Materials Science
Machine-learning-guided exploration of domain walls in the hybrid improper ferroelectric Ca3Ti2O7
Ida C. Skogvoll, Erik Fransson, Leo Ö. Westin et al. (+4 more)
Ruddlesden-Popper phases are highly tunable and naturally layered structures, in which polarization can arise via a hybrid improper ferroelectric mechanism. This enables a complex domain wall (DW) structure where multiple order parameters, like octahedral rotations, polar distortions and strain, interact. In this work, we explore the rich set of DW structures in prototypical Ca3Ti2O7, mapping out the DWs in the {100}, {110} and {001} pseudo-tetragonal planes using group theory and machine-learned interatomic potentials (MLIPs). The trained potential reproduces the density functional theory (DFT) order parameter and polarization profiles for all wall types and orientations considered. A charge-aware training framework combined with reference Born effective charges reduces the prediction errors for the DW formation energies by 70%, revealing the importance of including long-range electrostatics to model
symmetry-broken interfaces. Finally, the MLIP is used to identify minimum energy pathways at the atomic scale with nearly the precision of DFT calculations, revealing a low-energy antipolar configuration for polarization switching.
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All authors Ida C. Skogvoll, Erik Fransson, Leo Ö. Westin, Benjamin A. D. Williamson, Nicholas C. Bristowe, Sverre M. Selbach, Paul Erhart
Sound
Probing Large Audio-Language Models for Compositional Understanding of Sounding Actions
Michel Olvera, Paraskevas Stamatiadis, Changhong Wang et al. (+1 more)
Large audio-
language models (LALMs) excel at understanding and
reasoning tasks over atomic sound events, yet their ability to infer higher-level human activities from such fine-grained events remains largely unexamined. Everyday human actions and activities, such as setting a table, cleaning the house, or preparing a breakfast emerge compositionally from temporally distributed sound events, requiring abstraction beyond the event-centric granularity that dominates current training and evaluation paradigms. Our
benchmark evaluates a wide set of LALMs under a principled framework that tests how
language-based
reasoning, grounded in acoustic perception, structures sound abstractions into higher-level understanding. By systematically varying exemplar typicality and distractor similarity, our evaluation exposes \added{that current models do not reliably perform compositional inference from atomic acoustic events to higher-level human activities solely from audio.} All data, taxonomies, and evaluation scripts are publicly available on our companion website: https://alm-sounding-actions.onrender.com/
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All authors Michel Olvera, Paraskevas Stamatiadis, Changhong Wang, Gaël Richard
High Energy Physics (Phenomenology)
Resummation-scale uncertainties in PDF determinations
Hamed Abdolmaleki, Valerio Bertone, Giuseppe Bozzi et al. (+7 more)
We investigate the impact of resummation-scale variations on parton distribution function (PDF) determinations. These variations introduce an additional source of theoretical uncertainty related to the
evolution of PDFs and strong coupling $\alpha_s$ that has never previously been accounted for in PDF fits. Using the open-source xFitter framework, we quantify this uncertainty in fits to HERA deep-inelastic scattering data and examine its implications for predictions of top-
quark pair production at the LHC. We show that the resulting resummation-scale uncertainties have a sizable impact on LHC observables, highlighting the importance of including this source of uncertainty in precision QCD analyses.
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All authors Hamed Abdolmaleki, Valerio Bertone, Giuseppe Bozzi, Francesco Giuli, Alexander Glazov, Valentina Guglielmi, Francesco Hautmann, Fred Olness, Pavel Starovoitov, Oleksandr Zenaiev
Astrophysics of Galaxies
Extreme MgII Emission in Recently-Quenched Galaxies: A New Sample of Intermediate-Redshift Post-Starburst Quasars from the DESI Early Data Release
Margaret E. Verrico, Aayan Verma, K. Decker French et al. (+8 more)
Post-starburst
galaxies are
galaxies which have recently and rapidly shut off
star formation. AGN activity is often invoked to explain this rapid quenching, but most post-starburst selection methods select against optical AGN, motivating searches for "post-starburst
quasars." We present DESI observations of ten post-starburst
quasars with significant MgII emission ($L_{\text{MgII}} \geq 3 \times 10^{41}$ erg/s). This is the first sample of post-starburst
quasars to be selected from a post-starburst
galaxy parent sample rather than a
quasar catalog.
Quasars make up $4.6^{+1.6}_{-1.2}\%$ of the post-starburst parent sample at $0.49 \leq z \leq 1.39$. Using multiwavelength AGN diagnostics, we find that $26^{+3.0}_{-2.8}\%$ of post-starbursts in the parent sample host AGN. We find that post-starburst selection methods are biased against AGN with $\text{L}_{\text{Bol}}\gtrsim10^{45} \textrm{erg s}^{-1}$, potentially removing the
quasars responsible for driving
outflows that aid in quenching. Finally, we find that 9/10 post-starburst
quasars in our sample have no detected broad H$\beta$, similar to so-called "MgII emitters" that may be the remnants of fading
quasars; if confirmed, these objects suggest a link between post-starburst
galaxies and variable AGN. Our new sample of post-starburst
quasars provides a link between previously reported local and high
redshift post-starburst
quasars during the epoch when
star formation throughout the universe was declining.
