Probability
On the $\ell^2$ distortion of random triangulations
Jason Miller, Julian Ransford and Fredy Yip
For each $n \in \mathbf{N}$, let $T_n$ be a uniformly random (rooted, Type I) triangulation of the sphere with $n$ vertices, viewed as a metric space equipped with its graph distance. We show that for every $\delta>0$, with probability tending to $1$ as $n \to \infty$, every
embedding of $T_n$ into a separable
Hilbert space has distortion at least $(\log n)^{1/4-\delta}$.
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Machine Learning
Game-Guided Skill Discovery through Self-Play for Playable Agent Control
Seungeun Rho, Jeonghwan Kim, Xue Bin Peng et al. (+1 more)
We present Game-Guided Skill Discovery (GGSD), a framework that uses self-play in games to discover motor skills that are directly playable by humans. Playable skills provide a compact abstraction for controlling
embodied agents through a small set of learned behaviors rather than low-level actions. To be effective, these skills should be semantically distinct, interpretable, and expressive; properties that existing unsupervised skill-discovery methods often fail to achieve simultaneously. GGSD achieves these desiderata by grounding skill discovery in competitive gameplay. A hierarchical
agent competes against its past selves, with a high-level policy selecting from a small discrete skill set and a skill-conditioned low-level policy learning the corresponding behaviors. After training, a human can replace the high-level policy and directly control the
agent through the same discrete skills. Despite the small number of high-level actions, skill transitions give rise to emergent combo behaviors, expanding expressivity beyond individual primitives. Across Ant, Franka-arm, and Unitree G1 environments, we show that GGSD produces human-playable skills that humans can compose to solve unseen tasks, such as Maze and CubePush, without additional training. An interactive demo is available at https://ggsd-demo.github.io.
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All authors Seungeun Rho, Jeonghwan Kim, Xue Bin Peng, Sehoon Ha
Data Structures and Algorithms
Sharper Gaussian Covers in the Bansal–Huang–Lee Coloring Framework
Konstantin Makarychev and Yury Makarychev
Bansal, Huang, and Lee recently gave a
polynomial-time
algorithm that colors every $3$-colorable graph on $n$ vertices with $O(n^{0.19539})$ colors. We improve their bound to $O(n^{0.17794})$ colors. The improvement comes from a sharper rule for combining Gaussian covers. We prove the rule from Ehrhard's inequality by comparing the probability that a Gaussian vector misses a polyhedron at two thresholds. At the farther threshold a union bound records how many halfspaces define the polyhedron, and this information reduces the loss in the combination. We then organize the successive neighborhood steps of the Bansal-Huang-Lee argument into a single recursion. The smaller loss lets the recursion run one step farther than before, and at that step it would require more distinct vertices than the graph contains. This rules out the remaining case. Combining the resulting bounded-degree guarantee with the dense-graph
algorithm of Kawarabayashi, Thorup, and Yoneda gives a randomized
polynomial-time
algorithm that colors every $3$-colorable graph on $n$ vertices with $O(n^{0.17794})$ colors.
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Chemical Physics
Smite: A quasiclassical trajectory (QCT) program for bimolecular collisions and unimolecular dynamics on ab-initio, and machine-learned potential energy surfaces
Péter Szabó, Jenne van Veerdeghem, Jérôme Loreau et al. (+2 more)
We present Smite, a Python toolkit for quasiclassical trajectory (QCT) simulations of reactive and inelastic bimolecular collisions, unimolecular dynamics, and molecular collisions with finite surface models. A central feature is the explicit control of reactant preparation: harmonic normal modes admit fixed
quantum numbers, prescribed energies, thermal
quantum populations, or ground-state Wigner sampling; rotation is prepared at fixed angular-momentum magnitude or from thermal distributions appropriate to diatomic and polyatomic rotors. Rotating-Morse sampling provides a coupled anharmonic treatment of diatomic vibration and rotation, while saved molecular-dynamics phase points provide an alternative source of initial conditions. The same
nuclear propagators operate with on-the-fly electronic-structure calculations or user-supplied analytical and machine-learned potential energy surfaces. Additional modules provide constrained rigid-fragment dynamics, thermostat-based preparation, photoionization initial conditions with energy and
recoil constraints, and fewest-switches surface hopping (FSSH) on multiple PESs with approximate
curvature-derived couplings. Geometry optimization, transition-state searches, crossing-point optimization, intrinsic-reaction-coordinate following, and thermochemistry use the same energy and derivative interfaces. Analysis tools connect trajectories to product energy partitioning, stereodynamical correlations, time-resolved vibrational signatures, and independent-atom x-ray scattering.
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All authors Péter Szabó, Jenne van Veerdeghem, Jérôme Loreau, Jean-François Müller, Jeremy N. Harvey
Robotics
Tactile Curiosity Drives Robot Interaction
Klemens Iten, Alexander Proshkin, Bhavya Sukhija et al. (+4 more)
Mastering
robot manipulation skills via reinforcement learning (RL) remains largely sample-inefficient. The most common RL
algorithms rely on random action sampling to discover new strategies, resulting in
agents that allocate most of their training budget to motions in free space, away from the contacts from which manipulation skills emerge. Existing intrinsic motivation methods based on model disagreement or epistemic uncertainty improve on isotropic noise, but they can also reward uncertainty in functionally irrelevant transitions, such as erratic motions in free space. In this work, we argue that tactile feedback provides a natural signal for exploration, and introduce TacEx, a framework that incorporates touch into epistemic uncertainty-driven exploration by decomposing model uncertainty across sensory modalities and directing curiosity toward the tactile channel. By anchoring curiosity to the sense of touch, TacEx drives the
robot to discover complex contact dynamics, learning to manipulate and grasp objects without task rewards or expert demonstrations during exploration. The interaction-dense
dataset collected through this tactile-driven curiosity supports offline learning of downstream pick-and-place policies without additional environment interaction. We further use tactile-driven exploration to post-train
vision-
language-action (VLA) models. Although the VLAs are initially pre-trained without tactile feedback, post-training with TacEx substantially improves downstream performance while remaining highly sample-efficient.
