High Energy Astrophysical Phenomena
Is accretion flow magnetically arrested in M87?
Yuao Ma, Xinwu Cao, Jia-Wen Li et al. (+2 more)
It is still debating on whether the disc is magnetically arrested in M87. We assume that a weak external
magnetic field is dragged inwards by the
accretion disc, which is substantially enhanced to drive strong jets near the black hole horizon via Blandford-Znajek mechanism. The jet power of M87 has been well constrained with the observational data, while the
accretion rate in the inner region of the
accretion flow in M87 is estimated by fitting the multi-waveband continuum spectrum and the data of the Faraday rotation measurement, with which the surface density of the disc is derived. Our calculations show that, in order to produce the observed jet power $P_{\rm jet}=3.2\times 10^{43}~\rm erg~s^{-1}$, an external field with several hundred $\mu \rm G$ at the outer edge of the disc is required to be amplified in the disc to hundreds G at the BH horizon, and the
accretion flow in M87 must be magnetically arrested. A standard and normal
evolution (SANE) disc is allowed in M87, only if the jet power is significantly lower than $\sim 1.75 \times 10^{43} \rm erg~ s^{-1}$,
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All authors Yuao Ma, Xinwu Cao, Jia-Wen Li, Jianchao Feng, Qingwen Wu
Numerical Analysis
A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems
Tianhao Hu, Bangti Jin, Fengru Wang et al. (+1 more)
In this work, we propose a hybrid iterative deep Ritz method (H-IDRM) for a class of interface problems for second-order
elliptic operators. It is based on a new mixed formulation of the problem and involves solving a sequence of convex minimization problems. We employ a level-set neural network architecture, featuring a level-set representation of the interface, to accommodate the piecewise smoothness of the solution and the flux. The approach involves only volumetric representations instead of duality pairing on the interface and avoids explicit interface sampling that is inconvenient for complex interface geometries. Further, we present an analysis of the method, including the errors arising from the neural network approximation, Monte Carlo approximation, iterative scheme, and penalty parameters. Numerical experiments indicate that the H-IDRM outperforms existing neural solvers on problems with high-dimensional domains, intricate interface geometries, and lower subdomain regularity.
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All authors Tianhao Hu, Bangti Jin, Fengru Wang, Yifeng Xu
Strongly Correlated Electrons
Mobility-Gap Robustness and Středa-Hall Separation in Disordered Axion Pumping
Bryan Leung and Emil Prodan
We show that the noncommutative second Chern number of a $(3+1)$D disordered
axion pump remains quantized beyond global spectral gap closure at $W_g \approx 14.5$. Large-scale computation of the second Chern number and finite-size scaling demonstrate convergence of $\mathrm{Ch}_2$ toward $-1$ well into the mobility-gap regime ($W \lesssim 16.5$), while the Středa-
Hall response $\partial_\phi \mathrm{Ch}_{0,3}$ departs rapidly after global spectral gap closure, serving as an internal control that distinguishes bulk mobility-gap protection from finite-size artifacts. Level statistics identify a 3D
unitary Anderson transition at each pump slice and locate the mobility-edge bottleneck at $\tau=0$, with critical disorder $W_c \approx 18$.
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Optics
DNNsolver: Accurate and Efficient Deep Learning Modeling of Polarization-Sensitive Diffractive Neural Networks
Shuyi Wang, Hong-Bo Sun and Linhan Lin
Diffractive neural networks (DNNs), composed of cascaded diffractive layers, offer a promising platform for high-speed optical computing. However, accurate and efficient modeling of high-density, polarization-sensitive DNNs remains challenging. Conventional model based on thin element approximation (TEA) fails to capture electromagnetic coupling within layers, while full-wave simulations such as finite-difference time-domain (FDTD) methods are computationally expensive. Here, we propose DNNsolver, a deep learning-based electromagnetic surrogate model that learns the scattering response of diffractive layers. By predicting the scattering
matrix rather than source-dependent output fields, DNNsolver decouples the incident wavefront from the model and could be applied to arbitrary input fields. A local scattering kernel and sliding-window strategy further allow efficient modeling of DNNs with arbitrary spatial sizes. For single diffractive layer under random speckle illumination, DNNsolver achieves an average mean squared error (MSE) of 0.0095 and about 10^6-fold speedup compared with FDTD simulations. DNNsolver is further applied to the optimization of a trilayer polarization-multiplexed image classifier, which exhibits better agreement with FDTD simulations than its TEA-based counterpart. Our work provides an accurate and efficient framework for the design and optimization of high-density, polarization-sensitive DNNs.
