Statistics Applications
On the Benefit of Blocking for Online Experiments with Skewed Data
Abbas Zaidi, Matthew Reimherr, Rina Friedberg et al. (+2 more)
This paper advocates for using blocked (stratified) assignment in online A/B tests to handle highly skewed population data. While blocking yields only modest precision gains (5-10%) due to the limits of discretization, the authors demonstrate it offers two crucial structural benefits over post-hoc statistical adjustments. First, fixed-weight blocking correctly targets the true average treatment effect, avoiding the severe bias introduced by efficiency-weighted alternatives. Second, blocking localizes extreme outliers, enabling targeted within-block winsorization that effectively controls noise without destroying the tail-end treatment effect.
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All authors Abbas Zaidi, Matthew Reimherr, Rina Friedberg, Fabian Martinez, Richard Mudd
Instrumentation and Methods for Astrophysics
BOLT: Imaging Lightning and Terrestrial Gamma-ray Flashes at the Pierre Auger Observatory
Eric-Teunis de Boone for the Pierre Auger Collaboration
Lightning-related phenomena are known to interact with and influence all detector systems of the Pierre Auger Observatory. Notably, the Surface Detector has recorded unique signals associated with Terrestrial Gamma-ray Flashes (TGFs), which are rare phenomena linked to the initial processes of lightning. Studying TGFs in coincidence with their parent lightning discharges helps to constrain the mechanisms responsible for their production, providing key insights into how these high-energy emissions are generated and evolve within thunderstorms. To image the parent lightning discharges, we are developing the Broadband Observatory of Lightning and TGFs (BOLT), an interferometric lightning mapping array that enhances the unique capabilities of the Observatory by providing high-resolution 3D (spatial and temporal) imaging of lightning propagation. BOLT consists of VHF
radio detectors that have been previously developed for the Auger Engineering
Radio Array, sensitive in the 30 MHz to 80 MHz range. The array is co-located with the Surface Detector to enable direct correlation between lightning activity and candidate TGF signals at the Pierre Auger Observatory. The BOLT array is in commissioning, with successful station firmware modifications to acquire and stream multi-second waveforms.
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Combinatorics
The replica symmetric solution for hypergraph independent sets in the critical regime
Matthew Jenssen, Will Perkins, Aditya Potukuchi et al. (+1 more)
We prove a variational formula for the logarithmic asymptotics of a non-existence probability in a broad class of combinatorial problems such as avoiding cliques in random graphs and $k$-term arithmetic progressions in random subsets of integers. These results follow from a formula for the probability that a binomial random subset of the vertices of a locally sparse hypergraph is an independent set. The formula holds throughout the critical regime, interpolating between the regimes in which Janson's inequality and the method of hypergraph containers give the respective asymptotics. The formula is the replica-symmetric Bethe free energy formula from statistical physics applied to a hypergraph hardcore model. The proof uses two new techniques. The first, for the upper bound, involves revealing a small `window' of a random independent set and then applying
entropy methods. The second, for the lower bound, involves the analysis of a random greedy
algorithm guided by a Belief Propagation fixed point. In the case of avoiding cliques in random graphs, the variational formula can be expressed as an optimization problem over graphons. Moreover, typical random graphs conditioned on not containing $K_r$, when suitably normalized, approach the set of optimizing graphons in cut distance.
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All authors Matthew Jenssen, Will Perkins, Aditya Potukuchi, Michael Simkin
Quantum Physics
Dynamically protected erasure qubit via low-frequency charge driving
Ahmed Hajr, Ke Wang, Bingcheng Qing et al. (+6 more)
Dynamical protection via strong driving can enable resilient
quantum processing on imperfect physical hardware. However, the practical utility of such schemes is frequently limited by parasitic processes such as drive-induced dephasing and leakage. Here, we demonstrate that sub-GHz charge driving of superconducting Kerr oscillators (KOs) in the transmon regime circumvents this trade-off, simultaneously activating fast parametric interactions and protecting the encoded
qubit from low-frequency noise. The key is the frequency dependence of the charge sensitivity: using the AC Stark shift as a probe, we find that the KO frequency sensitivity to a charge drive grows quadratically with both drive frequency and amplitude, making the oscillator weakly sensitive to $1/f$ charge noise yet strongly coupled to drives near 1~GHz. Exploiting this, we first demonstrate cooling and reset of the KO in 82~ns, to a residual population below $0.7\%$—lower than its $2.5\%$ steady-state thermal population. Next, using two KOs, we demonstrate logical control and dynamical protection of a dual-rail
qubit with nearly fourfold erasure bias. Finally, using a single end-of-
circuit erasure check, we achieve an error per Clifford of $5.6\times10^{-4}$, which falls to $1.5\times10^{-4}$ after post-selection, with 25~ns gates.