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All authors Klemens Iten, Alexander Proshkin, Bhavya Sukhija, Stelian Coros, Andreas Krause, Pieter Abbeel, Carmelo Sferrazza
Atmospheric and Oceanic Physics
reGRAF: a global MPAS reforecast data set with convection-allowing refinements over the US and Europe
Thomas M Hamill, Akshay Subramaniam, Montgomery Flora et al. (+8 more)
NVIDIA and The Weather Company (TWC) have generated a data set of reforecasts from TWC's GRAF (Global high-Resolution Atmospheric
Forecasting) model, a version of the National Center for Atmospheric Research (NCAR) Model for Predictions Across Scales (\href{https://ncar.ucar.edu/what-we-offer/models/model-prediction-across-scales-mpas}{\underline{MPAS}}). GRAF is global, but the configuration for this reforecast had a mesh refinement to \textasciitilde4 km over the US, Caribbean Basin, and Europe, and 15 km elsewhere. This model was designed to run much of the computation on graphical processing units (GPUs), with this development assisted by NVIDIA. The 1836 reforecast cases (\textasciitilde5 years) were generated from ECMWF reanalyses (ERA5) for selected initial condition dates spanning more than 20 years, 2004–2024. These dates of the chosen initial conditions were mostly selected based on high-impact weather in the contiguous US (CONUS) and Caribbean. Sampling in this way, the reforecast spanned a wider range of interesting, high-impact weather scenarios than had we performed five contiguous years of once-daily reforecasts. The reforecast still provides many samples in non-precipitating regions with more ordinary weather. GRAF reforecasts were mostly run to $+$27 h lead time, assuming a 3-h
spin-up followed by a full diurnal cycle. Data were saved in zarr format on the native model vertical coordinate. Most fields were archived at 15-min intervals, though several precipitation variables were saved at 5-min cadence. Data are made publicly available to all through Amazon Web Services' Open-Data Initiative at https://registry.opendata.aws/graf-reforecast.
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All authors Thomas M Hamill, Akshay Subramaniam, Montgomery Flora, Raghu Raj Prasanna Kumar, Karthik Kashinath, Carl Ponder, Tao Ge, Sepideh Khajehie, John Wong, Brett Wilt, Peter Neilley
Plasma Physics
FIREWALL: A surrogate model for the rapid assessment of tokamak wall loading and melting by runaway electrons
Victor Johan Svensson, Tommaso Rizzi, Svetlana Ratynskaia et al. (+4 more)
Runaway electron (RE) beams generated during tokamak disruptions can deposit highly localized heat loads on
plasma-facing components, posing a serious risk of melting and damage. Monte Carlo particle transport simulations coupled with three-dimensional thermomechanical response modeling can quantify this damage but are too computationally demanding for device-scale assessments and extensive scenario scans. We present FIREWALL (Fast Integrated Runaway Electron WALL loads), a surrogate model that combines a database of Geant4 volumetric energy-deposition profiles with a one-dimensional heat-
diffusion solver for each wall element. FIREWALL retains the energy and incident angle distributions of impacting REs and predicts the spatiotemporal temperature
evolution of detailed three-dimensional wall geometries up to the melting threshold. FIREWALL thus provides a fast physics-based framework for translating global RE simulations into global wall melting predictions, enabling large-scale screening of disruption scenarios while directing high-fidelity costly workflows to the limited wall regions where they are actually required.
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All authors Victor Johan Svensson, Tommaso Rizzi, Svetlana Ratynskaia, Hannes Bergström, Luca Venerando Greco, Matthias Hoelzl, Panagiotis Tolias
Machine Learning
Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity
Eftychios Protopapadakis, Konstantinos Makantasis and Konstantinos M. Giannoutakis
Rank-constrained tensor neural networks reduce the parameterization of high-order inputs, but they do not explicitly constrain class geometry in the learned representation. This study investigates whether a differentiable prototype-rule can provide a complementary inductive bias for Rank-R tensor learning under limited supervision. The proposed framework augments the Rank-R objective with prototype-based regularization and optionally fuses prototype evidence with neural logits at inference. Four hyperspectral
benchmarks are evaluated with four Rank-R configurations under both seven-fold stratification and spatially separated folds that mitigate leakage; a separate spatial study varies the class support budget from 2 to 20 samples. Under spatial evaluation, full neurosymbolic inference changes Macro-F1 score by +8.82 percentage points on Botswana, +5.49 on Indian Pines, +1.59 on Pavia University, and -0.62 on Salinas. Most of the benefit arises from training-time regularization, whereas inference fusion is small and
dataset dependent.
