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All of arXiv

Thursday 17 September

Robotics

Learning Slope-Adaptive Whole-Body Locomotion for Humanoid Robots in Roofing Construction

Songyang Liu and Shuai Li

Roofing requires workers to coordinate locomotion, balance, and work-related body motions on pitched surfaces, creating a challenging application for humanoid robots. Directly retargeted human demonstrations, however, may preserve motion appearance while placing the robot's feet or hands incorrectly relative to the roof. This study presents a task-semantic scene-grounded framework for learning roofer-style whole-body motions on a Unitree G1. Human demonstrations are captured using a tracking system and retargeted to the robot, while a metric roof model supplies the spatial reference unavailable from the tracking system. A trajectory-level optimization grounds inferred support contacts and annotated work relations to the roof, and execution-aware reinforcement learning encourages the resulting policy to preserve these relations under dynamic tracking errors. The framework is evaluated through a multi-motion tracking study, a roof-pitch coverage matrix, a five-way nailgun ablation, cross-task experiments on hammering and lateral pushing, and comparisons with pure reinforcement learning and zero-shot teleoperation. Our method enables the robot to satisfy support, work-clearance, and nonpenetration criteria across all evaluated seeds. Across nailgun, hammering, and pushing, it achieves work-clearance errors between 0.256 and 0.531 cm and 3/3 successful evaluations per task. Physical experiments reproduce uphill walking, nailgun, hammering, and bending motions with mean base-frame motion errors below 80 mm. These findings establish scene-grounded human motion learning as a promising basis for construction-oriented humanoid motion primitives.
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High Energy Physics (Phenomenology)

A quantum representation of $\pi$ fragmentation functions through variational quantum circuits

David F. Rentería-Estrada, Roger J. Hernández-Pinto, Germán Rodrigo et al. (+2 more)

We present a variational quantum-circuit model for fragmentation functions (FFs). Isospin and charge-conjugation symmetries are imposed to construct an independent six-flavor basis describing charged and neutral pion production, while physics-inspired Ansätze, including logarithmic feature maps and mass thresholds, encode the relevant kinematics. This quantum architecture substantially reduces the quantum circuit redundancies and improve optimization convergence. Using the DSS14 pion FF set as a benchmark, we first develop a one-dimensional variational representation (FF-VQR) in the momentum fraction at fixed energy scale, and show how entanglement between quark and gluon FFs yields a significant improvement, with accurate results already obtained using just two variational layers. A spectral analysis further demonstrates that the quantum model achieves high expressivity with a limited number of Fourier modes, supporting its use as a compact non-perturbative parametrization suitable for DGLAP evolution. We then extend the FF-VQR to two dimensions by incorporating the energy-scale dependence. By encoding all flavor channels within a single entangled quantum circuit, the quantum model provides a unified representation with higher accuracy than an independent encoding for each partonic species.
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All authors David F. Rentería-Estrada, Roger J. Hernández-Pinto, Germán Rodrigo, Rodolfo Sassot, German F. R. Sborlini

Numerical Analysis

Incremental Column Subset Selection via Conditional Determinantal Point Processes

Laura Grigori and Zhipeng Xue

Column subset selection aims to seek a small set of representative columns that accurately approximates a given matrix. We study this problem from the perspective of determinantal point processes (DPPs) and their relation to several existing algorithms. To support incremental column selection, we introduce conditional DPPs, which can be applied to any column selection strategy. In particular, we combine it with adaptive randomized pivoting(ARP), and develop a multi-stage ARP (MSARP) algorithm. We establish theoretical guarantees on the expected Frobenius-norm approximation errors for these methods. In addition, we propose a fixed-precision variant of ARP that adaptively determines the number of selected columns. Numerical experiments on column subset selection and Nyström approximation show that MSARP achieves accuracy comparable to standard ARP while enabling incremental selection.
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Functional Analysis

Zero-product problem for Toeplitz operators on the Fock space

Jie Qin

We answer Bauer and Le's question on zero products of Toeplitz operators on the Fock space $F^2(\mathbb C^n)$[JFA, 261 (2011), 9, 2617–2640]. For $n\ge2$, we construct two bounded nonradial Schwartz symbols on $\mathbb C^n$ whose Toeplitz operators are nonzero and have zero product on $F^2(\mathbb C^n)$. For $n=1$ and each $c\in(1/2,1)$, we construct two smooth nonradial symbols of growth at most $Ce^{c|z|^2}$ for some constant $C>0$. Their extended Toeplitz operators in $F^2(\mathbb C)$ are nonzero and have zero product on all holomorphic polynomials. Moreover, the second symbol is bounded when $c\geq3/4$. Our proofs use Gaussian kernel calculations, matrix identities, theta functions and Fourier transform.
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General Economics

