench}.
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All authors Yibo Ma, Qianqian Zhang, Peng Liu, Tiancheng Zhao

Solar and Stellar Astrophysics

A Comprehensive Study of the Long-Period Cataclysmic Variable V630 Cassiopeiae

Ivan Mora Zamora, Gagik Tovmassian, Juan Echevarria et al. (+1 more)

We present a comprehensive review of V630 Cassiopeiae, which is a very long-period cataclysmic variable. Based on new observations combining spectroscopy and high-resolution photometry provided by TESS and precise distance data from GAIA, we confirm and extend previously described characteristics. The light curves show differential behaviors between different epochs, attributed to changes in the disk's brightness distribution, likely due to non-axial structures such as precessing eccentric disks. The spectroscopy reveals complex Ha line profiles, with dual components and an emission distribution that suggests a large, asymmetric, and possibly precessing disk, rather than a classic shock structure in the matter-flow impact region. Doppler tomography indicates that the emission originates at the periphery of the disk, distributed in an asymmetric pattern rather than a compact point, complicating the interpretation of radial velocities and limiting their use for accurately determining masses. Through photometric and spectroscopic analysis, we established a donor mass estimate with an approximate value of 0.38 Ms at the adopted distance of 2409 pc, with significant uncertainty related to distance and other systematic factors. Finally, using the parameters of V630 Cas, binary evolution simulations were conducted with MESA incorporating CARB magnetic braking prescription to identify an evolutionary sequence that explains its properties.
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All authors Ivan Mora Zamora, Gagik Tovmassian, Juan Echevarria, Diogo Belloni

Analysis of PDEs

Long-time Korteweg-de Vries approximation for the Fermi-Pasta-Ulam-Tsingou system

Younghun Hong and Junyeong Jang

We prove that, as the lattice spacing $h$ tends to zero, general solutions to the infinite Fermi–Pasta–Ulam–Tsingou (FPUT) system can be approximated in $L^2$ by two counter-propagating Korteweg–de Vries (KdV) waves on time intervals of order $\log(1/h)$. This resolves an open question raised by the first author and collaborators~\cite{HKY2021}. Our proof combines the FPUT conservation law with an $h$-uniform local well-posedness theory in $L^2$ and persistence of Sobolev regularity. We also introduce a frequency-localized auxiliary equation to overcome the difficulty of comparing the Fourier restriction norms associated with the FPUT and KdV flows.
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Computer Vision

StarWM: Self-Supervised Trained Attention Routing for Robust World Models

Zeqiang Zhang, Fabian Wurzberger, Maximilian Otte et al. (+4 more)

A robust world model must strike the balance between faithfully capturing environmental dynamics and abstracting away from irrelevant content. While reconstruction-based world models ensure faithful supervision, they misallocate representational capacity by pixel area rather than dynamics relevance for visual tasks, which can cause task-irrelevant content to dominate the learned representation. Alternatively, reconstruction-free methods avoid this bias but risk discarding possibly relevant information. We propose StarWM, which uses a cross-attention module trained on self-supervised dynamics to decide where reconstruction applies. A dual-stream decoder then restricts reconstruction to the attended regions, with stop-gradient barriers preventing interference between the two objectives. These components allows reconstruction to supervise the visual content of attended regions without contaminating the latent with non-predictive information. On DeepMind Control with dynamic video backgrounds, default (reward-free) StarWM achieves the strongest performance under random-frame distractors and substantially outperforms reconstruction-based baselines under sequential video. In addition, its reward-augmented variant matches or exceeds reconstruction-free methods on sequential video, achieving the highest overall return across all distractor regimes. Mechanistic probing confirms \starwm{} preserves state attributes with near-perfect fidelity through long-horizon imagination while systematically discarding distractors. Code is available on GitHub.
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All authors Zeqiang Zhang, Fabian Wurzberger, Maximilian Otte, Daniel Schmid, Sebastian Gottwald, Arne Peter Raulf, Daniel Alexander Braun