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Atomic Physics
Nuclear moments, charge radii, and magnetization distribution parameters of Ag isotopes from laser spectroscopy and ab initio electronic-structure calculations
Leonid V. Skripnikov, Bram van den Borne, Michail Athanasakis-Kaklamanakis et al. (+2 more)
The
nuclear electromagnetic moments and mean-square charge radii of several silver (Ag) isotopes deduced from recent
laser spectroscopy studies in the mass region $A=$ 96-121 are determined using high-accuracy electronic structure calculations performed in this work. We report hyperfine structure and isotope-shift atomic factors calculated with the relativistic coupled cluster approach, including single, double, triple, and perturbative quadruple excitations, CCSDT(Q). Following a systematic theoretical uncertainty analysis, we show that at the precision now achieved (sub-percent uncertainties in some cases),
quantum electrodynamic effects become significant. We also show that the isotope-dependent effect in the hyperfine structure due to the non-point-like
nuclear magnetization distribution can be extracted with negligible dependence on the assumed
nuclear magnetization model at the present level of precision. This also yields a
nuclear magnetic dipole moment that is corrected for the hyperfine anomaly induced by the Bohr-Weisskopf effect. In terms of the
nuclear electric quadrupole moments, the uncertainty in the electric-field gradient used to extract the quadrupole moments from
laser spectroscopy has also been reduced by one to two orders of magnitude relative to values used in previous studies. Finally, the
nuclear charge radii of Ag isotopes are extracted using field- and mass-shift factors from our coupled cluster calculations, and the difference in mean-square charge radii between $^{107,109}$Ag agrees with the value deduced from muonic X-ray spectroscopy.
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All authors Leonid V. Skripnikov, Bram van den Borne, Michail Athanasakis-Kaklamanakis, Gleb Penyazkov, Ruben P. de Groote
Computer Vision
VR-JEPA: Learning Contrastive-State Latent Guidance for Generation-based Video Reasoning
Zehua Ma, Kun Xiang, Yunshuang Nie et al. (+9 more)
Reasoning through
video generation offers a promising path toward visual intelligence by modeling latent visual states and their dynamics. However, current
video generation models often lack explicit guidance on how these states should evolve, leaving generated trajectories prone to physical and structural inconsistencies that undermine
reasoning reliability. While the
Video Joint-
Embedding Predictive Architecture (V-JEPA) provides rich spatiotemporal priors learned through latent prediction, these general priors do not naturally adapt to the logical
reasoning capabilities required for complex visual tasks. To bridge this gap, we propose VR-JEPA, a framework that aligns the V-JEPA predictor with task-specific
reasoning logic through localized contrastive-state learning and uses its predicted latent trajectories to guide
video generation for visual
reasoning. Specifically, (i) we pair successful trajectories with generated alternatives under the same input conditions and use discrepancies in their V-JEPA representations to identify informative states and
tokens for localized contrastive supervision. (ii) We further equip the V-JEPA predictor with skill-specific experts trained on anchor-task data, allowing the model to adaptively specialize its shared spatiotemporal priors across diverse cognitive domains. Together with skill-specific experts, this contrastive supervision enables VR-JEPA to predict latent trajectories that provide task-specific logical guidance for
video generation. Comprehensive experiments on the large-scale VBVR-Pro-Bench
dataset demonstrate that VR-JEPA achieves an $11.33\%$ relative improvement over the cutting-edge generation-based
reasoning baseline, significantly mitigating physical artifacts and enhancing logical consistency.
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All authors Zehua Ma, Kun Xiang, Yunshuang Nie, Quanlin Chen, Haoyuan Li, Xiuwei Chen, Jiang Ji, Haijun Wu, Zhenyu Xie, Michael Kampffmeyer, Hanhui Li, Xiaodan Liang
Quantum Physics
Optimal Resource Scaling for Early Fault Tolerant Iterative Quantum Phase Estimation under Cost Error Tradeoffs
Mrudula A Mahindrakar and Avhishek Chatterjee
The iterative
quantum phase estimation
algorithm (IPEA) is better suited for NISQ and early fault-tolerant hardware compared to the original
algorithm, which requires the inverse
quantum Fourier transform. However, current error mitigation and correction implementations lead to imperfect
unitaries, causing erroneous phase feedback in IPEA. To improve the reliability of phase bits is to repeat the k^th iteration for the 2^k-th power of the
unitary $N_k^*$ times, followed by a majority decision. However, due to variations in their
circuit complexities, different iterations incur varying resource costs ($w_k$) and different per-shot error probabilities ($q_k$). Given tight resource constraints, we ask what the optimal number $\{N_k^*: 1\le k \le L\}$ of shots per bit is: $$\arg \max_{\{N_k\}} \mathbb{P}(\text{all } L \text{ bits correct}) \text{ s.t.} \sum_{k=1}^L w_k N_k \le W$$ We obtain closed-form expressions for $N^*_k$ under the conditions: $W \gg \sum_k w_k $(enough for at least one shot per iteration), $w_k$ increases with $k$, $q_k$ are small enough and $L$ is large. We do so by analyzing tractable upper and lower surrogate problems derived via tight concentration and anti-concentration bounds and showing that their solutions converge when $q_k\ll 1$. We observe that when $W\gg \sum_k w_k \ln\! \left(\sum_k w_k\right)$, the optimal $N_k^*$ is proportional to $\frac{\ln\! \left(\sum_k w_k\right)}{c_k}$ and does not depend on individual $w_k$, where $c_k=-\ln\left(2\sqrt{\left(1-\frac{q_k}{2} \right) \frac{q_k}{2}}\right) \propto \ln\frac{1}{q_k}$. However, when $\sum_k w_k \ll W\ll\sum_k w_k \ln\! \left(\sum_k w_k\right)$, the allocation is also (additively) influenced by $\frac{1}{c_k}\ln\frac{1}{w_k}$ for larger values of $k$, i.e., higher powers of
unitary. These results lead to simple rules of thumb for resource allocation that may benefit the design of practical systems.
