Quantum Physics
Martino Bernasconi and Giulio Malavolta
We study a multilinear optimization problem for tensors with bounded Frobenius norm, where each of the $k$ local factors of dimension $d$ is chosen from a convex set. We give a deterministic
algorithm running in time $d^{O(k)}$ for constant additive approximations. As applications, we obtain the first
polynomial-time
algorithms at constant accuracy for weak membership in the
nuclear-norm unit ball of high-order tensors and for multipartite
quantum separability in Frobenius norm. Our approach views tensor optimization as a cooperative multiprover game and combines this perspective with a recursive spectral compression procedure. We then show that related ideas admit a
quantum implementation when the input state is given through copies, rather than an explicit classical description. In these settings we obtain an
algorithm to solve Frobenius-norm separability testing using $\text{poly}(k)$ copies and $\text{poly}(k\log d)$ time.
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Computer Vision
LoGo: Local-Global Rewards for Consistent Long-Horizon Video Generation
Ziqi Ma, Shreya Sharma, Mohamed El Banani et al. (+8 more)
Camera-controlled
video models are rapidly advancing toward long generation horizons and complex camera control. A key failure mode is 3D inconsistency: as the camera moves, objects lose permanence and scene structures shift. Existing post-training techniques, which assign a single scalar reward to the entire generation, are poorly suited to correcting these inconsistencies over long horizons. We introduce LoGo, which blends global and spatially localized rewards for camera-controlled
video models. The local reward provides fine-grained credit assignment, which substantially improves 3D consistency, while the global reward preserves camera following and
video quality. Across three base models, LoGo shows a clear advantage on DL3DV and TrajectoryBench, a new
benchmark for long-horizon, complex-camera-control generation that current evaluations lack. LoGo effectively reduces local object shifts, artifacts, and global scene changes, illustrating the importance of credit assignment in post-training
video models. Project website: https://ziqi-ma.github.io/logo-website/
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All authors Ziqi Ma, Shreya Sharma, Mohamed El Banani, Katja Schwarz, Chongjie Ye, Chao-Yuan Wu, Li Fei-Fei, Ben Mildenhall, Georgia Gkioxari, Justin Johnson, Gowthami Somepalli
Earth and Planetary Astrophysics
Temporal Variability of Titan's Middle-Atmospheric Zonal Winds from Southern Fall to Late Winter (2016-2023)
Martin A. Cordiner, Yuan Lian, Juan M. Lora et al. (+10 more)
Previous ALMA observations have revealed unexpectedly strong and rapid variations in Titan's high-altitude equatorial zonal winds, which present a challenge to our understanding of this moon's atmospheric dynamics. Here we report further measurements of Titan's zonal wind field at middle atmospheric altitudes $\approx200$-490 km, based on ALMA observations of spatially and spectrally resolved CH$_3$CN emission between 2016-2023 (corresponding to a
solar longitude $L_s=81.6^{\circ}$-$156.4^{\circ}$, spanning Titan's late southern autumn to late winter). These observations indicate substantial, ongoing, rapid temporal variability of Titan's zonal winds, on timescales as short as $\approx1$ Earth month ($0.9^{\circ}$ in $L_s$). The strongest variability is at (near-)equatorial latitudes where the zonal winds are fastest (up to $240\pm26$ ms$^{-1}$), with repeated $\sim40$ ms$^{-1}$ fluctuations occurring between $L_s=146.0^{\circ}$-$156.4^{\circ}$. The observed longer-term trends are qualitatively well-reproduced by two independent, state-of-the-art general circulation models (GCMs), which match the observed decrease in zonal wind speeds over a broad range of latitudes between $L_s=81.6^{\circ}$-$146.0^{\circ}$, followed by a more moderate increase between $L_s=146.0^{\circ}$-$156.4^{\circ}$. The wind speeds at mid-to-high latitudes ($\sim-45^{\circ}$ south) are also typically reasonably well reproduced by the GCMs (differing by $\lesssim30$%). However, the equatorial wind speeds are up to a factor of $\sim2$ faster than model predictions (with the greatest discrepancy around solstice; $L_s\approx90^{\circ}$). Rapid temporal variability of the retrieved zonal winds indicates the presence of strong atmospheric instabilities that are not well reproduced by models, suggesting a need for future GCM improvements.
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All authors Martin A. Cordiner, Yuan Lian, Juan M. Lora, Nicholas A. Lombardo, Lucy Wright, Jonathon Nosowitz, Richard Cosentino, Nicholas A. Teanby, Conor A. Nixon, Alexander E. Thelen, Claire E. Newman, Steven B. Charnley, Eliot F. Young
Artificial Intelligence
Credit Where It Matters: Dependency-Aware Policy Optimization for Terminal Agents
Yu Li, Guangfeng Cai, Long-Fei Li et al. (+5 more)
Terminal-using
agents benefit from reinforcement learning (RL) in coding, debugging, and other multi-step terminal tasks. In these tasks, later commands often depend on information or intermediate results produced by earlier commands. However, existing trajectory-level and step-level credit assignment methods do not explicitly trace the read-write dependencies through which commands affect the final outcome. Consequently, training signals could still be assigned to irrelevant operations, weakening learning from relevant steps. In this paper, we propose Dependency-Aware Group Policy Optimization (DepGPO), which uses execution dependencies between commands to guide credit assignment for terminal
agents. Specifically, we construct a command dependency graph from execution traces and trace backward from the resources inspected by the task verifier. We then assign credit to relevant writes and their supporting reads along these paths, and use it to redistribute trajectory advantages across steps. Extensive comparative experiments and ablation studies demonstrate that DepGPO improves task performance and training stability on complex terminal tasks.
