Papers

Model-based reinforcement learning has shown superior sample efficiency by leveraging the learned latent dynamics either in the form of derivative-free planning/imagined rollout training or dynamics gradient-based policy updates. While these approaches achieve comparatively fast learning, they all suffer, to varying degrees, from issues of recurrent compounding errors, high inference-time latency, and instability in backward propagation through time (BPTT). In this work, we propose a model-based RL approach that uses the chunk world model as a differentiable training-time evaluator to optimize the chunk actor without recurrent model invocation. Through the collaborative chunk-wise prediction of the world model and policy, we can generate H-step hypothetical rollouts in a single forward pass and directly optimize value expansion, avoiding the costly and unstable BPTT. We evaluate our method on 19 challenging high-dimensional humanoid tasks from HumanoidBench and deploy our method to the real-world for quadruped bipedal walking. Project Website: https://song-wx.github.io/cmpo.github.io/

We establish sharp projection inequalities for $k$-antichains under orders defined by open convex cones. For integers $n\geq2$ and $k\ge 1$, let $C\subsetneq\mathbb R^n$ be a nonempty open convex cone. A set $A\subseteq\mathbb R^n$ is a $k$-antichain with respect to the order $x\prec_C y\iff y-x\in C$ if it contains no chain $x^1\prec_C\cdots\prec_C x^{k+1}$. For every such set $A$ and every $v\in C$, we prove \[ \mathcal H^{n-1}(A) \leq k\frac{\|v\|}{\alpha_C(v)} \mathcal H^{n-1}(P_v(A)), \] where $P_v$ is the orthogonal projection onto $v^\perp$, $\mathcal H^{n-1}$ denotes normalized Hausdorff outer measure, and $\alpha_C(v)$ is the minimum of $\langle\xi,v\rangle$ over unit vectors in the dual cone $C^*$. In particular, every weak antichain $A\subseteq\mathbb R^n$ satisfies $\mathcal H^{n-1}(A)\leq\mathcal H^{n-1}(\Delta_i(A))$ for each $i$, where $\Delta_i(x)=(x_j-x_i)_{j\ne i}$. This proves the skewed projection conjecture of Engel, Mitsis, Pelekis and Reiher. As an application, we recover the bound $\mathcal H^{n-1}(A)\leq kn$ for $k$-antichains in the unit cube under the coordinatewise order.

The Gromov-Wasserstein (GW) distance provides a principled framework for comparing two probability distributions supported on different metric spaces by matching their individual intrinsic geometric structures. In practice, the GW distance is estimated from finite samples and often incorporates regularization for statistical and computational tractability. This motivates a quantitative understanding of the stability and estimation error of regularized GW distances. In this work, we study a general family of divergence regularized GW distances, including entropy and Tsallis regularizations over the full range of powers, from a nonasymptotic perspective. Specifically, we establish Lipschitz continuity of the value of regularized GW and Hölder continuity of its optimal coupling under Wasserstein perturbations of the input probability measures. Moreover, we derive the parametric rate of convergence for the empirical regularized (2,2)-GW distance on compactly supported Euclidean spaces.

Most existing approaches rely on video or motion-capture data for reinforcement learning (RL) training; however, all of these methods require an upper-level module to generate reference trajectories in real time. In object carrying tasks, the humanoid can only lift objects from designated locations along the reference trajectory, resulting in poor spatial generalization. Moreover, existing policies can only be evaluated inside a motion-capture studio. To address these limitations, we propose MOVER, a multi-stage, Teacher-Assistant-Student, RL training framework for humanoid object carrying. We first collect data from videos and employ GENMO and GMR to retarget the video data, combining this with data augmentation techniques to generalize the data across objects of varying shapes and sizes. In the first stage, building upon the DeepMimic \cite{peng2018deepmimic} motion-training framework, we train the humanoid to transport objects from specified locations along designated trajectories. In the second stage, we relax the tracking of the reference motion and adjust the reward so that the humanoid learns to transport objects from different positions. In the third stage, we apply a Dagger-PPO distillation method to distill away the proprioceptive position observations and reference joint position of the humanoid. This allows the deployed policy to operate without relying on global position information from a motion-capture system; instead, the humanoid can directly perceive the object's pose from its onboard RGB-D camera to complete the carrying task. We design a series of simulation experiments to compare the success rates across stages (Stages 1 vs. 2) and before versus after distillation. We further transfer the policy to a real humanoid, successfully transporting objects at varying positions in a motion-capture-free setting.