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All authors Margaret E. Verrico, Aayan Verma, K. Decker French, David J. Setton, Omar Almaini, Jenny E. Greene, Stephanie LaMassa, Yuanze Luo, Pallavi Patil, Kate Rowlands, Dharlenny Soto
Artificial Intelligence
Jev thinks "I don't know”, but doesn't say it: Introducing Sys1Cal-v1 Dataset for Probability Calibration
Riccardo Porcedda
The appearance of Jev marked the era of System One Models, foundation models that return structured decisions with probability distributions rather than text. Aside from low cost and great speed, Jev's central promise is that these probabilities are calibrated: such claim is not backed by any public test and available external
benchmarks evaluate confidence calibration, not whether every returned option probability has the right numerical meaning. To tackle this issue, we introduce Sys1Cal-v1, a
dataset of True/False questions about a proposition $A$ for which the exact probability $P(A)$ is known by construction. Each item is queried through the three Jev primitives - Noul, Choice and Score - and evaluated by total variation distance from the ground-truth distribution, which can be used to estimate a soft accuracy of System One Models. We showcase the utility of Sys1Cal-v1 as a
benchmark dataset by evaluating Jev and SemIf, an open-source Choice-style baseline. In this work, however, we focus even more deeply on Jev, by studying the calibration of its Score and Choice answers. In particular, we discover a peculiar behaviour that can be explained by assuming that Jev suppresses a third truth value, going beyond True and False. In other words, in Choice answers, $P(A)$ and $P(\neg A)$ are presented as if $P(A)+P(\neg A)=1$, while a term $P(U)\neq0$ is missing in the sum. Recovering $P(U)$ leads to an improvement of median soft accuracy in Choice answers from $0.771$ to $0.978$, suggesting that, even in binary decisions, Jev wants to answer with a third option:“I don't know”.
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Computer Vision
Generative Uncertainty as a Self-supervised Signal for Semantic Similarity Learning
Enrico Pallotta, Sina Raoufi, Lars Doorenbos et al. (+2 more)
Evaluating semantic similarity between
videos is a fundamental challenge in computer
vision, essential for tasks ranging from out-of-distribution (OOD) detection to
video retrieval. However, defining and labeling
video similarity is notoriously difficult and expensive due to the complex spatio-temporal nature. In this paper, we propose a novel self-supervised approach that leverages generative uncertainty from text-to-
video (T2V)
diffusion models to learn semantic similarity without human annotations. Our method is based on the observation that T2V models produce consistent outputs for familiar concepts but exhibit high variance and uncertainty when prompted with specialized concepts. We utilize this behavior to identify stable semantic features within existing pretrained representations, such as VideoMAE and V-JEPA. Specifically, we learn a mask over these
embeddings using purely generated data, encouraging the model to retain features that remain consistent across generations of general concepts while discarding those associated with generative noise or uncertainty. Experimental results across three key tasks demonstrate that our learned feature subspaces consistently outperform original pretrained features and baseline feature selection methods.
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All authors Enrico Pallotta, Sina Raoufi, Lars Doorenbos, Gianni Franchi, Juergen Gall
Geometric Topology
On pure braids and bonded braids
Sofia Lambropoulou and Lucrezia Beatrice Lorenzi
In this paper we investigate the relation between the bonded braid monoid BBn and the group of pure braids $P_n$, realised by an algebraic analogue of the topological tangle insertion, namely by replacing a bond by (a power of) a pure braid generator. To do so, we provide appropriate presentations for $P_n$ using cyclic relations and clasp generators, and extend them to presentations of $B_n$. We construct the monoid epimorphism $\Phi: BB_n \to Bn$, mapping bonds to pure braid generators, which is the main result of the paper. Using the isomorphism from the singular braid monoid $SB_n$ to the tight bonded braid monoid $BB_n$, we extend $\Phi$ to a new type of epimorphism $s \Phi: SB_n \to B_n$. The epimorphisms $\Phi$ and $s \Phi$ are extended to families of epimorphisms $\Phi_p$, $s \Phi_p$, $p \in \mathbb{Z}$.
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Quantum Physics
Zero Knowledge Proofs in Quantum Networks
Tuhin Paul, Srijani Das, Manasi Patra et al. (+1 more)
Zero-knowledge proofs (ZKPs) enable the verification of a statement without revealing any information beyond its validity and constitute a fundamental primitive in cryptography and information theory. However, existing constructions rely on computational assumptions and are predominantly confined to bipartite settings, leaving their information-theoretic realization in bipartite or network scenarios largely unexplored. Here we develop a framework for zero-knowledge verification based on the indistinguishability of
quantum states under operational constraints. Exploiting the fundamental limitations imposed by local operations, we show that a verifier is inherently restricted from extracting information about the underlying state while retaining the ability to verify correctness. We construct explicit protocols for multiparty
quantum networks that achieve information-theoretic security, ensuring that no subset of collaborating parties can gain knowledge beyond the validity of the statement, independent of their joint computational power.
