Differential Geometry
Parametrix Construction and Invertibility of $\Delta_g + 1$
Shih-Yu Chang
Given a
manifold $M$ with an asymptotically cylindrical end, we construct the parametrix for the shifted Laplace operator $\Delta_g + 1$ on the blown-up $b$-double space $M_b^2$. We will review the geometry of
manifold with a cylindrical end and construct the inverse directly via separation of variables, which motivates the parametrix construction. Next, we review the mapping properties and show how to get
elliptic regularity from the mapping properties of the parametrix. Through this explicit example, we hope this paper provides another reference for the theory of $b$-operators introduced by Melrose \cite{Mel93}.
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Machine Learning
PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media
Chunyang Wang, Mingrui Zhang, Yuyan Zhang et al. (+5 more)
Multiphase flow in porous microstructures is central to CO$_2$ storage, fuel-
cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear
evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D
datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native
lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB
dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.
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All authors Chunyang Wang, Mingrui Zhang, Yuyan Zhang, Linqi Zhu, Xin Ju, Edo Sicco Boek, Martin J. Blunt, Gege Wen
Optics
Visibility function and Stokes parameter analysis for non-ideal quarter-wave plates in a polarization contrast scheme
Stepan Kupavskii, Roman Malikov, Sergey Dyakov et al. (+6 more)
The match of the fourth power of the normalized third Stokes parameter for a single non-ideal quarter-wave plate (QWP) and the visibility function of the polarization contrast measured using a polarimetric setup with parallel polarizers and two identical QWPs was examined and observed. The behavior of the Stokes parameters of a single QWP and the visibility function of the polarization contrast scheme were investigated theoretically using the
Fourier-modal method (FMM) and described within the Jones
matrix formalism. This analysis was then generalized to a realistic case, accounting for the transmission anisotropy, phase deviation, and misalignment of optical components from their ideal orientations. An analytical expression for the visibility function of the polarization contrast scheme in terms of the normalized Stokes parameters was derived, along with the asymptotic expansions in terms of small parameters representing the phase deviation, transmission anisotropy, and angular misalignment of the polarization contrast scheme. For the investigated silicon-grating-based QWP, good quantitative agreement between the FMM-calculated fourth power of the normalized third Stokes parameter, and the visibility function (FMM-calculated and experimentally measured) was demonstrated over almost the entire investigated frequency range of 200-700 GHz.
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All authors Stepan Kupavskii, Roman Malikov, Sergey Dyakov, Sergei Tikhodeev, Arseniy Gavrilov, Kirill Dzhikirba, Sofya Andreeva, Igor Kukushkin, Nikolay Gippius
Solar and Stellar Astrophysics
ROSE (Red-giant Oscillations Spectra Estimator): A Modular Machine-Learning Framework for Automated Asteroseismic Characterisation. I. $\nu_{\max}$ and $\Delta\nu$ from TESS
Nipun Ghanghas, Dinil B. Palakkatharappil, Rafael A. Garcia et al. (+1 more)
Space-based photometry from Kepler and TESS has delivered oscillation spectra for hundreds of thousands of red
giants, and PLATO and the Roman
Galactic Bulge Time-Domain Survey will add more. We present ROSE, a modular machine-learning framework for automated asteroseismic characterisation of red
giants, and apply two of its modules to the frequency of maximum oscillation power, $\nu_{\rm max}$, and the large frequency separation, $\Delta\nu$. Each module is a neural network bundled with its own preprocessing transform and output binning, so that each parameter is measured in the representation that displays it most effectively: $\nu_{\rm max}$ from the power-density spectrum, and $\Delta\nu$ from the power spectrum of the power spectrum taken over a window centred on $\nu_{\rm max}$. Both are trained only on synthetic spectra generated at a one-year baseline and both return probability distributions rather than point estimates. This enables us to retrieve asymmetric uncertainty and a reliability index. Validating against held-out synthetic spectra, Kepler spectra at the training resolution and TESS continuous-viewing-zone
giants, we obtain robust dispersions of 1.4, 3.3 and 4.4% in $\nu_{\rm max}$ and 0.35, 0.61 and 1.3% in $\Delta\nu$, with the $\nu_{\rm max}$ uncertainties close to their nominal coverage. The fully automated pipeline was applied to 274,721 TESS red-
giant candidates observed for at least ten sectors, the framework returning reliable $\nu_{\rm max}$ for 56,224
stars and reliable $\Delta\nu$ for 39,939, taking 8 ms per
star. The sample follows $\Delta\nu = 0.278 \nu_{\rm max}^{0.757}$ with a scatter of 6.2%, and the red-clump phase stands out as a distinct overdensity, although neither module is provided an evolutionary label or asked to produce one.
