The Eaton--Moretó Conjecture Holds True for \(p\)-Solvable Groups
In this paper we prove that the Eaton--Moretó conjecture holds true for all $p$-solvable groups.
math.RT↗
arXiv subjects
Lizhong Wang
Publications and source records attributed to Lizhong Wang.
Closed-loop AI achieves certifiable engineering design
Agentic AI has automated parts of scientific discovery, including paper generation, expert-level coding, therapeutic proposal, and autonomous experimentation. Complex physical engineering design remains a gap, because candidates must satisfy simultaneous constraints in fluid dynamics, solid mechanics, and structural stability. We introduce The AI Engineer, an agentic framework that couples large language models (LLMs) to deterministic engineering backends in a closed loop: natural-language requirements are converted into design-domain geometry and mesh; topology is optimized with bi-directional evolutionary structural optimization (BESO) coupled to the CalculiX solver; and member sizes are refined with particle swarm optimization (PSO) coupled to Zwind under offshore aero-hydro-servo-elastic load cases. To explore many designs without per-candidate certification cost, an Automated Reviewer scores each candidate on five dimensions (capacity, steel intensity, unit cost, constructability, and fatigue life) using piecewise-linear functions calibrated on 11 real floating-wind projects. Search terminates only when a candidate reaches a composite score $S \ge 85$ (grade A) with no subscore below 60. We validated this gate by submitting the top-scoring design to the China Classification Society (CCS) for Approval in Principle (AIP), which it passed; AIP is thus an external check that the reviewer tracks professional judgment, not the daily objective. The certified design outperforms the human-optimized TuQiang baseline, reducing steel mass and unit capital cost by 8.1% each while meeting all AIP criteria. This verification-closed regime, in which every proposal is judged by deterministic physics and codified limit states, distinguishes The AI Engineer from open-ended generative systems. Remaining limits include detailed design and fabrication-hard constraints.
cs.AI↗
Thompson's Conjecture for Finite Simple Groups of Lie Type over Small Fields
We prove that every finite simple group of Lie type over a field of order at most 8 contains a conjugacy class whose square is the whole group. Together with the previously established cases, our results complete the proof of Thompson's conjecture. We explicitly construct the required class, address all low-rank identifications, and provide the precise computational certificates used in the exceptional character calculations.
math.GR↗
MobileMem: Learning from a Year of Mobile Experiences
The next generation of AI agents is increasingly moving beyond systems that answer isolated questions toward persistent personal assistants that can understand, remember, and continuously learn from users' experiences. Such assistants require long-term memory to accumulate and leverage user-specific experiences over time, yet existing benchmarks remain inadequate for realistic mobile settings, where experiences are heterogeneous, multimodal, evolving, and deeply personal. We introduce MobileMem, a benchmark and framework for studying on-device long-term memory, grounded in a year-scale collection of mobile experiences. MobileMem employs a knowledge-grounded synthesis pipeline to construct coherent and temporally consistent long-horizon trajectories from user-app sessions. It provides complementary text and multimodal settings covering multi-hop and temporal reasoning, knowledge updating, and implicit preference inference. Specifically, MobileMem enables agents to remember the past, understand the present, and adapt to the future. By modeling experiences rather than isolated facts, MobileMem moves memory beyond information retrieval toward experiential intelligence for continuous personal learning.
cs.AI↗
ToolRec: Calibrated Preference Alignment for Query Recommendation in On-Device Assistants
Large Language Models (LLMs) have significantly advanced generative query recommendation. However, while alignment is crucial for tailoring LLMs to human preferences, existing alignment methods primarily focus on standard chatbot scenarios, falling short in on-device intelligent assistants where users predominantly expect the rapid invocation of system-level tools. Moreover, directly aligning LLMs with real-world click logs introduces severe noise due to varying user activity levels and the failure to emphasize execution-oriented queries. To address these challenges, we propose ToolRec, a calibrated preference alignment framework tailored for on-device query recommendation. To ground query recommendation with executable tools, we first construct SysToolKit, a comprehensive repository of 708 system tools, paired with a context-aware tool retrieval mechanism to ensure that the extracted tools closely match the user's intent. A dual-level calibration mechanism is then proposed to refine raw click data, effectively mitigating user behavioral noise by calibrating signals based on user activity (user-level), while simultaneously up-weighting click signals on tool-invoking queries (system-level). Guided by these refined preference signals, we then align the model using a sample-level weighted Kahneman-Tversky Optimization (KTO). Extensive online A/B tests on our mobile assistant platform OPPO Xiaobu, which has over 150 million monthly active users, demonstrate that ToolRec can significantly improve Click-Through Rate (CTR) and total click volume over strong baselines while maintaining high query relevance.