Does Training on Future Data Pay? Look-Ahead Bias in Forecasting with Pretrained Models

Haiqiang Chen, Li Chen, Yunlong Chen et al. (+2 more)

We examine whether post-origin training information inflates the measured accuracy and economic value of financial forecasts. We evaluate five sets of financial time-series foundation models, each comprising independently trained annual vintages under U.S., global, and factor-augmented training environments, across 14 equity markets and four forecast horizons. Rolling comparisons vary the annual vintage for a fixed forecast; fixed-vintage comparisons hold the vintage fixed as target windows move across its training cutoff. Each alternative forecast is paired with an origin-aligned point-in-time (PIT) benchmark using identical numerical histories and inference protocols. In the U.S.-trained reference environment, post-origin vintages materially revise informative PIT forecasts but generally reduce accuracy in both designs. Pooled rolling comparisons yield higher mean squared forecast errors in 18 of 20 U.S. model-set-horizon combinations. The origin-crossing update also performs worse on average than an equally long pre-origin update. Under a common constrained allocation rule using one-month forecasts, median exposed-minus-PIT differences in annualized certainty-equivalent returns are -1.77 percentage points in the United States and -2.14 points internationally. Global and factor-augmented training produce more mixed predictive effects. An exact squared-error decomposition shows that revisions improve accuracy when their error-correcting benefit exceeds their mean squared magnitude; under U.S. training, alignment with PIT errors generally falls short of this requirement. Temporal exposure therefore establishes an information-set violation, not sufficient evidence of inflated predictive accuracy or investor value.
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All authors Haiqiang Chen, Li Chen, Yunlong Chen, Difang Huang, Bo Zhang

Algebraic Geometry

Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I

Andrew Obus, Padmavathi Srinivasan and Connor Stewart

We prove conductor-discriminant inequalities for all $\mathbb{Z}/n$-covers of $\mathbb{P}^1$ defined over discretely valued fields $K$ with excellent valuation ring $\mathcal{O}_K$ and perfect residue field of characteristic not dividing $n$, modulo some calculations appearing in work of the third author (arXiv:2609.20585). Specifically, when such a curve $X$ is given by $y^n = f(x)$ with $f(x) \in\mathcal{O}_K[x]$ and $n\mid\text{deg}(f)$, and if $\mathcal{X}$ is its minimal regular model over $\mathcal{O}_K$, then the negative of the Artin conductor of $\mathcal{X}$ is bounded above by $(n-1)v_K(\text{disc}(\text{rad}(f)))$. This is a direct generalization of previous work of the first two authors on hyperelliptic curves, which in turn generalized work of Ogg, Saito, Liu, and the second author. When $f$ is monic, this strengthens a result of Kohls stating that the conductor exponent of the Jacobian of such a curve is bounded above by $(n-1)v_K(\text{disc}(\text{rad}(f)))$.
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Instrumentation and Detectors

Mineral Detection of Neutrinos and Dark Matter 2026 Proceedings

Alexey Elykov, Patrick Stengel, Natsue Abe et al. (+81 more)