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All authors Nipun Ghanghas, Dinil B. Palakkatharappil, Rafael A. Garcia, Shravan Hanasoge
Machine Learning
Fault-tolerant foundation models
Trevor McCourt, Ila R. Fiete and Isaac L. Chuang
Emerging computer hardware often trades reliability for energy efficiency; here we show that large-
language models (LLMs) can be trained to tolerate this unreliability, and that rather than degrading, their error resilience actually increases as they grow. Modified neural scaling laws inferred from 40,000 GPU-hours of training runs on simulated faulty digital hardware quantify this trend and suggest that models learn to compute within "good" error-correcting codes, whose relative overhead remains finite no matter how large the model gets. This finding leads us to
conjecture that appropriately trained LLMs may be formally fault-tolerant; if true, running AI inference on low energy, faulty hardware may be a path to substantial energy savings over the status quo.
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Machine Learning
RSIGym: A Flexible Environment for Recursive Self-Improvement
Fanqing Meng, Lingxiao Du, Haocheng Lu et al. (+6 more)
Recursive self-improvement requires carrying accepted changes into later improvement cycles, while studying
agent-proposed changes also requires substantial research infrastructure. Existing settings often leave
agents to rebuild routine infrastructure or restrict exploration to individual components. We introduce RSIGym, an
agent-native research environment based on Everything as a Service (EaaS). RSIGym exposes training, inference, rollout, evaluation, and sandbox execution through reusable services, with shared budget and permission controls supporting Data, Harness, and Joint improvement tracks. This design enables
agents to investigate individual interventions and jointly optimize data, training settings, and execution harnesses within the same environment. We define RSI-Index as the mean fraction of the remaining performance gap closed across five
benchmarks covering software engineering, terminal interaction, mathematics, scientific
reasoning, and skill-based tasks. Comparing six frontier research models in independent Joint runs, Opus 5 achieves the highest RSI-Index of 0.4809 under a $500 platform-service budget per
benchmark run. Its selected systems improve all five
benchmarks, raising SWE-bench Verified from 17.67% to 50.33% and AIME from 31.67% to 97.78%. Additional experiments examine DSH-harness refinement, budget variation, and restricted network access, while recorded trajectories reveal how
agents diagnose failures and select candidates. We open-source the full RSIGym codebase and results to support reproducibility and further research.
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All authors Fanqing Meng, Lingxiao Du, Haocheng Lu, Qiguang Chen, Ziqi Zhao, Zijian Wu, Jiayuan Zhuo, Mengkang Hu, Michael Qizhe Shieh
Signal Processing
Antenna Coding by Pixel Antennas: Unlocking A New Dimension for Wireless Communications
Zixiang Han, Shanpu Shen, Yifei Yuan et al. (+3 more)
Conventional wireless communication systems employ
antennas with fixed radiation patterns. Enhancing system performance by increasing the number of
antennas would push the limits of cost and size for communication devices. To overcome this issue, novel
antenna technologies are urgently desired to break through the fundamental performance bottleneck and engineering limits. Pixel
antennas provide a general framework for highly reconfigurable
antennas, which can flexibly adjust radiation patterns via controlling variable lumped elements placed across adjacent pixels, unlocking novel degrees of freedom (DoF) in the beamspace domain. Recently, an emerging
antenna coding technique links wireless system performance to the
antenna configurations. This enables the use of pixel
antennas to enhance system performance by leveraging the DoF from the
antenna side. In this article, we provide a comprehensive overview on
antenna coding by pixel
antennas. Specifically, based on the pixel
antenna model, the concept of
antenna coding is firstly introduced, followed by a discussion on the classifications of
antenna coding. Two cases for channel gain and multiplexing gain enhancement are highlighted to show the effectiveness of
antenna coding in wireless communications. Besides, various optimization approaches for
antenna coding design are investigated. Finally, the challenges and opportunities are outlined, providing guidance for future works.
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All authors Zixiang Han, Shanpu Shen, Yifei Yuan, Jiangzhou Wang, Ross Murch, Chih-Lin I
Earth and Planetary Astrophysics
Two Low-Mass-Ratio Microlensing Planets from High-Magnification Events: KMT-2021-BLG-0247 and MOA-2023-BLG-169
Kansuke Nunota, Andrew Gould, Takahiro Sumi et al. (+56 more)
We present an analysis of two planetary microlensing events, KMT-2021-BLG-0247 and MOA-2023-BLG-169, both of which exhibit high magnifications and low
planet–host mass ratios, but with markedly different levels of parameter constraint. For KMT-2021-BLG-0247, the finite-source effect and microlens parallax are both clearly detected, leading to unusually tight constraints on the physical properties of the lens system. The host mass and lens distance are approximately $M_{\rm L}=0.9\pm0.1\,M_\odot$ and $D_{\rm L}=6.7^{+1.0}_{-0.3}\,\mathrm{kpc}$, respectively, and the
planet mass is $M_{\rm p}=41\pm5\,M_\oplus$. The projected
planet–host separations are $a_\perp=3.4^{+0.7}_{-0.3}\,\mathrm{au}$ and $3.0^{+0.6}_{-0.3}\,\mathrm{au}$ for the wide and close solutions, respectively. In contrast, MOA-2023-BLG-169 involves an extremely faint source, with $I_{S,{\rm OGLE}}=26.73$, such that the light curve permits a broad family of strongly correlated solutions. We therefore construct the physical-parameter likelihood using approximate invariant combinations of the light-curve parameters and supplement it with post-event Euclid/VIS imaging from the Euclid Q2
Galactic Bulge Survey (Beaulieu et al. 2026). The Euclid data reveal a component at the event position with ${\rm VIS}_{\rm AB}=23.05\pm0.09\,{\rm mag}$. Interpreting this component as the combined light from the source and any luminous lens, the resulting posterior gives $M_{\rm L}=0.48^{+0.23}_{-0.17}\,M_\odot$, $D_{\rm L}=3.50^{+2.82}_{-1.20}\,\mathrm{kpc}$, $a_\perp=1.62^{+0.77}_{-0.43}\,\mathrm{au}$, and $M_{\rm p}=143^{+103}_{-63}\,M_\oplus$. MOA-2023-BLG-169 demonstrates that, for an extreme faint-source event, even the event timescale and angular Einstein radius can remain strongly dependent on the
Galactic prior and independent flux constraints.