Analysis of PDEs

Stability of oblique sonic shocks in steady supersonic potential flow past a wedge

Geng Lai

When a uniform steady supersonic oncoming flow impinges on a straight wedge, if the wedge angle is smaller than the detachment angle, two types of steady oblique shocks satisfying the entropy condition will form in the flow field: weak shocks with supersonic or subsonic downstream flow, and strong shocks with subsonic downstream flow. There have been many results on the stability of oblique shocks with subsonic or supersonic downstream flow. However, much less is known about the stability of oblique shocks with sonic downstream flow, since the flow behind the shock wave is very sensitive to disturbances. This paper investigates the stability of oblique sonic shocks under the assumption of a straight wedge with non-uniform incoming flow. We reduce the problem to a degenerate hyperbolic free boundary problem. A local Lipschitz-continuous solution with sonic-supersonic downstream flow to the free boundary problem is constructed, using the classical Ascoli-Arzelà theorem and a diagonal argument. The main difficulty of this free boundary problem lies in the hyperbolic degeneracy on the sonic line. By adopting a weighted characteristic decomposition method, we establish a delicate estimate of the downstream flow near the sonic line.
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Dynamical Systems

On Standard perturbations of the Affine twist map

Salvador Addas Zanata

For any $t\in\mathbb{R}$, consider the Affine twist map $\rm{Aff_t}:\mathbb{T}^2\to\mathbb{T}^2$ given by $$\rm{Aff_t}(x,y)=(x+y \text{ mod 1}, y+t \text{ mod 1}).$$ The map $\rm{Aff_t}$ clearly possesses an invariant foliation by horizontal curves. If $t$ is rational, each leaf is periodic, and if $t$ is irrational, the orbit of each leaf is dense in the torus. In both cases, the vertical rotation set of the proper lift of $\rm{Aff_t}$ to the vertical cylinder is reduced to $\{t\}.$ Now, for $k\in\mathbb{R},$ define $$f_{k,t}(x,y):=(x+y+k\sin (2\pi x)\text{ mod 1},y+k\sin (2\pi x)+t\text{ mod 1}).$$ We show that: 1) when $t=p/q$ for integers $p$ and $q>0$, KAM theory implies the existence of a constant $k_{p/q}>0$ such that for $|k|<k_{p/q}$, the vertical rotation set of an adequate lift of $f_{k,p/q}$ is just $\{p/q\}.$ 2) when $t$ is irrational, for any $k\neq 0$ the vertical rotation set of the adequate lift of $f_{k,t}$ is a non-degenerate interval which contains $t$ in its interior. In other words, it is not easy to build area-preserving twist maps whose vertical rotation sets are reduced to a single irrational number. From Theorem A of \cite{eujul}, such a map needs to have an invariant foliation by Lipschitz graphs over the horizontal coordinate. In particular, all its iterates must satisfy a twist condition. This is precisely what does not hold for $f_{k,t}$, for all non-zero values of $k$.
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Analysis of PDEs

Rigidity of stationary and uniformly rotating planar Euler flows in the $C^1$ Yudovich class

Boquan Fan, Yuchen Wang, Chunjing Xie et al. (+1 more)