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All authors Ahmed Hajr, Ke Wang, Bingcheng Qing, Akel Hashim, Bibek Bhandari, Dominic Briseño-Colunga, Justin Dressel, Andrew N. Jordan, Irfan Siddiqi
High Energy Astrophysical Phenomena
The NANOGrav 15 yr Dataset: Modified Functional Forms for Profile-Evolution Time Delays in Pulsar Timing Models
Sofia V. Sosa Fiscella, Michael T. Lam, Olivia West et al. (+49 more)
Radio pulsars exhibit frequency-dependent variations in the shape of their pulse profiles that introduce systematic delays in the observed pulse times of arrival (TOA) across an observing band. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) models these delays using a frequency-dependent (FD) log-
polynomial function whose coefficients are fit to TOA measurements at different
radio frequencies. However, FD parameters are prone to absorbing power from other chromatic effects, such as interstellar dispersion, leading to fitted FD values that overestimate profile
evolution and vary significantly across
datasets. To separate these effects, we introduce two new mathematical formulations of profile
evolution: a monomial expansion (IFD) and a Legendre
polynomial expansion (LIFD). We test these models on observations of 11
pulsars in the NANOGrav 15-year
dataset and on simulated data, and also compare their performance to that of frequency-resolved pulse templates. We find that Legendre-based models generally predict timing delays that more closely replicate the true profile
evolution, reducing the residual offset relative to FD by as much as 85% for the simulated data. Additionally, we find that the choice of profile
evolution model can bias the fitted dispersion model, with FD-based models overestimating the injected DM by 0.013 pc cm^-3 compared to 0.0002 pc cm^-3 for LIFD. These results support the use of Legendre bases to mitigate covariances between chromatic effects, directly benefiting targeted timing studies of these effects and the development of advanced noise-modeling techniques for nanohertz gravitational-wave detection.
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All authors Sofia V. Sosa Fiscella, Michael T. Lam, Olivia West, Ruggero Valdata, Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Paul T. Baker, Paul R. Brook, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Timothy Dolch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Nate Garver-Daniels, Peter A. Gentile, Joseph Glaser, Deborah C. Good, Jeffrey S. Hazboun, Ross J. Jennings, Megan L. Jones, David L. Kaplan, Matthew Kerr, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Alexander McEwen, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Cherry Ng, David J. Nice, Timothy T. Pennucci, Benetge B. P. Perera, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Ann Schmiedekamp, Carl Schmiedekamp, Brent J. Shapiro-Albert, Taylor Starkman, Ingrid H. Stairs, Kevin Stovall, Abhimanyu Susobhanan, Joseph K. Swiggum, Haley M. Wahl
Fluid Dynamics
Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields
Peng Liu, Shaoxiang Qin, Theodore Potsis et al. (+3 more)
Rapid and accurate prediction of urban wind and temperature fields is important for urban microclimate design and
climate adaptation. Large-eddy simulation (LES) effectively resolves these instantaneous fields, but its application is limited in iterative design of urban microclimate applications due to high computational cost. Existing regressive data-driven models offers quick outputs, but they produce only deterministic point predictions that inherently fail to represent turbulent stochasticity. This paper adopts a novel generative framework of Conditional Flow Matching (CFM) that uses building geometry and mean flow as guidance to generate plausible three-dimensional instantaneous velocity and temperature fields for urban microclimate in seconds. To overcome the GPU
memory bottleneck of pixel space 3D generation, the model operates in parallel on overlapping pixel space through a shared-noise initialization that preserves high spatial continuity of flow structure across the entire domain. Against reference LES data, the CFM surrogate can rapidly and accurately restore the first-order statistics with Normalized Root Mean Square Error (NRMSE) of 2.99% for wind and 1.77% for temperature, second-order
turbulence metrics with NRMSE of 7.17% for wind and 8.84% for temperature, turbulent kinetic energy with NRMSE of 7%, probability density function and vertical profiles in representative locations. Wind engineering application of local gust prediction demonstrate that the speed and accuracy of CFM, supporting the use of generative AI for making
turbulence-aware resilient urban design and
climate adaptation more computationally feasible.
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All authors Peng Liu, Shaoxiang Qin, Theodore Potsis, Lili Ji, Dingyang Geng, Liangzhu Leon Wang
Computer Vision
SGF+: Decoupling Gradient Flows for Autoregressive Video Generation
Zihan Su, Junhao Zhuang, Yaowei Li et al. (+10 more)
Autoregressive
video generation requires denoising the current frames while writing their key-value representations as context for future predictions. However, these two roles typically share parameters, and we find that their gradients exhibit distinct patterns and systematic negative
alignment, hindering the joint optimization of visual quality and temporal consistency. We introduce Self Gradient Forcing Plus (SGF+), which assigns separate parameters to context writing and denoising while preserving their interaction through causal
attention. Both roles are jointly optimized using the original generation objective without auxiliary losses, with context writing supervised through its contribution to future predictions. This simple change improves visual quality and long-horizon consistency over the evaluated baselines in both framewise and chunkwise generation, without additional
video training data or a longer training horizon. Trained on only 5s rollouts, SGF+ supports continuous generation for up to 24 hours without long-
video fine-tuning. These results highlight role-specific parameterization as an effective design principle for high-quality autoregressive
video generation and native long-horizon extrapolation.
