Machine Learning
Stability-Plasticity Balance via Singular-Vector Selection in LLM Continual Learning
Lingxiang Wang, Hainan Zhang, Liang Pang et al. (+2 more)
Domain-specific continual adaptation of LLMs risks catastrophic forgetting, creating a fundamental tension between acquiring new capabilities and preserving those learned during pretraining. PEFT mitigates this problem by restricting the number of trainable parameters, but existing methods lack a principled unit for deciding where plasticity should be allocated and stability should be preserved. We identify the singular-vector channel as a natural unit for managing this trade-off. Each channel represents an input-output transformation, which can be updated to acquire new knowledge or fixed to preserve pretrained capabilities. Based on this perspective, we introduce SVC, a parameter-efficient continual-learning method that selectively updates Singular-Vector Channels. Before fine-tuning, SVC uses domain-specific data to estimate each channel's adaptation benefit and a fixed public general-domain corpus only as a history activation proxy for estimating forgetting cost. It then adaptively selects trainable channels based on these scores via knee-based cost screening, Pareto-front filtering, and Otsu thresholding. Experimental results across four LLM families and eight downstream tasks show that SVC better preserves pretrained capabilities while achieving strong downstream performance relative to existing PEFT baselines. Further analysis of channel scoring and selection demonstrates that selective plasticity at the singular-vector-channel level enables effective continual LLM adaptation.
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All authors Lingxiang Wang, Hainan Zhang, Liang Pang, Hongwei Zheng, Zhiming Zheng
Number Theory
A combinatorial proof of the quadratic Gauss sum
Adan Medrano Martin del Campo
We provide an elementary approach to computing the quadratic Gauss sum, emphasizing the method employed to compute the sum corresponding to multiples of 4. The proof method employed does not rely on the law of quadratic reciprocity, but only on exploiting
symmetries among the sum's components, together with a recursive approach.
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Machine Learning
Optimally Pacing Budget Spending and Learning
Mark Braverman, Jingyi Liu, Jieming Mao et al. (+2 more)
We establish near-optimal regret bounds for budget-constrained online learning against arbitrary classes of budget-pacing experts in the
adversarial setting. In particular, given any class of $F$ experts and a candidate budget pacing schedule, we provide a full-information
algorithm which obtains regret $O(D \sqrt{\log F}+ \sqrt{T\log F})$ against all experts whose cumulative spending stays within distance $D$ of this schedule, matching lower bounds established by Braverman et al. (2025). We additionally show that our technique extends to various problems in online resource allocation, where the learner gets to see the rewards and costs of the current options available to them, and establish $O(D\sqrt{\log F})$ regret bounds when fractional allocation is allowed. This is the first
algorithm we are aware of which can achieve $o(\sqrt{T})$ guarantees for such tasks.
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All authors Mark Braverman, Jingyi Liu, Jieming Mao, Jon Schneider, Eric Xue
Software Engineering
IRONPROOF: COBOL-to-Python Transpilation with SMT-Based Equivalence Checking
Dominik Blain
Translating COBOL to a modern
language can change what a program computes, and LLM translations carry no guarantee of equivalence. We present IRONPROOF, which parses COBOL into an intermediate representation, generates Python, encodes both as Z3 formulas over shared inputs, and emits either a machine-checkable equivalence certificate (UNSAT) or a counterexample (SAT). On 2,345 COBOL files (GnuCOBOL tests, NIST CCVS85, open-source collections, and programs we generated or wrote), 782 enter the checking path: 606 (77.5%) are proved equivalent, 101 are partially verified, none is refuted, and 75 fail inside our pipeline and stay in the denominator. On independently authored programs the rate is 52.6% (153 of 291), against 92.3% on programs we wrote. Of the 153 independent proofs, 37 cover a single execution of a program that reads input the encoder does not model, and across all 606 proofs only 14 quantify over an input that a proved output depends on. On two public business-application corpora (AWS CardDemo and IBM GenApp), the encoder models no program end to end. An April 2026 LLM-only baseline failed on 54 of 94 independently authored programs, counting translations our encoder could not verify. PIC-bounded overflow detection flags an out-of-range output in 22.1% of the programs it can analyze, an upper bound. An earlier confrontation with GnuCOBOL 3.2.0 found 24 of 49 executable independent proofs disagreeing with the runtime on a variable in the proof's domain. A proof establishes that the generated Python computes what our intermediate representation says the COBOL computes, not equivalence to a COBOL implementation.