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All authors Kansuke Nunota, Andrew Gould, Takahiro Sumi, Ian A. Bond, Jennifer C. Yee, Valerio Bozza, Fumio Abe, David P. Bennett, Aparna Bhattacharya, Kotaro Daimon, Ryusei Hamada, Yuki Hirao, Takuto Inoue, Stela Ishitani Silva, Shuma Makida, Shota Miyazaki, Yasushi Muraki, Seiya Nakayama, Ryo Ogawa, Ryunosuke Oishi, Greg Olmschenk, Hideaki Ose, Clément Ranc, Nicholas J. Rattenbury, Yuki K. Satoh, Daisuke Suzuki, Takuto Tamaoki, Sean K. Terry, Paul J. Tristram, Chihiro Ueda, Aikaterini Vandorou, Hibiki Yama, Michael D. Albrow, Sun-Ju Chung, Cheongho Han, Kyu-Ha Hwang, Youn Kil Jung, Yoon-Hyun Ryu, In-Gu Shin, Yossi Shvartzvald, Hongjing Yang, Weicheng Zang, Dong-Jin Kim, Chung-Uk Lee, Byeong-Gon Park, Andrzej Udalski, Przemek Mróz, Radosław Poleski, Jan Skowron, Michał K. Szymański, Igor Soszyński, Paweł Pietrukowicz, Szymon Kozłowski, Krzysztof Ulaczyk, Krzysztof A. Rybicki, Patryk Iwanek, Marcin Wrona, Mariusz Gromadzki, Mateusz J. Mróz
Combinatorics
Positive Lin-Lu-Yau curvature, planar graphs, and forbidden minors
Louis Esperet and Julie Semaan
Over the past few decades, several notions of graph
curvature have been introduced. Among them, Ollivier
curvature, defined through optimal transport, and its Lin–Lu–Yau variant provide notions of
curvature for graphs which retain several features of their counterpart in Riemannian geometry. A classical problem in this context is to understand the global structure of positively curved spaces. Lu and Wang proved that there are only finitely many positively curved planar graphs of minimum degree at least 3. In this paper, we study two directions motivated by this result. We first show that for fixed $2\leq s\leq t$, there are only finitely many positively curved $K_{s,t}$-minor-free graphs with minimum degree at least $s$. In particular, this generalizes the result of Lu and Wang to graphs embeddable on any fixed surface. We then give a complete classification of positively curved 5-connected plane triangulations. In particular, we show that there are only five examples, on 12, 14, 15, 16, and 17 vertices.
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Computer Vision
One-Shot Adaptive Segmentation For Scientific Images
Tejaswi V. Panchagnula, Allison M. Davis and Fengqing Zhu
Scientific image
segmentation methods rely on extensive annotation and task-specific training, limiting adaptation across imaging modalities and experimental conditions. We present a training-free, one-shot framework that specializes
vision foundation models using a single annotated reference image. The framework combines DINOv3 representations with background-adaptive feature orthogonalization to suppress artifact-related feature directions, after which cosine similarity localizes candidate regions for SAM
segmentation. We evaluate the framework on red-blood-
cell microscopy, structured-illumination pool boiling, and chest radiography. Relative to the strongest baseline, the proposed method improves mean IoU by 5.91% and 78.62% on the microscopy and pool-boiling
datasets, respectively, while achieving comparable performance on chest radiographs. These results demonstrate that one-shot reference conditioning can adapt general-purpose
vision models to specialized scientific
segmentation tasks.