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Machine Learning
Learning Functional Subspaces for Neural Network Compression
Massimo Bini, Anders Christensen, Stephan Alaniz et al. (+5 more)
Modern
transformers pair impressive capabilities with substantial
memory and compute demands. Low-rank weight factorization reduces both while keeping the
matrices dense, and thus efficient on standard hardware. Existing methods, however, choose the subspace to remove from each weight
matrix with local closed-form criteria: activation energy, layer-wise reconstruction error, or a quadratic approximation of the loss. These criteria ignore how errors propagate through the network, so at high compression the errors compound with depth and performance collapses. We introduce Learnable Subspace Projections (LSP), which instead learns the subspaces to discard end-to-end. Each linear layer, or tied group of layers that read the same activations, is assigned an orthogonal projector. All projectors are optimized jointly against a global objective–the KL divergence to the dense model's output distribution or the model's original training loss–while the pretrained weights remain frozen. Projectors are initialized from a whitened SVD truncation, and ranks are allocated by the output KL each projector induces per parameter saved. After training, the projectors merge into standard low-rank factors, with each tied group sharing one factor. In
attention, this also lets the model cache one narrow latent in place of full keys and values. Across LLMs (OPT-125M/1.3B, Qwen3-4B, Llama-2-7B) and ViT-B/16, LSP outperforms baselines, and its advantage widens as compression increases. At -70% compression, LSP brings Llama-2-7B to 10.9 WikiText-2 perplexity and 42.2% mean zero-shot accuracy, versus 13.3 and 36.0% for the strongest baseline. The factorized model decodes up to 1.6x faster than the dense model at small batch sizes, and aching the shared latent shrinks the combined
memory of weights and KV cache by 13.5x at a 128k-
token context, versus at most 6.5x for untied baseline factorizations.
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All authors Massimo Bini, Anders Christensen, Stephan Alaniz, Judah Goldfeder, Ole Winther, Yann LeCun, Ravid Shwartz-Ziv, Zeynep Akata
Human-Computer Interaction
Who Asked for This? Inline Annotations as Authoring Transactions for Provenance in Agentic Authoring
Chang Xiao
Writing with AI
agents turns a paragraph into the outcome of many requests, yet the finished document rarely explains which request produced which change. We introduce Reactant, an interaction paradigm in which authors place typed inline annotations in their original documents. A verified transaction protocol records each request, skill identity, and the correspondences that identify additions, deletions, and transformations. The kernel validates the witness against the recorded states to establish word-level longitudinal lineage. We demonstrate Reactant through this paper's revision history, and report four months of three colleagues' self-directed use. Their uses include conversational inquiry into history and deriving reusable skills from recurring requests, illustrating how the transaction record serves as an extensible substrate for agentic authoring.
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Cosmology and Nongalactic Astrophysics
Improved Constraints on Cosmic Microwave Background Circular Polarization with CLASS
Thomas Essinger-Hileman, Caleigh Ryan, Yunyang Li et al. (+25 more)
We present improved constraints on circular polarization in the
cosmic microwave background (CMB) from the Cosmology Large Angular Scale Surveyor (CLASS) experiment using data at 90, 150, and 220 GHz to complement previous results based on 40 GHz data alone. We extend constraints on circular polarization from the atmosphere to all CLASS frequencies and compare with a model of the atmospheric circular polarization spectrum. The inclusion of data at all CLASS frequencies improves upper limits on circular polarization, Stokes $V$, in the CMB by a factor of $\sim 5$ at the largest angular scales ($10 < \ell < 30$) and extends the constraints to smaller angular scales, $\ell = 700$. In combination with Planck temperature data, we provide the first limits on the temperature-circular-polarization ($TV$) power spectrum to date. Both circular polarization ($VV$) and $TV$ power spectra are consistent with zero, and CLASS places upper limits of $5.4 \times 10^{-3}$ $\mu$K$_{\text{CMB}}^2$ on $VV$ at large angular scale ($10 < \ell < 30$) and $5.8 \times 10^{-1}$ $\mu$K$_{\text{CMB}}^2$ on $TV$ at 95% confidence at $30 < \ell < 50$.