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Robotics
Haoyu Xi, Siwei Cheng, Xiangyuan Liu et al. (+2 more)
Autonomous
navigation in cluttered and constrained environments typically assumes a fixed environment and searches only for paths within existing free space. However, a route can be blocked by an articulated structure, a movable object, or a pedestrian, and reaching the goal may therefore require appropriate
embodied interaction with the environment. This paper formulates Path-Creative
Navigation (PCN), a
navigation paradigm in which the
robot recovers free space by coordinating locomotion and
embodied interaction, and addresses one class of PCN tasks with a mapless framework. The
vision-
LiDAR-odometry framework integrates local observations, obstacle geometry, and
robot-state estimates through a unified
navigation system, providing stable semantic and
geometric information for
navigation and interaction. The traversability-aware decision method utilizes visual and
LiDAR distance information to determine whether a blockage is actionable and whether it can be safely bypassed, enabling the
robot to interact only when necessary while supporting articulated structure pushing, movable object pushing, obstacle avoidance, and pedestrian requests. We design simulation scenarios and evaluate different methods in both simulation and two real-world tasks that cannot be completed by conventional
navigation alone without
embodied interaction. These results demonstrate that our framework achieves higher task completion than the baseline methods by coordinating
navigation and interaction in cluttered and constrained environments.
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All authors Haoyu Xi, Siwei Cheng, Xiangyuan Liu, Brenda Li, Wei Zhang
Quantum Physics
Analog quantum simulation of $\phi^4$ field theory with a superconducting transmission line
Ilan T. Rosen, Neill C. Warrington, Max Hays et al. (+4 more)
Understanding the dynamics of interacting
quantum fields remains a fundamental challenge. We propose a superconducting transmission line for analog
quantum simulation of $(1+1)$-dimensional $\phi^4$ field theory. The transmission line comprises fluxonium-like
circuit elements whose continuous and unbounded phase variables encode a scalar field without
Hilbert-space truncation. Their anharmonic potentials provide strong interactions. Tuning the
circuit parameters provides access to two distinct regimes. In the first, the transmission line emulates $\phi^4$ field theory with a single-well potential. We confirm this correspondence through
lattice Monte Carlo calculations of the low-energy spectra of both the
circuit and
lattice $\phi^4$ theory. This regime enables scattering experiments between counter-propagating particle wave packets. The second parameter set yields a double-well potential that emulates $\phi^4$ theory in the
symmetry-broken phase and hosts degenerate
vacua. Interfaces between the two
vacua form topological kinks, and the transmission line can simulate kink-antikink collisions. We present state preparation and measurement protocols for both collision experiments, enabling spatially resolved, real-time studies of particle and
soliton scattering in an interacting
quantum field theory.
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All authors Ilan T. Rosen, Neill C. Warrington, Max Hays, Christopher McNally, Joshua Lin, Stephen Sorokanich III, Julian Bender
Computer Vision
No Distillation Needed: Single-Pass Real-Time Talking Heads via Acausal Noise Shaping
Yu Han, Dejan Markovic, Alexander Richard et al. (+4 more)
Audio-driven facial animation underpins real-time avatars, telepresence, and
embodied virtual
agents. And it must run online: each frame emitted from audio observed up to the current time, at interactive rates. Recent progress is dominated by
diffusion models, which need many network evaluations per sample and are therefore a poor fit for streaming. We argue the cost is unnecessary in this domain. Audio-conditioned facial motion occupies a comparatively low-dimensional
manifold, a regime where a single-pass GAN suffices. The obstacle is not capacity but
stochastic structure. We show that a causal, time-invariant generator driven by i.i.d. noise cannot suppress its output spectrum over a band without collapsing its per-step innovation. We proposed FaceGAN, which dissolved the limitation by shaping the noise pathway acausally. Because the driving noise is synthetic, its future can be sampled now, so the audio-to-expression path stays causal, and the model supports fully causal operation. FaceGAN emits expression and head pose in a single forward pass per frame and matches or outperforms state-of-art approaches in generation quality. Being feed-forward with bounded
attention windows, it generates indefinitely without drift.
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All authors Yu Han, Dejan Markovic, Alexander Richard, Wojciech Zielonka, Akshay Venkatesh, Cheng-hsin Wuu, Michael Zollhoefer
Computation and Language
Clinician use of language models diverges from how the models are evaluated
Krithik Vishwanath, Haitong Lin, Anton Alyakin et al. (+19 more)
Large
language model (LLM) assistants are being deployed to clinicians across health systems, and judgments about their readiness rest largely on
benchmark scores, most of them derived from examination questions or curated cases. A
benchmark predicts performance in deployment only to the extent that its items resemble real use, yet whether
benchmarks reflect the work these systems receive has rarely been measured. Here we analyze 127,833 queries sent by 6,342 physicians, advanced practice providers and nurses in 35 specialties to an institutional assistant during an eight-month roll-out. We characterize each query with RCQ-Map, a clinician-validated framework grounded in taxonomies of clinical questions and of LLM evaluation, which records its task, intent, answerability, missing information and potential harm. Documentation and administration (36.2%) and knowledge
retrieval (28.9%) made up nearly two-thirds of use, and diagnosis 3.7%; more than a third of queries could not be answered well as posed. Applying RCQ-Map to 58 public
benchmarks drawn from major evaluation suites and frontier model reports, which we assemble into the Clinical AI
Benchmark Atlas, showed that the median
benchmark contained no documentation requests and shared 31% of the task mix of real use, less than an even spread across task categories would.