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Number Theory
Geometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groups
Yifan Jing and Yuchen Meng
We develop a
geometric lifting method for inverse sumset problems in compact connected abelian groups. The first result is an analogue of Freiman's $3k-4$
theorem, that is every compact set $A\subseteq G$ of sufficiently small Haar measure satisfying $\mu_G(A+A)<3\mu_G(A)$ is contained in a one dimensional Bohr set of measure at most $\mu_G(A+A)-\mu_G(A)$. This resolves a question of Christ and Iliopoulou. The proof combines Bilu's
theorem with a
geometric refinement of the spillover argument. We also establish a sharp projection
theorem. Under a continuous surjective homomorphism with connected kernel, a compact set of sufficiently small positive measure and doubling at most $K$, where $2\le K<3$, has image of doubling at most $2K-2$, and this factor is best possible. Further consequences include variants of the $3k-4$
theorem for popular sumsets and an inverse
theorem for Tao's convolution inequality.
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Artificial Intelligence
Verifiable Hidden Dynamics Play: Generating Agentic RL Environments from Solved Mechanisms
Xinjie Shen, Wei Fan, Xudong Guo et al. (+5 more)
Language-model
agents increasingly face long-horizon tasks with evolving state, interdependent decisions, and delayed outcomes. Scaling their training requires diverse agentic environments, dependable outcome signals, and low extension cost. Existing generation pipelines commonly construct an environment before defining its outcome rule or annotating its trajectories, leaving dynamics and evaluation to be aligned post hoc. VHD-Play reverses this dependency by sampling and solving a mathematical model before a corpus-grounded setter renders its decision process as stateful tools. The executable dynamics and trajectory-scoring reference are inherited from the same solved model. The pipeline produces 3,300 diverse agentic environments at a cost of a few cents each. Training Qwen3.6-35B-A3B on three families raises its mean agentic score from 0.204 to 0.815 in a five-family diagnostic. Gains also appear on held-out instances from all three training families and eight unseen mechanism families, then extend beyond the generated substrate to external
benchmarks for general function calling, travel planning, and 365-day e-commerce. On E-Commerce Bench, the trained checkpoint completes every run without bankruptcy and exceeds Qwen3.7-Max. We compare written-out problems with stateful versions that reveal or hide their parameters. The comparison shows that most of the learnable gap lies in stateful interaction rather than underlying problem solving. A frozen 35B setter realizes larger environments, and scale-matched training retains gains as mechanism size and horizon grow, indicating the potential for an evolving training substrate.
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All authors Xinjie Shen, Wei Fan, Xudong Guo, Jianhong Tu, Yang Su, Chuqiao Kuang, Yinger Zhang, Dayiheng Liu
Commutative Algebra
Dimensions of permanental varieties in arbitrary size
Ying Xie
Let $I_h(a,b)$ be the ideal generated by the $h\times h$ permanents of a generic $a\times b$
matrix over a field of characteristic different from two. We prove that $\dim K[X]/I_h(a,b)=\max(a,b)(h-1)$ whenever $1\le h\le\min(a,b)$ and $h<\max(a,b)$. Consequently, the critical locus of the permanent of order $n$ has codimension $2n$ for every $n\ge 2$. We also prove that the maximal permanents of a generic $k\times(k+1)$
matrix generate a geometrically reduced complete intersection. The dimension argument uses a pivot expansion and cubic relations in the border variables. Two successive comparisons with highest-degree equations reduce the relevant fibers to a coordinate-support calculation. Reducedness follows from a separate regular-sequence argument and a dimension estimate excluding components over the exceptional locus.
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Hardware Architecture
Exploiting Decompression Latency for Covert Channels in Inter-Line-Compressed LLCs
David K. Oh and Hiroshi Sasaki
The recently proposed XOR cache is an inter-line-compressed last-level cache (LLC) that leverages the data-inclusion relationship between the private caches and the LLC, compressing two cache lines into one by XORing them. The architecture relies on the cache coherence protocol for data decompression. In this paper, we demonstrate that this mechanism - specifically the latency asymmetry between a cache hit on an uncompressed vs. compressed line - introduces microarchitectural vulnerabilities. Based on this observation, we propose a covert channel attack targeting the XOR cache. A colluding sender controls the receiver's access latency by triggering decompression through targeted write requests to partner cache lines. By exploiting the data-dependent compression behavior of the XOR cache, the sender and receiver establish the channel using pre-agreed data values. The channel achieves higher bandwidth than the
Prime+Probe baseline for two reasons: first, each bit is encoded in the compression state of an individual line rather than the occupancy of a cache set, so a single set carries multiple bits; second, each bit is resolved by manipulating coherence-protocol state rather than forcing shared-cache evictions, so it costs fewer LLC accesses and demand misses than
Prime+Probe. Full-system simulations show a bandwidth of 2.9 Mbps at an observed 0.98% bit-error rate (BER) over 50,000 transmitted bits, 13.1 times the bandwidth of
Prime+Probe under the same sub-1%-BER selection rule.