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Machine Learning
Eduardo Santos-Escriche, Valerie Engelmayer, Ya-Wei Eileen Lin et al. (+1 more)
Training
Transformer-based architectures with finite data augmentation has become an increasingly popular approach in
geometric machine learning. Despite its empirical success, the interplay between the
Transformer architecture, invariance to different
symmetries, and augmentation budgets remains underexplored. In this paper, we study the ability of a vanilla
Transformer to learn various
symmetries through finite data augmentation for point cloud
datasets. We identify an ordering of increasing learnability across the following
symmetry groups: (i) non-angle-preserving
symmetries, (ii) angle-preserving
symmetries, and (iii) base angle-preserving subgroups, such as translation, rotation, and scale. For the base angle-preserving groups, we further investigate the
Transformer's extrapolation behavior and conduct a structural analysis of the trained models, allowing us to identify interpretable mechanisms that induce invariance. Finally, we extend our analysis to equivariant functions and show that the detected mechanisms for approximate invariance can also provide a key building block for learned equivariance. Our project page is available at https://
transformers-learn-
symmetries.github.io/
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All authors Eduardo Santos-Escriche, Valerie Engelmayer, Ya-Wei Eileen Lin, Stefanie Jegelka
Machine Learning
SemanticFold: Latent Sequence Compression SeparatesLanguage Modeling, Decodability, and Reasoning
Mingyan Liu and Min Huang
We study whether latent sequence compression of
prompt prefixes preserves the capabilities that large
language models rely on during inference. We introduce SemanticFold, a compression scheme that folds prefix hidden states at learned boundaries, and evaluate it across five model scales: Qwen3-1.7B, Qwen3-8B, SmolLM2-1.7B, Pythia-1.4B, and Pythia-6.9B. We use a fixed-target protocol: a frozen prefix is executed natively or compressed, and both arms teacher-force identical continuation
tokens. This design rules out target-selection explanations for likelihood changes. We examine five endpoint families: fixed-target negative log-likelihood, finite-label
reasoning accuracy, linear probe accessibility, open-ended generation, and systems-level
memory and latency. We find that compression moves these endpoints non-monotonically and that they do not share a single compression threshold. On Qwen3-1.7B at compression ratio R=1.7, compressed-minus-native mean NLL decreases by 0.135 under paired bootstrap with 10000 draws. On SmolLM2 at R=1.2, the mean change is 0.013 higher than native. On both Pythia checkpoints, NLL is effectively unchanged. An NLL decomposition separating sequence shortening from the learned residual transform shows that the favorable Qwen likelihood is attributable primarily to residual adaptation rather than to shortening alone. MLP-only, which applies the transform without shortening, achieves 0.082 lower NLL than Full SemanticFold. Linear probe accuracy and macro AUC change by less than 0.03 in absolute value across conditions, with confidence intervals crossing zero. We conclude that preservation under latent compression has no single scalar certificate:
language-model fit, decodability, and
reasoning behavior answer different questions and can move in different directions under the same compression operation.
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Computer Vision
Junhyeok Kim, Jinyeong Kim, Jae Wan Park et al. (+1 more)
The standard
Transformer architecture relies on a rigid pattern that alternates
Attention and Feed-Forward Network (FFN) layers. Despite its widespread adoption, the inductive bias imposed by this strict separation has not been systematically examined. In this work, we investigate the necessity of the
Attention-FFN dichotomy in
Vision Transformers (ViTs). To facilitate this analysis, we introduce the AttenFeed module, a unified component that integrates the functional properties of both
Attention and FFN. Based on this module, we devise the unified
Vision Transformer (uViT), which replaces the conventional alternating
Attention-FFN structure with a sequence of AttenFeed modules. We then use uViT as a control group that relaxes the
Attention-FFN dichotomy of the standard ViT and systematically compare the two models across multiple
datasets and model scales. Our experiments reveal that the
Attention-FFN dichotomy can hinder performance at smaller model scales due to the rigid parameter allocation of ViTs. The AttenFeed module and uViT serve as new analytical tools for understanding the
Attention-FFN structure and offer theoretical insights into the heuristically designed architecture of conventional ViTs.
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All authors Junhyeok Kim, Jinyeong Kim, Jae Wan Park, Seong Jae Hwang
Machine Learning
Continual Graph Multi-Agent Reinforcement Learning
Tommaso Marzi, Ahmed Hendawy, Jan Peters et al. (+3 more)
In Continual Multi-
Agent Reinforcement Learning (CMARL),
agents learn cooperative policies across sequences of tasks, aiming to adapt effectively to new tasks while preserving the ability to solve previously encountered ones. In many applications, tasks differ in their underlying structure, which can represent, for example, distinct operational conditions or target configurations (e.g., different network
topologies in power grids or arrangements in formation control). Existing CMARL methods lack dedicated mechanisms to leverage this structural information when learning new tasks, failing to promote transfer and mitigate forgetting. To fill this gap, we propose Continual Graph Multi-
Agent Reinforcement Learning (CGMARL), a novel framework for CMARL problems in which task sequences are mapped into a series of attributed graphs, each modeling a task-specific structure. In CGMARL, each graph determines the environment dynamics (next states and/or rewards) and the number of
agents for the corresponding task. Then, we present Graph-based Formation (GRAFO), the first CGMARL
benchmark, and show how forgetting arises in this setting. Finally, to address this limitation, we propose Frozen Graph Encoder (FROG), a method that relies on a frozen graph backbone to preserve past structural information in graph-based CMARL policies. Experiments on GRAFO show that pairing FROG with existing CL methods substantially improves performance on multiple CGMARL scenarios.