We prove a rigidity theorem for stationary and uniformly rotating solutions of the two-dimensional incompressible Euler equation with vorticity $ \omega_0\in C^1(\mathbb{R}^2)\cap L^1(\mathbb{R}^2) \cap L^\infty(\mathbb{R}^2). $ If the angular velocity $\Omega$ satisfies \[ \Omega\leq\frac12\inf_{\mathbb{R}^2}\omega_0 \qquad\text{or}\qquad \Omega\geq\frac12\sup_{\mathbb{R}^2}\omega_0, \] then $\omega_0$ is radially symmetric, in particular, every stationary vorticity of one sign in the class $C^1(\mathbb{R}^2)\cap L^1(\mathbb{R}^2) \cap L^\infty(\mathbb{R}^2)$ must be radially symmetric about some point. Furthermore, for $\Omega\neq0$, the center is necessarily the origin; The proof is based on the analysis for level-set geometry of a normalized stream function. A componentwise Bernoulli formula, together with the isoperimetric inequality and Pohozaev identities, yields a nonnegative defect measure encoding both geometric defects and topological branching. An analysis at infinity forces this measure to vanish, reducing the problem to a semilinear elliptic equation with a bounded nonnegative Borel nonlinearity. Radial symmetry then follows from a theorem of P.-L.\ Lions.
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All authors Boquan Fan, Yuchen Wang, Chunjing Xie, Weicheng Zhan

Functional Analysis

Symmetric Kahane–Salem–Zygmund Inequalities and the Supremum Norm

Daniel M. Pellegrino, Anselmo B. Raposo Jr. and Eduardo V. Teixeira

The Kahane–Salem–Zygmund inequality provides unimodular $m$-linear forms with small supremum norm. We consider its dimension-free symmetric constant $C_m^{\mathrm{sym}}$ over the real scalar field, defined by the requirement that, for every $n$, some real symmetric unimodular $m$-linear form $A:(\ell_\infty^n)^m\to\mathbb R$ satisfy \[ \|A\|\le C_m^{\mathrm{sym}}n^{(m+1)/2}. \] For complex scalars, Boas obtained under permutation symmetry an upper bound of order at most $\sqrt{m\log m}\,\sqrt{m!}$; over the real scalar field, an elementary argument gives the sharper order $\sqrt m\,\sqrt{m!}$. We prove \[ C_m^{\mathrm{sym}}\ge \left(\sqrt{\frac2e}+o(1)\right)\frac{\sqrt{m!}}m, \] using the square-free Walsh spectrum of the diagonal polynomial. In the opposite direction, we establish \[ C_m^{\mathrm{sym}}\le C_0\sqrt{m!}, \] where $C_0$ is absolute, removing the factor $\sqrt m$ from the real upper bound. This estimate follows from a geometric argument in which rigidity for Gram permanents reduces the relevant configurations to sets controlled by Gaussian width. For unrestricted unimodular forms, we also obtain a quantitative rectangular estimate from truncated Hadamard matrices; in equal dimension, the normalized minimum is at most $1+o(1)$ whenever $m=o(n^{5/6})$.
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Artificial Intelligence

LLM Parkinsonism: Executive-Control Failure, Token-Inefficient Persistence, and an Uncertainty-Aware Global Executive Control Architecture for Autonomous Language-Model Agents

Dongsheng Xiao, Zeyuan Wang, Xuzhe Xia et al. (+2 more)

Large language models (LLMs) can plan, use tools, write code, and execute long-horizon workflows, yet strong local competence does not guarantee project-level executive control. Agents may continue acting after the original objective is satisfied, producing low-value refinements, repeated verification, and repairs to self-created complexity. We use LLM Parkinsonism as a narrowly defined, non-clinical metaphor for this pattern of persistent action despite diminishing task-level value. We argue that the problem is not explained by autoregressive next-token prediction alone, but more directly by concentrating proposal generation, scope interpretation, progress assessment, and stopping authority within the same self-conditioned loop. We therefore introduce Global Executive Control (GEC) v0.2, an uncertainty-aware governance architecture that separates action generation from project-level control. In a 24,000-episode matched-candidate benchmark under a common 40,000-token ceiling, a first-candidate baseline achieved 67.42% hard-goal success, a candidate-set local control achieved 96.53%, and GEC achieved 96.57%. The candidate-set control shows that access to multiple candidate actions explains most of the success gain; relative to that control, GEC preserved success while reducing mean token use from 19,782 to 12,574 (36.4%) and restricted mean tokens to completion at the 40,000-token ceiling from 16,136 to 13,114 (18.7%), while eliminating measured pre-completion drift and sharply reducing gross complexity. Governance-overhead sensitivity remained favorable through an additional 500 synthetic governance tokens per cycle. These mechanistic simulations support explicit governance of scope, evidence, resource use, and stopping, while live-model validation remains necessary.
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All authors Dongsheng Xiao, Zeyuan Wang, Xuzhe Xia, Bo Zhao, Yankai Cao