The fourth "Mineral Detection of Neutrinos and Dark Matter" (MDvDM'26) meeting was held April 14-17, 2026 in Karlsruhe, Germany, hosted by the Institute for Astroparticle Physics (IAP) at Karlsruhe Institute of Technology (KIT). These proceedings detail the contributions that were presented during MDvDM'26, illustrating the unprecedented progress in theoretical, computational and experimental studies towards the realization of the concept of mineral detectors. Mineral detectors represent an emerging particle detection concept that has risen in prominence in recent years due to the advent of modern computational and high-resolution microscopy techniques. Natural and synthetic crystals are capable of retaining microscopic damage features induced by nuclear recoils, which could be then read out with a variety of micrometer and nanometer resolution microscopy techniques. On laboratory time scales mineral detectors could be employed for reactor neutrino monitoring and dark matter detection, with the potential to measure the directions as well as the energies of the induced nuclear recoils. Uniquely, ancient natural crystals (so-called paleo-detectors) that have been recording nuclear recoils over geological timescales could be used for studying astrophysical neutrinos, cosmic rays, dark matter and heavy exotic particles, as well as the variation of their fluxes over our Galaxy's lifetime. In recent years the international MDvDM community has been successfully tackling the challenges associated with realizing the concept of mineral detectors, opening the pathway towards a fully fledged experimental program and potential future discoveries.
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All authors Alexey Elykov, Patrick Stengel, Natsue Abe, Daniel Ang, Lorenzo Apollonio, Levente Balogh, Laura Baudis, Chinmay Bharathulwar, Priyanshu Bhattacharya, Yilda Boukhtouchen, Joseph Bramante, Vincent Breton, Andrew Buchanan, Jens Burkhart, Lorenzo Caccianiga, Andrew Calabrese-Day, Mason Camp, Jordan Chapman, Anson Cook, Reza Ebadi, Denis Erkal, Katherine Freese, Audrey Fung, Shota Futamura, Claudio Galelli, Kevin Gao, Peter W. Graham, Thomas Haddock, Minako Hashiguchi, Alexander Hayes, Adam A. Hecht, Samuel C. Hedges, Shigenobu Hirose, Luisa M. Hötzsch, Patrick Huber, Yohei Igami, Vsevolod Ivanov, Florian Jörg, Ayuki Kamada, Takenori Kato, Yoji Kawamura, Katharina Kehl, Chris Kelso, Holger Kluck, Emilie M. LaVoie-Ingram, Matthew Leybourne, Gavishta H. M. Liyanage, Thalles Lucas, Brenden A. Magill, Paolo Magnani, Jennika McIntosh, Naoki Mizutani, Kohta Murase, Tatsuhiro Naka, Lina Necib, Pranav Parvathaneni, Andre Peterson, Zachary S. C. Picker, Rabeya Rabu, Harikrishnan Ramani, Anupam Ray, Morteza Roostaeinia, Hannah Ross, Issei Saikyo, Lukas Scherne, Maximilian Shen, Aaron Shugar, Joshua Spitz, Kai Sun, Jiashen Tang, Erwin H. Tanin, Dionysios P. Theodosopoulos, Yoichi Usui, Pieter Vermeesch, Aaron Vincent, Ronald Walsworth, Jin-Wei Wang, David Waters, Samuel S. Y. Wong, Audrey Wu, Gregory Wurtz, Wen Yin, Xiuyuan Zhang, Zhexian Zhang

Astrophysics of Galaxies

Interstellar disparity: N- vs O-bearing molecules: A multidisciplinary perspective across interstellar environments

Mathilde Bouvier, Joan Enrique-Romero and Marta De Simone

Observations of O- and N-bearing molecules reveal systematic chemical differentiation across a wide range of interstellar environments. This pattern is peculiar and its origin likely reflects a combination of physical conditions, chemical pathways, and observational effects rather than a single mechanism. In this paper, we provide a comprehensive overview of the current understanding of the N-bearing and O-bearing species and their relative behaviour in the interstellar medium, integrating results from observations, laboratory experiments, chemical modelling, and theoretical studies. While inspired by discussions at the Lorentz Center workshop held in Leiden in August 2025, this work goes beyond a summary of the meeting and instead synthesizes the state of the field, highlights key open questions, and outlines future directions. We identify several key observational, experimental, and theoretical challenges that must be addressed to determine the origin of this chemical differentiation.
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Statistics Theory

Principal component error in high-dimensional factor models

Alex Bernstein, Lisa R. Goldberg, Nicholas Gunther et al. (+4 more)

In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of principal directions, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics, genomics, machine learning and signal processing. Out-of-subspace error measures the distance from an estimate to the subspace spanned by population factor exposures. It can be expressed in terms of data, providing an estimable floor for asymptotic error. In-subspace error is driven by a rotation error within that subspace, which arises from the fixed sample size of the latent factor returns and cannot be estimated from data alone. We illustrate our error analysis with a three-factor simulation of the US public equity market, showing the dependence of the magnitude of the error and its components on dimension and sample size. In that simulation, out-of-subspace error dominates. Researchers who rely on principal component analysis to estimate factor models can use our results to quantify errors in model-based predictions and attributions.
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All authors Alex Bernstein, Lisa R. Goldberg, Nicholas Gunther, Alec N. Kercheval, Tian Lan, Yian Lin, Dayi Yao

Quantum Physics

Scalable logical qubits

Matthias Troyer, Chetan Nayak and John Martinis

Utility-scale quantum computing will require executing long, complex algorithms with end-to-end error rates far below what physical qubits can support directly. Error-corrected logical qubits are needed to achieve this goal. To make the progress on logical qubits measurable and comparable we introduce the definition of scalable logical qubits: logical qubits preserved for long computations by repeated quantum error correction, capable of fault-tolerant universal operations with low-latency real-time decoding and feedback, and replicable to the hundreds or thousands, as required by applications. We characterize these scalable logical qubits along four coupled dimensions: reliability, scale, capability, and performance, and discuss trade-offs among these dimensions.
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Machine Learning