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Quantum Physics
Minimal representations of topology-preserving quantum-like states
William Horvat, Debadrita Saha, Nicolás Gigena et al. (+2 more)
We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from
quantum-like bits that preserves the relevant spectral and topological properties. We show that this result follows from the fact that the operations of taking the Cartesian product of graphs and constructing equitable partition of the graphs commute. Numerical simulations illustrate the preserved emergent eigenstates in the reduced structures. Additionally, we provide a construction of the minimal structure without passing through the Cartesian product. Finally, we frame
quantum-like structures in the
language of
topology and fibrations.
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All authors William Horvat, Debadrita Saha, Nicolás Gigena, Prineha Narang, Gregory D. Scholes
Computer Vision
Breaking Weather-Content Coupling: Type-Severity Guided Progressive Disentanglement for All-in-One Infrared Restoration
Xinyao Wang, Lijun He, Zhihan Ren et al. (+1 more)
Infrared (IR) imaging is crucial for autonomous driving, remote sensing, and other perception tasks. However, adverse weather may introduce fake structural responses that are entangled with real thermal structures. Existing IR restoration methods are typically designed for a single degradation type or directly reconstruct from degradation-entangled representations. Consequently, they struggle to distinguish intrinsic thermal structures from weather-induced fake responses and to accommodate spatially varying degradation severity, leading to artifacts or the over-suppression of weak but meaningful thermal responses. To address these issues, we propose TSGPD-IR, a type-severity guided progressive disentanglement network for all-in-one infrared restoration that factorizes restoration guidance into task-level weather semantics and region-level degradation severity. Specifically, a Weather and Semantic Co-Guided Multi-Level
Prompt Generation Module combines global weather semantics with stage-wise local features to generate adaptive
prompts that progressively suppress degradation-induced responses while preserving intrinsic thermal structures. To complement global weather semantics with spatial restoration control, a Proxy-Supervised Regional Degradation
Estimator derives severity supervision without manual annotations and predicts spatially varying degradation priors. Guided by these cues, a Multi-Source Collaborative Expert Selection Strategy uses a shared branch to preserve weather-invariant thermal structures and hierarchical routing to select weather-specific expert pools and severity-compatible regional experts. This design progressively separates degradation interference from genuine thermal content and enables region-adaptive restoration, reducing both residual artifacts and over-suppression.
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All authors Xinyao Wang, Lijun He, Zhihan Ren, Fan Li
Functional Analysis
Critical surface for two component Bose-Einstein Condensates
Wenshuai Peng, Xiaoyu Zeng, Qidi Zhang et al. (+1 more)
We investigate the existence of ground states for two-component Bose–Einstein condensates with intraspecies interactions $a_1, a_2 \in (0, a^*)$ and interspecies interaction $\beta>0$. By carefully investigating an associated auxiliary minimization problem, we prove the existence of a unique, continuous, critical surface $\gamma = \gamma(a_1, a_2)$ between $\beta_*:= \sqrt{(a^* - a_1) (a^* - a_2)}$ and $\beta^*:= a^* - \frac{a_1 + a_2}{2}$. This surface provides a complete classification for the existence of minimizers: ground states exist for $\beta \in (0,\gamma)$ and do not exist for $\beta > \gamma$. Additionally, when the trapping potentials are continuous at a common zero point, there is no ground state for $\beta = \gamma$. Our results close the gap case $\beta \in [\beta_*, \beta^*]$ when $a_1\ne a_2$ in literature, significantly extending the results in \cite{Bao-Cai-1,guoBlowupSolutionsTwo2017a}.
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All authors Wenshuai Peng, Xiaoyu Zeng, Qidi Zhang, Huan-Song Zhou
Audio and Speech Processing
Beyond DER: Speaker Counting in Crowded End-to-End Diarization
Lahiru Samarakoon and Hongxu Zhu
Speaker diarization must solve two problems: counting how many speakers are present in a given conversation, and assigning
speech to each one. This becomes harder in crowded conversations with five or more speakers. We evaluate how end-to-end neural diarization models count speakers, and find systematic under-counting in crowded recordings. The standard diarization error rate (DER) hides this failure, because it is duration-weighted and barely penalizes the dropped, low-activity speakers. We therefore also report the Jaccard error rate (JER) and explicit counting metrics. We propose a gated loss that couples speaker existence with frame activity. This loss can be computed in two ways, duration-weighted or speaker-weighted, and the speaker-weighted variant, used as a regularizer, reduces the under-count. On real-world crowded recordings our method clearly improves the counting metrics, lowering JER by about 6% relative and DER by about 9% relative, while leaving sparse recordings unharmed.