cs.IR↗
Self-Evolving Just-In-Time Memory for Proactive Embodied Safety
While Vision-Language Models (VLMs) have empowered embodied agents to execute complex household tasks, they struggle to proactively handle dynamically emerging hazards during closed-loop interactions. Existing safety approaches often rely on runtime guardrails to block unsafe actions or induce excessive caution, which severely stalls task progress instead of actively resolving the underlying risks. To break this safety-progress trade-off, we introduce the Self-Evolving Just-In-Time Memory framework, which reframes embodied safety from progress-stalling guardrails to proactive hazard mitigation. The framework consists of a Risk-Sufficient Topological Belief Graph (RSG) for persistent safety-relevant state tracking under partial observability, an Agency-Grounded Factual Memory for precise hazard anticipation, and an Experience Memory that injects procedural Meta-Skills to guide executable, progress-preserving mitigation. Furthermore, we propose an automated Test-Verify-Write loop, allowing agents to continually refine their mitigation Meta-Skills from execution traces at test time. Experiments on IS-Bench demonstrate that our framework substantially boosts the Safe-Success rate across multiple VLM backbones (e.g., +30.3% on Qwen3-VL-8B), enabling agents to proactively mitigate hazards without stalling task progress. Code is available at https://github.com/DyMessi/JIT-Memory.
cs.LG↗
PACT: Self-Evolving Physical Safety Alignment for Diffusion Policies in Embodied Manipulation
Diffusion policies have achieved remarkable success in robotic manipulation, yet they often fail to satisfy strict physical constraints required for safe deployment. Existing approaches impose safety either prematurely during training or reactively via external guardrails at test time, limiting policy expressivity and overall scalability. We propose Physical safety Alignment for Constrained Trajectories (PACT), a self-evolving post-training framework that projects pretrained diffusion policies onto constraint-feasible regions without accessing demonstration data or task rewards. PACT distills constraint gradients into the diffusion model through a reverse-KL objective with dense supervision across timesteps. It incorporates a curriculum that progressively tightens constraints while maintaining theoretically bounded policy shift and monotone improvement, mitigating the safety-performance trade-off from catastrophic forgetting. On simulated and real-world embodied manipulation benchmarks, PACT significantly reduces safety violations by 31.0% on average while improving task success by 30.7%.
cs.RO↗
Reinforced Rate Control for Neural Video Compression via Inter-Frame Rate-Distortion Awareness
Neural video compression (NVC) has demonstrated superior compression efficiency, yet effective rate control remains a significant challenge due to complex temporal dependencies. Existing rate control schemes typically leverage frame content to capture distortion interactions, overlooking inter-frame rate dependencies arising from shifts in per-frame coding parameters. This often leads to suboptimal bitrate allocation and cascading parameter decisions. To address this, we propose a reinforcement-learning (RL)-based rate control framework that formulates the task as a frame-by-frame sequential decision process. At each frame, an RL agent observes a spatiotemporal state and selects coding parameters to optimize a long-term reward that reflects rate-distortion (R-D) performance and bitrate adherence. Unlike prior methods, our approach jointly determines bitrate allocation and coding parameters in a single step, independent of group of pictures (GOP) structure. Extensive experiments across diverse NVC architectures show that our method reduces the average relative bitrate error to 1.20% and achieves up to 13.45% bitrate savings at typical GOP sizes, outperforming existing approaches. In addition, our framework demonstrates improved robustness to content variation and bandwidth fluctuations with lower coding overhead, making it highly suitable for practical deployment.
eess.IV↗
Reinforced Embodied Active Defense: Exploiting Adaptive Interaction for Robust Visual Perception in Adversarial 3D Environments
Adversarial attacks in 3D environments have emerged as a critical threat to the reliability of visual perception systems, particularly in safety-sensitive applications such as identity verification and autonomous driving. These attacks employ adversarial patches and 3D objects to manipulate deep neural network (DNN) predictions by exploiting vulnerabilities within complex scenes. Existing defense mechanisms, such as adversarial training and purification, primarily employ passive strategies to enhance robustness. However, these approaches often rely on pre-defined assumptions about adversarial tactics, limiting their adaptability in dynamic 3D settings. To address these challenges, we introduce Reinforced Embodied Active Defense (Rein-EAD), a proactive defense framework that leverages adaptive exploration and interaction with the environment to improve perception robustness in 3D adversarial contexts. By implementing a multi-step objective that balances immediate prediction accuracy with predictive entropy minimization, Rein-EAD optimizes defense strategies over a multi-step horizon. Additionally, Rein-EAD involves an uncertainty-oriented reward-shaping mechanism that facilitates efficient policy updates, thereby reducing computational overhead and supporting real-world applicability without the need for differentiable environments. Comprehensive experiments validate the effectiveness of Rein-EAD, demonstrating a substantial reduction in attack success rates while preserving standard accuracy across diverse tasks. Notably, Rein-EAD exhibits robust generalization to unseen and adaptive attacks, making it suitable for real-world complex tasks, including 3D object classification, face recognition and autonomous driving.