Mitigating Retaliatory Algorithmic Collusion in Repeated Games

Karthik Sivachandran and Rohan Paleja

Reinforcement learning agents trained to maximize their own reward in repeated interactions can converge to supra-competitive outcomes resembling explicit collusion, without communication or shared design. Existing mitigation approaches are largely tied to specific economic settings, like two-sided platforms and auctions, leaving open how to design interventions for general repeated games. We address this gap by formalizing the connection between empirical observations from prior work on Q-learning collusion and classical theory of Simple Penal Codes (SPCs). We show any non-trivial SPC induces a quantifiable conditional dependence in agents' policies, detectable via the total variation distance between an agent's action distributions across cooperation and defection histories. Building on this connection, we propose CURB (Collusion Unwinding via Reward shaping and Belief injection), a reward-shaping framework that penalizes this Total Variation (TV) distance signal during Q-learning and is guaranteed to convert any SPC fixed point of the dynamics into a trivial one, thus precluding collusive equilibria sustained by punishment threats. Empirically, CURB substantially reduces collusion by Q-learning agents in both Bertrand and Cournot Competition Repeated Games. We further demonstrate that CURB extends to deep Q-network agents in Bertrand competition, suggesting the mechanism generalizes beyond tabular Q-learning.
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Representation Theory

Representations of formal Lie groups and Lie pairs

Fulin Chen, Binyong Sun and Chuyun Wang

Formal Lie groups, which generalize Lie groups in differential geometry, are analogous to formal group schemes in algebraic geometry. In a previous paper, we established the basic theory of formal Lie groups, including a formal Lie theory theorem that identifies formal Lie groups with Lie pairs. In this paper, we develop the foundations of the representation theory of formal Lie groups and Lie pairs. In particular, we construct modules of Lie pairs on function spaces over formal manifolds and prove that the category of representations of a formal Lie group is isomorphic to the category of modules of the corresponding Lie pair.
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Combinatorics

Fractional expectation thresholds and the "second" Kahn-Kalai conjecture

Tuan Tran

We show that the uniform probability measure on copies of a nonempty graph $H$ in $K_n$ is $Cq_H\log(2e(H))$-spread, where $q_H$ is its graphic expectation threshold. Consequently, the fractional expectation threshold of $H$ is at most $Cq_H\log(2e(H))$. We remove the logarithmic factor for trees and for graphs whose average degree is at least the logarithm of their maximum degree. This proves the “second” Kahn-Kalai conjecture for these two classes, which encompass most of the standard families studied in random graph containment problems.
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Lattice Field Theory

Computability of GPDs near $x=\pm\xi$ in Lattice QCD

Yushan Su, Xiangdong Ji, Yizhuang Liu et al. (+1 more)

In lattice QCD computations of generalized parton distributions (GPDs), the large momentum expansion generally requires all hard scales, $2|x\pm\xi|P^z$ and $2|1\pm x|P^z$, to be much larger than $\Lambda_{\rm QCD}$. We show that this condition can be relaxed for $2|x\pm\xi|P^z$ at large $\xi$, making the important $x\sim\pm\xi$ regions accessible to lattice calculations and considerably expanding the region of computability. Revisiting previous lattice results with complete one-loop matching, we obtain the expected partonic threshold behavior—GPDs continuous at $x=\pm\xi$ but with discontinuous derivatives—which has not previously been observed on the lattice. We thus obtain, for the first time, important prediction for GPDs in the distribution-amplitude-like region, which smoothly connects the quark and antiquark PDF-like behaviors.
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All authors Yushan Su, Xiangdong Ji, Yizhuang Liu, Rui Zhang

Optimization and Control

Convergence rate of the moment-SOS hierarchy for univariate polynomial optimization

Didier Henrion and Mohab Safey El Din

We study the convergence rate of the moment-SOS (sum-of-squares) hierarchy for polynomial optimization problems (POPs) on a bounded subset of the real line described by arbitrary polynomial inequalities. We prove that, for every fixed univariate POP, the relaxation error is bounded by $O(1/r^2)$, where $r$ is the relaxation order. In particular, boundary degeneracies in the polynomial description of the feasible set affect the constant but not the convergence exponent. The proof combines the structure of finitely generated univariate quadratic modules with a Chebyshev polynomial construction that approximately recovers the natural generators of the feasible set while controlling the degree of the certificate. We also give an elementary degree-four example for which the relaxation error is exactly $1/(2r(r-1))$, showing that the quadratic rate is optimal. Equivalent reformulations connect this example to a cubic univariate problem and to a bivariate POP whose feasible set has a cusp singularity at the minimizer.
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Artificial Intelligence

Language-model groups overstate consensus when replaying human deliberation on a reasoning task