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Robotics
CoRe-WAM: Correspondence-Aligned Temporal Residuals for World Action Models
Bin Zhou, Jialong Liu, Jianan Wang et al. (+2 more)
Comparing current and past observations helps
robots understand scene changes and select subsequent actions during manipulation. However, comparing visual features at the same image location can mix different scene content when objects or the camera move. We introduce CoRe-WAM, a world-action model that incorporates correspondence-aligned visual changes through a parameter-efficient temporal interface. Its TraceDelta module uses correspondences from a frozen tracking model to transport historical visual features to current locations before computing signed differences in a shared pretrained feature space. Correspondence thus determines which historical content is compared with the present, rather than entering the policy as a separate trajectory representation. A lightweight adapter converts these differences into validity-gated residuals that supplement current visual conditioning, allowing the policy to use recent changes alongside current-scene information. Built on Motus, CoRe-WAM keeps the pretrained backbone weights frozen and optimizes 1.59 million parameters. With a 5,000-update adaptation budget, CoRe-WAM achieves 92.22% clean success across 50 RoboTwin 2.0 tasks, 3.56 percentage points above Motus; on randomized evaluation, it achieves 89.60% success, a 2.58-point gain. Integrating TraceDelta into a StarVLA-based policy improves clean success from 58.10% to 67.62%, supporting transfer of the temporal interface beyond Motus.
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All authors Bin Zhou, Jialong Liu, Jianan Wang, Changhao Chen, Kani Chen
Dynamical Systems
Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts
Paulina Cecchi-Bernales and Sebastián Donoso
We develop a method for constructing minimal subshifts with a prescribed bound on the factor complexity within any strong orbit equivalence (SOE) class. This implies realizations of topological
entropies within any SOE class, strengthening a series of classical results by Sugisaki. While prior work established complexity controls for zero-
entropy systems, the approach of the present work extends to positive-
entropy regimes. Our construction introduces the class of pseudo-Toeplitz subshifts, and we show that they exist in any SOE class. More precisely, for any $\alpha \geq 1$ and sequence $g_n$ growing exponentially at rate $\log(\alpha)$, we construct a system in this class whose topological
entropy is $\log(\alpha)$ and whose complexity grows strictly faster, or, under certain conditions, slower than $g_n$. As a consequence, any Choquet simplex can be realized as the set of invariant measures of a Toeplitz subshift with precisely controlled complexity, in either a zero or positive-
entropy regime.
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Robotics
Turning Safety into Competence: Minimally Exploitable Robot Policies via Safety-Filtered Reinforcement Learning
Ruihan Wu, Rui Yang, Donggeon David Oh et al. (+2 more)
Robots deployed for competitive tasks must outmaneuver their opponents without sacrificing safety. Existing approaches, including safe reinforcement learning (RL), train a single policy to achieve task success and avoid failures simultaneously. This coupling can complicate training and leave the learned policy exploitable by deliberate attacks. We propose Safety to Competence (S2C), a two-stage RL framework that separates safety synthesis from competitive task learning. We formulate competitive interactions as safety-critical Markov games and prove that perfect filtering preserves policy non-exploitability when all players commit to safe maneuvers. S2C learns a robust safety filter via
adversarial RL, embeds it in the environment during task policy training, and retains the same filter at deployment. In simulated touchdown games, S2C outperforms eight safe RL baselines, achieving the highest win rate and Elo rating, and the lowest exploitability. Hardware stress tests against a human opponent confirm S2C's competence.
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All authors Ruihan Wu, Rui Yang, Donggeon David Oh, Duy Nguyen, Haimin Hu
Cryptography and Security
Multi-View Fusion for Encrypted C2 Detection: A Leakage-Controlled Measurement Study of Evaluation Pitfalls
Hoang-Huy Nguyen-Huu, Van-Tri Phan and Khuong Nguyen-An
Command-and-control (C2) traffic increasingly hides within TLS, so defenders now apply machine learning to traffic metadata. Many studies assume that combining two metadata views, namely flow statistics and TLS handshake fingerprints, improves both accuracy and robustness. We tested this assumption on 17,577 TLS flows from 62 real Cobalt Strike captures. Our evaluation removes the data leakage that leads to overly optimistic reported scores. We report three findings that matter more than the fusion result itself. First, an incorrect preprocessing step increases the F1 score by 0.28. This step computes the frequency encoding across the entire
dataset rather than within each cross-validation fold. The increase is about ten times larger than any real effect we measured. Second, both the labels and the behavioral features depend on the destination address. Because of this, the 17,577 flows form only 2,132 independent groups, and the positive rate of 55.1%, which looks balanced, drops to 4.2%. Therefore, class balance is just a result of how we analyze the data, specifically whether we count flows or endpoints, and not a real feature of the task. Third, 20 of the 62 captures (32%) have no TLS flows to any known C2 address, so they contain only benign samples. We checked these captures directly and confirmed that this is a gap in the ground truth, not a labeling error. In this context, fusion beats the best single view by only 0.022 in F1. When an attacker forges both feature surfaces simultaneously, every model performs worse than a simple baseline that always predicts positive (F1 = 0.711). For encrypted C2 detection, the evaluation design is not a preliminary step. It is the main result.