Self-propelled Janus particles are promising active agents for microscale manipulation and microrobotic applications. However, when powered by a global external energy source, such as an electric, magnetic, or optical field, all particles respond simultaneously, preventing their independent and concurrent control. Achieving parallel, decoupled control without continuous particle-specific feedback, while preserving intrinsic self-propulsion, remains a significant challenge. Here, we present an optoelectronic (OE) strategy for simultaneously and independently controlling electrically driven, self-propelled metallo-dielectric Janus particles (JPs) using spatially programmable virtual electrodes. These electrodes are generated by projecting a single predefined illumination pattern from a digital micromirror device onto a photoconductive surface. The resulting confinement landscape enables multiple JPs to follow distinct trajectories without continuous monitoring, feedback, or pattern reconfiguration. We demonstrate controlled pairing of JPs with passive polystyrene particles and biological cells. For automated multi-agent operation, an image-based assignment framework identifies optimal agent-target pairs, excludes intersecting trajectories, and generates a single composite pattern for simultaneous, selective pair formation without real-time updating. Finally, we demonstrate independent manipulation of multiple magnetically rolling JPs under a globally applied magnetic field. Overall, this programmable open-loop strategy provides a versatile framework for multi-agent microrobotic manipulation, with potential applications in in-vitro micromanipulation and microfluidic systems.

This paper considers a class of structured cardinality penalized optimization problems with nonsmooth convex loss functions, for which the proximal mapping associated with the structured $\ell_0$ penalty is generally unavailable. To overcome this difficulty, we develop a chain of exact reformulations based on variable splitting, exact penalization, and continuous relaxation, and establish rigorous equivalence relationships among these resulting models. In particular, we define a class of strong local minimizers for the original problem and show that these minimizers are equivalent to weak $d$-stationary points of the relaxation problem. Further, we propose a safeguarded accelerated proximal alternating direction method of multipliers (SAP-ADMM). We prove that the sequence generated by SAP-ADMM converges to a weak $d$-stationary point of the relaxation problem. Depending on the parameter settings and algorithmic regime, we establish $O(1/k)$ or $o(1/k)$ convergence rates for both the objective function value gap and the KKT residual. Numerical experiments on signal and image denoising demonstrate the effectiveness of both the proposed models and SAP-ADMM in terms of reconstruction quality and computational efficiency.

Large pretrained models have achieved remarkable success across diverse domains, yet adapting them to multiple downstream tasks remains challenging: full fine-tuning is costly, while maintaining separate task-specific models is storage-inefficient and fails to produce a unified multi-task model. Low-Rank Adaptation (LoRA) offers an efficient alternative for Model Merging by representing each task adaptation as a low-rank update over frozen pretrained weights. However, existing LoRA merging methods often treat task-specific updates as directly comparable objects and merge them in their original low-rank parameter spaces. This overlooks two key factors: which update directions provide reliable shared support across tasks, and how these directions should be re-parameterized with respect to the pretrained weights before merging. To address this limitation, we propose Pretrained-Guided Shared Basis (PGSB), a two-stage framework for LoRA model merging. PGSB first identifies shared directions among task-specific LoRA updates, and then re-parameterizes these directions using their interaction with the pretrained weights, producing a more suitable basis for merging. Extensive experiments demonstrate that PGSB consistently outperforms state-of-the-art baselines across multiple benchmarks. Codes are available at https://github.com/Kitschnada/Pretrained-Basis .