Tengfei Shao

Full-consensus rates are often treated as indicators of collective cognition, yet depend on how participation and final states are operationalized. We replayed 100 held-out human Wason groups with matched large language model (LLM) agent groups, seeding one belief-anchored agent per participant's pre-discussion answer and scoring agents and people with the same code. Across human scoring definitions, estimates ranged from 24.0% to 57.0%; about one fifth of participants never posted, whereas agents almost always did. Agent groups remained more consensual in two post-unblinding sensitivity analyses: the submit-based comparison (n = 98) yielded gaps of 34.0 and 43.9 percentage points for chat and reasoning modes, and the participation-matched comparison (n = 45) yielded gaps of 34.1 and 44.4 points. These complementary routes reduced different measurement asymmetries yet converged within 0.5 percentage points. The gap persisted without early stopping and under a reparameterization removing the memorizable answer; reasoning-mode groups then agreed nearly unanimously, mostly on incorrect answers. Simulated consensus did not track collective accuracy, and belief-anchored agent groups were biased estimators of the human group-outcome distribution in this setting. These analyses provide a scoring-explicit basis for assessing simulated-group estimates of human deliberative outcomes.
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Quantum Physics

Technical Report OFDM-Assisted Simultaneous Quantum and Classical THz Communications

Xin Liu, Chao Xu, Soon Xin Ng et al. (+4 more)

The feasibility of cost-effective simultaneous quantum and classical communication (SQCC) transmitting both the quantum key and classical information via a superimposed coherent state is investigated both in optical and Terahertz (THz) bands. Since the existing THz SQCC schemes assume single-carrier (SC) transmission over flat fading channels, we embark on investigating SQCC in realistic frequency-selective multipath THz fading channels. We then propose an orthogonal frequency division multiplexing (OFDM) based SQCC system for time-invariant frequency-selective THz scenarios, supported by low-density parity-check coded (LDPC) multidimensional QKD reconciliation schemes. Our simulation results demonstrate that the OFDM-based SQCC scheme is capable of achieving a practical secret key rate (SKR) over a wide range of power sharing scenarios between the classical and quantum signals. By contrast its single-carrier counterpart requires the classical signal to be at least 100 times stronger than the quantum signal in THz SQCC.
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All authors Xin Liu, Chao Xu, Soon Xin Ng, Mohammed El-Hajjar, Phuc V. Trinh, Shinya Sugiura, Lajos Hanzo

Computation and Language

An Analysis of Training-Free Self-Reported Confidence in Language Models

Lukas Meyer, Sofia Rossi, Wei Chen et al. (+2 more)

Large language models can report a numerical confidence together with generated content, but it is unclear whether this report is more than calibrated rhetoric. We analyze three training-free signals: confidence verbalized with the answer, post-hoc $P(\mathrm{True})$, and agreement with three additional generations on the same 100 TriviaQA questions for two model families. Direct verbalization is a surprisingly strong baseline: after auditing benchmark errors, it reaches AUROC 0.956 and 0.937 for correctness prediction. Three-sample agreement is substantially weaker (0.765 and 0.790), and a fixed interpolation with verbalized confidence has no statistically reliable benefit. Four of nine errors from one model and two of eight from the other receive unanimous sample support, showing that self-consistency can amplify shared misconceptions. Re-eliciting confidence for the same fixed answers with equivalent prompts changes scores by 0.043 to 0.084 on average and flips 4% to 9% of decisions at a 0.8 threshold. An exploratory audit of 100 confidence-tagged biography claims further finds only a modest confidence gap between supported and contradicted claims. These results argue that useful self-reports remain sensitive to elicitation, correlated errors, and benchmark noise.
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All authors Lukas Meyer, Sofia Rossi, Wei Chen, Thomas Laurent, Yiming Li

Robotics

Integrated Guidance and Control of a Mother-Child UAV-UGV System for Cooperative Missions

Aashish Sahu and R. Prasanth Kumar

Autonomous recovery of a small multirotor onto a hovering multirotor carrier differs from recovery onto ground or shipborne platforms because the recovery surface is itself an actively controlled, thrust-limited aerial vehicle. This paper presents a field-validated autonomy framework for a heterogeneous rover-mothership-child system executing rover supervision, mothership transit, child deployment and sortie, autonomous return, aerial recovery, and synchronized descent. The recovery stack combines jerk-bounded reference generation, disturbance-observer-augmented planar tracking, feasibility-aware vertical control, a discrete-time barrier-based safety filter for relative vertical geometry, and communication-aware carrier-state prediction. The contribution is the coordinated system-level integration of these methods for recovery onto a hovering multirotor and its full-scale outdoor validation. The framework is implemented on a PX4-ROS 2 architecture using RTK-enabled GNSS, IMU, and barometric fusion, with mothership-side 1D lidar used only as an auxiliary near-contact cue. RTK-fixed positioning was maintained throughout testing. Across 20 outdoor cooperative missions, 17 successfully completed deployment, sortie, and recovery, giving an observed mission success rate of 85%. For successful recoveries, mean terminal-alignment time was 6.3 s, mean planar alignment error at acceptance was 0.18 m, maximum terminal planar deviation was 0.32 m within a 0.40 m capture radius, and minimum logged relative vertical separation during coupled descent was 0.41 m. Mothership planar station-keeping RMS error was 0.25 m. The three unsuccessful trials occurred at different mission stages and are analyzed separately. Results demonstrate practical autonomous aerial recovery within the tested outdoor operating envelope.
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Machine Learning