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Number Theory
Completed cohomology of Hilbert modular varieties below middle degree
Lue Pan
We study the locally analytic vectors of completed
cohomology of
Hilbert modular varieties below middle degree. Our main result says that the universal enveloping
algebra action has to factor through certain quotients. Application includes bounds on the Gelfand-Kirillov dimension and a density result. The method is a continuation of our joint work with Kai-Wen Lan.
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Software Engineering
FairTest: Search-Based Fairness Testing for Multi-Agent Reinforcement Learning Systems
Xiaotong Wang and Xuan Xie
Multi-
agent Reinforcement Learning (MARL) trains a team of
agents that share one environment and learn their policies together. Training maximizes the team return, and a high return does not imply that the rewards are shared fairly among the
agents in every episode. Testing is an established way to discover the failures of deep reinforcement learning, yet few methods address the
fairness of MARL. In this work, we propose FairTest, a search-based testing approach that seeks the unfair executions of a MARL policy. The design combines search guidance with test prioritization. The guidance scores each candidate with three fitness functions. One measures the
fairness of the runs already performed, another predicts the
fairness from abstract states and
fairness features, and the third reads the decision uncertainty from the policy. Crossover and mutation derive further candidates from the observed executions. The prioritization ranks the candidates by the predicted
fairness and the decision uncertainty, so that the runs reach the candidates where failures are expected. FairTest is evaluated on three environments and two MARL
algorithms, and four baselines are given the same budget. It detects the most
fairness failures compared to three baselines with statistical significance and large effect sizes. The failure count exceeds that of the strongest baseline by 221% on average and coverage improves by an average of 23%.
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Robotics
EmbodiedSWE: Coding Agents for Long Horizon Dexterous Robotics
Zeyu Shen, Haoxiang You, Yilang Liu et al. (+16 more)
We study coding
agents for long-horizon, dexterous robotics and ask whether their solutions can provide scalable supervision for learning general
robot policies. To test this, we develop EMBODIEDSWE-BENCH, a simulation
benchmark for coding
agents spanning contact-rich manipulation, deformable objects, and long-horizon tasks requiring up to half an hour of continuous interaction. We find that frontier coding
agents can solve complex long-horizon tasks and transfer prior solutions across both tasks and embodiments. We also design supporting tools that help
agents more effectively solve these tasks. However, the resulting solutions require substantial iterative interaction and are typically specialized to individual task instances. We therefore introduce EMBODIEDSWE-GEN, which expands a single solution from coding
agent into large diverse trajectories for training a VLA. VLA performance improves with more generated demonstrations, and
agent-aided diversification improves generalization to held-out task variations. We also show that a VLA finetuned solely on coding-
agent-generated simulation demonstrations completes a long-horizon task on real
robot. Together, our framework uses coding
agents to solve complex robotics tasks and turn verified solutions into scalable supervision for
robot policies.
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All authors Zeyu Shen, Haoxiang You, Yilang Liu, Zhicheng Zheng, Lihan Zha, Kashu Yamazaki, Mingtong Zhang, Suning Huang, Jiankai Sun, Qianzhong Chen, Lucy He, Kaiyuan Liu, Haoran Chang, Katerina Fragkiadaki, Dhruv Shah, Mac Schwager, Peter Henderson, Ian Abraham, Canwen Xu
Artificial Intelligence
Learn How to Act from Your Own Interactions: On-Policy Self-Distillation for GUI Agents
Yan Zhang, Daiqing Wu, Huawen Shen et al. (+7 more)
Graphical User Interface (GUI)
agents enable the fulfillment of complex user instructions through multi-turn interactions with software environments, requiring step-wise
reasoning and long-horizon
memory to guide actions and retain task-relevant information, respectively. Recent on-policy self-
distillation (OPSD) methods have achieved strong performance on GUI grounding, a foundational subtask for GUI
agents, owing to dense
token-level supervision from privilege-conditioned self-teachers. However, extending existing OPSD methods to multi-turn GUI
agents is hindered by self-teachers' limited privilege-following ability and insufficient privileged guidance. In this paper, we introduce GUI-SD-v2, the next version of GUI-SD, which extends OPSD from GUI grounding to multi-turn GUI interaction and addresses key limitations through a two-stage training framework. Specifically, GUI-SD-v2 first strengthens privilege following by jointly optimizing rollouts with and without privileged guidance from the same GUI states. Furthermore, it selectively distills step-specific
reasoning and
memory guidance through a privilege-conditioned self-teacher, supporting action decisions and the retention of task-relevant information for subsequent interactions. Extensive experiments on two representative GUI
agent benchmarks, AndroidWorld and MobileWorld, show that GUI-SD-v2 compares favorably with existing OPSD baselines while consistently outperforming the evaluated state-of-the-art methods in both Pass@1 and Pass@3 success rates. Code and training data will be publicly released.