Machine Learning

Population loss in shallow ReLU networks: Bias & families of critical points

Michael Field

The main result presented is a formula for the population loss in the student-teacher kernel model that is applicable to shallow ReLU networks with bias. This extends previous work of Choo and Saul (2009) and Brutzkus and Globerson (2017). The formula makes essential use of Owen's T-function. The necessary theory of the T-function is given and a high precision coding using MPFR for the T-function, based on an algorithm of Komelj (2023), is available on request. It is shown that various families of spurious minima described in past papers of Arjevani and the author extend to biased networks and that the loss is always strictly decreased when bias is added. The change in landscape geometry caused by adding bias appears to be relatively mild. Only the simplest examples are described in this paper where it is assumed that the number of inputs is equal to the number of neurons (this restriction is for reasons of length). A review of relevant previous results on unbiased networks is included. Aside from Gaussian statistics, the main mathematical tools and ideas come from analytic geometry (analytic and subanalytic sets, the Curve Selection Lemma).
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General Relativity and Quantum Cosmology

Geometry as Thermodynamics:Entropy Stationarity and Horizon Residues

Wen-Xiang Chen

Thermodynamic descriptions of gravity involve both variational conditions for spacetime dynamics and analytic structures associated with horizons. We examine their relation while keeping their assumptions distinct. First, we present an explicit derivation of the Einstein equation from the established null-vector entropy functional, including the null constraint, the matter term, and the integration constant associated with the cosmological constant. Second, for an analytic static spherical geometry with a nondegenerate Killing horizon, we define a meromorphic radial one-form whose residue is the inverse of twice the surface gravity. Euclidean regularity then fixes the Hawking temperature. Combining this residue with the Einstein–Hilbert Noether charge gives a normalized contour representation of the Wald entropy. The construction reproduces the Schwarzschild temperature, entropy, and Smarr relation, but does not constitute an independent microscopic derivation of the area law. We establish the limits of a stronger identification between pole structure and dynamics: an asymptotically flat family can retain the Schwarzschild horizon residue, area, surface gravity, and mass while violating the vacuum Einstein equation, and an extremal charged solution possesses a higher-order pole. We also show why exponentiating an unspecified entropy functional does not produce a universal entropy residue. The resulting framework separates entropy stationarity, horizon analyticity, and charge normalization, providing explicit consistency tests for further thermodynamic interpretations of gravitational singularities.
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Image and Video Processing

Image Reconstruction from Phase with Untrained Neural Priors

Ene Meco and Ahmet Enis Cetin

Fourier phase encodes important spatial image structure, but recovering an image without measured spectral magnitude requires additional constraints and leaves absolute intensity ambiguous. We propose a projection-based two-stage framework that combines Fourier-phase and spatial-support constraints with an image-specific neural prior. The first stage alternates constraint enforcement with regularized neural-prior updates, while the second performs phase/support refinement alone with guaranteed convergence. We evaluate two neural-prior implementations on the same 77 microscopy images and compare them with a constraint-only baseline. After 500 final refinement passes, the best-performing variant achieves 31.41 dB pooled PSNR, 35.75 dB mean PSNR, and 0.9531 mean SSIM, improving pooled PSNR by 1.51~dB and reducing pooled MSE by 29.3% relative to the baseline. The results demonstrate the benefit of combining neural guidance with explicit constraint refinement at the evaluated iteration budget, while showing that lower phase residual alone does not guarantee greater reconstruction accuracy.
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Graphics