Synthetic three-dimensional (3D) light fields provide a new route to imprinting chirality on achiral matter through light–matter interaction. Although previous work has numerically demonstrated that chirality can be imprinted on the photoelectron momentum spectrum of atoms, a transparent analytical physical picture that links the structure of the driving field to the chirality of the spectrum is still an open question. Here, using frequency-domain theory based on nonperturbative quantum electrodynamics (QED), we demonstrate that this chirality originates from coherence between adjacent quantum transition channels. We further find that a symmetry transformation introduces into the coherence term a symmetry-breaking phase shift ($\Phi_{\mathrm{SBPS}}$), which can be tuned by varying the laser-field parameters to preserve or break the corresponding symmetry in the spectrum. Once all such symmetries are broken, the momentum spectrum becomes chiral. In particular, for the noncollinear two-color 3D light field considered here, the spectrum is chiral for even $f=\omega_2/\omega_1$ and achiral for odd $f$. Our results provide a microscopic interpretation of chirality imprinting and establish a framework for predicting and controlling chiral electron wave packets with synthetic 3D light fields.

Fermi surface transformation accompanied by quantum phase transition is widely observed in correlated electron systems including heavy fermion materials and van der Waals quantum heterostructures. The unified Anderson lattice description for this phenomenon suggests that their interacting ground states in the case of electron half filling always destabilize the metallic phase in the strong Kondo-coupling regime. We examine this issue within the paramagnetic phase of a Kondo lattice system with a heterotic layered structure. In the weak Kondo-coupling regime, the system exhibits a fractional Dirac liquid involving the massless or massive Dirac fermions and a charge neutral spinon Fermi surface. In the strong Kondo-coupling regime, the spinons hybridize with the Dirac fermions resulting in an intermediate nearly-flat hybridizing band together with the conduction and valence heavy fermion bands, yielding a large electric Fermi surface. Absence of the Kondo gap between these bands is observed depending on the stacking configurations of the layered structure. In particular, the system remains metallic even at the exact half filling in this regime and Luttinger's theorem is violated across the critical point. Implications of these results on the van der Waals quantum heterostructures are briefly discussed.

We study the three-dimensional primitive equations with full viscosity and horizontal thermal diffusion in bounded domains. We establish global well-posedness for admissible $H^1$ initial data and persistence of $H^2$ regularity on the flat-bottom cylinder. The higher regularity analysis combines fractional hydrostatic Stokes regularity with anisotropic estimates of the vertical transport. We also consider variable-depth domains with positive $h\in C^3(\overline M)$ and a diffusion operator adapted to the topography compatible with layers $z/h(x,y)=\mathrm{constant}$. This operator reduces to $\Delta_H$ at constant depth and generally differs from the Cartesian horizontal Laplacian over a varying bottom. Its weighted formulation yields global strong solutions for admissible $H^1$ data. Persistence of $H^2$ regularity is proved under the additional assumption $\partial_\nu h=0$ on $\partial M$, where $\nu$ is the outward horizontal unit normal.

For every $m\geq2$, we prove that any connected closed oriented smooth immersion $X:M^m\to\mathbb{R}^{m+1}$ satisfying \[ K=\left\langle X,\nu\right\rangle \] is an embedding onto the unit sphere. No convexity is assumed. At a point maximizing $|X|$, we find a strictly convex component of $\{K>0\}$. If this component does not coincide with $M$, its polar immersion bounds an unbounded convex set. A finite area lemma then extends the local surface area formula for the polar body to a global measure identity. Using the vanishing first moment of surface area measure, we show that the origin lies in the interior of the polar body, contradicting the existence of recession directions. Thus the hypersurface is strictly convex, and the classification of strictly convex shrinkers completes the proof.