Benchmarks in suites designed to resemble clinical practice were individually no closer to real use than those used in frontier model reports.
Benchmark scores therefore say little about how clinical AI performs on most of the work it is actually given, and evaluation should be matched to real clinical use.
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All authors Krithik Vishwanath, Haitong Lin, Anton Alyakin, Jin Vivian Lee, D. Brock Hewitt, Jie J. Yao, William Robert Small, Hammad A. Khan, Cordelia Orillac, Aakaash Varma, Brandon Ye, Daniel Alexander Alber, Gustavo Stolovitzky, Batia Wiesenfeld, Oded Nov, Wei Wu, Kang Zhang, Yindalon Aphinyanaphongs, Tim Requarth, Eric Karl Oermann, The International Digital Twin Consortium in Healthcare, Medicine
Statistical Mechanics
High-resolution mapping of the phase boundary of the honeycomb-lattice Blume–Capel ferromagnet
Eluiz C.M. Filho and Claudio J. DaSilva
We present a high-resolution numerical study of the
spin-1 Blume-Capel ferromagnet on the honeycomb
lattice ($z=3$). Using the Wang-Landau algorithm to estimate the joint density of states $\Omega(E_1,E_2)$ and field-mixing scaling, we map the first-order transition line and locate the tricritical point at $(\Delta_t,T_t)=[1.4820(2),0.4022(7)]$. Independent Metropolis histogram reweighting for $L=36$ and $48$ yields a crossing temperature near $0.4039$, consistent with the Wang-Landau extrapolation. The field-mixing parameter is $r=-1.585(19)$, while the coexistence-line slope gives $r=-1.587(5)$. Normalizing by the zero-temperature field $\Delta_0=zJ/2$, the results for honeycomb, square, and triangular
lattices give $r/\Delta_0$ between $-1.057$ and $-1.067$, about 6% larger in magnitude than the mean-field value. Simple-cubic estimates are compatible with this range but do not resolve dimensionality dependence. Finite-size scaling yields $y_t=1.795(7)$, consistent with the tricritical Ising value $9/5$, while the fourth-order cumulant scaling agrees with $y_g=4/5$. Deep in the first-order regime, the cumulant approaches the two-phase limit $U_Q\to2/3$. Multicanonical simulations up to $L=64$ yield an interface tension exponent $\mu=1.265(26)$, consistent with the tricritical prediction $(d-1)/y_g=5/4$. We also map the continuous phase boundary, obtaining $T_c(\Delta=0)=1.157$, and identify crossover effects from Ising to tricritical scaling near the tricritical point.
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Computer Vision
Diffusion Meta-Prompting and Steering for Generalizable Foundation Model Adaptation
Deepak Sridhar, Yi Li, Kartikeya Bhardwaj et al. (+7 more)
Prompt learning is a popular method for adapting foundation models, but learned
prompts are typically task-specific and fail to generalize to new classes, domains, or compositions of tasks. In this paper, we introduce a
Diffusion Meta-
Prompt (DMP) model , a framework that models the distribution of learned
prompts using
diffusion models. Given a repository of previously learned
prompts, DMP is trained and sampled without access to the original task examples or task losses, and synthesizes new
prompts conditioned on natural
language task descriptions. To improve the sampling stability, we introduce a test-time steering strategy for DMP, which uses the best training-selected
prompt in the repository as a latent anchor during
diffusion sampling, without retraining the DMP or accessing test classes. DMP improves generalization across classification,
retrieval and text-to-image generation tasks, supports concept composition and negative prompting without explicit training. It reduces storage and inference costs by over 90% compared to
prompt retrieval methods. For composite classification, DMP achieves upto 2.0% average gain over prior meta-learning methods across 55 pairs of
datasets with gains as high as 8.5% on specific pairs such as Eurosat and Flowers. DMP also enhances cross-task generalization with ~2-9% improvement for hierarchical classification task. We further provide a theoretical guarantee bounding the expected task loss of
prompts sampled from a DMP. Code is available: https://github.com/DeepakSridhar/dmp
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All authors Deepak Sridhar, Yi Li, Kartikeya Bhardwaj, Shuangjun Liu, Taotao Jing, Yuan Li, Shuai Zhang, Jiancheng Lyu, Dashan Gao, Nuno Vasconcelos
Functional Analysis
A Counterexample to Two Compactness Conjectures of Brudnyi
Jinghao Huang and Ran Xu
We construct a quasi-
Banach function
lattice $X$ on $\mathbb R$ whose quasi-norm is order continuous and invariant under every translation. Nevertheless, $X$ contains a bounded sequence with common compact support which is equicontinuous in $X$ and has no norm-convergent subsequence. This provides a counterexample to
Conjectures 2.5 and 2.11 proposed by Brudnyi in \cite{Brudnyi2015}.