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All authors Zihan Su, Junhao Zhuang, Yaowei Li, Siwen Lu, Haoran Li, Lingen Li, Haoyu Wu, Weiyang Jin, Songchun Zhang, Haoyang Huang, Chun Yuan, Zeyue Xue, Nan Duan
Machine Learning (Statistics)
Derivative Gaussian Processes on a Two-Direction Budget
Hyunseok Seung and Matthias Katzfuss
Gradient observations promise more accurate Gaussian process (GP) surrogates, but the cost of incorporating them has long stood in the way of realizing that promise. We propose a derivative GP with a budget of just two directions per observed gradient. One direction focuses on each gradient's direct contribution to target prediction, while the other aggregates its indirect contributions through correlations with the conditioning function values. Within a Vecchia approximation, where each prediction conditions on $m$ nearby inputs in $d$ dimensions, this construction represents their $md$ gradient coordinates using at most $2m$ directional derivatives, giving $\mathcal{O}(m^3)$ dense factorization cost per prediction target. For general conditioning sets, we bound the posterior approximation error relative to using full gradients and characterize when the error is small or the approximation is exact. In simulations, our method matches the accuracy of a leading exact gradient-reduction method at equal conditioning set size. Because its cost grows much more slowly with that size, it can use conditioning sets well beyond the
memory limit of the exact method, reaching lower prediction error with a small fraction of the time and
memory. Notably, our method can exploit gradient observations while requiring less computation time or
memory than function-only GP baselines.
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Quantum Physics
Design-Time Conformance Checking for Pulse-Level Quantum Control
Rylan Malarchick
A pulse-level
quantum control program is written against a device whose limits are recorded, if at all, in vendor documentation and source code. A program that exceeds them can be refused at compile time. It can also be accepted and silently altered, or compile and then fail at the board. In the last two cases the experiment runs, and the data does not correspond to the program that was written. We present qconform, a checker that decides whether a pulse program is realizable on a device, given a versioned capability descriptor for that device. Every constraint in a descriptor cites the toolchain observation that established it. The checker is design-time, offline, and deterministic, and it uses no floating point. It reports a verdict, the rules it applied, and a coverage manifest that names what it did not check. We evaluate qconform by differential testing against the QICK and Qblox toolchains, on three QICK board configurations and one Qblox cluster. Over 1263 program runs of 969 distinct programs, the checker accepted no program that a toolchain refuses. On both vendors, a descriptor pinned to one toolchain release accepts programs that older releases refuse. The evaluation also found ten defects in the checker and its descriptors, all fixed.
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Computation and Language
CoTrace: Data Recipes for Training Terminal Agents with Harness-Model Co-Evolution
Jixuan Chen, Jiaxin Zhang, Qinyuan Ye et al. (+11 more)
Terminal-
agent capability depends jointly on model weights and the runtime harness that formats
prompts, binds tools, and handles error recovery. Existing harness-model co-
evolution approaches improve both components, yet often treat trajectories produced during harness search as an undifferentiated replay buffer. This practice overlooks that a trajectory's value for model training depends on the harness under which it was generated. To systematically analyze this interface, we establish an alternating co-
evolution framework that decouples harness search and policy training through component-wise promotion decisions. Within this framework, we introduce CoTrace, a harness-aware data recipe that explicitly governs trajectory routing, provenance matching, and curriculum refresh. Under CoTrace, recurring execution failures guide harness synthesis, while policy training is strictly conditioned on verified rollouts matched to the adopted runtime for supervised fine-tuning (SFT) or fresh online interactions for reinforcement learning (RL). On the Tmax promotion split, CoTrace advances Qwen3.5-9B from 78 to 88 solved tasks under supervised fine-tuning while an online reinforcement variant reaches 90. Specifically, a compact harness-matched corpus produces steady model gains at substantially lower compute than much larger corpora pooled across sibling harnesses. Furthermore, evaluations on Terminal-Bench 2.1 and SWE-bench Lite show that out-of-distribution transfer depends fundamentally on harness compatibility, where maintaining consistency between training and evaluation runtimes prevents procedural execution breakdowns observed under foreign scaffolds.