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All authors Yan Zhang, Daiqing Wu, Huawen Shen, Liang Li, Gang Cao, Zhi Gong, Wei Dai, Xiaode Zhang, Can Ma, Yu Zhou
Machine Learning
Discrete Diffusion Models via Evolving Variational Autoregressive Networks
Kewen Pan and Ying Tang
Conventional score-based
diffusion models learn scores without representing normalized densities, whereas tractable normalized models support both sampling and direct likelihood evaluation. A recent tensor-network approach provides such a representation but is largely restricted to low-dimensional
lattices. Here we introduce a discrete
diffusion model that parameterizes normalized probability distributions using variational autoregressive networks. Explicit Markov jump operators govern the forward noising and reverse denoising dynamics, extending discrete
diffusion models with normalized distributions to
spin systems on higher-dimensional
lattices. We apply this framework to the two- and three-dimensional Ising models across ordered, critical, and disordered regimes, accurately computing thermodynamic quantities including free energy, energy, and magnetization. We further integrate the framework with Monte Carlo sampling, using adaptive
diffusion steps to maintain high acceptance rates even at low temperatures while enhancing sample diversity. These results establish a neural-network framework for the discrete
diffusion model with normalized probability distributions.
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Dynamical Systems
A strict amplitude lower bound for the van der Pol equation and extensions to symmetric Liénard systems
Changjian Liu and Ziwei Zhuang
We prove that the amplitude of the unique limit cycle of the van der Pol equation $\ddot{x}+\mu(x^2-1)\dot{x}+x=0$ is strictly greater than $2$ for every $\mu>0$. The proof combines orbit comparison in the relaxation oscillation regime, trigonometric comparison curves in the weakly nonlinear regime, and
polynomial energy estimates in the intermediate regime. The
polynomial sign conditions arising in the latter two regimes are certified using exact rational arithmetic and Bernstein coefficients. The orbit comparison method also applies to a class of symmetric Liénard systems. Under suitable monotonicity assumptions, we establish a sufficient criterion for the limit cycle amplitude to exceed a critical value determined by the damping function.
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Game Theory
The Power of Recruiting the Smaller Side: Two Additional Traders Suffice in Two-Sided Markets
Yang Cai, Vineet Gupta, Yanchen Jiang et al. (+5 more)
We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove that recruiting just two additional sellers enables Seller Trade Reduction (STR), a prior-independent mechanism, to achieve expected Gains From Trade (GFT) at least the first-best GFT of the original
market; symmetrically, when $m \le n$, Buyer Trade Reduction suffices with two additional buyers. This resolves open questions of Babaioff, Goldner, and Gonczarowski (SODA 2020) and Cai, Liaw, Mehta, and Zhao (STOC 2024). Moreover, this uniform bound is optimal: already for $m = n = 1$, no prior-independent mechanism (deterministic or randomized) that is dominant-strategy incentive-compatible (DSIC), individually rational (IR), and weakly budget-balanced (WBB) matches the first-best GFT with one additional seller. We further extend our characterization to $r$-dominance ($F_B \succeq_r F_S$), where $r \in (0, 1]$ and $1 - F_B(x) \ge r(1 - F_S(x))$ for all $x \in \mathbb{R}$ (recovering $F_B \succeq_{\mathrm{FSD}} F_S$ at $r = 1$). When $m \ge n \ge 1$, $c = \lceil 1/r \rceil + 1$ additional sellers suffice for STR to match or exceed the first-best GFT, while every prior-independent DSIC, IR, and WBB mechanism requires at least $\max(2, \lceil 1/r \rceil - 1)$ additional sellers even for $m = n = 1$, pinning down the optimal bound to within two traders. Finally, this $\Theta(1/r)$ bound cannot be asymptotically improved even by recruiting on both sides: for $r < 1/64$ and $m = n = \lceil 2/(5r) \rceil$, every prior-independent DSIC, IR, and WBB mechanism requires $c \ge \lceil 1/(64r) \rceil = \Omega(1/r)$ additional traders per side.