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All authors Tommaso Marzi, Ahmed Hendawy, Jan Peters, Carlo D'Eramo, Andrea Cini, Cesare Alippi
Machine Learning
Revisiting Explainable AI through Model-Independent Concept Dictionaries
Thomas Schnake, Doreen Schöppenthau, Alexander Meyer et al. (+3 more)
Modern applications of AI rely on increasingly complex models. Explainable AI (XAI) has emerged as a set of techniques aimed at improving model transparency. However, existing XAI methods typically assume input features to be inherently interpretable, or they rely on intermediate internal abstractions that are difficult to characterize and highly architecture-specific, hindering consistent use across models. To address these limitations, we propose DictXAI, a method that defines concepts directly in the input domain via a dictionary—a large, potentially overcomplete set of predefined elements, each carrying an interpretable meaning. Technically, DictXAI first computes a sparse code of the input and then attributes the model's prediction to the associated dictionary elements. We demonstrate the actionable nature of DictXAI explanations, showing that they can attribute AI malfunctions (e.g., Clever Hans effects) directly to identifiable artifact patterns in the data, while fostering human-AI
alignment on intricate biomedical signals. We further demonstrate our method's ability to operate across a wide variety of dictionaries, including learned image bases, analytically defined waveforms for electrocardiography, and experimentally acquired dictionary elements. Overall, our results show that DictXAI provides more interpretable, actionable, and architecture-agnostic insights than classical XAI or existing concept-based approaches.
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All authors Thomas Schnake, Doreen Schöppenthau, Alexander Meyer, Jacques Corbeil, Klaus-Robert Müller, Grégoire Montavon
Fluid Dynamics
Steady translation of a chemically active viscous drop along a rigid wall
Nikhil Desai and Sébastien Michelin
Chemically active drops release a chemical solute, gradients in whose concentration cause interfacial flows that advect the emitted solute. This non-linear coupling between solute distribution and fluid flow causes the drop to swim via an advective instability, if the system's Peclet number Pe–ratio of advective-to-diffusive solute transport–is larger than a finite threshold. Theoretical analyses often model active drops as diffusiophoresis-driven active particles, primarily to simplify the implementation of boundary conditions at the drop surface. However, physical insights about drop motion that rely on this simplification risk having limited applicability to fluid drops, especially when the drop is interacting chemo-hydrodynamically with its environment. Towards this, we study here the translation of a chemically active viscous drop parallel to a rigid wall, as an example of a common experimental configuration. We consider a propulsion mechanism where the drop swims due to interfacial Marangoni stresses and diffusiophoretic flows, and compare our results to those of the ”isotropic active particle” model, to examine the validity of the latter. Our analysis shows that, for the same confining force, a less viscous drop swims closer to the wall than a more viscous drop. This results in faster swimming, due to stronger concentration gradients driving the drop's motion. It is also shown that for moderate Pe, the swimming speed of the drop depends weakly on its mobility ratio (relative strength of diffusiophoretic and Marangoni flows). This weak dependence provides a quantitative justification for studying diffusiophoresis-driven active particles to infer the motion of Marangoni-stress-driven active drops.
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Machine Learning
Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss
Ruoyu Zhao, Yuting Chen, Jinheng Zhang et al. (+2 more)
What can a distribution-matching regularizer such as SIGReg in LeJEPA certify about contrastive learning? We study shared Gaussianization (SG), a characteristic-function Gaussianity test on the average of two normalized views, scaled by an independent $\chi_d$ radius. Because disagreeing views shorten the average, one test detects both misalignment and non-uniformity. SG vanishes exactly at the aligned, uniform minimizers of population InfoNCE, and under equal marginals it bounds the InfoNCE excess by $4\cdot 3^{3/4}\beta$ times the square root of the SG loss, plus a term linear in the loss. The square-root rate and this dimension-free constant are sharp, and no squared mean-
embedding distance on view pairs achieves a faster rate. With an explicit
alignment term, a rotation-invariant uniformity test gives a linear bound if and only if its spectrum dominates that of InfoNCE's kernel $e^{\beta u^\top v}$; SG's own test does, Gaussian kernels $e^{-\gamma \|u-v\|^2}$ qualify exactly when $\gamma \ge \beta/2$, and moment matching never does. Away from the optimum, the objectives differ. Along an isotropic nuisance channel, pure SG lowers its loss by adding per-view nuisance whenever the shared code is non-uniform. An
alignment weight above the channel's gain makes the nuisance-free solution a strict local minimizer; for LeJEPA, the same rule gives a critical SIGReg weight that decreases with the batch size. At finite batch size, an off-diagonal U-statistic removes a plug-in bias toward misalignment. In controlled latent-variable models, pure SG retains per-view style, an
alignment weight above the measured gain removes it, and for LeJEPA at three batch sizes the measured gain separates the encoders that retain style from those that do not. InfoNCE training also reaches a lower SG$_{0.2}$ loss than SG$_{0.2}$ training from scratch, which points to an optimization gap.
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All authors Ruoyu Zhao, Yuting Chen, Jinheng Zhang, Zhehao Zou, Tong Che
Machine Learning
Physics-Aligned Electronic Ground-State Learning Improves Generalization
Eike S. Eberhard, Xaver Kainz, Viktor Kotsev et al. (+2 more)
Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For
Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.