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All authors Yu Li, Guangfeng Cai, Long-Fei Li, Shuo Han, Shengtian Yang, Han Luo, Kaibing Yang, Lei Feng
Optimization and Control
Closing the Accuracy Gap in Stochastic First-Order Bilevel Optimization
Haihan Zhang, Wendao Wu, Chenheng Zhang et al. (+5 more)
We characterize the optimal accuracy dependence for smooth nonconvex–strongly-convex bilevel optimization with
stochastic first-order oracles. For globally unbiased fresh-gradient observations with bounded variance, we prove an $\Omega(\epsilon^{-6})$ lower bound matching the accuracy exponent of existing upper bounds. We consider globally Lipschitz gradients, a bounded upper gradient in the lower variable, and Lipschitz lower Hessian blocks, with target $\mathbb{E}|\nabla F(\widehat{x})|\le\epsilon$. Let $L$ be the common first-order scale, $\mu$ the lower strong-convexity modulus, $\rho$ the lower Hessian-variation budget, $\kappa=L/\mu$, and $\chi=1+\rho/\mu$. For $\rho\gtrsim\mu$, $\chi\lesssim\kappa$, sufficiently high accuracy, and sufficiently large dimension, we establish $\Omega\left(L\kappa^2\Delta\epsilon^{-2}+L^3\chi^2\kappa^8\sigma_g^2\Delta\epsilon^{-6}\right)$, where $\Delta$ is the initial gap budget and $\sigma_g^2$ is the lower-gradient variance budget. The bound holds over full Euclidean spaces against arbitrary randomized adaptive
algorithms, even when every sample is the gradient of a scalar function. In the common-scale regime $\rho=\Theta(L)$, the leading
stochastic term has condition-number dependence $\kappa^{10}$, compared with the achievable $\kappa^{11}$ dependence. The proof embeds a sequential hard objective into an exact lower response while preserving global regularity and finite gap. A multiscale decomposition limits the gradient signal carrying each new direction, yielding the required sample complexity. We complement this lower bound with a frozen-linear-tilt
estimator whose bias is proportional to lower Hessian variation. Its analysis makes this structural dependence explicit and yields matching leading rates in the specified
curvature-controlled and small-gap regimes.
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All authors Haihan Zhang, Wendao Wu, Chenheng Zhang, Yanyi Li, Chunyuan Zheng, Cong Fang, Haoxuan Li, Zhouchen Lin
Computer Vision
Yiqi Liu, Ruifeng Yuan, Yang Wang et al. (+7 more)
Physical fidelity has received increasing
attention in world models and
video generation, yet how
video representations encode physical information remains less understood. We introduce the World
Embedding Benchmark, comprising 8,000 controlled simulation cases from 80 families spanning fluid mechanics, solid mechanics, dynamics, and optics & electromagnetism. Each case pairs a rendered
video with simulation-derived physical annotations, supporting three complementary tasks: text-
video retrieval, physical-property regression, and multiple-choice
video-description pair classification. We use these tasks to distinguish cross-modal physical
alignment from the recoverability of quantitative physical information. Evaluated pre-trained omnimodal
embedding models show weak
retrieval and near-chance within-family pair classification, while lightweight probes recover useful physical information from frozen
video embeddings. Continual contrastive training with physics-specific
video-text pairs improves
retrieval and pair classification but degrades physical-property regression, revealing a trade-off between
alignment and quantitative information recoverability. Finally, we use the
embeddings to retrieve reference
videos for
retrieval-augmented generation with MiniMax-H3. Retrieved references improve the physical fidelity of generated
videos, with stronger
retrieval models yielding larger gains in our experiments. Together, these findings highlight the need to evaluate physical
alignment and property recoverability jointly, and demonstrate the utility of physical representations for improving
video generation.
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All authors Yiqi Liu, Ruifeng Yuan, Yang Wang, Long Li, Fengyu Cai, Hou Pong Chan, Jialin Yu, Hao Zhang, Chenghua Lin, Chenghao Xiao
Artificial Intelligence
NeutronGym: Physics-Graded Neutron Instrument Design for LLM Agents
Lijie Ding and Changwoo Do
Designing a scientific instrument tests whether
language-model
agents can do physics rather than recall it, provided the grading cannot be argued with. We introduce NeutronGym, to our knowledge the first executable environment for
neutron instrument design:
agents build instruments through validating tools, McStas ray-traces what they build, and a level-resolved ladder grades syntax, runtime, structure and science with no LLM judge. Procedural families supply unlimited instances of a fixed layout whose design parameters the
agent must set, with held-out parameter regimes; a curated slice, McStasBench, adds 16 tasks from published instruments behind memorization probes and a sandbox. Seven models reproduce at most 7 of the 16, none retrieves a reference, and none meets an improvement target. The environment also trains. Reinforcement learning on its reward takes Qwen3-8B from 11% to 77% of held-out instances of a family whose targets come from a hidden design (69% at a second seed), past an untrained Qwen3-32B, and the recipe holds, at one seed each, on three further gated families. The analysis says what that gain is. Without the ladder's partial credit it collapses by 60 points. From reward alone the trained model reaches what a classical optimizer reaches, at the
agent's simulation budget, only when handed the closed-form physics (77% against 81%, a gap that does not separate at this size), while frontier models still solve 98-99%. Getting a trustworthy result meant failing four task designs that no-model baselines could solve, and we release the probes that found them.