Autoregressive video generation models generate videos sequentially, with each new block conditioned on previously generated blocks. By training on the model's own rollouts, Self Forcing and its follow-up methods substantially mitigate exposure bias caused by the mismatch between training- and inference-time history distributions. However, these models still suffer from error accumulation during long-horizon generation. We identify a key underlying limitation: the model remains highly sensitive to errors in its generated history, allowing small deviations to be amplified through subsequent generations. We refer to this underexplored problem as the local history robustness gap. To address this gap, we introduce Adversarial Gradient Forcing (AGF), a framework designed to improve the robustness of few-step autoregressive video models to perturbations and accumulated errors in their own generated histories. AGF uses distribution matching gradients from future block predictions to select adversarial perturbations of self-generated histories. It then jointly trains the generator on the original and perturbed histories to improve the robustness of future generation. Extensive experiments show that AGF achieves the highest VBench Total score on 60-second video generation and the best visual quality on four-minute video generation. Notably, AGF achieves such long-horizon robustness while requiring only 5-second rollouts for training.

Protocol specifications rarely justify executable behavior in one place: a transition may inherit its source state from a remote control block, name its events only by number, and remain subject to a later correction. Recovering the nearby clause is therefore insufficient; the system must assemble a source-linked certificate and determine whether any stronger rule applies. We introduce LASER, a proof-carrying search method for sparse, defeasible protocol evidence. LASER represents missing support and unresolved corrections as explicit obligations, searches typed evidence routes, and lets an occurrence-aware symbolic checker alone decide whether a certificate warrants, refutes, or leaves a behavior unresolved. On 91 BehaviorCheck families under a matched 2K budget, LASER improves Joint Edge+Proof over the strongest local reader on two model families ($\Delta=+.132$, $p=.017$; $\Delta=+.198$, $p<.001$) while cutting false discoveries by 2–3$\times$. Controlled replays attribute the gain and its limits: neither reference routing nor deterministic citation expansion alone exceeds the local baseline; whole-document reading (29–65K tokens), two-round iterative retrieval, and even oracle minimal-certificate evidence all fail to reach LASER, localizing the bottleneck in typed obligation closure rather than evidence access. An authority-corruption replay shows source-link errors only cause abstention, while the only unsafe-warrant mechanism is mis-recording a Held erratum as Verified, confined to that erratum's family. LASER thus improves long-range dependency recovery while converting incomplete evidence and uncertain authority into explicit residual obligations rather than unsupported behavior.

In multi-robot manipulation, an action's value depends on how teammates respond. We present \method{} (Cooperative Action–Response Belief Estimation), a framework for learning team-response beliefs from local history. A predictive belief encoder represents the interaction and conditions a nominal action. Matched reactive and replay continuations separate each candidate's direct advantage from the utility contributed by teammate adaptation. A candidate-conditioned readout learns this response distribution alongside total advantage, and calibrated selection chooses an alternative or retains the nominal action. Our analysis characterizes when response changes the preferred action and how prediction and source errors limit the recoverable gain. With the representation, proposals, and data fixed, explicit response supervision improves candidate ranking and reduces selection regret relative to learning the same information through branch utilities. The benefit is concentrated in decisions where teammate adaptation changes the preferred action. Across RoboFactory, the MARS Control Track, and physical collaboration tasks, CARE achieves the highest average success among the evaluated policies, combining a capable nominal policy with selective coordination adjustments. Together, these results show that CARE turns predictions of teammate adaptation into effective decentralized action selection. Project page: https://jeong-zju.github.io/care/.

Dynamic Product Advertising (DPA) retrieval systems are a core component of modern e-commerce advertising; however, their evaluation remains challenging. Conventional offline engagement metrics are limited by sparse, biased feedback, while online evaluation is costly and time-consuming. In this work, we propose a user–product relevance metric for offline evaluation of DPA retrieval systems. The metric first compresses the engagement history into a compact set of intent representatives via Semantic-ID-grouped, event-stratified segmentation, then assesses the relevance of a recommended product to each individual intent and aggregates them as a user-level relevance score, yielding a stable and interpretable measure of retrieval quality. To compute this metric at scale, we leverage large language models (LLMs) as semantic relevance judges, capturing nuanced functional and semantic relationships that heuristic methods often miss. We propose an agentic, human-aligned prompting framework that generates multi-category relevance guidelines and distills teacher-model judgments into an efficient student model for scalable evaluation. The resulting metric strongly correlates with offline and online business metrics, enabling faster and more reliable DPA retrieval iteration before A/B testing.