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All authors Thomas Essinger-Hileman, Caleigh Ryan, Yunyang Li, Matthew A. Petroff, John W. Appel, Charles L. Bennett, Ricardo Bustos, Carol Yan Yan Chan, David T. Chuss, Joseph Cleary, Sumit Dahal, Rahul Datta, Jullianna Denes Couto, Kevin L. Denis, Joseph R. Eimer, Joseph E. Golec, Kyle R. Helson, Jeffrey Iuliano, Tobias A. Marriage, Jeffrey J. McMahon, Ivan Padilla, Carolina Morales Perez, Karwan Rostem, Rui Shi, Deniz A. N. Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack
Computation and Language
Debias It Yourself: Teaching LLMs Cognitive Bias Mitigation Interventions
Chahat Raj, Sina Mansouri, Aylin Caliskan et al. (+2 more)
Bias has long been studied in social psychology and cognitive science, where decades of research have produced a body of validated interventions that reduce stereotypical thinking and prejudiced responses in humans. We propose Debias It Yourself (DIY), a cognitively grounded framework that translates five such interventions into debiasing procedures for large
language models and delivers them through three established paradigms: Show (in-context examples), Train (instruction tuning), and Revise (guided self-revision). Across three models, five bias
benchmarks, eleven debiasing baselines, and three
reasoning benchmarks, Train+Revise and Revise alone attain the top two average ranks, lead the bias-
reasoning tradeoff (mean bias as low as 2% at 90%
reasoning accuracy), and reduce bias on unseen dimensions by up to 14.8%. Our code and data are publicly available.
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All authors Chahat Raj, Sina Mansouri, Aylin Caliskan, Antonios Anastasopoulos, Ziwei Zhu
Number Theory
Galois groups of random polynomials of large degree
Guy Blachar, Emmanuel Breuillard and Gady Kozma
We study random
polynomials of the form $R(x)=x^n+\omega_{n-1}x^{n-1}+\cdots+\omega_0$, where $\omega_0,\dots,\omega_{n-1}$ are independent, uniformly bounded integer-valued random variables, and $\omega_1,\dots,\omega_{n-1}$ have a fixed common law $\mu$. We prove (unconditionally) that, if the Rényi
entropy of order $2$ satisfies $H_2(\mu)=-\log\|\mu\|_2^2>12$, then $\mathbb{P}(\operatorname{disc}(R)\text{ is a square})=O_\mu(1/\log n)$. Combined with previous results, this shows that, for such measures $\mu$ and under additional hypotheses, $R$ has full Galois group $\mathrm{Sym}(n)$ with high probability, when conditioned on $\omega_0\ne 0$.
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Geometric Topology
Myopic Tutte polynomials and Khovanov homology in $\mathbb{R}P^3$
Keegan Boyle and Dean Spyropoulos
We present a "myopic" Tutte
polynomial for graphs on $\mathbb{R}P^2$ which takes only nullhomologous spanning subgraphs as input. It recovers the generalized Krushkal
polynomial and Drobotukhina's analogue of the Jones
polynomial for alternating, nullhomologous links in $\mathbb{R}P^3$. We use this myopic Tutte
polynomial to prove an analogue of the Kauffman-Murasugi-Thistlethwaite
Theorem, relating the Jones
polynomial of an alternating link to certain refinements of the crossing number. Finally, we construct a spanning tree model for the Khovanov homology of nullhomologous links, mirroring work by Champanerkar-Kofman and Wehrli for links in $S^3$. For alternating links, we use our model to prove that the Khovanov homology in $\mathbb{Z}/2\mathbb{Z}$ coefficients is determined entirely by the Jones
polynomial and signatures of the link.
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Computation and Language
On the (In)effectiveness of AMR Augmentation for Large Language Models
Hoa Quynh Nhung Nguyen, Jacopo Staiano and Michael Sullivan
While Abstract Meaning Representation (AMR) has historically improved performance on a range of NLP tasks, the benefit—or lack thereof—of AMR augmentation for modern LLMs is thus far unclear. In this paper, we attempt to reproduce recent work that reported substantial downstream gains from AMR augmentation, finding that these are likely due to specific choices in the experimental settings used: using a consistent and unified protocol for hyperparameter selection, we observe that text-only baselines consistently match or exceed the performance of AMR-augmented models. To investigate this null result, we introduce a perplexity-based probe measuring the degree to which AMR provides an LLM with supplemental relational knowledge not already available to the model. We find that AMR augmentation does not help LLMs improve their understanding of relational content in the sentence, indicating that augmenting these models with AMR offers no clear benefit on downstream tasks.
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Machine Learning
Scalable Cox Regression via Grouped Risk Sets and Sharper LogSumExp Rates
Elizaveta Iashchinskaia and Egor Gladin
Motivated by the computational challenges of large-scale Cox regression, we study
stochastic minimization of LogSumExp objectives over large sets. Mini-batch normalizer estimates generally yield biased gradients. We instead use a softplus surrogate that introduces one auxiliary scalar per normalizer and admits unbiased single-sample gradients. For smooth convex LogSumExp objectives, we prove an $O(T^{-1/2})$ averaged objective bound, improving the previous $T^{-1/4}$ analysis. With a strongly convex regularizer on the original variable, we also obtain a last-iterate squared-error rate of $\widetilde{O}(T^{-1})$ without strong convexity in the auxiliary variables. For Cox regression, the normalizers are defined over nested risk sets. We exploit this structure by grouping neighboring failures and sharing one auxiliary variable per group. The resulting compressed objective admits uniform score and
curvature bounds that control the errors from grouping and softplus approximation. Together with the general optimization result, these bounds give a mean-square rate of $T^{-4/5}$, up to logarithmic factors, relative to the full Cox solution. The compressed
estimator also matches the full
estimator's asymptotic distribution. Experiments on synthetic and real survival
datasets with slowly decreasing risk sets show a favorable performance relative to
stochastic baselines.