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All authors Tuhin Paul, Srijani Das, Manasi Patra, Ramij Rahaman
Machine Learning
NeuronDiscover: Agent-in-Twin for Mechanistic Discovery in Neuronal Microenvironments with World Action Models
Haowei Xu, Wanyi Fu, Hongbin Han et al. (+1 more)
Mechanistic discovery in neuronal microenvironments requires interventions and measurements that separate competing explanations of solute transport and neuronal response. Predictive accuracy cannot settle the question: a real mechanistic change and an error in the computational twin leave the same signature in sparse observations. We formalize this twin confounding and reason over a joint mechanism–discrepancy belief, designing experiments that separate the two. NeuronDiscover is an
Agent-in-Twin framework whose shared, mechanism-grounded World Action Model (WAM) couples prediction, intervention proposals, and observation design; independently adjudicated outcomes revise a scoped Mechanism–Intervention–Observation–Outcome (MIOY) graph, whose supported relations compile into executable programs carrying discrepancy-adjusted acceptance bounds. We evaluate on simulated
brain-fluid tracer-transport worlds adjudicated by an independently frozen finer-mesh reference solver, and on donor-disjoint public current-clamp recordings of cortical
neurons. Counting only relations that reach a certified terminal status, and scoring abstentions as unresolved for every method, at a matched budget of 16 experiments over 32 source units NeuronDiscover resolves 4.0 relations per assigned world against 3.4 for the strongest baseline and 3.2 without graph revision, at 5% false support and 82% scope accuracy. Joint mechanism–discrepancy acquisition resolves 3.8 relations versus 2.9 for plug-in expected information gain; discrepancy-adjusted verification lowers accepted-program failure from 15% to 9% at 60% acceptance coverage; and transfer to the recordings yields 1.94 versus 1.53 relations per assigned world. Correctness is adjudicated within declared model worlds and archival recordings.
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All authors Haowei Xu, Wanyi Fu, Hongbin Han, Zhaoheng Xie
Data Structures and Algorithms
Pure Tail Constraints for Online Problems
Mateusz Basiak, Marcin Bienkowski, Yongho Shin et al. (+1 more)
Controlling tail risk is an important objective in online optimization, and recently it has been studied in the context of competitive analysis. Continuing this line of research, we investigate pure tail constraints, which capture the tradeoff between expected and worst-case competitiveness. For two fundamental search problems, online bidding and line search, we derive the Pareto-optimal frontiers of this tradeoff. We then investigate another classic problem, TCP acknowledgment, which has structure similar to the iterated ski rental problem. There, we construct an
algorithm whose tradeoff coincides with the known Pareto-optimal tradeoff for ski rental. The lower bounds for this problem are substantially more involved as the problem exhibits adaptive structure: an online
algorithm observes requests of the adversary (packet arrivals) and may adaptively adjust its actions (acknowledgments) on this basis. We emphasize that all previous work on tail risk in the context of competitive analysis was restricted to non-adaptive problems, where the feedback given to an
algorithm was essentially limited to a binary indicator of whether the
algorithm has succeeded or not. Nonetheless, we identify a set of constraints implied by tail bounds in this adaptive setting, and show that they imply a nontrivial lower bound on the TCP acknowledgment problem.
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All authors Mateusz Basiak, Marcin Bienkowski, Yongho Shin, Agnieszka Tatarczuk
Artificial Intelligence
TMCS: Tool-Grounded Multi-Agent Reasoning for Compositional Chemical Problem Solving
Shengqin Wang, Jie Jin, Yu Cheng et al. (+4 more)
Despite the promise of Large
Language Models (LLMs) in computational chemistry, rigorous combinatorial chemistry problems remain difficult because they require quantitatively constrained molecular modification, candidate validation, and systematic revision after failed attempts. Existing tool-augmented chemical
agents demonstrate useful planning and tool use, but they rarely provide a unified loop for property-driven molecular optimization and workflow-level composition. To bridge this gap, we propose Tool-Grounded Multi-
Agent Reasoning for Compositional Chemical Problem Solving (TMCS), a step-by-step multi-
agent framework that formalizes chemical problem solving as an interpretable, tool-augmented workflow. At the task level, specialized
agents leverage external tools, few-shot trajectory
memory, and structured reflection to iteratively refine solutions. At the workflow level, TMCS chains generation, understanding, editing, description, and optimization into a closed-loop pipeline. Evaluations across multiple chemical tasks demonstrate that TMCS consistently enhances chemical
reasoning across both open- and closed-source base models, achieving state-of-the-art performance.