Physical systems and distributed AI workflows can retain past information, receive delayed feedback and combine conflicting signals. These features pose a common modeling problem: determining what information about past interactions a state must retain to account for future responses. Active Neural Matter (ANM) addresses this problem through a finite-window response framework. Forward analysis uses each system's dynamics to predict state and output responses to perturbations, separating propagation from output sensitivity. Inverse analysis tests whether a candidate state retains enough information for these responses. With the system and future inputs or interaction rules fixed, distinguishable responses from histories assigned the same state identify distinctions the representation must preserve. Their distributional separation gives a lower bound on the worst-case error of approximating behavior from that state. Uncertainty bounds distinguish rejection, support within a fixed tolerance on tested comparisons, and unresolved cases. Delayed-consensus simulations check analytical predictions of response amplitude and phase over a narrow range of delays; flocking illustrates dependence on the chosen observable. An exact delayed-return construction establishes a sufficient state for a specified program. The AI studies identify distinctions in interaction history and evidence order that a representation must preserve to reproduce observed response distributions. Tests on new histories in a controlled feedback task provide bounded support for a state specified by the task instructions; the instructed rule predicts every observed action. ANM connects response prediction to measurable information requirements, separating behavioral fidelity from task correctness and initial-state adequacy from a closed evolution law for that state.

We formulate a proof of Part~I of Martin's conjecture for order-preserving maps directly on the quotient of the reals by Turing equivalence. The assumptions are countable choice for reals, the perfect-set property for sets of reals, and continuous uniformization on a comeager domain. The argument applies under $\mathsf{AD}+\mathsf{DC}_{\R}$ and inside the choiceless Solovay model. We then determine the exact consistency strength of the unrestricted order-preserving dichotomy as an axiom over $\mathsf{ZF}+\mathsf{AC}_{\omega}(\R)$: it is equiconsistent with $\mathsf{ZFC}$ plus a strongly inaccessible cardinal.

To operate distributed applications with high availability, operators must rapidly diagnose and mitigate any incident. LLM-based agents can help, but unlike experienced human operators they do not improve as they handle more incidents. Each investigation starts from scratch, re-deriving likely causes and re-testing hypotheses even when a similar fault was resolved in the past. We present a self-defining operator (SDO) that improves with time by updating its operational behavior and memory. When SDO resolves an incident, it distills that experience into playbooks, which describe reusable diagnostic instructions for future incidents with similar faults, and detectors, scripts that take application telemetry as input and output relevant playbook(s). SDO continuously runs the detectors and invokes LLMs only when one fires, so its token cost scales with incident count rather than with operational time. Across 11 open-source microservice applications, SDO cuts resolution time by 52% on recurring faults while keeping per-incident cost low. SDO is open source at https://github.com/self-defining-systems/sdo.

We solve an open problem posed by Richard Guy in his book Unsolved Problems in Number Theory. We prove that, for every integer $n\geq10$, there exist infinitely many $n\times n$ integer matrices $A$ such that every entry is $\ge2$ and $\det A=\det A^{[3]}=1$, where $A^{[3]}$ denotes the entrywise cube of $A$. The matrices may be chosen compatibly, so they can form the leading principal blocks of a single infinite positive integer array. The order-ten case is reduced to an inhomogeneous system consisting of one linear and one diagonal cubic equation. The circle method then provides infinitely many positive integral solutions. To pass from order $n$ to order $n+1$, we introduce a bordering construction that preserves the signed cofactor vectors of both the matrix and its entrywise cube. Iterating this construction yields the result in every order $n\geq10$.