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Programming Languages
Automatically Building Machine-Checked Assurance Cases from C Codebases to Requirements
Haokun Li, Zhongyi Wang, Guanyan Li et al. (+4 more)
Large
language models (LLMs) have shown promise in automating interactive
theorem proving, yet verification of real-world C codebases requires more than discharging individual proof goals. The task involves jointly constructing expressive function specifications and their proofs, and ensuring that library interfaces compose along intended call sequences even without a designated client. This paper presents CCV, an LLM-assisted framework for building machine-checked assurance cases: structured, auditable artifacts supporting the claim that a C codebase meets its intended requirements. To model intended cross-interface use in open libraries, CCV constructs an interface protocol that exposes permitted call sequences and resource assumptions for review, with a conditional safety guarantee under verified contracts and caller obligations. CCV coordinates two complementary phases: (i) requirement-guided analysis and bottom-up construction of candidate specifications and protocols; and (ii) modular proof construction with feedback that revises the specifications and proofs. Implemented using VST in Rocq, CCV verifies
memory safety and leak freedom for all 299 function definitions across six C
benchmarks, including industrial cryptographic components, with less than one person-day of reported human effort per
benchmark. The guarantees depend on disclosed contracts and assumptions; human review supplies the conformance judgments connecting the formal artifacts to the intended requirements.
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All authors Haokun Li, Zhongyi Wang, Guanyan Li, Xiao Yi, Shengchao Qin, Jianwei Yin, Mingshuai Chen
Computation and Language
Persistent Context Graphs for Efficient Memory Compaction in LLM Agents
Jingbo Yang, Kwei-Herng Lai, Xiaowen Wang et al. (+6 more)
As LLM capabilities advance,
agents are tackling increasingly complex tasks over longer horizons. Their growing interaction histories make
memory compaction essential for staying within context windows and reducing prefill cost. Existing methods summarize the history or compress its KV cache, often adding model computation to preserve information for future requests. A new user request can change which history matters, but reassessing that history with the model requires re-encoding it if the KV cache has expired. Past
attention provides signals of historical importance and dependencies between messages, while relevance to the current task must be assessed using the new user request. We introduce ReCAP, a
memory compaction method that stores
attention-derived importance scores and dependency links in a lightweight, persistent context graph. For each new request, ReCAP combines stored importance with relevance cues from the request and follows dependency links to select messages and their supporting context, without additional model calls for selection. Compared with Codex's default summarization-based compaction, ReCAP reduces estimated latency for compaction and cold restoration by approximately 95% on both Qwen3-Coder and gpt-oss. It also roughly halves the historical context per call on SWE-Together at comparable task quality and improves accuracy on the code tasks of Lost-in-Conversation over full history by 19.8 and 41.2 points.
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All authors Jingbo Yang, Kwei-Herng Lai, Xiaowen Wang, Zhaoxuan Tan, Pei Zhou, Mengting Wan, Yaar Harari, Evgeniy Gabrilovich, Shiyu Chang
Machine Learning
Beyond Model Ranking: Regime Diagnosis for Distributional-Statistical Misspecification in Industrial Time-Series Forecasting
Pengyu Nie, Chenglang Xu, Yaoshi Chen et al. (+4 more)
Time-series
forecasting models achieve strong
benchmark performance but exhibit severe systematic bias in industrial deployments. This train–deploy gap is conventionally attributed to temporal-structural errors or distribution shifts. We characterize a complementary source that these explanations overlook: canonical losses embed fixed statistical priors, while industrial demand mixes benign and pathological regimes—zero-inflation, skewness, high variability—in which these priors are systematically violated. The induced bias persists even under perfect temporal modeling, remains in a distributional-shape component that normalization cannot remove, and creates an aggregation trade-off invisible to aggregate metrics. We turn these observations into an evaluation toolkit centered on the Regime-wise Relative Bias Vector (RBV): a metric-agnostic, regime-decomposed diagnostic that audits how pooled training allocates systematic mismatch across pathological subpopulations. A controlled attribution analysis decomposes RBV into a model-independent intrinsic floor, set by each loss's estimand, and an excess component attributable to training, tracing observed bias to the loss rather than the model. A large-scale study—13 loss objectives, 3 seeds, 60,000+ series spanning RetailShiftBench and M5, with random-split controls—shows that regime-aware diagnosis separates optimization-type from bias-type failure, and that regime-aware training resolves the pooling-induced bias that capacity scaling cannot, for mean-type losses. A formal structural observation, that risk under evaluation-distribution contamination is affine in the pathology mixture weight, grounds these findings. Our work complements model ranking with mechanism-grounded, regime-oriented evaluation.
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All authors Pengyu Nie, Chenglang Xu, Yaoshi Chen, Chaogan Ren, Wei Hu, Chao Yang, Jiangong Zhang
Quantum Physics
Quantum Advantage of Permutation-Invariant Functions in Communication Complexity
Yunqi Huang and Zekun Ye
We study how
symmetry affects
quantum advantage in two-party communication complexity. For any partial function $f$ on length-$n$ strings over a fixed alphabet of size $q$, invariant under simultaneous coordinate permutations, we prove $R^{\mathrm{pub}}(f)=O_q(t\log(2+n/t))$, where $t=\min\{n,Q^{\ast}(f)^2\}$, $R^{\mathrm{pub}}$ denotes public-coin randomized communication complexity, and $Q^{\ast}$ denotes
entanglement-assisted
quantum communication complexity. This bound is tight for set disjointness and extends the binary-alphabet result of Guan et al. with a smaller logarithmic overhead. The exponent of the logarithmic factor cannot be reduced by any fixed positive amount: for every fixed $\varepsilon\in(0,1)$, there are binary permutation-invariant partial functions with
quantum communication complexity $O_\varepsilon(\log\log n)$ and randomized communication complexity $\Omega_\varepsilon((\log n)^{1-\varepsilon})$. We also characterize
quantum communication complexity by a combinatorial parameter up to a logarithmic factor. Growing alphabets and graph
symmetries admit exponential separations. For every fixed $\varepsilon\in(0,1)$, we exhibit permutation-invariant partial functions on length-$n$ strings over an $n$-symbol alphabet with
quantum communication complexity $O_\varepsilon(\log n)$ and randomized communication complexity $\Omega_\varepsilon(n^{1-\varepsilon})$. For graph-invariant partial functions on $v$-vertex graphs, we obtain $O_\varepsilon(\log v)$
quantum versus $\Omega_\varepsilon(v^{2-\varepsilon})$ randomized communication complexity. All separation protocols require no prior
entanglement.