Parallelism, critical windows, and separations among diffusion language models

Sitan Chen and Liye Wang

A popular selling point of diffusion large language models (dLLMs) is their capacity for parallelism: the ability to generate sequences of text far more efficiently than autoregressive models, which require one forward pass per token. Yet among the many competing paradigms for dLLMs, from masked to uniform to Gaussian diffusion, principled understanding of how these different proposals compare in parallelism remains limited. In this work, we initiate a fine-grained comparison of the capacity for parallelism among these three leading approaches and prove the following: - Uniform and Gaussian diffusion can sample in a number of forward passes which scales with the dual total correlation of the underlying distribution, a measure of intrinsic complexity which can be much smaller than the context length. Previously, it was only known how to achieve this using masked diffusion. - For a certain family of random empirical measures, we show that $\widetilde{\Theta}(\sqrt{d})$ forward passes are necessary and sufficient to sample using uniform or Gaussian diffusion, yet there exist approximate score oracles for which $\widetilde{\Omega}(d)$ forward passes are needed for masked diffusion. This establishes the first provable separation in parallelism between the three prevailing dLLM paradigms. Contrary to popular intuition that masked diffusions are harder to parallelize because they must commit to token values, the latter separation instead comes from the fact that the critical windows in masked diffusion sampling are asymptotically narrower than those in uniform and Gaussian diffusion sampling.
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Artificial Intelligence

Refuse, Decompose, Refresh: A Claim-Safe Protocol for Closed-Loop AI Evaluation

Peiying Zhu and Sidi Chang

An AI evaluation can be perfectly reproducible and still support the wrong claim. This risk is acute in closed-loop systems: policy determines visited states, observable components, and which failures leave a measurable trace. We propose a claim-safe protocol with three actions. Refuse: abstain when a clean reference stream or matched runtime comparison lacks support. Decompose: report protocol execution, operational false admission, and structural hypotheses separately rather than as one PASS/FAIL label. Refresh: treat distribution-shift alarms as requests to invalidate and recompute a reference map, not as fault evidence. We instantiate the protocol in an aggregate-only simulator with 24 policy components, three demand regimes, two fault-mask families, and independent development and heldout seeds. The preregistered heldout contains 1,440 cases and 21,600 partition rows. Only 55/72 regime-component units were reference-admitted and 54/55 remained runtime-admitted, making abstention part of the result. Stable false admission was 0/20 represented components, with a one-sided exact 95% upper bound of 0.1391 under a frozen 0.20 rule. Within admitted units, affected clean traffic outpredicted nominal fault-cell fraction: across 540 unit-arm rows nested in 20 component clusters, the cell-minus-traffic negative-log-likelihood difference was 0.1264 nats per row, with a 95% component-cluster interval of [0.0593, 0.1918]. A drift log shows why "null" must be reference-relative: clean fault-null streams triggered 15/15, 0/15, and 14/15 alarms across three regimes, while only the middle regime matched the frozen detector reference. Rather than a universal threshold, we contribute an executable contract linking observable support, statistical calibration, and justified claims.
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Quantum Physics

Coherent error threshold for quantum LDPC codes

Zhengyi Han, Yuanchen Zhao, Yijia Xu et al. (+2 more)

A key appeal of quantum low-density parity check (qLDPC) codes is their ability to suppress stochastic Pauli noise below nonzero thresholds. Coherent errors are fundamentally different: they produce superpositions of error patterns whose amplitudes can interfere even after syndrome measurement. Rigorous understanding of coherent errors remains limited. Here we show that general qLDPC codes admit a nonzero code capacity threshold against local coherent noise and more generally local channel noise. For any family of qLDPC codes with distance $d=\Omega(\log n)$, we show that there is a constant noise strength below which the logical recovery error in diamond distance decays exponentially with the code distance. The result is established for optimal recovery as well as the minimum-weight decoder. The key technical ingredient is what we call a cluster resummation: rather than bounding superposed error configurations one by one, we isolate a large connected error cluster in the channel expansion and exactly resum all errors disconnected from it before taking norms. Standard cluster counting then yields exponential suppression. This work resolves a longstanding challenge in fault tolerance theory, providing general robustness guarantees for qLDPC codes against coherent noise and laying a rigorous foundation for future studies of fault-tolerant quantum technologies.
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All authors Zhengyi Han, Yuanchen Zhao, Yijia Xu, Yixu Wang, Zi-Wen Liu