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All authors Eike S. Eberhard, Xaver Kainz, Viktor Kotsev, Abdulrahman Aldossary, Stephan Günnemann
Robotics
Energy-Efficient Gait Adaptation via Hierarchical Reinforcement Learning for Quadrupedal Locomotion Across Diverse Terrains
Ammar Issa, Anubhav Singh, Anton Tsaritsin et al. (+1 more)
While energy efficiency is a critical objective for legged-
robot locomotion control, achieving low energy consumption while maintaining robust performance across different velocity ranges and terrain conditions remains a key challenge. This is particularly true for end-to-end RL policies, where gait generation, motion execution, and energy optimization are tightly coupled, leading to high sensitivity to reward design. In this work, we propose a hierarchical reinforcement learning (HRL) framework that separates a high-frequency policy for stable and robust joint-level motion execution from low-frequency gait adaptation that explicitly minimizes the cost of transport (CoT). The three-stage Isaac-based training procedure enables zero-shot sim-to-real transfer with improved tracking accuracy, robustness, and energy efficiency. The learned hierarchy exhibits automatic speed-dependent gait adaptation, transitioning from pacing at low speeds to trotting at higher speeds. We validate the proposed approach in simulation against representative single-policy and hierarchical locomotion baselines, demonstrating reduced CoT over a broad range of commanded velocities, while maintaining robust locomotion across flat, uneven rough, and inclined terrains. We further demonstrate its practical feasibility through zero-shot deployment on a physical Unitree AlienGo quadruped.
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All authors Ammar Issa, Anubhav Singh, Anton Tsaritsin, Sergey Kolyubin
Group Theory
Frattini Geometry of Non-Generating Complexes: Symmetry, Homology and Betti Numbers
Luis Alfredo Dupont García
For a finite group \(G\), let \(N(G)\) be the simplicial complex of subsets that do not generate \(G\). We separate a general Frattini-topological reduction from the structure special to finite \(p\)-groups. For every finite noncyclic group, the non-cone Frattini core is homotopy equivalent to the order complex of the proper part of the subgroup
lattice of \(G/\Phi(G)\). For a finite \(p\)-group this quotient is an elementary abelian vector space, and the core becomes the non-spanning complex of a uniform parallel extension of \(\mathrm{PG}(r-1,p)\), where \(r=d(G)\) and \(q=|\Phi(G)|\). We use this geometry to determine the exact simplicial isomorphism data and full simplicial
automorphism group, identify top homology equivariantly with the appropriate restriction of the Steinberg module, and derive modular consequences. We also give an explicit supportwise formula for every multigraded Betti number and compare it with a closed single-sum formula for the \(\mathbb Z\)-graded Betti numbers. Known matroidal and building-theoretic inputs are stated separately from the group-specific consequences. The resulting framework also yields the homotopy type, depth, regularity, projective dimension, face enumeration, and the complete Cohen–Macaulay classification.
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Game Theory
Sharper bounds on the thresholds for sensitive and Blackwell optimality
Xavier Allamigeon, Stéphane Gaubert, Julien Grand-Clément et al. (+1 more)
In perfect-information two-player
stochastic games, the notions of Blackwell and sensitive optimality provide generalizations of the classical mean-payoff optimality and discount optimality criteria to account for more farsighted preferences. We provide bounds on the Blackwell threshold $\alpha_{\sf bw}$ and the $d$-sensitive thresholds $\alpha_{\sf d}$, defined as the smallest discount factors above which discount optimal policies coincide with Blackwell optimal policies and $d$-sensitive optimal policies respectively. Our refined bounds improve upon prior work by focusing on “reduced” families of
polynomials and, crucially, our bounds are tight in terms of controlling the degrees and heights of the minimal
polynomials of the Blackwell thresholds. We apply classical root separation based on Mahler's and Cauchy's bounds to our reduced families to derive the strongest upper and lower bounds on $\alpha_{\sf bw}$ in the literature, and we are the first to obtain bounds on $\alpha_{\sf d}$ in the multichain
stochastic setting.
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All authors Xavier Allamigeon, Stéphane Gaubert, Julien Grand-Clément, Ricardo Katz
Optics
Sub-shot-noise mid-infrared photothermal measurements using twin beams
Kazuki Hashimoto and Takuro Ideguchi
Mid-infrared photothermal (MIP) measurement probes refractive-index changes induced by mid-infrared (MIR) absorption using visible or near-infrared light and has recently emerged as a powerful modality for MIR spectro-imaging in the life sciences. Reducing measurement noise allows the probe power to be lowered without compromising the signal-to-noise ratio (SNR), thereby mitigating the risk of sample damage. However, even in the absence of classical noise, the SNR of conventional MIP measurements using a classical coherent probe is fundamentally limited by shot noise. Here, we demonstrate sub-shot-noise MIP measurement using twin beams generated through seeded optical parametric amplification. Balanced detection of the twin beams suppresses the noise by more than 5 dB below the shot-noise level established using a coherent beam. As a proof-of-principle demonstration, we measure the MIP signal from
liquid water using balanced twin-beam detection and achieve an SNR enhancement of more than 2 dB over the balanced coherent-beam detection.