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All authors Jixuan Chen, Jiaxin Zhang, Qinyuan Ye, Yada Pruksachatkun, Haoxiang Zhang, Jingming Zhuo, Yifan Zhang, Yutong Dai, Juntao Tan, Xiangyu Peng, Silvio Savarese, Zeyuan Chen, Lianhui Qin, Chien-Sheng Wu
Differential Geometry
Compact toric Einstein four-manifolds
Mingyang Li and Song Sun
This is a continuation of our previous paper on toric gravitational instantons. We develop a systematic theory of compact simply-connected Einstein four-
manifolds with toric
symmetry. Applications include (1) The construction of simply connected positive Einstein four-
manifolds with arbitrarily large $b_2$. Our method is based on local gluing combined with a global virtual counting argument. The key idea involves a particular design of rod structures to enable a gluing construction and restrict possible degenerations. (2) A topological characterization of algebraically special toric Einstein metrics. This uses special
curvature identities for $W^+$ in the toric setting. (3) Uniqueness, up to scaling and isometry, on toric four-
manifolds admitting algebraically special Einstein metrics. The proofs uses a variational study of the Einstein–
Hilbert functional. (4) Diffeomorphism classification of compact toric Einstein four-
manifolds in terms of an improved Hitchin-Thorpe inequality $\chi\geq3|\tau|$. In particular, our construction recovers all the classical toric Einstein metrics, including the Page and Chen–LeBrun–Weber metrics, starting from the round sphere through
moduli spaces of conical Einstein metrics.
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Combinatorics
A counting version of Petersen's $2$-factor theorem
Hyunwoo Lee
A classical result of Petersen states that every regular graph of even degree has a $2$-factor. We prove that every $n$-vertex $2r$-regular simple graph contains at least $\left((1 + o_r(1))\frac{2r}{e}\right)^n$ distinct $2$-factors. This improves the previously known lower bound $\left((1 + o_r(1))\frac{r}{e}\right)^n$ by a factor of $2^{(1 + o(1))n}$ and is asymptotically tight for large $r$. As a direct consequence, we determine asymptotically tight bounds on the number of $2$-factorizations of a given $2r$-regular simple graph for every sufficiently large $r$.
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Computer Vision
GraphRectify: Graph-Based Transfer of Adversarial Example Detectors Across Neural Networks
Arash Vashagh and Roozbeh Razavi-Far
Adversarial example detectors are often tied to the classifier backbone they were trained on, limiting reuse when the protected model is replaced or upgraded. Directly transferring such detectors across backbones is challenging because different networks generally produce incompatible internal representations. We propose GraphRectify, a graph-based framework for transferring
adversarial image detectors across classifier backbones. GraphRectify learns a structured representation of intermediate classifier features and adapts representations from a new backbone to the detector learned on the original model, enabling detector reuse. We evaluate GraphRectify across multiple
datasets, backbone architectures, and
adversarial attacks, including detector-aware adaptive attacks that jointly target the classifier and detector. Across the complete evaluation
matrix, GraphRectify achieves higher aggregate ROC-AUC than training a detector from scratch on the new backbone and the evaluated transfer ablations. The gains are particularly strong for transfers between different backbone families and when sufficient data are available. In contrast, training from scratch remains competitive in the most data-limited settings. These results show that
adversarial detection knowledge can transfer effectively across heterogeneous classifier architectures rather than being relearned whenever the protected backbone changes.
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Machine Learning
Which Rollout Taught It That? BehaviorTrace and the Limits of Training-Data Attribution in Online RL
Amit Nautiyal
When reinforcement learning teaches a
language model a new behavior, can we find the training rollouts that taught it? And when an attribution method says it can, how do we know the answer is real? We study both questions on online RL fine-tuning with GRPO, using a planted behavior with a known cause. We release BehaviorTrace, an open evaluation harness that combines full-gradient sketching, the planted-behavior setup, and controls for gradient magnitude, fluency, headroom, and variation across seeds and generation draws. Across three seeds on Qwen2.5-1.5B, much of the apparent attribution signal comes from confounds. A control that ranks training steps by gradient size alone, with no behavior target, reaches 4.2 to 4.5 times chance and matches or beats the best targeted
estimator on two of three seeds. At saturated checkpoints, model fluency predicts the behavior label at least as well as every gradient method we compared it with. Once fluency is controlled, the per-rollout results change from seed to seed and from one generation draw to the next, so a single run cannot settle the question. One signal does hold on all three seeds. The gradient of the trigger
tokens aligns with a target built where the behavior actually occurs. We turn these findings into a checklist for evaluating attribution in RL. We test existing
estimators, including GAS (renormalized TracInCP) and a TRAK-style
estimator, and do not propose a new one.