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Artificial Intelligence
Unlearnable, or Unmeasured? On the Reliability of Difficulty Labels in RLVR
Chandak Chakma, Syed Nazmus Sakib, Nafiul Haque et al. (+1 more)
Reinforcement learning with verifiable rewards (RLVR) has become an important approach for improving
reasoning during post-training. Recent work suggests that some difficult
prompts remain resistant to learning even when they occasionally produce correct solutions. We revisit this unlearnability phenomenon and find that the affected
prompts do improve, at roughly one third of the learnable rate, while the difficulty-defined set used to study them is much less reproducible than expected. These difficulty labels are estimated from a limited number of sampled responses. Combining them across seeds can further change which
prompts are selected instead of simply reducing measurement noise. We develop a sampling-based framework for quantifying this instability and determining how much evaluation is required for difficulty assignments to reproduce reliably. We also revisit the gradient-similarity evidence proposed to explain unlearnability and show that part of the observed separation arises because difficult
prompts provide fewer correct rollouts from which their gradients can be estimated. Matching this sample count weakens the gradient difference but does not remove it. Overall, the slow-learning phenomenon survives our reanalysis, while both the
prompts used to define it and the evidence used to explain it require more careful measurement.
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All authors Chandak Chakma, Syed Nazmus Sakib, Nafiul Haque, Shifat E. Arman
Analysis of PDEs
Dispersion for the wave equation with Neumann boundary condition inside general strictly convex domains
Oana Ivanovici and Diego Sanchez Sanz
We consider the wave equation on a
manifold of dimension d>1 with smooth strictly convex boundary, with Neumann boundary condition. We construct a sharp local in time parametrix for the Neumann wave equation near glancing, extending the classical Melrose-Taylor construction for the Dirichlet problem to the Neumann boundary condition. Our construction is based on the microlocal framework and the parametrix developed in [10] for the Dirichlet problem, together with the Melrose-Taylor argument for solving the transport equations under more general, affine-type boundary conditions. Once the Neumann parametrix is constructed, the dispersive and Strichartz estimates follow the analysis developed in [10] for the Dirichlet problem. We therefore only recall the main ingredients of that argument. In particular, the fixed time decay rate for the Green function exhibits the same loss of 1/4 with respect to the boundaryless case, associated with swallowtail type singularities in the wave front set, and this decay is optimal. Moreover, the corresponding Strichartz estimates are obtained by balancing lossy long time estimates at a given incidence with short time ones with no loss: for d=3, this heuristically means that, on average, the decay loss is only 1/6 .
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Soft Condensed Matter
Liquid crystalline order and its impact on shape evolution of fluid lipid membranes
Ingo Nitschke, Maik Porrmann and Axel Voigt
We consider extensions of the classical
curvature-elasticity free energy for a fluid lipid membrane, explicitly treating the
liquid crystal structure of the membrane, which results from the lipid molecules that are, on average, oriented normal to the surface. Locally varying
liquid crystal order leads to local variations in bending
rigidities and surface viscosity and thus influences the shape
evolution. This provides a multiscale coupling between the local membrane mechanics on the level of the lipids and the mesoscopic length and time scales of biological functions. Numerical simulations in the one-constant approximation demonstrate the impact of local membrane mechanics on the emerging
equilibrium shapes. These shapes not only depend on the specified conserved surface area and enclosed volume, as for the classical
curvature-elasticity free energy, but also the elastic parameter and are characterized by a reduced
liquid crystal order at highly curved regions. The modified shapes and their varying
liquid crystal order, as function of
curvature, provide experimentally testable properties. Exploring the dynamic
evolution demonstrate a tight coupling of tangential flow, shape
evolution and
liquid crystalline order. We further point to model extensions towards lipid phase separation and asymmetric lipid
bilayers and biological implications.
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Chemical Physics
Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz
Yaolong Zhang, Bin Jiang and Hua Guo
Directly solving the full electron-
nuclear Schrödinger equation remains one of the grand challenges in
quantum mechanics. Here, we propose a
quantum-chemically motivated orbital-based neural network wavefunction ansatz with explicit many-body electron-electron correlation terms, with parameters depending on the entire electron-
nuclear configuration, enabling an accurate description of strongly correlated and/or multi-reference electronic structures by a single Slater-determinant across a broad
nuclear configuration space. To train this wavefunction, we further develop an efficient hybrid optimization strategy that combines the variational Monte Carlo technique with local-energy constraints, mitigating the intrinsic sampling bias of the former and considerably reducing the statistical error. These advances are embedded in a unified neural network framework, Schrödinger, enabling the determination of globally accurate potential energy surfaces with a single training for systems ranging from strongly correlated diatomic molecules, triatomic reactions containing conical intersections, to polyatomic multi-reference molecules. This work offers a practical machine-learning tool for solving the electron-
nuclear Schrödinger equation and capturing full
quantum effects beyond the Born-Oppenheimer approximation.