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All authors Shengqin Wang, Jie Jin, Yu Cheng, Yihang Chen, Weilin Luo, Yuan Xie, Zhizhong Zhang
Machine Learning
Large Language Models for Automated Cross-Domain Machine Learning Task Type Identification: A Benchmark Dataset and Evaluation
Petros Tsialis, Steffen Limmer, Tobias Rodemann et al. (+1 more)
Machine learning task type identification is essential for constructing valid ML pipelines, yet in practice it is typically specified manually. We investigate whether large
language models (LLMs) can infer both the data domain and the downstream prediction task directly from
dataset-level information when only the target feature is provided by the user. Together with our LLM-based system we also release an annotated
benchmark comprising 625 public tabular and time series
datasets. We evaluate the proposed approach in three settings: (i) tabular
datasets in comparison with established AutoML heuristics, (ii) cross-domain evaluation across tabular and time series
datasets, and (iii) a practical deployment scenario using smaller local models. The results show consistent advantages for LLM-based task type identification, with increasing difficulty in heterogeneous and resource-constrained settings. LLM-based approaches outperform AutoGluon in the tabular setting, reaching 0.98 F1 macro compared to 0.93. In the cross-domain setting, the best model achieves 0.90 F1 macro, while smaller locally deployable models reach 0.75, indicating a trade-off between deployment feasibility and accuracy.
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All authors Petros Tsialis, Steffen Limmer, Tobias Rodemann, Martin Heckmann
History and Overview of Mathematics
Leiden Declaration on Artificial Intelligence and Mathematics
Jarod Alper, Michael Barany, Alain Chavarri Villarello et al. (+13 more)
This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research. Technological developments have repeatedly transformed the practice of mathematics. Recent artificial intelligence technologies, including symbolic and neural methods for the generation and formalization of mathematics, may already have initiated a significant chapter in this long history. Among researchers, artificial intelligence has produced a wide range of reactions: enthusiasm for its potential to yield new discoveries; intimidation by the pace of developments; indifference to these rapid changes; and concern for the implications, both for mathematics and in wider society. Mathematicians have a choice about whether and how to adopt artificial intelligence in the conduct of their research. They also have a responsibility to ensure the continued flourishing of the discipline. This Declaration calls upon mathematicians to exercise this responsibility, and provides recommendations for individuals, institutions, government, and industry. Although we adopt the perspective of mathematical research, much of what we write applies equally to other aspects of mathematics. This includes work in the broader mathematical sciences, education, mentoring, publishing, funding, science policy, and use of mathematics in the wider world.
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All authors Jarod Alper, Michael Barany, Alain Chavarri Villarello, Sander Dahmen, Walter Dean, Karthik Ganapathy, Michael Harris, David Holmes, Mateja Jamnik, Steven Kelk, Bryna Kra, Ursula Martin, Bartosz Naskręcki, Rodrigo Ochigame, Jim Portegies, Johannes Schmitt
Machine Learning
Scalable In-Context Reinforcement Learning with Recurrent Algorithm Distillation
Yuanqing Ma, Zhenrui Zheng and Chenjun Xiao
Algorithm Distillation (AD) has demonstrated the remarkable ability of
Transformers to perform in-context reinforcement learning without explicit weight updates. However, capturing long-term learning progress necessitates expansive context windows, which incur prohibitive
memory costs and limit scalability in complex, long-horizon tasks. To address this bottleneck, we propose Recurrent
Algorithm Distillation (RAD). RAD employs a dual-component architecture: a Compression
Transformer that distills extended interaction histories into compact latent
tokens, and an AD
Transformer that auto-regressively generates actions using a hybrid context of these compressed
memories and recent transitions. By maintaining a fixed-size latent buffer, RAD decouples the effective history length from computational complexity, functionally providing the model with a long-horizon
memory. Empirical evaluations across diverse environments demonstrate that RAD matches the asymptotic performance of standard AD with significantly reduced context window sizes, offering a scalable solution for efficient in-context decision-making.
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Probability
Central Limit Theorems for Finitary Factors of iid Processes
Raimundo Briceño, Zemer Kosloff and Nicolò Paviato
We study statistical limit
theorems for time-series generated by multidimensional random fields that are finitary factors of iid random processes. Based on the decay of the tail of the coding radius, we establish the Central Limit
Theorem with explicit rates of convergence, as well as the weak convergence to a Brownian sheet, for suitably regular functions. Our results can be applied to a variety of classical models in statistical mechanics, such as the Ising model, the hard-core model, and proper colourings.
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Game Theory
Reverse Sequential Proportional Approval Voting Rule: Proportionality and Approximation Guarantees
Georgios Papasotiropoulos
We study the Reverse Sequential Proportional Approval Voting Rule (RevSeqPAV) in approval-based committee elections. Despite its historical prominence and practical use, its properties and guarantees are much less understood than those of Sequential PAV. We analyze it along two dimensions: proportional representation (measured by Extended Justified Representation, its approximations, and proportionality degree) and approximation of the maximum PAV score of instances. We first establish strong negative results for general, unrestricted election instances and then identify settings in which the rule provides meaningful
fairness and optimization guarantees.