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Statistical Methodology
Adaptively Combining Randomized and External Control Data Using a Mixture Prior in the Presence of Heterogeneity
Xinyi He, Peter F. Thall, Ying Yuan et al. (+1 more)
When resources are limited in a randomized trial, a common strategy is to augment data from the control arm with external controls. We propose a hybrid group sequential
Bayesian design that uses this approach to compare time-to-event distributions. The design allows between-treatment effects to differ between patient subgroups, and adaptively combines subgroups that have similar hazard functions. The aim is to reduce the control arm sample size without compromising the validity of comparative inferences due to systematic trial-versus-external data differences. The model borrows external control data dynamically by using a self-adapting mixture prior, which is a weighted average of a non-informative prior and an informative prior constructed from the external controls. The amount of borrowing is proportional to the agreement between the randomized and external controls. At each interim analysis, the design compares the treatments in each subgroup, and if inferiority or superiority is concluded stops accrual for that subgroup. Simulations show that the proposed design outperforms other methods for incorporating external control data in a randomized trial, and improves efficiency.
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All authors Xinyi He, Peter F. Thall, Ying Yuan, Suyu Liu
Combinatorics
A near-linear Chvátal–Erdős condition for Hamilton cycles in digraphs
Chengli Li and Bo Ning
For a digraph $D$, let $\alpha_2(D)$ be the largest size of a vertex set containing no directed $2$-cycle. Let $f_2(a)$ be the least positive integer $k$ such that every $k$-strongly connected digraph $D$ with $\alpha_2(D)\le a$ has a Hamilton cycle. Jackson and Ordaz conjectured that $f_2(a)\le a+1$. Towards this
conjecture, we establish the near-linear bound $f_2(a)=O\!\left(\frac{a(\log a)^4}{(\log\log a)^2}\right),$ and hence $f_2(a)=O_\varepsilon(a^{1+\varepsilon})$ for every fixed $\varepsilon>0$. We also disprove the pancyclicity
conjecture of Jackson and Ordaz that every digraph $D$ with $\kappa(D)\ge\alpha_2(D)+1$ contains a directed cycle of every length from $2$ to $|V(D)|$.
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Numerical Analysis
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: IMEX time-stepping and full effective field
Michele Aldé, Dirk Praetorius and Agus L. Soenjaya
We extend the BDF2-type finite-element integrator proposed in [M. Aldé, M. Feischl, D. Praetorius; BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions. (Math. Comp., 2026, doi:10.1090/mcom/4210)] to the Landau-Lifshitz-Gilbert (LLG) equation with lower-order effective-field contributions and current-induced non-conservative torques arising in micromagnetic applications. To incorporate these additional terms while retaining a linear solve at each time step, we employ an implicit-explicit (IMEX) time splitting. Our main
theorem proves unconditional weak convergence of the fully discrete approximations towards weak solutions of the LLG equation. The analysis removes the mild but artificial CFL-type restrictions required at the first and final time steps in [Aldé M., Feischl M., Praetorius D.; Math. Comp., 2026]. Furthermore, in the presence of the Dzyaloshinskii-Moriya interaction (DMI), the convergence is likewise unconditional and does not require the CFL-type restriction imposed in [G. Hrkac, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, A. Segatti, and B. Stiftner. Convergent tangent plane integrators for the simulation of
chiral magnetic skyrmion dynamics. (Adv. Comput. Math., 2019. doi: 10.1007/s10444- 019-09667-z)]. Numerical experiments support the theoretical findings.
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Differential Geometry
CR Orbits on the complex flag manifolds of $G_2$
Donato Mancini, Stefano Marini and Costantino Medori
We give an explicit description of the orbits of the split real form $G_{2(2)}$ on the complex flag
manifolds of $G_2$ and study their induced invariant CR structures. In particular we study their Levi forms and show that all possible cases in the simple homogeneous setting occur, namely Levi nondegeneracy, $k$-nondegeneracy for $2\leq k\leq 3$, and holomorphic degeneracy. Moreover, following the classical approach to orbits on flag
manifolds, we give equations for these homogeneous CR
manifolds.
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Probability
Exact bounds on the distribution function of isotropic log-concave distributions
Iosif Pinelis
For each real $b$, exact upper and lower bounds on the probability $\mathsf P(X\ge b)$ over all random variables $X$ with log-concave p.d.f.'s such that $\mathsf E X=0$ and $\mathsf E X^2=1$ are obtained, as well as the best constant factor $C$ in the inequality $\mathsf P(X\ge b)\le C e^{-b}$ for all real $b\ge0$. Exact upper and lower bounds on the corresponding exponential moments (Proposition 9.4) and explicit exponentially decreasing upper bounds on the mentioned p.d.f.'s (Propositions 9.2 and 9.3) are given as well. Some general results concerning log-concave p.d.f.'s are also obtained.