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All authors Yang Cai, Vineet Gupta, Yanchen Jiang, Christopher Liaw, Aranyak Mehta, Grigoris Velegkas, Di Wang, Mingfei Zhao
Machine Learning
Live Assistant: Learning Whether, When, and Whom to Assist in Real-World Live Social Streams
Shujian Gao, Jiamei Yan, Yuchen Yang et al. (+6 more)
Livestreams are long-lasting interactive environments where audiovisual content, viewer activity, host behavior, and platform signals evolve together, creating assistance needs that emerge from the stream itself. We introduce \liveassistant, a framework for mixed-initiative, role-conditioned assistance that formulates livestream interaction as four coupled decisions: whether to act, when to act, whom to address, and what to communicate. At each 10-second interval, one autoregressive policy consumes native audio and
video with synchronized comments, gifts, viewer dynamics, and room metadata, then selects OBS, MEM, or ANS. OBS remains silent, MEM records a private semantic update, and ANS specifies a recipient, task, and grounded message. To support this task, we build a trajectory engine that reconstructs real livestream sessions into structured causal supervision, yielding over 320 hours of optimization trajectories and a human-reviewed
benchmark of 275 clips and 13,812 decision intervals. We train the policy with Marker-Aware Multiturn Supervised Fine-Tuning (MA-MSFT), which strengthens sparse structured decisions, followed by Streaming Multiturn GSPO (SM-GSPO), which optimizes self-generated trajectories with turn- and trajectory-level credit. On the held-out
benchmark, \liveassistant reaches 71.14 state accuracy, 72.67 recipient accuracy, and 58.41 task accuracy, with consistent gains over representative streaming and general
multimodal baselines. Together, the formulation,
benchmark, and training framework establish livestream assistance as selective participation in a shared social stream.
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All authors Shujian Gao, Jiamei Yan, Yuchen Yang, Penghao Zhou, Qinglei Wang, Tiehan Fan, Yuan Wang, Zuxuan Wu, Yu-gang Jiang
Mesoscale and Nanoscale Physics
Unmodeled states and uncertain action outcomes in agentic scanning tunneling microscopy
Siyu Cheng, Muxian Xu, Christopher Candelora et al. (+1 more)
In physical experiments, interventions can alter hidden experimental states in ways that cannot be predicted in advance. Autonomous scientific
agents must therefore interpret the consequences of their interventions while operating with incomplete knowledge of the experimental state. Here we investigate this problem using scanning tunneling microscopy (STM) tip conditioning, traditionally a human-expert-intensive task governed by inaccessible tip apex conditions and uncertain action outcomes. We introduce quailbot, an
agent harness that places the LLM inside the instrument feedback loop by linking physical interventions with experimental readbacks. After a brief apprenticeship with a human expert, frontier LLM
agents autonomously completed end-to-end tip conditioning on an STM and passed an independent verification. The contingencies that arose during the experiments further exposed the limits of LLM agentic autonomy when relevant experimental states or dynamics were hidden or unmodeled. Our results show that future autonomous physical experimentation requires
agents to infer hidden and unmodeled experimental states, track the outcomes of their actions, and operate within the observability and action limits of real instruments.
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All authors Siyu Cheng, Muxian Xu, Christopher Candelora, Ilija Zeljkovic
Algebraic Geometry
Lengths of Hodge characters in Fermat varieties
Maximiliano Miranda, Hossein Movasati, Lucas Rufino et al. (+1 more)
We revisit the Hodge
conjecture for Fermat (and weighted Fermat) varieties. We review the reduction of the Hodge
conjecture in terms of Hodge characters introduced by Shioda and its further reduction in terms of the formal module of tuples introduced by Aoki. Following Aoki, we introduce several lengths on this formal module, and by means of Kang's
theorem on the Hodge
conjecture for Fermat fourfolds we reduce the
conjecture to bound the lengths of exceptional tuples by 6. By applying length reduction
algorithms we prove the Hodge
conjecture for all Fermat varieties (of any dimension) of degree less than 65 and different from 44, 51 and 52. The main novelty of our length reduction method is the introduction of a lift operation on the degree of the tuple.
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All authors Maximiliano Miranda, Hossein Movasati, Lucas Rufino, Roberto Villaflor
Cryptography and Security
SoK: You Find What You Seek: Rethinking Oracles, Guidance, and Input Generation in Hardware Fuzzing
G Abarajithan, Zhenghua Ma, Cristian Tirelli et al. (+4 more)
Hardware fuzzing is an active area in security verification research, yet its industrial adoption remains in its early stages. This SoK examines which lessons from software fuzzing carry over to hardware and where unique approaches are needed. By analyzing 52 fuzzers across RTL/IP, CPU, NoC, and SoC designs, we introduce an analytical framework that frames verification as a bounded search. This search is defined by its objective, oracle, guidance, input generation, target abstraction, and budget. Consequently, a campaign only uncovers failures it can effectively reach, recognize, and prioritize before exhausting its resources. We distinguish two roles for hardware fuzzing: (1) augmenting constrained-random verification (CRV) via feedback-guided coverage and (2) directed
adversarial testing based on threat models and security specifications. Through our framework, we identify what each campaign can observe and generate, providing a basis for assessing the evidence behind reported results. Our analysis suggests that mainstream adoption of hardware fuzzing will require reusable interfaces, target-specific verification assets, reproducible evaluations, and transparent reporting of cost and user effort.