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Astrophysics of Galaxies
ViCTORIA project: A pilot study of the M49 region in the Virgo cluster in polarisation
A. Spasic, A. Benati, M. Brüggen et al. (+7 more)
Large-scale
magnetic fields permeate the Intracluster Medium (ICM) of
galaxy clusters. Understanding these fields gives an insight into the origin of
cosmic magnetic fields and the interaction of cluster
galaxies with the ICM. Using MeerKAT observations of the Virgo cluster as part of the ViCTORIA project, we probe
magnetic fields via Rotation Measure (RM) synthesis. The aim of this work is to characterise the
magnetic fields in and around the infalling group M49 in the Virgo cluster. We will probe the interaction of M49 with its surrounding medium through its imprint on the polarised emission and Faraday rotation. We use L-band MeerKAT data in full polarisation calibrated with the ViCTORIA MeerKAT Survey (ViMS) pipeline, which is designed for the calibration, imaging, mosaicking and RM Synthesis of the fields in the Virgo cluster, to achieve high-fidelity reconstruction of, both, total intensity and polarised emission. We analyse the background sources of the cluster for potential local changes in the
magnetic field, by calculating the RM distribution. In the final polarised image, consisting of four pointings of 45 min, we reach a noise level of $23.3 \mu \textrm{Jy/beam}$. We detect 101 background sources in the $\sim 2.5\, \textrm{deg}^2$ region around M49, corresponding to a source density of 40 sources/$ \textrm{deg}^2$. Across the $112\, \textrm{deg}^2$ observations of the Virgo cluster, this implies a total number of 4000 polarised sources. In M49 we find structured, diffuse polarised emission extending in the direction of the total intensity
radio tails. A higher polarisation fraction across the upper edge of the source indicates the effect of
magnetic field draping. Around M49 we find a larger RM scatter (at $3.8\sigma$) in the wake of M49 compared to the region in front of it. This can inform the modelling of the
turbulence created by
galactic motions.
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All authors A. Spasic, A. Benati, M. Brüggen, H. W. Edler, F. De Gasperin, V. Gustafsson, P. Serra, A. Bonafede, A. Boselli, H. McCall
Classical Analysis and ODEs
Algorithmic Implementation of Multi-Window STFT Phase Retrieval
Ting Chen, Hanwen Lu, Wenchang Sun et al. (+1 more)
STFT phase
retrieval aims to reconstruct a signal from spectrogram magnitudes. While two compactly supported windows theoretically guarantee uniqueness, a complete algorithmic framework remains lacking. This paper systematically constructs numerical schemes for multi-window STFT phase
retrieval. We theoretically provide a nonuniqueness counterexample for the single-window case. We then propose a two-window reconstruction
algorithm based on Shannon interpolation and analytic square-root extraction. To overcome the instability of the global sign choice, we introduce a third window and a robust $K$-sign method that determines the sign locally. We also adapt SCR
algorithm to the STFT setting. For the $K$-sign method, we establish deterministic stability on a finite contiguous block of frequency samples, with the contribution of the complementary tail explicitly included in the error bound. Numerical experiments validate the effectiveness of all schemes.
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All authors Ting Chen, Hanwen Lu, Wenchang Sun, Yutong Zhao
Artificial Intelligence
Hyper Algorithm Design Agent: Evolving Learnable Optimizer from Zero
Zipei Yu, Yue-Jiao Gong, Zeyuan Ma et al. (+2 more)
Meta-Black-Box Optimization (MetaBBO) is one of the highlights in the recent AI for Optimization trend. This paradigm's bi-level workflow leverages the learnable
algorithm design policy at meta level to ensure the performance and generalization improvement on the low-level optimization task. While MetaBBO helps advance the performance lower bound of the resulted optimization system, it is currently handcrafted and customized case by case to adapt different optimization problems, which inevitably introduces inherent subjectivity and hence restricts the performance upper bound and usability in practice. In this paper, we address this issue by regarding MetaBBO's design loop as coding task, where we could introduce openendedness into MetaBBO with recursive self-improvement capability of advanced coding
agents. Specifically, we propose a dual-
agent framework: i) a task
agent continuously refines the codebase of a target MetaBBO approach through code
evolution; ii) a hyper
agent progressively modifies the task
agent and itself to provide open-ended design behavior; iii) the evolved MetaBBO codebase is evaluated and all in-execution information is fed back to the
agents for recursive self-referential improvement. As a result, given a naive MetaBBO template, our framework automates a design
evolution and finds novel variants superior to up-to-date human-made MetaBBO baselines. Surprisingly, the experimental results also demonstrate that our framework supports fast adaption across different optimization domains. Solid interpretation analysis further reveals interesting design principles emerge in such open-ended process. This work serves as the first exploration on automating design of complex learning-assisted optimization
algorithms.