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Robotics
AirGroundVLN: A Large-Scale Benchmark for Goal-Oriented Air-Ground Collaborative Vision-and-Language Navigation
Zhenxuan Zeng, Qingle Wu, Wei Suo et al. (+4 more)
Goal-oriented
Vision-and-
Language Navigation (VLN) requires
agents to locate and reach targets described in natural
language without prescribed routes. Air–ground collaboration is valuable for tasks requiring both wide-area search and fine-grained localization. However, systematic study of goal-oriented air–ground collaborative VLN remains limited by the lack of large-scale, diverse
benchmarks and two core challenges: 1) substantial differences between aerial and ground views, together with useful observations becoming unavailable as
navigation proceeds, make it difficult to maintain spatially consistent context across platforms and over time; and 2) asymmetric spatial observability makes ground perception locally detailed but spatially limited and aerial perception broad but locally coarse, limiting the reliability of single-platform planning. To address these limitations, we introduce AirGroundVLN, a
benchmark containing 10,281
navigation episodes and 955 target instances across 19 Unreal Engine environments, with seen/unseen splits and an aerial-visibility protocol for systematic evaluation. Alongside the
benchmark, we propose AG-CoNAV, a trainable reference framework comprising two key components: Spatiotemporally Anchored Collaborative
Memory (SACM) and Aerial-Guided Regional-to-Local Planning (AGRLP). SACM maintains and retrieves spatially consistent historical context across aerial and ground observations. Meanwhile, AGRLP combines regional aerial guidance with fine-grained ground
navigation. Extensive experiments demonstrate the effectiveness of AG-CoNAV and establish AirGroundVLN as a comprehensive
benchmark for future exploration.
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All authors Zhenxuan Zeng, Qingle Wu, Wei Suo, Maojia Wu, Bairong Zhang, Hangzheng Yu, Peng Wang
Optics
Lattice tuning of optical and mechanical interactions in gold nanodisk metasurfaces
Juan I. Sangiorgio, Diya Xie, Emiliano Cortés et al. (+2 more)
The interaction between neighboring plasmonic nanoparticles can modify their intrinsic optical and mechanical resonances, enabling collective responses to be controlled through the geometry of their arrangement. Periodic arrays therefore provide a means of controlling both electromagnetic and mechanical interactions through a common geometrical parameter, the
lattice pitch. Joint control of these two channels is particularly useful for engineering how coherent mechanical excitations couple to the substrate and are optically read out at the nanoscale. Here, we investigate the optical and mechanical response of gold nanodisk metasurface patches on silica as a function of
lattice pitch using two-color pump-probe spectroscopy and numerical simulations. Optically, simulations show that varying the pitch tunes a Rayleigh anomaly across the broad localized surface plasmon resonance of the nanodisks, producing a strongly asymmetric collective optical response. Pump-probe measurements further reveal a pronounced wavelength dependence of the optical readout of coherent mechanical vibrations. Mechanically, we investigate how coupling between the nanodisks and the substrate depends on the character of the nanodisk resonances. The intrinsic nanodisk modes exhibit markedly different sensitivities to the periodic environment. One remains nearly independent of pitch, whereas another undergoes a pronounced frequency shift mediated by elastic interactions through the substrate. Numerical simulations further reveal that a third nanodisk resonance couples resonantly to a
lattice-selected acoustic mode, giving rise to an avoided crossing and mode hybridization. These distinct mechanical responses are governed by how efficiently each mode couples to near-surface elastic motion in the substrate. These results demonstrate that
lattice periodicity can simultaneously tune optical sensitivity and substrate-mediated mechanical coupling, providing a versatile platform for tailoring nanoscale optomechanical responses in the GHz regime.
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All authors Juan I. Sangiorgio, Diya Xie, Emiliano Cortés, Gustavo Grinblat, Andrea V. Bragas
Numerical Analysis
A hat function based positive contact discontinuity capturing Boltzmann scheme
Balwinder Singh and S. V. Raghurama Rao
The suitable moments of the Maxwell velocity distribution function recover the conserved variable and flux vectors of the Euler equations of gas dynamics. However, the Maxwellian has infinite support in velocity space, which poses challenges for the numerical analysis of kinetic schemes based on it. Although Maxwellian is a natural choice, it is not the only distribution function that preserves these key moments. In his seminal paper, Perthame (1990) introduced a compactly supported hat function as an alternative. This paper presents the formulation and analysis of a contact discontinuity capturing Boltzmann scheme based on peculiar velocity, constructed using the hat function. Owing to the compact support of the hat function in velocity space, the numerical analysis of the proposed scheme is considerably simplified, allowing for a direct proof of its positivity. The scheme, extended to second-order accuracy without compromising the positivity-preserving property of its first-order counterpart, is tested on several
benchmark inviscid flow problems in one- and two-dimensions.
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Algebraic Geometry
Pablo Portilla Cuadrado
Let $\boldsymbol{n}=(n_1,n_2,n_3):(\mathbb{C}^2,0)\to(\mathbb{C}^3,0)$ be a holomorphic map germ admitting an injective representative. We prove that if $(d\boldsymbol{n})_0=0$, then $\mathrm{ord}_0(\boldsymbol{n})\in\{2,3,4\}$. This reduces Lê's
conjecture to excluding potential counterexamples $\boldsymbol{n}$ of orders $2$, $3$, and $4$. The proof combines techniques from the theory of plane curve singularities, explicit cobordism constructions, and genus bounds obtained by applying properties of the $\Upsilon$ invariant coming from
knot Floer homology.