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Quantum Physics
Entanglement of purification for Werner states: canonical purification and nonadditivity
Zahra Baghali Khanian and Amir-Reza Negari
We prove that the von Neumann
entanglement of purification is nonadditive. For two-
qubit Werner states $W(f)$ with singlet weight $1/64\le f\le1/4$, we show that canonical purification is globally optimal: its
entanglement, also known as reflected
entropy, gives the exact
entanglement of purification. In contrast, the regularized
entanglement of purification lies strictly below the reflected
entropy for $0<f<f_\ast$, where $f_\ast\approx0.017$. Together, these results establish nonadditivity throughout $1/64\le f<f_\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\le\alpha<1$ using classical two-
qubit states. We thus resolve the additivity question at $\alpha=1$. Remarkably, nonadditivity is again witnessed by separable states and no
entanglement in the underlying states is required.
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Quantum Physics
Discriminating Lindbladian Dynamics
Robert Salzmann, Ludovico Lami, Martin B. Plenio et al. (+1 more)
The fundamental task of
quantum hypothesis testing, which consists in discriminating
quantum objects, has been extensively studied for
quantum states and channels. Here, we investigate the fundamental limits of discriminating an arbitrary pair of
quantum Markovian dynamics generated by Lindbladians, focusing on the roles of total exposure time and temporal resolution. We allow adaptive choices of
evolution durations and arbitrary instantaneous controls between them. We characterise the optimal type-II error exponent (Stein exponent) as the largest instantaneous increase of
quantum relative
entropy, and give an algebraic criterion for its finiteness in terms of the Lindbladians. Remarkably, an infinite exponent is equivalent to a vanishing type-II error probability at sufficiently large finite total time, for every positive type-I tolerance. While some dynamics admit a finite protocol with zero type-II error, others require increasingly fine temporal control. For the latter, the error vanishes as the minimum allowed
evolution duration, or resolution time, tends to zero at fixed sufficiently large total time, but remains bounded away from zero at every fixed positive resolution time. We achieve this using
quantum Zeno protocols, establishing temporal resolution as a resource for discrimination. When the null hypothesis is the identity
semigroup, an infinite asymptotic error exponent has a stronger consequence: at a fixed finite total exposure time, the type-II error can be made arbitrarily small while keeping the type-I error exactly zero. This is impossible in the corresponding classical setting. Discriminating the identity
semigroup from generalised amplitude damping on a
qubit provides examples of all three regimes: a finite asymptotic error exponent, zero type-II error attainable at positive resolution time, and vanishing type-II error requiring the resolution time to tend to zero.
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All authors Robert Salzmann, Ludovico Lami, Martin B. Plenio, Susana F. Huelga
Logic
On differentiability in weakly o-minimal expansions of fields
Juan Pablo Acosta, Yatir Halevi, Assaf Hasson et al. (+2 more)
We show that every definable function in a weakly o-minimal expansion of a field $K$ is generically differentiable, where the derivative takes values in the Cauchy completion of $K$, i.e. it is a definable nonvaluational cut. As a consequence, every definable field is definably isomorphic to either $K$ or its algebraic closure.
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All authors Juan Pablo Acosta, Yatir Halevi, Assaf Hasson, Will Johnson, Ya'acov Peterzil
Biological Physics
Cost convexity controls the architecture of resistance-optimal networks
Hugo Tovar, Genaro Vázquez-Victorio, Enrique Hernández-Lemus et al. (+2 more)
A conducting network improves access to its interior only by spending material, so architectures compare only at equal budget. We redistribute conductance under a power-law resource law $\C_{\alpha}=\sum_e a_e w_e^{\alpha}$ and measure access by the reciprocal of the mean pairwise effective resistance. When the cost is strictly convex the allocation is unique and every admissible edge keeps positive conductance; at $\alpha=1$ uniqueness survives but an edge can be priced out. The marginal worth of an edge is then its squared biharmonic distance, a Murray-type balance whose balanced quantity is global rather than junction-local. The same optimum scores any weighted network at its own budget, separating an allocation factor from a topological one. Under concave cost the marginal price of an incipient channel diverges, the feasible set is nonconvex, and conductance condenses onto sparse backbones. The uniform
star and the uniform complete graph cross at $\alpha_c(n)=\log(n/2)/\log(n-1)$, near which intermediate states beat both. Up to $n=64$ the best states found grow approximately linearly in $n$, so channels per node change much less than the active fraction does. Loops are governed instead by a collapse exponent $\alpha^{*}(n)$, resolved to $0.005$ at every size: it rises from $0.555$ at $n=8$ to $0.675$ at $n=64$, and the collapse across it is abrupt, the support at $n=64$ falling from $133$ active edges to the $63$ of a spanning tree. A fixed exponent therefore changes character with size by crossing this boundary. One prescribed source and sink instead gives a loopless optimum.