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All authors Zipei Yu, Yue-Jiao Gong, Zeyuan Ma, Yuncheng Jiang, Zhiguang Cao
Quantum Physics
Distributional Variants of the Aaronson-Ambainis Conjecture
Uma Girish, Kunal Mittal, Barak Nehoran et al. (+1 more)
A longstanding
conjecture in
quantum complexity theory asserts that, under the uniform input distribution,
quantum query
algorithms can be polynomially simulated by classical query
algorithms. More precisely, the acceptance probability of any
quantum query
algorithm can be approximated, on average over uniformly random inputs, by a classical query
algorithm, with only
polynomial query overhead. The
conjecture is central to understanding whether exponential
quantum advantages for decision problems necessarily rely on additional structure. We study analogues of this
conjecture under other natural input distributions and prove that they are all equivalent to the original uniform-distribution
conjecture. We first consider the product distribution $\mu_p$, where the input bits are independent Bernoulli variables with fixed bias $p$. We show that for every fixed $p \in (0, 1)$,
quantum query
algorithms under the $\mu_p$ distribution admit
polynomial-overhead classical simulations if and only if the same holds under the uniform distribution. Second, we consider the distribution $\nu_p$ that is uniform over the slice of strings with Hamming weight $\lfloor pn \rfloor$ and prove a similar equivalence for the $\nu_p$ distribution and the uniform distribution. The Aaronson-Ambainis
conjecture is a stronger statement that implies the above-mentioned
conjecture and is formulated in terms of bounded low-degree
polynomials on the Boolean hypercube. It asserts that under the uniform distribution, any such
polynomial with nonnegligible variance must have an influential variable. We formulate analogues of this
conjecture, where the underlying distribution is a biased product distribution or a uniform distribution over a slice, and prove that all these variants are equivalent to the original Aaronson-Ambainis
conjecture.
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All authors Uma Girish, Kunal Mittal, Barak Nehoran, Ran Raz
Computational Complexity
$\mathrm{Almost}\text{-}\oplus\mathrm{P} = \mathrm{BP}\cdot\oplus\mathrm{P}$ and a Random-Oracle Proof of Toda's Theorem
Lance Fortnow
Using the recent exponential correlation bounds of Chattopadhyay, Hatami, Lee, Lovett, Tal and Viola between $\mathbb{F}_2$-
polynomials and the XOR of majorities, we show that $\mathrm{Almost}\text{-}\oplus\mathrm{P} = \mathrm{BP}\cdot\oplus\mathrm{P}$, where $\mathrm{Almost}\text{-}\oplus\mathrm{P}$ is the class of
languages that lie in $\oplus\mathrm{P}^R$ with probability one for a random oracle $R$. This is the parity analogue of Bennett and Gill's $\mathrm{Almost}\text{-}\mathrm{P} = \mathrm{BPP}$ and Nisan and Wigderson's $\mathrm{Almost}\text{-}\mathrm{PH} = \mathrm{PH}$. The key ingredient is a pseudorandom generator with
polynomial seed length that fools $\mathbb{F}_2$-
polynomials of
polynomial degree on exponentially many variables. As an application we complete a random-oracle proof of the first half of Toda's
theorem, $\mathrm{PH} \subseteq \mathrm{BP}\cdot\oplus\mathrm{P}$, following an approach of Regan and Royer. Relative to a random oracle, the
polynomial hierarchy collapses into $\oplus\mathrm{P}$ by applying Valiant-Vazirani and Papadimitriou-Zachos level by level, with no probabilistic quantifier ever moved through an oracle. Our result then removes the oracle. We compare this argument with the simple proof of Toda's
theorem by Fortnow (2009).
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Representation Theory
A proof of Frenkel's bound for the hyperbolic Kac-Moody Lie Algebra A_1^++
Gabriel B. Legros
We give a computer-assisted proof of Frenkel's root-multiplicity bound for the rank-three
hyperbolic Kac–Moody Lie
algebra $A_1^{++}$. For every root $\alpha$, we prove $\dim g_\alpha\le p(1-(\alpha,\alpha)/2)$, where $p$ is the ordinary partition function. The proof combines exact affine characters with a coefficientwise logarithmic majorant derived from
parabolic homology. After Weyl reduction, analytic estimates establish the inequality on infinite regions of large depth or large level. The remaining finite region is verified by computer. Together with the known low-level formulas, the assembly of these estimates establish the
conjecture for every root of $A_1^{++}$.
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Optics
Contactless Continuous-Variable Quantum Optical State Conditioning With Classical MmWave Phase
Niloy Ghosh and Sarang Pendharker
This paper establishes the Heisenberg's picture framework for seamless mmWave-to-photonic data transduction. Based on this framework, contactless modulation of continuous-variable (CV)
quantum optical states with digitally modulated classical mmWave beams is shown for the first time. Our analysis reveals the direct influence of mmWave phase variation on the Wigner-space
evolution of modulated optical coherent and squeezed states. Furthermore, the analysis indicates that classical mmWave phase not only governs the displacement but also modulates the quadrature uncertainty of squeezed states, revealing a novel technique for
embedding information onto multiple
quantum-optical degrees of freedom. This work builds the theoretical and analytical foundation for wireless conditioning of
quantum light without conventional on-chip metallic interconnects and complex electronic control circuitry, thereby opening a key pathway toward seamless bridging of integrated
quantum photonics with emerging mmWave or THz communication technology.