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Group Theory
On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group
Ayrton Anjos Teixeira and Dessislava H. Kochloukova
We show some sufficient conditions ( in terms of properties of $A$, $B$ and $X$) for the non-abelian exterior square $G \wedge G$ to be residually finite, where $G $ is the wreath product $A \wr B$ or the combinatorial wreath product $G = A \wr_X B$, in the latter case $B$ is a free group. We prove that for the Grigorchuk group $G$ the non-abelian exterior square $G \wedge G$ and the non-abelian tensor product $G \otimes G$ are residually finite. We show conditions that imply that $A \wr B$ is not (cohomologically) good in dimension $\leq 2$.
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Combinatorics
The local dynamical structure of $\Delta^*$ sets via a new Furstenberg family algebra
Angelina Blahodatna, Lauren Detmold, Daniel Glasscock et al. (+1 more)
In this paper, we strengthen the connection between the combinatorics of difference sets and the dynamics of group rotations. Our main result shows that sets which have non-empty intersection with all difference subsets of a commutative
semigroup possess local Bohr structure. This generalizes results of Bergelson, Furstenberg, and Weiss and Host and Kra from the integers to arbitrary commutative
semigroups. We accomplish this by A) utilizing a recent result showing that the regionally proximal relation is an equivalence relation for minimal actions of commutative
semigroups and by B) describing a new, DeMorgan-type
algebra on Furstenberg families that allows for efficient manipulation and computation. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.
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All authors Angelina Blahodatna, Lauren Detmold, Daniel Glasscock, Anh N. Le
Sound
Steerspeech: Activation Steering For Emotion Control In Generated Speech
Afsara Benazir, Darius Pétermann, Felix Xiaozhu Lin et al. (+1 more)
Pretrained text-to-
speech (TTS) models can generate expressive
speech, but reliable inference-time
emotion control remains challenging:
prompts and reference audio offer coarse, inconsistent control, whereas specialized conditioning and model adaptation require costly training. We present SteerSpeech, a lightweight activation-steering framework that controls
emotion by injecting steering vectors into hidden activations. For each target
emotion we train a lightweight low-rank transform, using a multi-expert objective that encourages monotonic
emotion control while preserving speaker identity and linguistic content, constraining steering drift, and keeping the TTS backbone frozen. To optimize through discrete
speech tokens, we introduce a two-pass generation-and-replay pipeline using a straight-through
estimator to backpropagate expert supervision through sampled
tokens. At inference, a target-
emotion steering direction is optimized with its respective transform and injected into the base TTS model. Objective and subjective evaluations with Qwen3-TTS across seen, unseen, and accented speakers show stronger continuous
emotion control with limited speaker and content degradation. SteerSpeech achieves 1.08x-7.12x baseline target-
emotion scores and for a representative
emotion subjectively, it receives 78.1%-96.8% intensity preference and 1.43x-1.46x speaker-identity preservation at high steering strengths.
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All authors Afsara Benazir, Darius Pétermann, Felix Xiaozhu Lin, Salar Rahili
Quantum Physics
CV-QKD with noisy coherent states and realistic displacement receivers
L. F. Melo, J. J. Lacerda, John A. Mora Rodríguez et al. (+1 more)
Near-optimal binary coherent state discrimination can be achieved by performing a displacement operation followed by
photon detection. This displacement serves as a control parameter that can be tuned to optimize a chosen figure of merit, which makes such receivers attractive beyond state discrimination. Here, we turn this discrimination strategy into a complete continuous-variable
quantum key distribution (CV-QKD) protocol based on a binary alphabet of noisy coherent states (displaced thermal states) and displacement receivers. We develop a strategy for estimating the channel parameters with the same displacement receiver, since standard quadrature-based methods do not apply. While a key map can be obtained with on/off detection, we demonstrate that reliable parameter estimation requires
photon-number-resolving detection with sufficient resolution. Finite detector resolution underestimates the observed noise and constitutes a potential security loophole, which we quantify and show to be mitigable with modest resolution. We analyze the protocol's security against entangling-cloner collective attacks in the asymptotic regime, for both direct and reverse reconciliation, and show that it can generate secret keys even under noisy state preparation and imperfect detection. Interestingly, we find that the displacement that minimizes the discrimination error probability also performs well for key generation, thus providing a useful and analytically tractable tuning strategy for the CV-QKD receiver. We evaluate the protocol's performance over a range of transmittances and noise parameters, showing that the displacement receiver can outperform conventional homodyne detection in experimentally relevant regimes. Together, our results point to displacement receivers as a promising alternative for CV-QKD implementations.