Lattice Field Theory

Numerical Investigations of Phase Transitions in Lattice Field Theories

Vamika Longia

The study of phase transitions plays an important role in understanding qualitative changes in the behaviour of physical systems at criticality. Despite decades of progress, there is still a strong demand for high-precision numerical tools capable of resolving subtle critical phenomena. Motivated by this need, in this thesis, we present two complementary numerical investigations of phase transitions in lattice systems. The first uses GPU-accelerated higher-order tensor renormalization group (HOTRG) techniques to study the two-dimensional generalized XY model, characterizing its ferromagnetic, nematic, and paramagnetic phases and mapping their phase boundaries using thermodynamic observables in the thermodynamic limit. The second develops and benchmarks a configurational temperature estimator, constructed from gradients and Hessians of the Euclidean lattice action, in compact U(1) lattice gauge theories. On one hand, tensor network methods capture rich phase structures when truncation and finite-bond effects are adequately controlled. On the other hand, the configurational temperature estimator provides an independent, low-overhead means of validating thermal sampling across different algorithms and models, and can also be used as a runtime diagnostic to identify sampling pathologies before large-scale production runs.
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Artificial Intelligence

FreqCondNorm: Towards Cross-domain Predictive Maintenance through a Frequency-Conditioned Transformer Foundation Model

Zaynab Raounak, Camille LHermine and Zhiguo Zeng

Deep learning predictive maintenance models suffer from poor transferability across machines and operating conditions, especially when labelled data are scarce and signals span five orders of magnitude in sampling frequency (1 Hz to ~100 kHz). We propose FreqCondNorm, a Transformer-based architecture that introduces a FiLM-style frequency-conditioned normalization layer to unify heterogeneous time-series within a single model. The architecture is pretrained on five public predictive maintenance datasets (CWRU, MFPT, UOC18, PRONOSTIA, CMAPSS) using masked auto-encoding and contrastive learning with balanced domain sampling. On fault diagnosis, the model achieves 99.2% accuracy on CWRU (+6.4 pp over CNN) and 82.1% zero-shot accuracy on MFPT, demonstrating strong transfer across sampling frequencies. However, the approach does not improve remaining useful life prediction, suggesting a mismatch between pretraining and RUL objectives that warrants future investigation.
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High Energy Physics (Theory)

Holographic correlators with non-supersymmetric multi-particle states

Michele Giorgi and Stefano Giusto

We consider heavy-heavy-light-light (HHLL) holographic correlators in which the heavy states are coherent superpositions of $n$-particle operators. In the limit of large $n$ and large central charge, $c$, with $n/c$ held fixed, these HHLL correlators are described by a classical supergravity computation. When the multi-particle operators are half-BPS, it has been shown that the $n/c\to 0$ limit of the HHLL correlator encodes the tree-level connected contribution to the 4-point function with the heavy operators replaced by two $n$-particle operators with finite $n$. We provide evidence that this relation continues to hold when the multi-particle operators are non-supersymmetric. Although our checks are carried out in the AdS$_3$/CFT$_2$ setting, we expect that our conjecture extends to more general holographic dualities.
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Category Theory

Cocompactness and Presentability

Thorger Geiß, Phil Pützstück and Maxime Ramzi

We give a short proof that $\kappa$-cocompact objects in a presentable category are subterminal. As our main result, we extend this to the setting of presentable $\infty$-categories. A consequence is that an $\infty$-category $\mathcal{C}$ such that both $\mathcal{C}$ and $\mathcal{C}^\mathsf{op}$ are presentable is a small complete lattice, extending a classical theorem of Gabriel-Ulmer. Along the way, we prove a nilpotence result for phantom maps in general pointed presentable $\infty$-categories. Additionally, we show that a strengthening of our main result is equivalent to the existence of a proper class of measurable cardinals.
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Cryptography and Security

Towards TEE-Certified DP: Verifiable Differentially Private Training on Legacy GPUs

Li Ge, Wenjie Qu, Weitao Feng et al. (+4 more)