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Machine Learning
CityDeploy-Bench: Benchmarking Physics-Grounded Spatial Set Planning for Multi-Transmitter Network Deployment
Chenyang Yuan and Xiaoyuan Cheng
Automating city-scale wireless deployment remains challenging under complex urban propagation and network-wide interference. We introduce CityDeploy-Bench, a
benchmark that reframes multi-transmitter deployment as physics-grounded spatial set planning under a unified ray-tracing verifier. The
benchmark separates utility representation from planning dynamics, enabling controlled comparison between direct scalar rewards, relational models, and higher-order interaction structures across diverse planners. Our experiments reveal a clear transition in planning behavior as physical coupling grows. Deployment quality becomes increasingly dependent on whether the learned utility captures collective transmitter interactions, whereas stronger search alone cannot compensate for missing relational structure. This establishes multi-transmitter deployment as a coordination problem over physically interacting sets rather than a collection of independent spatial decisions. We release CityDeploy-Data and the
benchmark framework as a reproducible testbed for research linking decision learning with physically grounded wireless network design.
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Machine Learning
Measuring and Mitigating Solution Mode Collapse in RLVR
Liv G. d'Aliberti, Marwa Abdulhai, Sofiia Druchyna et al. (+2 more)
A
language model (LM) can usually answer the same question in more than one way, but reinforcement learning with verifiable rewards (RLVR) is indifferent to which correct answer a model produces. A solution will earn the same reward whether it is the thousandth copy of a familiar answer or one the model has never produced before. Yet, there is potential value in having the model retain multiple correct solutions as it is trained. For instance, multiple modes may give users a choice and provide problem-solving strategies that improve overall model performance. Here, we introduce ModeBench, a
benchmark of multi-solution tasks in which the verifier returns both correctness and mode discovered. We then use ModeBench to measure how solution diversity changes under RLVR post-training. We find that RLVR post-training concentrates probability onto fewer correct modes even as accuracy holds or improves, and moreover, that frontier models are already highly concentrated. We then introduce our solution, Re:Max, which stores one verified example per discovered mode in a replay buffer and trains on those stored modes uniformly. A solution found once is, therefore, practiced as often as one found repeatedly. Across three model scales, two RL objectives, and harder task constructions, replay improves both how often a policy succeeds and how many different ways it can succeed.
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All authors Liv G. d'Aliberti, Marwa Abdulhai, Sofiia Druchyna, Peter Henderson, Manoel Horta Ribeiro
Machine Learning
Emergent Inverse-Depth Scaling From Nonlinearity In Attention
Zirui Peng, Yizhou Liu, Ziming Liu et al. (+1 more)
Scaling laws describe power-law improvements in model performance with
dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-
attention models, this scaling is tied to a power-law data spectrum: unable to selectively attend to relevant
tokens, these models learn according to global spectral strength, with stronger directions learned before weaker ones. Large
language models, however, can be strongly nonlinear. Here, we show that nonlinear
attention yields inverse-depth decay of loss across all tested data spectra. Nonlinearity enables
attention to focus selectively on relevant
tokens, allowing strong and weak spectral directions to be learned in parallel. Similar focusing across layers motivates a connection to the central limit
theorem: shared error across layers sets the loss plateau, while aggregation turns layer-specific differences into continued gains with depth. Our findings suggest that depth scaling may arise from nonlinearity in
attention, which allows large
language models to focus locally and may make the global covariance structure less relevant.
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All authors Zirui Peng, Yizhou Liu, Ziming Liu, Jeff Gore
Materials Science
Bond-Switching Reconstruction in Bare Ti3C2 MXene
Kui Lin
MXene properties are typically tuned through composition, surface termination, and intercalation, while the metal-carbon framework
topology is considered fixed. Here, we demonstrate that this framework can reconstruct. Unconstrained relaxations of biaxially strained bare Ti3C2 yield a dynamically stable polymorph, N, featuring a 15-atom primitive
cell, six distinct Ti-C bond classes, and 2.55 Å Ti-Ti pairs. The coherent transformation pathway crosses an 8.47 eV barrier per
cell but first reaches another reconstructed minimum, N', lying 1.08 eV below N, revealing a family of bond-switched networks. Phase N lies 7.58 eV per
cell above the parent. Reverse barriers along the calculated pathway are 1.50 and 1.98 eV per
cell for N and N', respectively. Reconstruction quenches the parent
spin polarization, yielding a nonmagnetic metal with a nearly fourfold increase in
Fermi-level density of states. Bader and electron-localization analyses suggest charge redistribution from C toward Ti associated with Ti-Ti pairing. In multilayers, reconstructed layers form interlayer Ti-C bonds. A 10% biaxial tension halves the phase-energy difference, and pressure reverses phase ordering near 85 GPa. These results establish bond-switching reconstruction as a mechanically controllable structural degree of freedom in MXenes.