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All authors L. F. Melo, J. J. Lacerda, John A. Mora Rodríguez, Alexandre B. Tacla
Analysis of PDEs
Stability for a formally determined Lorentzian inverse problem
Spyridon Filippas and Lauri Oksanen
We consider the inverse problem of recovering a potential $q$, depending on space and time, in the wave equation $(\Box_g+q)u=0$ on a Lorentzian
manifold. We prove Lipschitz stability for a formally determined version of this problem under a null-cone foliation assumption. As a consequence, we obtain uniqueness for the Lorentzian Calderón problem in a fixed conformal class. Our approach uses distorted spherical waves.
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Materials Science
Magnetic Order from First-Principles Linear Response
Yaroslav Zhumagulov, Emiliano Cruz-Aranda, Denis Kochan et al. (+1 more)
The
magnetic order of a material is usually predicted by comparing the energies of trial
spin configurations, a strategy that cannot reach orders outside the chosen set and rapidly becomes intractable as the number of
magnetic sites grows. We show that the order can instead be identified directly from the paramagnetic state: the leading eigenmodes of its self-consistent magnetization response, obtained with
spin–orbit coupling at arbitrary wavevector within the primitive
cell, determine both the ordering wavevector and the pattern of moments, with no candidate configurations. With no prior assumption about the order, the method correctly reproduces the G-type stacking with out-of-plane moments in the altermagnet candidate KV$_2$Se$_2$O, the $3{:}1$ ferrimagnetic tetrahedra of Cu$_2$OSeO$_3$, and the incommensurate spiral instability of monolayer NiI$_2$. Our results establish the response of the paramagnetic state as a predictive and unbiased route to assessing
magnetic order, enabling systematic searches for complex magnets.
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All authors Yaroslav Zhumagulov, Emiliano Cruz-Aranda, Denis Kochan, Oleg V. Yazyev
Machine Learning
Training Parallel Speculative Draft Models by Directly Minimizing Expected Decoding Rounds
Yunxiao Zhao and Changxiao Cai
Speculative decoding accelerates large
language model inference by using a low-cost draft model to propose
tokens that the full-size target model verifies in parallel. Parallel and semi-autoregressive (semi- AR) drafters improve drafting efficiency by proposing an entire block in a single forward pass, but training them raises a new difficulty: the draft distribution for a given position depends on where the decoding round starts, and where rounds start depends on how many
tokens earlier rounds accepted. Existing training objectives typically rely on block-local surrogates that ignore this cross-round coupling, and therefore do not directly optimize the global decoding efficiency. In this work, we develop a theoretical framework for training and evaluating these drafters by representing speculative decoding as a Markov reward process. This formulation yields the Expected Decoding Rounds (EDR) objective, which weights local rejection costs by state occupancies and exactly equals the expected number of decoding rounds. Unlike prior surrogate objectives, EDR introduces no auxiliary hyperparameters. We then derive an exact temporal-difference gradient that supports unbiased
stochastic optimization from target-model rollouts. The same framework also yields an exact offline evaluator for round counts, enabling paired drafter comparisons on shared target rollouts without running speculative decoding. Finetuning two state-of-the- art drafters, DSpark and DFly, with EDR consistently improves mean accepted length and outperforms existing training objectives across nine
benchmarks spanning math
reasoning, code generation, and chat.
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Algebraic Geometry
Transverse rational curves and the LeBrun–Salamon conjecture
Zhengyu Hu, Kefeng Liu and Xueyuan Wan
We prove that every compact connected positive quaternionic–Kähler
manifold of real dimension $4n$ with $n\ge2$ is isometric to a Wolf space after rescaling the metric by a positive constant. This proves the LeBrun–Salamon
conjecture. The proof uses transverse rational curves and the contact structure of the twistor space.
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Robotics
RobotWorld: Benchmarking Multimodal Agents for Robot Use Across Diverse Tasks and Embodiments
Zhiqin Yang, Chenxin Li, Xiaomeng Hu et al. (+30 more)
General-purpose
agents increasingly write code, use tools, and complete complex digital tasks, raising the question of how far these capabilities carry into the physical world. To investigate this, we introduce RobotWorld, a challenging simulation testbed for
robot use: turning instructions and observations into physical task execution through
robot interfaces. Its 84 tasks span manipulation, mobile manipulation, locomotion, driving, and aerial control, with explicit interaction budgets and executable success checks. By analysing task outcomes alongside execution traces, we identify both the capabilities that transfer and the gaps that prevent reliable completion. Furthermore, we find that current
agents can construct sophisticated perception and control workflows, including image
segmentation, camera calibration, spatial estimation, and dynamics-based computation. These capabilities, however, do not consistently compose into successful behaviour:
agents lose task-relevant object states despite reaching commanded poses, fail to correct ineffective actions, recover too late, or mistake unfinished tasks for completion. This uneven transfer also differs across models: Astra succeeds more often on spatial and constrained-contact goals, whereas Opus 5.5 succeeds more often on continuous-balance and timed-interaction goals. By linking these outcomes to execution behaviour, RobotWorld provides both a rigorous proving ground and an empirical account of the remaining capability gaps, thereby establishing concrete targets for training and designing more reliable physical-world
agents.