Wide adoption of machine learning has created growing policy and regulatory demand for protecting sensitive training data, with differential privacy (DP) emerging as a key mechanism. Yet a less-studied problem is how to certify the faithful execution of DP during training: an external verifier should be able to check that a released model was trained with proper DP protection, without accessing the private training data. Existing cryptographic approaches, such as zero-knowledge proofs, provide strong guarantees but often incur prohibitive overhead, in some cases by orders of magnitude. Trusted Execution Environments (TEEs) offer a more efficient alternative, but the multi-GPU TEE support needed for training and fine-tuning large language models remains limited to recent platforms and is absent or inefficient on legacy GPUs. To address this, we propose a practical framework for verifiable DP training using CPU-side TEEs together with untrusted GPUs. Our design addresses a fundamental efficiency-security tension: training entirely inside a CPU TEE is too slow, while unrestricted GPU offloading can allow malicious deviations from DP. We therefore offload expensive gradient computation to GPUs, while using the CPU TEE to efficiently verify the correct enforcement of DP on gradients through probabilistic checking. Our framework detects frequent full deviations from DP with high probability; for the utility-oriented forged-gradient attacks evaluated in this work, sparse deviations provide limited utility benefit and show no measurable additional membership leakage. Experiments further show that our approach nearly achieves a “free lunch”: it incurs only modest overhead compared with standard GPU-based DP training, while effectively constraining malicious deviations from the claimed DP execution.
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All authors Li Ge, Wenjie Qu, Weitao Feng, Yi Zeng, Jiaheng Zhang, Xiaofeng Wang, Wei Dong

Classical Analysis and ODEs

Sharp mixed $A_p$-$A_\infty$ estimates for sparse operators on filtered and nonhomogeneous measure spaces

Francisco Gonçalves and Emiel Lorist

We prove mixed $A_p$-$A_\infty$ estimates for sparse operators in two non-doubling settings. In the first setting, we consider sparse operators defined using stopping times in continuous time. We obtain both strong- and weak-type bounds with the same powers of the weight characteristics as in the classical setting. Some of our weak-type bounds are even new for the dyadic filtration on $\mathbb R^d$ and, in particular, imply a sharp weak-type $(2,2)$ estimate for Rubio de Francia square functions, solving a problem left open by Garg, Roncal and Shrivastava [J. Geom. Anal., 31:748-771, 2021]. In the second setting, we consider dyadic sparse forms in which distinct cubes may interact, provided their dyadic distance is bounded. We obtain strong-type bounds with the same powers of the weight characteristics as in the classical setting. As a one-dimensional application, we obtain strong-type bounds for Haar shifts over balanced non-doubling measures, answering a quantitative question posed by Conde-Alonso, Pipher, and Wagner [Math. Ann., 391:2209-2253, 2025].
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Computation and Language

Relational Attention for Data-Efficient Language Modeling

Adrian Brasoveanu, Ece Takmaz and Jakub Dotlačil

We present Relational BabyLM, a system submission to the BabyLM 2026 challenge that combines two cognitively motivated inductive biases in a single decoder-only Transformer. Architecturally, we replace standard self-attention with a Dual Attention Transformer (DAT), which separates the routing of object-level ("sensory") lexical features from structural/relational information (Altabaa and Lafferty, 2025; Altabaa et al., 2024; Webb et al., 2024; Kerg et al., 2022; Webb et al., 2021). Relational attention (RA) disentangled from self-attention greatly increases data efficiency and out-of-training-sample generalization on purely relational tasks, but language modeling requires object-level and relational information to be integrated as well as disentangled, and RA-based LMs have remained largely unexplored. BabyLM's data-constrained training and comprehensive evaluation is an ideal testing ground for whether that data efficiency transfers. As a training intervention, we add a Next-Latent Prediction (NextLat; Teoh et al. 2026) objective that encourages hidden states to compress history incrementally into a dense belief state. Architecture is the dominant factor for structural linguistic generalization; the objective is secondary but still significant. DAT's three relational attention types (full RA vs. the simpler RCA and DisRCA variants) are largely interchangeable at 10M words; full RA pulls ahead at 100M. We also introduce a novel symbol-retrieval mechanism (RoPE-based, as opposed to learned, relative symbols) that matches learned symbol libraries while adding no parameters. On the strict (100M-word) track, our best model ranks 6th of 55 overall and 3rd of 55 on the leaderboard's NLP-task subset at the time of writing; our two strongest models outperform the GPT-2 baseline on most benchmarks, with one attaining the highest EWoK score among strict-track entries.
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Statistics Theory

Approximation Theorems for High-Dimensional Canonical U-Statistics: Gaussian Chaos and Phase Transition

Leheng Cai and Qirui Hu

We study simultaneous inference for maxima of canonical order-two $U$-statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibration can fail even after exact variance normalization. We show that the appropriate general target is a joint signed Gaussian quadratic chaos and establish a general approximation result that permits indefinite kernels. The general anti-concentration bound is too crude for high-dimensional inference, and we obtain sharper bounds under additional spectral structure. We also identify a phase transition from a non-Gaussian signed-chaos maximum to its covariance-matched Gaussian counterpart driven by the effective rank. For feasible inference, we propose a Gaussian multiplier bootstrap that avoid estimating eigensystems, and establish its validity. Two applications and extensive numerical simulations further illustrate the scope and practical performance of the proposed framework.
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