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All authors Hugo Tovar, Genaro Vázquez-Victorio, Enrique Hernández-Lemus, Alejandra Cervera, Daniel Pérez-Calixto
Artificial Intelligence
Depth as Time in One-Step Generative Models
Arnold Caleb Asiimwe, William Yang, Sanghyuk Chun et al. (+2 more)
The recent wave of one-step generative models, which compress the multi-step trajectory of
diffusion via either
distillation or learned flow maps, has reached an inflection point where they can generate high-quality images. Here, we ask a natural question that follows from these advances: what happens to the denoising trajectory of multi-step
diffusion when generation is compressed into a single forward pass? We offer an empirical observation we call depth as time: the denoising computation that multi-step
diffusion performs across sampling steps appears to unfold across the depth of a single forward pass, and can be recovered by decoding intermediate layers with the model's own output head. Most interestingly, we show that this depthwise computation depends on the transport task a flow map is trained to solve. The most surprising case is MeanFlow, where probing shorter transport intervals reveals both denoising and renoising within a single network evaluation. In contrast, generators trained without a time-indexed transport task, such as drifting models, do not exhibit the same depthwise denoising. Consequently, we show that models that exhibit the depthwise denoising phenomenon are more compressible across the layerwise computation: a MeanFlow SiT-L/2 model can be compressed by $16.6\times$ in parameters into a single time-conditioned block. We offer an explanation for this denoise-then-renoise behavior and show that, when we treat the layerwise computation explicitly as a flow, a single time-conditioned block can be trained to denoise across layers, compressing a MeanFlow SiT-L/2 model by $16.6\times$ in parameters. Together, these results suggest that the temporal computation of
diffusion is not eliminated by one-step generation, but reorganized across network depth.
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All authors Arnold Caleb Asiimwe, William Yang, Sanghyuk Chun, Esin Tureci, Olga Russakovsky
Computation and Language
FALCON: A Model and Dataset Agnostic Framework for Synthetic Data Generation for NL2SQL Pairs
Darian Lee, Shannon Rumsey, Jack St. Clair et al. (+3 more)
Relational databases are among the most widely deployed forms of structured knowledge, and natural
language access to them requires grounding
language onto schema entities and relations while handling the ambiguity inherent in how people phrase requests. Existing synthetic NL-to-SQL data generation methods largely ignore this ambiguity and produce oversimplified queries that fail to prepare models for the complexity of real-world structured knowledge access. We present FALCON, a framework that generates realistic, ambiguity-aware NL-to-SQL data matching the complexity of challenging real-world
benchmarks, at low cost using compact open models. Our approach combines reserved-word SQL seeding and persona-based prompting to generate structurally complex queries, while
alignment-based filtering preserves difficulty by distinguishing genuinely incorrect examples from complex but valid queries. Human evaluation confirms consistent high quality across model sizes, and our generated data exceeds existing
benchmarks in both SQL complexity and natural
language richness. Difficulty-stratified analysis shows models trained on FALCON data increasingly outperform baseline-trained models as query complexity increases, validating our pipeline's success in generating challenging training data. When combined with a small proportion of existing
benchmark data, mixed training recovers performance on simpler queries while preserving these advantages on complex ones. The model- and database-agnostic design enables organizations to generate high-complexity NL-to-SQL training data locally without external APIs.
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All authors Darian Lee, Shannon Rumsey, Jack St. Clair, Xinyi Tang, Aditya Bansal, Yuanming Shi
Quantum Physics
Maryam Mudassar, Zhi-Yuan Wei, Alexander Schuckert et al. (+3 more)
Fault-tolerant
quantum simulation requires compiling
symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous
symmetries even when the target
evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2)
symmetry exactly. We characterize the number-theoretic obstruction preventing
symmetry-preserving
unitary Clifford+T
circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the
symmetry-preserving operator
algebra rather than introducing
symmetry-breaking perturbations. We demonstrate the
algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our
symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge
symmetries in
lattice gauge theories and to particle-number and
spin symmetries in fermionic models relevant to
quantum chemistry and the
Fermi-Hubbard model. These results show that
symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for
quantum simulation.
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All authors Maryam Mudassar, Zhi-Yuan Wei, Alexander Schuckert, Michael J. Lawler, Michael J. Gullans, Daniel Gottesman
Networking
Beyond Idealized Orbits: Realistic Network Topology and Spatio-Temporal Traffic Emulation for LEO Satellite Constellations
Suryansh Aryan, Josh Smith, Alexa Houck et al. (+5 more)
Large low-earth orbit (LEO) satellite constellations are revolutionizing network access globally by delivering potential high-capacity, low-latency communication, fueling innovation and accelerating research in advanced space-based non-terrestrial network architectures. Consequently, a research testbed that allows flexibility in designing realistic network routing schemes, traffic load balancing and inter-shell communication methods to emulate real-world multi-shell network becomes an important tool for industry developers and academic researchers. This study broadens the scope of the SpaceNet testbed, now including emulation of multi-shell constellations and computation of routes with the existing global web of terrestrial terminals. Furthermore, the testbed produces accurate trends in return trip time (RTT) and throughput metrics due to its support of high-level congestion modeling and the necessary local and global congestion routing. To evaluate the efficacy of the testbed, the network performance of emulated results for the Starlink constellation is evaluated and compared with data from real Ping and iPerf tests between Starlink terminals. Two important communication scenarios have been discussed that highlight the testbed's potential for realistic multi-shell
topology generation and handling various types of traffic distribution with well-informed congestion routing. Predictions of network performance using SpaceNet accurately addresses temporal behaviors for different traffic levels with strong temporal predictability in its throughput and RTT time-series, as well as enhanced ground truth coverage within a 95% confidence interval.