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All authors Zhiqin Yang, Chenxin Li, Xiaomeng Hu, Yibin Liu, Weidong Huang, Jiankai Sun, Haitao Li, Zijian Wu, Yuzhi Huang, Fanding Huang, Hanwen Sun, Jiashun Liu, Jingqi Tong, Mingxin Huang, Shaoli Hu, Shijue Huang, Tianyi Bai, Xinyuan Wang, Yunlong Lin, Zhengyang Tang, Zhexin Zhang, Zhuo Chen, Xierui Song, Juntao Dai, Boyuan Chen, Jiaming Ji, Fangneng Zhan, Mengkang Hu, Wei Xue, Yonggang Zhang, Han Hu, Tsung-Yi Ho, Yike Guo
Computer Vision
Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry
Subhransu S. Bhattacharjee, Dylan Campbell and Rahul Shome
Procrustes-Wasserstein
alignment jointly estimates a matching and rotation without supplied correspondences, but alternating minimization can stop at suboptimal solutions. Rubix solves the equally weighted planar problem globally under squared Euclidean loss. Each matching $\sigma$ of two centered $n$-point sets defines a complex correlation $z_\sigma=\sum_i\bar x_i y_{\sigma(i)}$. Their convex hull is the permutation polygon: supporting vertices give optimal matchings at fixed rotations, and the farthest vertex gives the global
alignment. We prove the sharp bound of $n(n-1)$ vertices for $n\ge2$, answering Rote's rotation-assignment open problem. In exact arithmetic, assignment queries recover the polygon in $\mathcal O(n^5)$ operations. Assignment-based bounds extend the approach to three-dimensional rotations and partial matching at a supplied translation through branch-and-bound. On timed MPEG-7 shape pairs, Rubix attains every numerical reference value in 12 ms on average, 50 times faster than a rotation grid at the same accuracy. Its distances improve
gravity-aligned matching of real 3D scans, shape
retrieval and noisy
crystal classification over alternating minimization.
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Artificial Intelligence
SOTA: Stock Options Trading Agents Guided by Option-Implied Return Distributions
Yizhen Xie and Mengyang Liu
As option
markets grow and AI advances, agentic systems for option trading are gaining increasing
attention.
Language-model-based
agents can reason over contextual information such as news, but option trading presents a particularly challenging decision problem: a single stock can have thousands of contracts, and the
agent must decide both which contracts to trade and how to combine them. Existing approaches often sidestep this complexity by restricting the policy to a fixed strategy structure, such as a straddle, limiting their ability to switch strategies as
market conditions change. We present SOTA (Stock Options Trading
Agents), an agentic trading framework for structured option-strategy selection. SOTA abstracts the large option universe into strategy-level decisions while deterministic resolvers handle portfolio implementation. We develop SOTA by post-training Qwen3.8-27B with supervised fine-tuning followed by reinforcement learning. SOTA is evaluated on options on nine large-cap U.S. equities and SPY against rule-based and machine-learning strategy selectors in the same trading environment. Over a six-month out-of-sample period, SOTA earns an 18.3% total return with a Sharpe ratio of 1.60 and a maximum drawdown of 8.96%. We also document an asymmetric role of news: news improves frontier-teacher trajectories, but retaining news during reinforcement learning reduces out-of-sample return from 18.3% to -2.7%.
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Rings and Algebras
$W$-algebras with involution: polynomial identities and asymptotic growth
Ginevra Giordani, Antonio Ioppolo and Carla Rizzo
Let $W$ be an
algebra with involution over a field of characteristic zero. We develop a theory of $W$-
polynomial identities with involution for finite-dimensional $(W,*)$-
algebras $A$, using the multiplier
algebra with involution of $A$. We prove that the $(W,*)$-exponent of $A$ exists and coincides with the ordinary $*$-exponent. We then consider a four-dimensional subalgebra $M$ of the
algebra of $4\times4$ upper triangular
matrices, endowed with the reflection involution, and study two non-equivalent $(W,*)$-
algebra structures on it. For both structures, we determine the corresponding $T_W^*$-ideals of $W$-
polynomial identities with involution and compute the $(W,*)$-codimension sequences explicitly; for one of them, we also determine the complete $(W,*)$-cocharacter sequence. Finally, we prove that these two $W$-
algebras with involution generate distinct varieties of almost
polynomial growth.
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