cs.CV↗
Control of fusion by elementary abelian subgroups of rank at least 2
In this paper, we focus on the subgroups control $p$-fusion, and we improve the Theorem B of [4] for odd prime. For odd prime, we prove that elementary abelian subgroups of rank at least 2 can control $p$-fusion(see our Theorem B).
math.GR↗
Multi-Roller Structure Triboelectric Nanogenerator for Enhanced Water Wave Energy Harvesting and Energy Management
Wave energy harvesting is critical for advancing the development and utilization of marine resources. In this study, we present a novel multi-roller structure triboelectric nanogenerator (MR-TENG) designed specifically for efficient water wave energy harvesting. The MR-TENG leverages a coupled multi-roller design to significantly enhance its energy harvesting capabilities. The triboelectric layers are composed of polytetrafluoroethylene (PTFE) film and paper, with a grid copper electrode serving as the conductive element. Through an optimized energy output strategy, a single MR-TENG is capable of generating 602.045 μJ of electrical energy within 100 s. The device achieves a short-circuit current (Isc) of approximately 2.06 μA and an open-circuit voltage (Voc) of around 166 V. We further investigate the impact of different connection modes, including parallel and series configurations, on the performance of MR-TENG arrays. Notably, the electrical energy produced by the MR-TENG array is sufficient to power 40 blue commercial light-emitting diodes (LEDs). This research not only introduces a versatile optimization approach and energy management strategy for roller-structured TENGs but also contributes significantly to the advancement of ocean-based TENG technology.
physics.app-ph↗
Character triples and relative defect zero characters
Given a character triple $(G,N,θ)$, which means that $G$ is a finite group with $N \vartriangleleft G$ and $θ\in{\rm Irr}(N)$ is $G$-invariant, we introduce the notion of a $π$-quasi extension of $θ$ to $G$ where $π$ is the set of primes dividing the order of the cohomology element $[θ]_{G/N}\in H^2(G/N,\mathbb{C}^\times)$ associated with the character triple, and then establish the uniqueness of such an extension in the normalized case. As an application, we use the $π$-quasi extension of $θ$ to construct a bijection from the set of $π$-defect zero characters of $G/N$ onto the set of relative $π$-defect zero characters of $G$ over $θ$. Our results generalize the related theorems of M. Murai and of G. Navarro.
math.GR↗
The RoboDrive Challenge: Drive Anytime Anywhere in Any Condition
In the realm of autonomous driving, robust perception under out-of-distribution conditions is paramount for the safe deployment of vehicles. Challenges such as adverse weather, sensor malfunctions, and environmental unpredictability can severely impact the performance of autonomous systems. The 2024 RoboDrive Challenge was crafted to propel the development of driving perception technologies that can withstand and adapt to these real-world variabilities. Focusing on four pivotal tasks -- BEV detection, map segmentation, semantic occupancy prediction, and multi-view depth estimation -- the competition laid down a gauntlet to innovate and enhance system resilience against typical and atypical disturbances. This year's challenge consisted of five distinct tracks and attracted 140 registered teams from 93 institutes across 11 countries, resulting in nearly one thousand submissions evaluated through our servers. The competition culminated in 15 top-performing solutions, which introduced a range of innovative approaches including advanced data augmentation, multi-sensor fusion, self-supervised learning for error correction, and new algorithmic strategies to enhance sensor robustness. These contributions significantly advanced the state of the art, particularly in handling sensor inconsistencies and environmental variability. Participants, through collaborative efforts, pushed the boundaries of current technologies, showcasing their potential in real-world scenarios. Extensive evaluations and analyses provided insights into the effectiveness of these solutions, highlighting key trends and successful strategies for improving the resilience of driving perception systems. This challenge has set a new benchmark in the field, providing a rich repository of techniques expected to guide future research in this field.
cs.CV↗
On polynomial representations of finite groups
By generalizing Frobenius' polynomial method to good partition algebra, we will develop new character theories for a finite group $G$. A uniform defining equations are derived for these kinds of character theories. The new character theories leads to various factorizations of the group determinant. We will show that these new character theories are equivalent to the Frobenius polynomials of the correspondent good partition algebras. In particular, the character table of a finite group $G$ can be replaced by the Frobenius polynomial of $G$ which is a kind of degenerate of the group determinant. As applications, we find a new series of invariants $p_{ijl}$ for a finite group. In particular, a finite simple group is determined by these invariants. As further applications, the degrees of all irreducible characters can also be realized as the solutions of a polynomial of $G$ and we can combine the refined McKay conjecture and part of Galois conjecture of Navarro on degrees of irreducible characters into a new general conjecture.
math.RT↗
Relatively Projectivity and the Green correspondence for complexes
We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same for a subgroup $H$, often the normalizer of a $p$-subgroup of $G$. We present a basic formula for deciding when categories of modules or complexes have a Green correspondence and apply it to many examples. In several cases the equivalence is an equivalence of triangulated categories, and in special cases it is an equivalence of tensor triangulated categories.
math.RT↗