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All authors Suryansh Aryan, Josh Smith, Alexa Houck, Rahul V. Chintalapati, Alexander Kedrowitsch, Jeffrey H. Reed, Nishith D. Tripathi, Samantha Parry Kenyon
Robotics
CORNAV: Construction-Aware Reasoning for Robot Navigation on Active Worksites
Parastoo Ali Pour, Deepak Prakash Kumar, Tommy Zhou et al. (+2 more)
The construction industry faces persistent labor shortages, low productivity that costs the global economy over $1.6 trillion annually, and one of the highest injury rates among major industries. These factors motivate the use of autonomous
robots to improve efficiency and worker safety. Existing
language-grounded
navigation systems, however, rely on semantic scene understanding alone and lack access to construction-specific context such as architectural plans, evolving work schedules, and safety constraints. As a result, they localize permanent building features unreliably and cannot safely navigate active jobsites. We present CORNAV, a blueprint-grounded, schedule-aware
navigation framework that operates from 2D CAD drawings and project schedules without requiring a Building Information Model. CORNAV aligns architectural blueprints against hierarchical open-vocabulary 3D scene graphs to ground object queries, converts project schedules into time-varying
navigation constraints, and validates requests through an LLM-based safety module that escalates hazardous zones before planning. An A* planner then enforces mandatory exclusion zones while preferentially avoiding higher-risk areas. Across an indoor office and a real construction site, blueprint grounding raises task success from 13.0% to 72.2% over semantic
retrieval alone, schedule awareness eliminates all hard-zone violations, and the safety module correctly rejects hazardous requests arising from mislabeled project schedules.
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All authors Parastoo Ali Pour, Deepak Prakash Kumar, Tommy Zhou, Pramod Khargonekar, Mohammad Abdullah Al Faruque
Game Theory
Normal-Form Correlation in Markov Games
Ioannis Anagnostides, Constantinos Daskalakis, Gabriele Farina et al. (+3 more)
There has been a surge of recent work on correlated
equilibrium concepts in Markov games. However, existing results focus on concepts weaker than normal-form correlated
equilibria (NFCEs), leaving open the more challenging question of computing such
equilibria, which goes back to the seminal work of Papadimitriou and Roughgarden (JACM'08). Here, we establish the first efficient
algorithm for NFCEs in finite-horizon Markov games with a fixed number of players $n$. In particular, with $S$ states, horizon $H$, and at most $A$ actions per player, it computes an $\epsilon$-NFCE in time $S(AH/\epsilon)^{O(n)}$. This is the first
algorithm polynomial in $1/\epsilon$ and the description of the game for NFCEs in an interesting class of problems beyond the normal-form setting. Moreover, under the usual assumption that recommendations are independent across states, we show PPAD-completeness—that is, computational equivalence to Nash
equilibria—either in many-player games or when the precision is exponentially small. The key idea behind our approach is to run backward induction on a sequence of auxiliary stage games, but with the twist that in each step we compute a constant-expectation correlated
equilibrium. This is a natural refinement of correlated
equilibrium in which the conditional expected payoff from obeying is independent of the recommendation. In fact, our reduction goes both ways, establishing an equivalence between constant-expectation CEs and NFCEs in Markov games. For a fixed number of players, we observe that a constant-expectation CE can be computed approximately by combining linear programming with suitable discretization. In contrast, it is PPAD-hard in i) polymatrix (many-player) games at constant precision, and ii) two-player games at exponentially small precision. The latter result follows from an unexpected connection to rank-2 two-player games.
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All authors Ioannis Anagnostides, Constantinos Daskalakis, Gabriele Farina, Noah Golowich, Tuomas Sandholm, Brian Hu Zhang
Machine Learning
UniIntervene++: An Adaptive Intervention Agent for Efficient Real-World Reinforcement Learning
Yudong Lin, Haoyuan Deng, Zhuoxuan Yuan et al. (+3 more)
Online reinforcement learning (RL) enables
robot policies to improve through physical interaction, but the assistance they require changes as their competence evolves. Existing intervention strategies based on offline estimates or fixed decision rules can therefore become mismatched to the current policy. To address this, we propose UniIntervene++, an adaptive intervention
agent that learns to allocate control between autonomous execution and heterogeneous assisted behaviors during online RL. Specifically, UniIntervene++ first formulates the evolving RL policy, trajectory correction, and a task-structured CodePolicy as Options in a unified semi-Markov decision process and learns their relative values online. Building on this, competence-adaptive intervention periodically probes the RL policy through unassisted execution, keeping control allocation responsive to its evolving capability. Finally, coupled experience learning allows assisted behaviors to improve the RL policy, whose evolving outcomes in turn reshape future intervention decisions. In this way, UniIntervene++ jointly determines when to intervene, how to intervene, and when to return control as the RL policy improves. Across five real-world manipulation tasks, UniIntervene++ achieves an average success rate of 89.67%, outperforming all baselines by at least 6 percentage points, while reducing human intervention to 0.77%, a relative reduction of at least 94.6% from the best baseline. Code is available in our \href{https://github.com/dannyyudong/An-Adaptive-Intervention-
Agent-for-Efficient-Real-World-Reinforcement-Learning}{GitHub repository}.