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Plasma Physics
Beam filamentation instability drives deuterium-tritium fusion with polarized neutron emission
Guanqi Qiu, Deji Liu, Dongchi Cai et al. (+3 more)
Filamentation instabilities are generally regarded as detrimental to fast-electron transport in fusion
plasmas because they increase beam divergence and redistribute deposited energy. Here, we use two-dimensional particle-in-
cell simulations coupled to a
spin-dependent deuterium-tritium fusion module to investigate whether filamentation can instead transfer energy from counterstreaming electrons to prepolarized fusion ions. The simulations show that
magnetic filaments, together with longitudinal inductive and transverse charge-separation electric fields, accelerate initially stationary deuterons and tritons to energies at which fusion reactions occur. Over the parameter range examined, the calculated
neutron yield increases with the saturated
magnetic-field energy. The model further predicts anisotropic,
spin-resolved
neutron emission. The direction of maximum
neutron polarization is approximately perpendicular to the dominant deuterium-tritium collision direction and evolves with the angular distribution of the reacting ions. These results suggest that beam filamentation can couple relativistic-electron energy to fusion ions and that polarized
neutron emission may provide a reaction-weighted signature of the underlying
plasma dynamics.
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All authors Guanqi Qiu, Deji Liu, Dongchi Cai, Ronghao Hu, Zheng Gong, Xueqing Yan
Computer Vision
AffordDrive3D: Affordance-Aware World-Action Modeling with Spatial Understanding
Tianhui Cai, Xinglong Sun, Chao Fang et al. (+6 more)
World-action models have recently improved autonomous driving by jointly learning future scene prediction and trajectory generation. Most existing approaches model the future primarily through RGB appearance, and recent works have begun to incorporate
geometric prediction to improve spatial understanding. However, dense geometry describes the spatial layout of the entire scene without indicating which parts are most relevant to the ego vehicle's action. For driving, the model must also identify and anticipate where it can safely move and which regions may pose collision risks. Jointly modeling action-relevant regions and future geometry can provide the policy with both driving-relevant cues and their corresponding spatial structure. We therefore propose AffordDrive3D, an affordance- and geometry-aware world-action model that jointly learns future action-relevant regions and spatial structure. In order to capture the scene semantics and driving context needed for driving affordance prediction, we build AffordDrive3D on a VLM backbone to forecast drivable areas and collision-critical regions that directly affect ego motion, while predicting future geometry from RGB world-model latents. On NAVSIM, AffordDrive3D achieves state-of-the-art performance with 91.3 PDMS and 89.9 EPDMS, demonstrating the effectiveness of jointly modeling future affordances and geometry for trajectory planning. Project Page: https://afforddrive3d.github.io/
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All authors Tianhui Cai, Xinglong Sun, Chao Fang, Zhenxin Li, Rui Song, Jose M. Alvarez, Yunxiang Mao, Jiaqi Ma, Langechuan Liu
Systems and Control
A Latent Space Optimization Approach for Symbolic Discovery of Dynamical Models
Tongjia Liu and Ilias Mitrai
In this paper, we propose a hybrid latent-space
Bayesian Optimization (BO) and global optimization framework for solving symbolic regression tasks to discover dynamical models from data. Symbolic regression can discover equations from data without fixing the functional form of the expression a priori. The proposed framework uses the fact that if the functional form of the expression is fixed, the symbolic regression task reduces to a parameter estimation problem, which must be solved to global optimality. Motivated by this structure, first, we train a VAE to map the discrete space of expression trees into a continuous latent space. Then, we use BO to search this latent space while assessing a candidate expression's prediction error by solving the parameter estimation problem to global optimality. We evaluate our framework across two case studies: static reaction rate law discovery and dynamic concentration identification in a continuous stirred-tank reactor (CSTR). The results show that our framework identifies the true governing equations faster than MINLP formulations without solver timeouts and achieves higher sample efficiency than evolutionary baselines under tight evaluation budgets.