DiffusionShadow: Diffusion-based Shadow Caching for Neural Volume Rendering

Kai-Chen Tung, Qi Wu, David Bauer et al. (+3 more)

Implicit neural representations (INRs) have gained momentum in scientific visualization due to their compactness and scalability to large datasets, making them well suited for integration with direct volume rendering (DVR). However, real-time volume rendering of INR with advanced illumination effects, such as shadows, remains computationally expensive, as evaluating shadow terms via ray marching is costly. Alternatively, precomputing and storing shadows for many lighting directions is prohibitive in both memory and storage. To address this, we introduce a diffusion-based shadow caching framework that compresses a vast set of pre-calculated shadow INRs into a single diffusion model. Rather than focusing on generalizing to unseen directions, our method effectively memorizes and reconstructs a dense set of pre-trained lighting conditions on the fly. We first encode a collection of shadow coefficient volumes as shadow INRs, and then train a diffusion model conditioned on lighting direction to predict the corresponding shadow INR weights at inference time. This design integrates directly with standard INR renderers without additional runtime sampling. Experiments show that our approach achieves faster rendering than traditional methods while bypassing the massive storage bloat of independent INRs, producing shadows that closely match most of the reference results.
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All authors Kai-Chen Tung, Qi Wu, David Bauer, Mengjiao Han, Silvio Rizzi, Kwan-Liu Ma

Cryptography and Security

Prompt Injection Detection for Email Agents Through Attack Chain Modeling

Ahmad Hashmi, Dhyey Patel and Yunting Yin

Large language model email assistants are particularly vulnerable to indirect prompt injection because untrusted email content can be retrieved into the model context and influence subsequent tool use. Existing prompt injection detectors mainly formulate this problem as binary malicious text classification, which overlooks the important factor that harmful agent behavior often arises through a sequence of stages. We propose a detection framework that models this attack chain by combining a text detector, verifiers specific to each stage, explicit rule-based risk signals, user intent and action consistency analysis, and a logistic decision policy. To support this framework, we derive attack chain labels from prompt injection datasets, evaluate the proposed framework under random splits, temporal phase transfer, conditional stage transfer, cross-dataset transfer, and conduct ablation studies on multiple benchmarks. Results show that random train test splits substantially overestimate robustness under distribution shift, while later tool argument stages are more predictable than earlier stages in the framework. We also show that training on harmless emails that resemble attacks helps reduce false alarms while preserving the ability to detect real attacks. Across five binary benchmarks, our framework achieves a mean F1 score of 0.406 under the strict threshold setting policy, compared with 0.216 for the strongest of five pretrained detectors evaluated without additional training. These results highlight the value of combining attack stage predictions with checks for conflicts between the user's request and instructions in retrieved emails. Our experiments also demonstrate the importance of training with challenging benign examples to balance attack detection and false alarms.
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Information Retrieval

Component Benchmark: Hierarchical Model Profiling for Large-scale Recommendation Systems

Dharak Kharod, Yuzhen Huang, Zhou Wang et al. (+11 more)

Large-scale recommendation models pose distinct, under-explored profiling challenges. Most recommendation model architectures are structurally heterogeneous, intermixing memory-bandwidth-bound operations, small compute-bound dense layers, dynamic shapes from jagged categorical features, and low-arithmetic-intensity operations. Recommendation models evolve rapidly as modeling engineers experiment with compositions, often written without visibility into hardware execution characteristics. Standard profiling tools offer either end-to-end throughput or operator-level traces, but cannot attribute performance to the submodules that practitioners reason about. We present Component Benchmark (CB), a profiling system that independently characterizes each submodule performance in a hierarchical manner, providing a tree-structured, interactive visualization that brings performance clarity to ML practitioners. At its core, CB provides a simple yet extensible, submodule-based benchmarking framework with a plugin architecture that enables hierarchical performance analysis. These large-scale recommendation models are TB-scale, run on thousands of GPUs and ingest 100B examples per day. We demonstrate CB's effectiveness on common open sourced models and discuss how CB has been leveraged to accelerate modern recommendation model performance analysis and optimization.
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All authors Dharak Kharod, Yuzhen Huang, Zhou Wang, Jackie Xu, Fuzail Khan, Jacky Zhou, Hao Yan, Lidong Zhao, Xizhou Feng, Yvonne Liu, Karthik Jayaraman, Praveen Ramachandran, Vishwa Karia, Yashasvi Makin