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All authors Yudong Lin, Haoyuan Deng, Zhuoxuan Yuan, Zaijia Yang, Yuanjiang Xue, Ziwei Wang
Dynamical Systems
Beta-shifts without typical periodic optimization
Wen Huang, Oliver Jenkinson, Leiye Xu et al. (+1 more)
We show that beta-shifts whose lexicographically largest point is a Sturmian sequence do not have typical periodic optimization (TPO): on each such beta-shift there is a non-empty open set of Lipschitz functions whose unique maximizing measure is the Sturmian measure, which is not supported on a periodic orbit. These are the first known examples of beta-shifts without TPO, and, since they have the specification property, the first known examples of shift spaces with specification but without TPO. The corresponding beta-transformations do not have TPO in any space of Hölder functions on the interval. The main ingredient in the proofs is a
rigidity property of Sturmian subshifts: modulo constants and Lipschitz coboundaries, the space of Lipschitz functions on such a subshift is one-dimensional. We also show that the set of $\beta>1$ for which the beta-shift or the beta-transformation does not have TPO is dense in $(1,\infty)$, but has zero packing dimension. The density is proved by a tuning construction, analogous to Douady–Hubbard tuning in the Mandelbrot set, which produces non-Sturmian subshifts with the same
rigidity property. Finally, we show that every beta-shift has typical zero-
entropy optimization: for an open dense set of Lipschitz functions, the maximizing measure is unique and its support has zero topological
entropy.
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All authors Wen Huang, Oliver Jenkinson, Leiye Xu, Yiwei Zhang
Artificial Intelligence
Video-Time Priors for EEG-fNIRS Emotion Regression on Familiar Videos
Minghao Kong, Ying Gao, Jiurun Chen et al. (+4 more)
Do viewer-specific physiological signals improve continuous
emotion regression beyond the stimulus-driven response shared across viewers? We examine this question by predicting
emotion ratings for new viewers watching
videos that also appear in the training set. As a stimulus-only baseline, we define a
video-time prior:the smoothed median of training labels for each
video at each second. We then combine this prior, using a fixed fusion weight, with a graph-based model of electroencephalography (
EEG) and functional near-infrared spectroscopy (fNIRS) signals. On MER-PS 2026, five-fold cross-validation grouped by participant over 24 participants yields a mean absolute error (MAE) of 29.01 for fusion, compared with 29.06 for the prior alone. On an external cohort of four participants excluded from training, the corresponding MAEs are 27.72 and 28.04. In this cohort, most of the MAE reduction relative to a global-constant baseline comes from the prior, that is, from
video identity and playback time alone.Fusion lowers MAE for three of the four held-out participants and for nine of the fifteen
videos. The added value of physiological signals is therefore small and varies across participants and
videos. Because the model uses physiological signals recorded after each prediction time, it supports only offline prediction. Generalization to unseen
videos remains untested.
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All authors Minghao Kong, Ying Gao, Jiurun Chen, Muyao Chen, Zheng Ge, Jianxin Wu, Rongjie Wang
Computer Vision
DEPICT: Scoring Text-to-Image Alignment by Answer Agreement
Vasco Ramos, Sandra Godinho Silva, Joao Magalhaes et al. (+2 more)
Image-text
alignment is a core problem in computer
vision with applications in caption evaluation,
hallucination detection, data curation, and the benchmarking of text-to-image (T2I) generators. As T2I models improve, benchmarking has become demanding, requiring metrics capable of finding a series of issues like missing objects, swapped attributes, miscounts, and ignored negations. Recent work addresses this by fine-tuning evaluators on preference data or by prompting a
vision-
language model, either holistically with the caption or with decomposed verification questions. However, existing approaches fall short: fine-tuned metrics remain bound to one backbone and training distribution; holistic metrics miss fine-grained details; and decomposed metrics rely on a fixed-YES assumption that penalizes faithful images whenever that assumption fails. In contrast, we propose DEPICT, a training-free metric that replaces fixed reference answers with expected agreement between image-based and caption-only answers, weighting questions by how decisively the caption determines them. By replacing fixed references, our agreement rule increases negation accuracy from 19% to 88%. To recover the context lost during decomposition, DEPICT merges this agreement score with a holistic score. We evaluate DEPICT on five
benchmarks and eleven backbones from three model families and find that it surpasses all training-free metrics and exceeds fine-tuned evaluators on two out of three human-correlation
benchmarks.
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All authors Vasco Ramos, Sandra Godinho Silva, Joao Magalhaes, Ricardo Rei, Pedro Henrique Martins
Robotics
LLA-MPC on Embedded Hardware: Rapid Adaptive Control with Thousands of Parallel Models
Henry Z. Liao, Maitham F. AL-Sunni and John M. Dolan
We present a generalized implementation of Look-Back and Look-Ahead Adaptive Model Predictive Control (LLA-MPC), a learning-free framework for real-time, rapid adaptive system identification and control. The original formulation was demonstrated only in simulation, for autonomous racing with a fixed model structure. Our implementation has modular dynamics and integrators, and we validate it on the F1TENTH platform under constrained computation and noisy state estimation. The system identifies tire parameters online by evaluating thousands of candidate models in real time on an embedded computer. Experiments with low-friction tires across changing surfaces show that LLA-MPC completes high-speed tracking tasks where a fixed nominal model fails. Code,
videos, and our related work are available at: https://lla-control.github.io.
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Robotics
Bridging Frontier Reasoning and Robot Execution: From Autonomous Demonstration Generation to Dense Language Supervision
Bosung Kim, Alexander Trevithick, Ruiyi Wang et al. (+1 more)
Recent advances in frontier models enable
robot manipulation from only a few demonstrations, but high inference latency limits their use for real-time
robot control. To bridge this gap, we study two complementary approaches that connect frontier
reasoning with low-latency local execution. First, we use a frontier model to autonomously generate demonstrations that supplement human demonstrations for training a fast local policy. We augment its in-context examples with corrective demonstration segments that show how to recover from physical errors, improving generation reliability. Generation time and cost decrease as successful examples accumulate in context, suggesting a path toward more efficient data collection. At deployment, a harness combines frontier-generated instructions with a fast local policy, enabling efficient execution while preserving the frontier model's ability to guide and correct actions. With low-latency execution delegated to the local policy, the bottleneck shifts to its capacity to reliably follow the frontier model's diverse instructions. Our second bridge introduces dense
language supervision across three nested granularities—primitive, atomic, and composite—with multi-aspect descriptions at each level. Across long-horizon tasks in RoboCasa 365 and BEHAVIOR-1K, where instructions change as execution progresses, the combined supervision achieves the highest performance under both oracle and frontier-model instructors, demonstrating more reliable instruction following through the policy's
language interface. Finally, we evaluate both bridges together on a crossword task that combines semantic planning and manipulation within a fixed time budget. These results support autonomous demonstration generation and dense
language supervision as complementary components for connecting frontier
reasoning to low-latency local execution.