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Computer Vision
Refine Connections, Close the Gap: A Reliable Enhancement Framework for Driving Scene Topology
Xiaoqi Wang, Dingyi Zhuang, David Paz et al. (+6 more)
In autonomous driving, understanding scene
topology - the connectivity between lanes and traffic elements - is critical for safe path planning and motion control. While current methods excel at detecting individual map elements, their connectivity
reasoning often falls short of its theoretical potential, leaving a significant performance gap relative to the theoretical upper-bound achievable given the underlying detections. Furthermore, the decision-ready
topology graphs passed to downstream tasks often remain unreliable. Current approaches typically derive connectivity by thresholding continuous
topology scores; however, these scores often fail to reflect the true logical likelihood of connectivity, resulting in false positives or missing connections. Existing
benchmarks further overlook this issue by primarily evaluating continuous metrics, rather than assessing the discrete connectivity required for decision-making. To bridge these gaps, we propose TopoEnhance, a novel
topology enhancement framework designed to unlock the latent potential of existing methods and improve the reliability of decision-ready
topology. We formulate
topology enhancement as a denoising-based reconstruction process, where the model learns to recover structural consistency from stochastically corrupted ground-truth graphs. This formulation enables the model to resolve logical inconsistencies and rectify unreliable connections, producing robust discrete
topology graphs that closely approach theoretical maximum performance. Extensive experiments across different baselines show that TopoEnhance consistently improves both continuous
topology metrics (TOP score), and discrete connectivity measured by our adapted
Topology Jaccard Similarity (TJS) metric. As a flexible, source-agnostic framework, TopoEnhance delivers substantial gains across diverse state-of-the-art baselines without requiring retraining.
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All authors Xiaoqi Wang, Dingyi Zhuang, David Paz, Wenbin He, Yucai Bai, Peng Zhou, Rui Zhang, Jinhua Zhao, Liu Ren
Computer Vision
Learning What to Trust in Multimodal Learning under Noisy Supervision
Jiashuo Zou and Xiaobo Xia
Multimodal classification processes and relates information from multiple modalities to achieve more accurate predictions. However, existing methods typically rely on high-quality ground-truth labels, which are difficult to obtain in real-world scenarios. While sample-selection methods for learning with noisy labels aim to identify correctly labeled examples from noisy data, traditional methods primarily focus on unimodal settings and fail to exploit
multimodal information fully. This motivates us to build a more reliable noise detector in
multimodal learning. To this end, we theoretically analyze the relationship between representation structure and noise detection capability. Based on this analysis, we propose REFINE, which is a
multimodal label-noise detection framework that jointly uses fused and unimodal representations for label-noise detection. Specifically, REFINE constructs discriminative eigenvectors through discriminative analysis of the target and background classes and selects trusted representation spaces with better noise detection capability for each class. Within each trusted space, REFINE measures the
alignment between each instance representation and the discriminative eigenvectors. It then combines the subsets selected from these spaces. The combined set provides cleaner supervision for updating the
multimodal classifier, thereby reducing the influence of mislabeled examples during training and improving model generalization. Extensive experiments across diverse tasks demonstrate REFINE's superiority compared to baseline methods. The source code will be publicly available.
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Analysis of PDEs
Uniqueness and Symmetry Breaking for Singular $Q$-curvature Equations in $\R^n$
Haoyu Li, Tuoxin Li, Juncheng Wei et al. (+1 more)
For $n\ge3$ and $\gamma>-1$, we study normal solutions of \begin{equation*} (-\Delta)^{n/2}u=(n-1)!\,|x|^{n\gamma}e^{nu} \quad\hbox{in }\R^n. \end{equation*} We reformulate this problem on the cylinder via the Emden–Fowler transform. We first establish Kelvin
symmetry for normal solutions. We then prove existence and uniqueness, up to dilation, of the radial normal solution and establish its radial nondegeneracy. Next, we carry out a detailed spectral analysis of the linearized operator and construct branches of nonradial normal solutions by the Crandall–Rabinowitz
theorem. Finally, we prove that every normal solution is radial when $\gamma>0$ is sufficiently small.
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All authors Haoyu Li, Tuoxin Li, Juncheng Wei, Wen Yang
Operator Algebras
Banach non-isomorphism of type III and semifinite noncommutative $L_p$-spaces
Jinghao Huang and Fedor Sukochev
Let $M$ be a nonzero type III von Neumann
algebra with separable predual, and let $N$ be a semifinite von Neumann
algebra. We prove that $M_*$ is not isomorphic to a subspace of $N_*$. For $1<p<\infty$, $p\ne2$, we prove that $L_p(M)$ is not isomorphic to a complemented subspace of $L_p(N)$. In particular, the
Banach isomorphism class of $L_p(M)$ distinguishes type III
algebras from semifinite
algebras for $1\le p<\infty$, $p\ne2$.