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Group Theory
Free abelian quotients of commensurators
Adrien Le Boudec
For every group $\Gamma$, we define a homomorphism $d^\Gamma : \mathrm{Comm}(\Gamma) \to \mathbb{Z}^{(\mathcal{FS})}$ from the abstract commensurator $\mathrm{Comm}(\Gamma)$ to the free abelian group $\mathbb{Z}^{(\mathcal{FS})}$ with basis the collection $\mathcal{FS}$ of isomorphism classes of finite simple groups. We investigate the homomorphism $d^\Gamma$ when $\Gamma$ is a finitely generated free group $F$. We explicitly describe the image of $d^F : \mathrm{Comm}(F) \to \mathbb{Z}^{(\mathcal{FS})}$, which is a free abelian group of infinite rank, and we show that the kernel is the monolith of the group $\mathrm{Comm}(F)$. We deduce in particular that every proper quotient of $\mathrm{Comm}(F)$ is abelian. We use this to study the commensurator of a cocompact
lattice in the
automorphism group of a regular tree, which can be seen as a subgroup of $\mathrm{Comm}(F)$. We show that the image of this group under $d^F$ is again a free abelian group of infinite rank, showing in particular this group is not virtually simple.
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Machine Learning
Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Data
Jérémie Klinger, Raphaël Urfin, Giulio Biroli et al. (+1 more)
Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for multi-modal distributions, trajectories commit to modes of the target within a narrow time window, the speciation time. In this work, focusing on high-dimensional data, we decompose the integrated loss into its single-time contributions and analyze each at fixed signal-to-noise ratio $\Lambda(t)$: we show that $\Lambda(t)$ sets the rate at which each feature of a
multimodal target - the mode directions and their relative weights - is acquired during training. Crucially, at high $\Lambda(t)$ all mode directions are acquired together, on a single timescale insensitive to their amplitudes, while the relative weights are not learned at all. Only near the speciation time, where $\Lambda(t)$ becomes of order one, do all features become learnable, each on its own timescale: the weights are acquired jointly with the directions, and the directions at rates set by their relative amplitudes. For models trained on time-integrated objectives, the learning dynamics is then governed by how much of the weighting effectively sits near the speciation time, which provides insights on $w(t)$ design choices. These results follow from an exact high-dimensional analysis of the training dynamics of unbalanced and hierarchical Gaussian mixtures. Numerical experiments on image and human genome haplotype generation recover the predicted hierarchy of learning timescales in more complex settings.
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All authors Jérémie Klinger, Raphaël Urfin, Giulio Biroli, Marylou Gabrié
High Energy Physics (Phenomenology)
System-size dependence of jet quenching from light to heavy-ion collisions at LHC
Man Xie, Xiang-Yu Wu, Han-Zhong Zhang et al. (+1 more)
Single inclusive
hadron suppression in high-energy heavy-ion collisions provides a sensitive probe of parton energy loss and jet transport coefficient in
quark-
gluon plasma (QGP). System size dependence of jet quenching can provide further constraints on the dynamics of jet quenching and parton energy loss. Motivated by recent experiments on light-ion collisions at the Large
Hadron Collider (LHC), we perform a systematic study of single-inclusive
hadron suppression in O+O, Ne+Ne, Xe+Xe and Pb+Pb collisions at the LHC energies. The calculations are carried out within the next-to-leading-order perturbative QCD model, incorporating the
nuclear modified initial-state parton distributions, final-state parton energy loss in the higher-twist approach and the temperature dependence of the jet transport coefficient $\hat q/T^3$ from the
Bayesian analyses of previous experimental data at the Relativistic Heavy-ion
Collider (RHIC) and LHC. Our model calculations can simultaneously describe the measured single-inclusive charged
hadron $R_{AA}$ in O+O, Ne+Ne, Xe+Xe and Pb+Pb collisions over a broad range of event centralities and in the minimum-bias events. We further illustrate the system size dependence of jet quenching through the ratio $R_{\mathrm{NeNe}}/R_{\mathrm{OO}}$ and the modification factors $R_{AA}$ as a function of $\langle N_{\mathrm{coll}} \rangle$ which follow a common behavior at fixed $p_{\rm T}$, indicating the formation of QGP even in the smallest collision systems.
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All authors Man Xie, Xiang-Yu Wu, Han-Zhong Zhang, Xin-Nian Wang
Probability
Continuous phase transitions in the $k$-creation process without stirring in $d=1$
Rick Durrett
This paper is a companion to one in which we prove there is a discontinuous phase transitions in the $k$-creation process with fast stirring in $d=1$ when $k \ge 2$. Dickman and Tomé (1991) introduced models on $Z$ in which $k$ consecutive occupied sites give birth at rate $\lambda$ and individual particles die at rate 1. Here, we show that without stirring the models with $k\ge 2$ have qualitative properties much like the contact process, which is the case $k=1$. The critical value can be charracterized by the speed of interface when the process starts from the initial configuration $(-\infty,0]$. The process dies out at the critical value. In the supercritical phase the complete convergence
theorem holds which implies there is only one nontrivial stationary distribution, and convergence to the limit occurs exponentially rapidly. In the subcritical phase, the process dies out exponentially fast starting from any finite set.