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All authors Bosung Kim, Alexander Trevithick, Ruiyi Wang, Prithviraj Ammanabrolu
Analysis of PDEs
Quantitative uniqueness for bi-Laplace equations with $C^2$ lower-order coefficients
Zhiwei Wang
We study quantitative unique continuation for bi-Laplace equations \[ \Delta^2u+W(x)\Delta u+V(x)\cdot\nabla u=0 \] with $C^2$ lower-order coefficients. Using the weighted-frequency function, we establish an $L^\infty$ three-ball inequality whose exponential factor has coefficient dependence $\|W\|_{C^2}^{1/2}+\|V\|_{C^2}^{1/3}$. Under some normalization, we obtain a vanishing-order bound of size $C(\|W\|_{C^2}^{1/2}+\|V\|_{C^2}^{1/3})$.
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Soft Condensed Matter
Surface Charge–Potential Relation for Spherical Particles in Electrolyte Solutions
Olga I. Vinogradova and Elena F. Silkina
Predicting the relationship between surface charge density and electrostatic potential for spherical particles remains a fundamental challenge in colloid science. Because the governing non-linear Poisson–Boltzmann equation lacks a general exact analytical solution, researchers typically rely on numerical calculations or various semi-empirical approximations. In this paper, we overcome these limitations by developing a dual-asymptotic framework that provides explicit, closed-form expressions for this surface charge–potential relationship across the entire spectrum of particle
curvature. For weakly curved systems, where the Debye length $\lambda_D$ is much smaller than the particle radius $R$ ($\lambda_D/R \ll 1$), a formal mathematical derivation rigorously establishes the Ohshima–Healy–White formula as an exact regular perturbation expansion. Conversely, for highly curved spheres ($R/\lambda_D \ll 1$), we employ singular perturbation analysis using the scaled particle radius as the small parameter. This approach provides a first-principles mathematical justification for the spherical Debye–Hückel theory, proving that its leading-order expansion remains asymptotically exact within the full non-linear Poisson–Boltzmann framework due to the
geometric deactivation of non-linearity. Crucially, we map the exact limits of this
geometric regulation, demonstrating how non-linear screening re-emerges as the particle radius increases, with the breakdown threshold governed by the interplay between
curvature and surface charge density.
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Combinatorics
Signed seeds and G-gradings on cluster algebras
Lauren Williams and Alan Yan
The theory of cluster
algebras is closely connected to the theory of total positivity; indeed, the desire to better understand total positivity was one of the main motivations for Fomin and Zelevinsky's introduction of cluster
algebras [arXiv:math/0104151]. In particular, any cluster variety whose coordinate ring has a cluster structure has a natural notion of positive part: the subset of the variety where all cluster variables are positive. In this paper, we explain that there are other signed
cells contained in cluster varieties that are equally natural from a cluster-theoretic point of view. These come from signed seeds, which can be thought of as a $\mathbb{Z}/2\mathbb{Z}$-grading on cluster variables, and which were introduced in [arXiv:2310.17727] in the context of the amplituhedron. More generally, given any abelian group $G$, we introduce the notion of a $G$-graded seed for a cluster
algebra, which is a way of assigning elements of $G$ to each cluster variable which is compatible with the cluster structure. When $G$ is the multiplicative group $\{-1, 1\}$, this recovers the above notion of signed seed; when $G = \mathbb{C}^*$, this recovers the notion of cluster
automorphism group [GSV10] or cluster dilation group [arXiv:2603.17890]; and when $G = \mathbb{Z}^d$, this recovers the notion of graded cluster
algebra studied by Grabowski-Launois [arXiv:1301.2133], Grabowski [arXiv:1309.6170] and Gekhtman-Shapiro-Vainshtein [GSV10, Section 5.2] (which had previously appeared in special cases in work of Fomin-Zelevinsky [arXiv:math/0602259]). The examples we study include the space of square
matrices, symmetric
matrices, skew-symmetric
matrices, positroid varieties, and amplituhedron tiles. We also connect this notion to tropical mutation when $G = \mathbb{R}$ or $\mathbb{Z}$.