Systems and Control

Certificate-Carrying Distributed Model Predictive Control on Product Manifolds with $\mathrm{SO}(3)$

Shengjun Zhang, Tingyi Liu, Lei Xu et al. (+1 more)

This paper studies constraint certification in synchronous distributed model predictive control (DMPC) when neighboring predictions change between sampling instants. Before the parallel local solves, each agent communicates a shifted prediction and an announced update budget. A hard trajectory trust region makes that budget enforceable, while an edge-wise feasibility cap computed from the shifted packets keeps the fallback feasible without using any current optimizer output. Distance and relative-attitude constraints are tightened with explicit Lipschitz constants and two budget layers: one accounts for the simultaneous neighbor update and the other retains a checkable shift reserve. We prove hard pairwise constraint satisfaction and recursive feasibility under stated nominal-execution and terminal assumptions, give the additional residual caused by execution error, and derive a local practical value-decrease bound. A spacecraft formation example uses hard terminal and pairwise constraints, a geodesic relative- attitude constraint on $\SO$, and reproducible terminal-set checks. Comparisons with fixed, trajectory-only, and windowed online margins show that the proposed budget reduces conservatism while preserving a positive shifted-feasibility margin.
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All authors Shengjun Zhang, Tingyi Liu, Lei Xu, Tao Yang

Astrophysics of Galaxies

A Cyanopolyyne-rich but COM-poor Massive Protostar: The First Hot Carbon Chain Chemistry Source G28.28-0.36

Kotomi Taniguchi, Masao Saito, Prasanta Gorai et al. (+6 more)

We present molecular emission line data from the massive young stellar object (MYSO) G28.28-0.36 (G28.28) obtained with the Atacama Large Millimeter/submillimeter Array Band 3. Cyanopolyynes (HC$_3$N and HC$_5$N) and three complex organic molecules (COMs; CH$_3$OH, CH$_3$CN, and CH$_3$CHO) are detected from the MYSO G28.28. In addition, strong emission regions of cyanopolyynes are identified between G28.28 and a nearby ultracompact H II region. The HC$_5$N emission is coincident with the dust continuum peak, where an excitation temperature of 100 K is derived from CH$_3$CN. These results suggest that the Hot Carbon Chain Chemistry (HCCC) mechanism produces cyanopolyynes in the hot region around G28.28. We find that G28.28 exhibits a unique chemical feature: cyanopolyynes are abundant, but COMs are deficient, unlike the other MYSOs studied previously. These results imply that G28.28 is a counterpart of the Warm Carbon Chain Chemistry (WCCC) low-mass source L1527. G28.28 is the first HCCC source identified so far.
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All authors Kotomi Taniguchi, Masao Saito, Prasanta Gorai, Olli Sipilä, Kazuhito Dobashi, Paola Caselli, Tirupati Kumara Sridharan, Tomomi Shimoikura, Jonathan C. Tan

Information Theory

3GPP-Compatible Long-Range Sensing for LEO-ISAC: A Window-Grid Processing Framework

Yi Geng, Xun Fan, Chenfeng Xu et al. (+1 more)