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Computer Vision
TouchScale: 500 Hours of Human Vision and Touch for Visual-Tactile Learning
Dayou Li, Hao Wang, Qianqian Yang et al. (+23 more)
Large-scale
egocentric human interaction data is becoming an important source of physical supervision for
embodied learning, yet
video alone leaves the contact and pressure that characterize physical interaction unrecorded. Recent visual-tactile
datasets provide this missing supervision, but their synchronized tactile data remain far smaller in volume than human
video. Moreover, the largest resources often merge recordings from different sensors or annotation procedures, which makes the effect of data scale difficult to isolate. We therefore introduce TouchScale, a 500-hour
dataset of contact-rich human interaction recorded with a single unified wearable setup. Its approximately 2K predefined task descriptions span everyday activities and structured manipulation, and each recording temporally aligns
egocentric RGB-D
video with wrist RGB
video and dense full-hand bimanual tactile measurements. Compared with prior tactile data, training on the full TouchScale raises zero-shot contact IoU on data from an unseen tactile sensor from 0.134 to 0.383. Pretraining a visual encoder on TouchScale also yields the highest action recognition accuracy on three
benchmarks among the compared visual-tactile
datasets. Used for visual-tactile mid-training of a
robot policy, TouchScale improves the average real-world success rate across four contact-rich manipulation tasks from 22.5% to 57.5%. With the sensor and collection protocol held fixed, both zero-shot tactile prediction and
robot success show an overall upward trend as more TouchScale data is used. These results suggest that human visual-tactile data collected at scale with consistent sensing benefits both perception and
robot manipulation. We will publicly release TouchScale, including all synchronized visual-tactile recordings and reconstructed object models, to support future research on scalable visual-tactile learning.
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All authors Dayou Li, Hao Wang, Qianqian Yang, Zihao Zhu, Haoquan Fang, Ziyao Zeng, Yan Han, Zihan Wang, Yan Wang, Baoru Huang, Dilin Wang, Kenji Shimada, Yiyue Luo, Manling Li, Teresa Lv, Mustafa Mukadam, Rakesh Ranjan, Ruohan Zhang, Qi He, Changliu Liu, Xu Chen, Marco Pavone, Bangya Liu, Jiachen Li, Masayoshi Tomizuka, Zhiwen Fan
Optics
Thermal Holography with Nonlocal Metasurfaces
Mingze He, Lin Jing, Michele Guizzardi et al. (+7 more)
Thermal radiation and luminescence are among the most ubiquitous sources of light, yet their properties are difficult to engineer due to their incoherent nature. Recent advances in thermal emission control have endowed heat-generated light with spatial and temporal coherence, as well as control over its polarization, by judiciously patterning periodic arrays of nanostructures. However, custom wavefront engineering of incoherent light has remained an open challenge, as it requires not only sufficient spatial and temporal coherence but also arbitrary local phase control, which experimentally translates into sustaining long-range
lattice resonances in aperiodic systems while maintaining their robustness against local phase perturbations. In this work, we address this longstanding limitation and demonstrate programmable vectorial control over the thermal emission wavefront from single-layer aperiodic nonlocal metasurfaces, realized by manipulating local
geometric phases across a collective delocalized resonance. We exemplify the wavefront-shaping capabilities of our approach by demonstrating thermal beam steering,
spin-momentum-locked thermal focusing and the generation of a thermal vectorial hologram, providing custom spatial and spectral control over thermal light. Our platform addresses challenges in thermal emission engineering and provides a route for light generation and control without the need for external coherent sources or bulky setups. Future work may extend this design principle to other incoherent emission systems, such as photo- and electroluminescence.
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All authors Mingze He, Lin Jing, Michele Guizzardi, Shixiong Yin, Martina Riva, Yajun Gao, Shuwei Guo, Adam C. Overvig, Sander A. Mann, Andrea Alù
Computer Vision
$\Delta$Representation: Geometry Supervised Representation Learning of Phenotypes via Counterfactual Reasoning for Medical VLMs
Hao Wang, Qiwei Zeng, Jinghao Lin et al. (+6 more)
Medical
vision-
language models (VLMs) have shown increasing potential for radiological image interpretation. Medical VLMs encode radiological images into visual representations that capture both anatomical and phenotypic information for diagnosis. Existing approaches improve pathological phenotype representations through semantic-guided representation
alignment. However, pathological phenotypes arise as lesion-specific visual changes superimposed on underlying normal anatomy. Such semantic
alignment approaches fail to model the phenotype-specific increment relative to the corresponding normal anatomical representation. To address this gap, we propose \textbf{$\Delta$Representation}, a visual phenotype representation learning framework based on counterfactual
reasoning for medical VLMs. It comprises BaseAnatomy, a geometry-supervised representation learning module, and \textbf{$\Delta$Phenotype}, a counterfactual incremental representation learning module. BaseAnatomy provides fine-grained
geometric supervision through spatial relationships across and within anatomical structures. $\Delta$Phenotype computes the representation increment between lesion representations and their corresponding normal anatomical representations, and supervises increments associated with the same phenotype to cluster in the representation space. Experiments on ReXGroundingCT and LIDC-IDRI demonstrate that $\Delta$Representation effectively structures pathological phenotype representations and improves lesion grounding and phenotype characterization accuracy in medical VLMs. Code is available at https://anonymous.4open.science/r/deltarep-CF6D.
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All authors Hao Wang, Qiwei Zeng, Jinghao Lin, Shuchang Ye, Yuezhe Yang, Yige Peng, Haoyuan Che, Jinman Kim, Lei Bi