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Combinatorics
Counting Hamiltonian Sturm permutations: generating functions and Gaussian distributions
Bernold Fiedler and Carlos Rocha
Our combinatorial analysis is motivated by the PDE dynamics \begin{equation} \mathbf{u_t} = \mathbf{u_{xx}} + \mathbf{g}(\mathbf{u}),\qquad 0<\mathbf{x}<1, \end{equation} of solutions $\mathbf{u}=\mathbf{u}(\mathbf{t},\mathbf{x}),\ \mathbf{t}\geq 0$, under Neumann boundary conditions. For dissipative nondegenerate nonlinearities $\mathbf{g}$, the global attractors $\mathcal{A}=\mathcal{A}_\mathbf{g}$ of the PDE can then be classified by the orderings of their $2n+1$
equilibria $\mathbf{v}$ at the boundaries $\mathbf{x}=0,1$. We encode the boundary orders as
Hamiltonian Sturm permutations. The name ”Sturm” refers to nodal properties of PDE solutions $\mathbf{u}(\mathbf{t},\mathbf{x})$. ”
Hamiltonian” refers to the second order pendulum ODE for
equilibria $\mathbf{v}(\mathbf{x})$: \begin{equation} 0 = \mathbf{v_{xx}} + \mathbf{g}(\mathbf{v}). \end{equation} We determine the generating function $a(z)=\sum_n a_nz^n$ for the counts $a_n$ of
Hamiltonian Sturm permutations. For $n\rightarrow\infty$, this provides explicit asymptotics of $a_n$. We refine these counts as $a_n=\sum b_{rq}$. Here $b_{rq}$ counts
Hamiltonian Sturm permutations with $2r+1$ spatially homogeneous
equilibria and $2q$ spatially non-homogeneous
equilibria, such that $r+q=n$. We also determine the explicit generating function $b(x,y)=\sum_{r,q} b_{rq}x^ry^q$. This implies asymptotically Gaussian distributions of the probabilities $p_{nr}=b_{rq}/a_n$ with $r+q=n$, asymptotically for large $n$. We derive asymptotics for means and variances, with error estimates of order $1/n$. All asymptotics are based on work by Flajolet and Sedgewick. We conclude with numerical illustrations and remarks on nonlinearities $\mathbf{g}(\mathbf{u},\mathbf{u_x})$ under periodic boundary conditions $\mathbf{x}\in\mathbb{S}^1=\mathbb{R}/2\mathbb{Z}$, where rotating waves arise.
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Strongly Correlated Electrons
Decohering Kitaev's Sixteenfold Way: A Holographic Approach
Shuyu Zhang, Linhao Li, Zhen Bi et al. (+2 more)
We study anyon decoherence in 2D topological order, with the
fermion decoherence in Kitaev's sixteenfold way as explicit examples. The sixteenfold way includes
chiral topological phases, which are believed to admit no commuting projector
Hamiltonian, making it challenging to study their decoherence directly. We further
conjecture the density
matrix produced by this decoherence induced phase transition can be obtained by a three-step procedure: first lift the topological order to its Walker-Wang model, followed by a transition to another Walker-Wang model, and finally trace over the bulk degrees of freedom. This establishes a connection between the decoherence of a topological order and a pure state phase transition in its 3D counterpart. Many examples are given. In particular, we show that decohering the
fermion in each of the sixteen states always yields an intrinsically mixed-state topological order, a consequence of the fact the corresponding 3D bulk always transits into the 3D fermionic toric code (fTC). Our result suggests a systematic method for studying anyon decoherence in
chiral topological orders at the level of commuting projector
Hamiltonians.
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All authors Shuyu Zhang, Linhao Li, Zhen Bi, Tzu-Chieh Wei, Zijian Song
Quantum Physics
The QICK Box: A Modular RF Front-End System for Quantum Control and Readout
L. Arnaldi, D. Martin, S. Sussman et al. (+11 more)
The QICK (
Quantum Instrumentation Control Kit), first introduced in 2022, is a standalone open source control system for
quantum information science. Since then, QICK has been migrated to new hardware platforms, expanded its functionality for applications with different types of
qubits (superconducting, atomic, ion-trapped, and
spin defects), as well as
quantum sensors, and
quantum networks. QICK is a highly optimized control kit, with a library of functions that can be used for more than one application. In particular, the software and firmware are customized to minimize latency and maximize control performance and throughput. In this white paper, we describe hardware details and performance of the QICK Box. The QICK Box features up to 16 outputs, up to 8 inputs, and 8 20-bit DC biases. Modular output and input daughtercards give the choice of signal chains optimized for fast DC-coupled signals or RF signals up to 10 GHz. Power levels, step attenuation, and bandpass filtering are controlled by software. We demonstrate the system's performance through single-shot readout measurements of a six-transmon device at the
Quantum Underground Instrumentation Experimental Testbed (QUIET) at Fermilab, achieving (91.7 +/- 0.4)% readout fidelity limited by T1 decay during the readout. The single shot readout signal-to-noise ratio (SNR) is 4.4 +/- 0.1 without a
quantum amplifier, confirming that the QICK Box is suitable for high-fidelity
quantum control and measurement applications. Advances in firmware and software will be described in a separate paper.
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All authors L. Arnaldi, D. Martin, S. Sussman, S. Uemura, K. Treptow, N. Wilcer, A. Colón Cesaní, O. Seidel, K. Anyang, G. Bratrud, F. Abouzahr, J. Christiansen-Salameh, D. Baxter, G. Cancelo
Algebraic Topology
The Squire complex and its extensions revisited
Elton Pasku
The Squier complex $\mathcal{D}(\cP)$ has been defined in \cite{LDHM1} as a combinatorial 2-complex. Also several extensions of $\mathcal{D}(\cP)$ are defined and used extensively in \cite{LDHM2}, \cite{SES} and \cite{EP}. Since the results obtained in those papers rely on the assumption that $\mathcal{D}(\cP)$ and its extensions in \cite{LDHM2} and \cite{SES} are CW-complexes of dimensions 2 and 3, respectively, and no proofs are given to support these preconditions, we provide the respective proofs in the present paper.
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