This paper addresses long-range sensing in bistatic low-Earth-orbit integrated sensing and communication (LEO-ISAC). Conventional OFDM sensing fails in LEO-ISAC because millisecond-scale propagation delays destroy the transmitter–receiver symbol alignment and, with multiple targets, make the receive window longer than the transmitted block. We propose a window-grid (WG) processing framework that exploits the known beam-intersection swath to resolve both problems purely at the receiver, leaving the 3GPP symbol structure unmodified: the swath delay span is folded into cyclic-prefix-sized slices, each handled by one WG. With 103.2 MHz bandwidth at bistatic ranges beyond 640 km, simulations demonstrate meter-level ranging of two targets, and 1000 Monte-Carlo trials over random target–satellite geometries show that, with an ephemeris-based satellite-selection rule, every target is detected with a 90th-percentile range error of 2.4 m.
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All authors Yi Geng, Xun Fan, Chenfeng Xu, Yu Zhao

Computation and Language

Recursive Self-Improvement via On-Policy Distillation for Reasoning

Shangjian Yin, Zehao Zhao, Kavosh Asadi et al. (+7 more)

On-policy distillation (OPD) trains a student model by having it generate trajectories, then matching its next-token predictions with an external teacher's next-token predictions. This provides dense, token-level supervision to the student. On-policy self-distillation (OPSD) eliminates the need for the external teacher. Specifically, a second frozen copy of the student model, now given the ground truth in its context, serves as the teacher. The student model only receives the problem and learns to mimic the privileged teacher model, while the teacher remains frozen throughout training. Previous work showed that freezing the teacher is useful for training stability, but we argue that this can prevent the teacher from incorporating the improvements learned by the student during training. Our primary contribution is to address this limitation with a recursive framework built around two complementary components. First, we let the privileged teacher co-evolve with the student so that revision learned in one round can guide the next, a process we refer to as Dynamic Co-Evolution (DCE). Second, because stronger revision can also make responses too verbose and self-critical, we additionally train on shorter, verified rewrites of the model's own on-policy responses. We call this complementary objective Self-Refined Concise Learning (SRCL). Overall, our comprehensive evaluations show that DCE+SRCL outperforms OPSD across multiple model scales and four competition-level mathematics benchmarks. Specifically, on Qwen3-8B, DCE+SRCL reaches 65.97% Average@12, outperforming OPSD by 35.62 percentage points while reducing mean output length by 7.80% relative to DCE alone.
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All authors Shangjian Yin, Zehao Zhao, Kavosh Asadi, Rui Liu, Yuchen Lu, Shike Mei, Hang Cui, Luke Simon, Zhouxing Shi, Hamed Firooz

Programming Languages

Verification of Compiler-to-Accelerator Mappings for Machine Learning Accelerators

Akash Gaonkar, Mike He, Yi Li et al. (+8 more)

To meet the performance needs of modern machine learning (ML) applications, ML compiler frameworks support compiler-to-accelerator mappings that offload parts of application code to operations in specialized hardware accelerators. However, most of these frameworks do not verify these mappings down to the hardware level, potentially resulting in functional mismatches. In this paper we propose BOLT, the first framework for formally verifying the correctness of compiler-to-accelerator mappings for coarse-grained intrinsics in ML accelerators, with respect to a formal hardware semantics. BOLT does not require additional information from the compiler, and verifies the functional equivalence of the application code and the code for the mapped hardware accelerator intrinsic, including handling of complex loop nests and tensor data layouts in hardware. It effectively utilizes a pattern of *aligning* software loops with the hardware, followed by *relating* corresponding data layouts, to enable verification using well-aligned product programs. To support these steps, we propose two custom templates — the sync-skeleton and the layout-sketch — to guide users in aligning loops and specifying data layout relationships, respectively. We have developed a proof-of-concept prototype for BOLT and use it to successfully verify the correctness of several complex mappings for two recent open-source ML accelerators.
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All authors Akash Gaonkar, Mike He, Yi Li, Bo-Yuan Huang, Andrew Cheung, Vishal Canumalla, Gus Henry Smith, Zachary Tatlock, Grigory Fedyukovich, Sharad Malik, Aarti Gupta