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Machine Learning
Teacher-Student Gaps Are Not Enough: Outcome-Guided On-Policy Distillation for Multi-Turn Autonomous Agents
Tong Zhang, Zhou Liu, Yihao Liu et al. (+8 more)
On-policy
distillation (OPD) trains a student on its own trajectories with dense teacher supervision. Recent work on OPD for multi-turn autonomous
agents often treats large teacher-student
token-level distributional gaps as promising intervention points, linking larger gaps to a greater need for correction. Yet, our empirical analysis reveals a supervision-benefit mismatch: large gaps can be benign, while small gaps can be outcome-critical. Teacher-student gaps capture differences at the current turn, whereas the benefit of teacher guidance depends on how the current student interacts with the environment afterward. The student may still succeed despite choosing an action that differs from the teacher's, while a teacher-preferred action may lead to a state from which the student cannot complete the task. Local gaps alone are therefore not enough to determine whether teacher guidance benefits the current student. Effective supervision should instead emphasize guidance that the current student can translate into better final task outcomes. Accordingly, we propose Outcome-Guided On-Policy
Distillation (OG-OPD), which applies trajectory-relative weighting to teacher supervision and calibrates these weights using final task outcomes from paired student continuations. This calibration selectively strengthens supervision on the student's original trajectories at turns where teacher guidance benefits the current student. Across ALFWorld, ScienceWorld, and WebShop, OG-OPD consistently outperforms baselines under diverse settings. It improves task success rates by 3.6-17.7 percentage points over vanilla OPD and by up to 7.0 percentage points over the strongest baseline.
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All authors Tong Zhang, Zhou Liu, Yihao Liu, Jiahua Bao, Xuchen Li, Honglin Lin, Tao Cheng, Zhihan Yu, Kai Tang, Xiaoxi Jiang, Guanjun Jiang
Robotics
DexAgent: An Agentic Human2Sim2Robot Framework for Dexterous Manipulation with Self-Evolving Tool Library
Youhui Wang, Yunzhu Li, Li Fei-Fei et al. (+2 more)
Human
videos offer a scalable source of demonstrations for dexterous
robot manipulation. However, existing human-to-simulation-to-
robot (Human2Sim2
Robot) pipelines rely on predefined procedures that struggle to accommodate diverse object properties and interactions, particularly those involving articulated and deformable objects. We introduce DexAgent, an agentic Human2Sim2
Robot framework that converts a single
egocentric human
video and a task
prompt into physically grounded
robot trajectories for policy training. It operates through four stages: semantic understanding of human
videos, property-based simulation reconstruction,
robot trajectory optimization, and
robot data generation. At each stage, DexAgent adapts its approach to the task and object properties by selecting suitable skills from its tool library or developing new ones when needed. Property-specific verifiers assess stage outcomes for physical validity and task-specific requirements and provide feedback for refinement, preventing error propagation through the workflow. This adaptive, verification-guided process allows DexAgent to process diverse objects and long-horizon tasks. In the final stage, DexAgent varies object and
robot states in simulation to generate diverse
robot trajectories from a single human
video, then retextures the rendered observations to facilitate sim-to-real transfer. Newly developed skills and verifiers are retained in its tool library, making it self-evolving to accumulate reusable capabilities. This reduces processing time as DexAgent encounters more human
videos. Across eleven real-world tasks, policies trained with DexAgent-generated data achieve a 3.5x higher success rate than competing baselines. Project website: https://dexagent1.github.io/.
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All authors Youhui Wang, Yunzhu Li, Li Fei-Fei, Jiajun Wu, Huang Huang
Cosmology and Nongalactic Astrophysics
LISA bright sirens as a tiebreaker among cosmologies in tension
M. F. A. Medeiros, F. C. Carvalho and L. L. Sales
Gravitational waves from massive black hole binaries detected by LISA will deliver luminosity distances without any astrophysical calibration, offering a probe of the expansion history independent of the
cosmic distance ladder. Rather than asking how tightly LISA will constrain a single fiducial cosmology, we ask which of several mutually discrepant present-day cosmologies a future LISA
dataset would render most self-consistent. We build mock catalogues of LISA bright sirens under three fiducial cosmologies drawn from
datasets that participate in the current $H_0$ discrepancy (Planck 2018, Union3 and Pantheon+SH0ES), with a self-consistent error budget from instrumental noise, weak
lensing and host peculiar velocities. We compare the posterior from the simulated LISA data alone with that of a real-data combination of Type Ia
supernovae, DESI
baryon acoustic oscillations,
cosmic chronometers and the compressed Planck 2018 CMB, and quantify their internal tension in the $(H_0,\Omega_m)$ plane, crossing each fiducial with three SN Ia compilations. The fiducial drives the tension, from $2.08\sigma$ to well beyond $5\sigma$, while the
supernova compilation changes it by at most $1.2\sigma$. The discriminating power is strongly asymmetric: a Pantheon+SH0ES universe is inconsistent with every background we test, at a significance far in excess of $5\sigma$ and still at $3$-$5\sigma$ for the $10$-$20$ events expected from recent population models, whereas the Planck 2018 and Union3 fiducials, which differ by only $0.24$ km/s/Mpc in $H_0$, cannot be separated by any catalogue size. LISA bright sirens are therefore a sharp arbiter of the Cepheid-calibrated scenario and, on this error budget, silent between the other two.
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