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Artificial Intelligence
Agent Error Dataset: Scaling 50,000 Error–Diagnosis Pairs for Failure Analysis and Error-Aware Post-Training
Kunlun Zhu, Xuyan Ye, Yibo Li et al. (+3 more)
An unsuccessful LLM
agent rollout contains more information than its final reward: the observations available to the
agent, the actions it chose, and the environment's responses. Reusing this experience for learning requires identifying a decision to revise and testing a concrete alternative. We introduce the
Agent Error
Dataset (AED), comprising 50,228 error-diagnosis pairs from 9,961 source tasks across 33 environments, 19 harness families, and 23 policy models in text-based
agent systems. We retain source traces and execution metadata to support cross-setting failure analysis and re-diagnosis without repeating the original rollout. Our five-stage Agentic Error-to-Training (AET) pipeline collects natural failures, generates diagnoses and proposed corrections, and checks them against recorded evidence. Where replay is supported, we compare corrections with original-action retries from the same checkpoint under matched execution settings. We then construct separate training views for diagnosis and actor recovery. Across 3,062 matched replay pairs, first-proposal corrections raise verifier pass rates from 18.4% to 51.1%, a gain of 32.7 percentage points. Using a separately frozen diagnosis release, full-diagnosis fine-tuning on 1,656 source tasks raises Qwen3-8B's exact-step agreement with internal teacher labels from 47.2% to 63.6%, averaged over three seeds on a 943-case holdout. The strongest prompted reference in this comparison scores 54.7%, and mean agreement improves at each of four increasing training-set sizes. In a single-seed comparison of actor-training recipes, action-only repair training scores 6.67 percentage points higher on WebShop-lite than success-only training.
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All authors Kunlun Zhu, Xuyan Ye, Yibo Li, Cheng Qian, Beibin Li, Heng Ji
Quantum Gases
Collective excitations of driven-dissipative quantum fluids of light
Alberto Bramati and Iacopo Carusotto
In this work we give an overview on a couple of decades of theoretical and experimental research on the many-body physics of driven-dissipative
quantum fluids of light in optical cavities. These systems consist of a large number of
photons enclosed in a cavity device where spatial confinement induces a finite
photon mass and the Kerr optical nonlinearity of the cavity material mediates finite
photon-
photon interactions. Differently from standard Bose gases of material particles like
liquid Helium or ultracold atomic gases,
photons are inevitably subject to radiative and/or non-radiative losses, which must be compensated by some pumping mechanism. As a result, the properties of the steady state are not imposed by a thermal
equilibrium condition, but are determined by a dynamical interplay of pumping and losses. Among the many collective phenomena that are observed in these systems, we focus here on the collective excitations around the steady state and we characterize the impact of the driven-dissipative nature of the gas on their properties, in particular on their dispersion relation. Different pumping configurations give very different behaviors: a specific discussion is provided for the most important configurations used in the experiments. Observable consequences of the various forms of the dispersion -gapped, gapless, sonic, band-sticking, diffusive Goldstone- are illustrated with a special eye towards their consequences on the superfluidity properties. We conclude the article with a presentation of a few research avenues that we personally find most exciting for the next years, namely the osbervable consequences of the concurrently superfluid and solid nature of supersolid states of light and the collective dynamics of
quantum correlated states of strongly interacting
photon gases in the presence of strong nonlinearities, in particular Mott
insulator states.
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Strongly Correlated Electrons
Probing Collective and Individual Kondo Screening: Multi-Stage, Multi-Channel Kondo Effects in a $C_3$-Symmetric Four-Impurity Model
Danqing Hu, Jiangfan Wang, Zixiang Hu et al. (+1 more)
Collective screening has been proposed to underlie the basic physics of multi-
impurity and
lattice Kondo systems. But how to establish this picture and distinguish it from individual (local) Kondo screening remains a grand challenge. The recently developed auxiliary-bath numerical renormalization group (AUNRG) method provides a key step towards resolving this issue. Its application to the $C_3$-symmetric three-
impurity Kondo (3IK) model with a shared electron bath reveals fully screened
Fermi liquid ground states arising from collective screening of cluster
spin degrees of freedom at small Kondo coupling $J_{\rm K}$ and individual (local) screening of local
impurities at large $J_{\rm K}$. Here we design a four-
impurity Kondo (4IK) model where the probe
impurity couples only to the original three Kondo
impurities to detect the nature of the screened states. We show that the collective and individual Kondo screenings give rise to emergent multi-stage, two-channel Kondo effect and unstable three-channel Kondo effect, respectively. This suggests a special helicity structure of the screened states and confirms the idea of collective screening in multi-
impurity Kondo systems. Our work also demonstrates that the same auxiliary-bath construction can be readily extended to models with additional
impurities to explore novel many-body
quantum states with emergent cluster degrees of freedom.
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All authors Danqing Hu, Jiangfan Wang, Zixiang Hu, Yi-feng Yang