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All authors G Abarajithan, Zhenghua Ma, Cristian Tirelli, Andres Meza, Francesco Restuccia, Cynthia Sturton, Ryan Kastner
Statistical Methodology
Beyond the Illusion of Power: Calibrating Quasi-Experiments in Observational IS
Spandan Ghose Chowdhury
Information systems (IS) researchers increasingly use quasi-experimental methods such as difference-in-differences (DiD) and instrumental variables (IV) to recover causal effects from observational panel data. Power calculations that justify these designs assume i.i.d. errors, but the deeper problem is what even a cluster-robust calculator cannot see. We report a Monte Carlo study over 9837 parameter conditions (approx 9.8 million
datasets) and decompose the planned-versus-achieved power gap. The serial-correlation component is recoverable by an AR(1)-aware calculator when rho is known, and partially when rho must be estimated from short pre-periods, but panel attrition, staggered-adoption bias, and parallel-trends pretesting are captured by no closed-form formula; exogenous attrition alone costs approx 8 to 11 percentage points at the few-hundred-to-thousand sample sizes IS studies use. Treatment-correlated, outcome-dependent attrition instead induces bias, not just power loss. For IV, holding first-stage F fixed, larger N neither raises power nor curbs exclusion bias, though with a fixed instrument more data does sharpen the first stage, so identification rests on instrument strength, not sample size.
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Artificial Intelligence
StateComp: Learning When to Compress History in Long Horizon Agents
Mingxuan Wang, Hongyue Chen, Yinglong Guo et al. (+6 more)
Long-horizon
agents continuously accumulate interaction history during task execution, yet the importance of past interactions changes as the
agent state evolves. Existing context management methods largely compress history based on fixed windows, periodic schedules, or current relevance, overlooking a more fundamental question: when has a past interaction become safe to replace? Premature compression may remove information still needed for future actions, while overly conservative retention leads to substantial context overhead. To address this, we propose State Conditioned Compression (StateComp), a framework that determines when historical interactions can be safely compressed according to the current
agent state. StateComp constructs KEEP and READY supervision through a two-stage annotation procedure and trains an imbalance-aware router on hidden representations from a frozen
language model. A bounded state representation further reduces the cost of evaluating long histories, while adjacent READY interactions are grouped into continuous spans and replaced with compact summaries during execution. Experiments on WorkBuddyBench show that StateComp reduces total
agent and summarization
tokens by 52.27% while maintaining task performance, and achieves a 12.67-fold speedup in representation extraction.
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All authors Mingxuan Wang, Hongyue Chen, Yinglong Guo, Fei Luo, Chao Ning, Bo Wang, Guorun Yao, Yanbiao Ma, Jungong Han
Artificial Intelligence
Large Knowledge Model: A Knowledge Foundation for Agentic Science at Scale
Yuan Huang, Sihan Hu, Hongyu Gu et al. (+18 more)
Agentic science envisions many autonomous
agents investigating concurrently while building on a shared, evolving body of scientific knowledge. This requires a knowledge foundation that supports high-concurrency access, preserves traceable and reusable
reasoning, and grows incrementally. We propose the Large Knowledge Model (LKM), a growing,
agent-native knowledge foundation that provides a general representation of scientific knowledge across disciplines. LKM organizes the scientific literature into
reasoning graphs, with claims as the core nodes and associated
reasoning chains that make explicit how premises and evidence support conclusions. These source-grounded objects are persistent and addressable; cross-paper links organize them into aligned question, workflow, and evidence views. Newly extracted papers extend the foundation incrementally while preserving existing object identities. Building on this foundation, we develop an
agent-native,
reasoning-aware scientific
retrieval system that retrieves claims together with their
reasoning chains and sources, enabling
agents to inspect and reuse the evidence underlying scientific conclusions. Across
benchmarks,
agents using LKM retrieve more evidence, cite more faithfully, and answer scientific questions more accurately: LKM nearly doubles the known supporting and contradicting evidence retrieved on SciFact-Open (818 versus 443 claim-paper pairs),
reasoning graphs raise citation F1 on ScholarQABench by more than 5 points over the same retrieved papers, and LKM
retrieval improves a fixed answering model by 9.3, 4.2, and 14.7 points over no
retrieval on ChemBench, PubMedQA, and SciBench. LKM lays the foundation for a scientific ecosystem in which AI scientists not only recall accumulated knowledge but also extend it, returning new questions, workflows, and evidence to a
memory that every subsequent investigation can build on.
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All authors Yuan Huang, Sihan Hu, Hongyu Gu, Chao Ma, Jiaxing Zhang, Zhiyong Zou, Caiyu Fan, Yan Xiao, Mingjun Xu, Chenyu Xie, Mingzhen Ju, Zhehao Ma, Qi Zhang, Baozong Wang, Yu Li, Zhiyuan Yao, Ruoxue Liao, Xinyu Li, Linfeng Zhang, Kun Chen, Weinan E