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Robotics
A Reconfigurable Fabric Based Pneumatic Actuator with Button Fastened Constraint Modules for Multi Mode Actuation
Kentaro Kimura, Hiroki Ishizuka, Yusuke Sakaue et al. (+2 more)
Soft pneumatic actuators are widely used in soft robotics. However, their actuation modes are typically fixed by internal chamber designs or reinforcements, making post fabrication reconfiguration difficult. This paper presents a reconfigurable fabric-based pneumatic actuator that enables rapid, tool free, and reusable switching among multiple actuation modes by attaching constraint fabric modules to a buttoned textile sleeve. By rearranging low-stretch constraint parts on a single actuator body, the proposed system realizes four actuation modes isotropic expansion, contraction, bending, and twisting without redesigning or disassembling the actuator.We further introduce an attachable capacitive fabric-based tactile sensor module that can be mounted at arbitrary locations on the actuator surface for task dependent contact sensing. Experiments demonstrated an elongation ratio of 1.2, a maximum bending angle of approximately 60 degrees, and a twisting angle of approximately 90 degrees at 24 kPa, while achieving blocking forces exceeding 10 N across all modes. The tactile sensor exhibited a monotonic, force-dependent increase in capacitance with low hysteresis (approximately 12%) and stable cyclic responses under preload. Finally, we constructed soft robotic arms composed of multiple actuators and demonstrated in situ motion reconfiguration for grasping by changing the attached constraint patterns. These results indicate that the proposed modular constraint and sensing framework improves the functional adaptability of fabric-based soft
robots while preserving a simple, robust actuator structure.
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All authors Kentaro Kimura, Hiroki Ishizuka, Yusuke Sakaue, Sei Ikeda, Osamu Oshiro
Other Condensed Matter
Three-dimensional dopant distribution from a single, out-of-focus spectroscopic image
Michael Deimetry, Timothy Petersen, Matthew Weyland et al. (+1 more)
Increasing miniaturization of nanoscale devices makes determining the three-dimensional distribution of dopants increasingly important. In out-of-focus spectroscopic scanning transmission electron microscopy images, we show that dopant atoms appear as disks with radii relating to dopant depth, allowing the three-dimensional distribution of dopants to be determined from simple
geometric analysis of a single out-of-focus image. Through numerical experiments on Si-doped
graphene we validate statistical detection and
Bayesian inference methods to quantify confidence and uncertainties while making the analysis more robust at lower dose. We present proof-of-concept experimental data from an Fe-doped spinel, retrieving dopant depth to within around 2 nanometres.
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All authors Michael Deimetry, Timothy Petersen, Matthew Weyland, Scott Findlay
General Relativity and Quantum Cosmology
Accounting for detector calibration uncertainty in black-hole ringdown analysis
Rowina S. Nathan, Shingo Hido, Neil Lu et al. (+3 more)
Detector calibration systematics can bias measurements of a remnant black hole's mass and
spin, producing spurious evidence against general relativity if unaccounted for. The ringdown phase in the gravitational-wave signal produced by a binary black-hole merger encodes the remnant properties: at sufficiently late times, the signal is well described by a superposition of quasinormal modes, each with a frequency and damping time set only by the remnant mass and
spin. Here we present two complementary approaches for analyzing the ringdown portion of the data to estimate the remnant mass and
spin in the presence of a nonnegligible detector calibration error, using the quasinormal-mode rational filter (QNMRF). With a well-measured error, we apply the best-estimated calibration correction to the strain before conducting the standard analysis; with an unknown error, we instead jointly sample the remnant mass,
spin and the frequency-dependent calibration error, marginalizing over an uncertainty prior. By injecting the numerical-relativity waveform SXS:BBH:0305 into colored detector noise, at a full-signal matched-filter signal-to-noise ratio of $\sim60$ and with simulated calibration errors of $\pm25\%$ in magnitude and $\pm25^\circ$ in phase, marginalizing over the calibration uncertainty recovers the true mass and
spin within the 90% credible interval, whereas the estimated values are biased if the calibration errors are ignored. We apply the method to GW250207, an event recorded while the Hanford detector response was not well characterized, and recover a remnant consistent with the inspiral-merger-ringdown prediction using the ringdown portion alone, both by correcting for a best-estimated calibration error and by marginalizing over a broad uncertainty prior.
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All authors Rowina S. Nathan, Shingo Hido, Neil Lu, Mallika R. Sinha, Sizheng Ma, Ling Sun
Game Theory
Optimal Multi-Item Auctions with I.I.D. Values
Boyu Liu, Zhengyang Liu and Zihe Wang
We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a
polynomial-time
algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate
algorithms under different parameter restrictions. Exact
polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a
polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these
algorithms satisfy DSIC and ex-post individual rationality.
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Artificial Intelligence
AgentHorizon: Evaluating Agentic Judges for Long-Horizon Computer-Use Tasks
Xing Han Lù, Dheeraj Vattikonda, Sina Hajimiri et al. (+7 more)
Computer-use
agents are capable of completing complex tasks, increasing the use of automatic judges to determine success, either for training or for evaluation without human involvement. Despite their flexibility, their reliability on long tasks spanning multiple applications remains unclear. A trajectory, composed of long sequences of screenshots and actions, may appear complete, but in reality violates constraints from the instruction or introduces an unwanted side effect. To identify these errors, a judge needs to examine the trajectory with respect to the user's instruction. To this end, we introduce AgentHorizon, a
benchmark of 1,373 computer-use tasks (instruction-trajectory pairs) drawn from 166 hours of human-recorded trajectories spanning three operating systems. By recording trajectories for closely related instructions, we can construct negative tasks by swapping the instructions. This paired design evaluates judges on their ability to distinguish a successful trajectory from one that completed a similar (but incompatible) request. We release the
benchmark under three splits: a frontier split, AgentHorizon (AH), a simplified split, AgentHorizon-Simple (AH-S), and a development split, AgentHorizon-Development (AH-D). We further evaluate eleven judges by (1) directly passing the full trajectory (with up to 300 screenshots and actions), and (2) using them as coding
agents across five
agent harnesses. We find that our best agentic judge, GPT-5.5, achieves 80.9% balanced accuracy on the AH subset. We find that tool-use improves certain models but results in worse performance for open-weight models, and that judges differ drastically in their ability to accept a valid trajectory and reject failed ones. Our findings highlight the need for judges that are capable of locating and verifying often hidden evidence that a task was properly completed inside long interaction histories.
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All authors Xing Han Lù, Dheeraj Vattikonda, Sina Hajimiri, Fatemeh Pesaran Zadeh, Parishad BehnamGhader, Ghazwa Darwiche, Amirhossein Kazemnejad, Christopher Pal, Alexandre Drouin, Siva Reddy
Computer Vision
SatFix: Absolute Visual Localization of UAVs in Satellite Maps from a Single Oblique Image
Jiarui Zeng, Kun Shi, Chiman Vong et al. (+1 more)
We study absolute metric
UAV localization within a provided geo-referenced satellite region, recovering continuous map position and viewing heading from a single oblique image or a short multi-view clip. Existing cross-view geo-localization methods retrieve the most similar satellite tile from a gallery and report Recall@K, but
retrieval depends on gallery sampling, provides no heading estimate, and returns a tile index rather than a continuous coordinate. We propose SatFix, a feed-forward
UAV–satellite localization framework built on VGGT-$\Omega$. Satellite-grid features act as queries that aggregate
UAV visual evidence, and two lightweight heads regress a 3-DoF pose in the satellite-map frame: continuous 2D position and heading. SatFix requires no explicit 3D map, rendered bird's-eye image, auxiliary sensor, or test-time pose
alignment. A single model supports both single- and multi-view inputs, with trajectory constraints used during multi-view training. For metric evaluation, we introduce University-Metric, where satellite imagery is re-collected over a region up to 10.7$\times$ longer on a side (about 114$\times$ the ground area) than the original University-1652 tiles, with continuous position and heading labels for the original
UAV tours. With one
UAV view, SatFix localizes 52.08% of test frames within 50 m and 17.34% within 10 m, with median position and heading errors of 45.66 m and $20.81^\circ$, respectively. Inference takes under 0.1 s per single-view query on an NVIDIA RTX 4090. With nine
UAV views, the median position error falls to 21.96 m and the median heading error to $8.73^\circ$. Compared with a fine-tuned VGGT-$\Omega$ baseline, SatFix reduces median position error by 34.0% and nine-view median heading error from $25.43^\circ$ to $8.73^\circ$.
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All authors Jiarui Zeng, Kun Shi, Chiman Vong, Zhedong Zheng
Classical Analysis and ODEs
Revisiting Positive Exponent power weighted Stein-Weiss inequalities in $L^1$
Wen Qi Zhang
We obtain the necessary and sufficient conditions on input functions for a family of positive exponent power weight $L^1$ Stein-Weiss inequalities. Earlier work by De Nápoli and Picon showed that a certain cocanceling condition was necessary and sufficient in $L^1$, but it was unknown if this condition remained necessary in the positive exponent power weight setting. This present article identifies weaker necessary conditions for positive exponent power weights, some of which were shown to be sufficient for positive, non-integer exponent power weights in the author's earlier work.
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Combinatorics
Almost all graphs are determined by their generalized spectrum
Ziqing Xiang
Haemers'
conjecture for the generalized spectrum asserts that almost all graphs are determined by their generalized spectrum, that is, for almost all graphs $G$, every graph with the same spectrum as $G$ whose complement has the same spectrum as the complement of $G$ is isomorphic to $G$. We prove this
conjecture by showing that the random graph $G(n,1/2)$ is determined by its generalized spectrum with probability tending to one. The proof combines a local theory of the denominators of the rational orthogonal
matrices that relate generalized cospectral graphs,
Fourier analysis of random symmetric
matrices over finite rings, Seidel switching, inverse Littlewood–Offord theory over finite fields, rank estimates for random symmetric
matrices modulo
primes, and a study of the rational factors of the characteristic
polynomial of a random symmetric $\pm1$
matrix with zero diagonal.
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