Large-scale multimodal data are a key enabler for integrating large generative artificial intelligence models into wireless networks. However, existing wireless datasets offer limited support for heterogeneous environments, particularly in terms of reusable high-fidelity scenes, scalable differentiable ray tracing, and synchronized multimodal data. These limitations are more pronounced in mobile and aerial scenarios with time-varying environments and channels. To address these limitations, we propose DeepTelecom, a material-aware, high-fidelity multimodal channel dataset and reproducible generation framework for networks involving unmanned aerial vehicles (UAVs) and reconfigurable intelligent surfaces. DeepTelecom refines coarse indoor/outdoor reconstructions and uses a large language model to map segmented surfaces to frequency-dependent electromagnetic parameters, yielding material-aware Level of Detail 3 digital twins. Then, a differentiable GPU-accelerated Sionna ray tracer simulates propagation across the sub-6 GHz/millimeter-wave/sub-terahertz bands, and specifically captures rotor-induced micro-Doppler signatures of stationary or moving UAVs at different pitch angles and translational velocities. The framework synchronously produces channel tensors, coverage maps, transmission videos, multi-view images, and weather-conditioned renderings, and supports differentiable material calibration from sparse channel anchors. The released dataset contains 10 material-aware indoor/outdoor scenes and 50,000 synchronized UAV samples; the framework supports scalable generation of additional data for user-defined scenes and system configurations. In 3D UAV localization, DeepTelecom reduces the 90th-percentile error from 31.05 m to 2.43 m compared with schemes considering only channel state information, demonstrating its significance for artificial-intelligence-enabled wireless systems.

Roadside 4D occupancy forecasting predicts future semantic occupancy in a fixed infrastructure coordinate system. Roadside scenes are globally structured yet locally evolving, requiring comprehensive scene-level context while precisely modeling sparse localized motion. However, existing forecasting paradigms struggle to tackle both requirements. To address this limitation, we propose InfraWorld, a world model formulating roadside occupancy forecasting as selective state evolution. InfraWorld maintains a dense BEV state for the complete scene and persistent motion queries for moving regions, assigning complementary states to global context and local dynamics. Specifically, we propose Dynamic Query Initiation (DQI) to initialize queries in regions supported by motion in the observed history. During rollout, the dense state is updated through Long–Short Temporal Fusion (LST), which combines short-term adjacent-frame continuity with long-term motion trends to preserve stable context while capturing scene evolution. Motion-Aware Query Injection (MAQI) then refines the queries and injects confidence-weighted query information into corresponding BEV tokens, enabling targeted dynamic updates without perturbing global context. Together, InfraWorld concentrates predictive capacity on evolving traffic regions. Extensive experiments on the InfraOcc and Occ3D–nus datasets demonstrate that InfraWorld achieves state-of-the-art performance for roadside 4D occupancy forecasting while retaining its effectiveness under ego-centric settings. Code will be released.

The construction of fault-tolerant atomic registers is a fundamental problem in distributed computing. GPUs, widely used in scientific computing and machine learning, face Byzantine thread behaviour, while their shared memory lacks access control, allowing any thread to modify shared objects. This raises the question of whether atomic register semantics can be maintained when any thread, including the designated writer, may behave Byzantine. We study this problem in the GPU-inspired shared-memory model of Georgiou et al. and present implementations of a Byzantine-linearizable single-writer multi-reader (SWMR) register. CAReg uses constant memory with a quantifiable probability of invalid reads, while SnapObject maintains a bounded window of authenticated writes, eliminating invalid reads and tolerating up to \(n-1\) Byzantine processes through lock-free and wait-free variants. Our results demonstrate how GPU phase-based, lock-step execution can partially compensate for the absence of access control.

Multimodal benchmarks are central to evaluating whether models can reason over information from multiple modalities. However, existing literature has revealed that some benchmarks may contain shortcut items that can be answered from a single modality or from answer-option regularities alone, thus failing to reflect models' true cross-modal inference ability. Existing methods for assessing benchmarks typically rely either on intrinsic item structure or extrinsic model response behavior, which are not adequate for a comprehensive diagnosis. To fill in this gap, we propose SRCoD, a structure-response co-calibrated diagnosis framework for item-level diagnosis of modality dependence in multimodal benchmarks. SRCoD estimates sample-wise multimodal information structure from benchmark content and target answers, and uses this signal as a soft structural anchor for modality-conditioned item response modeling. The learned model produces a calibrated item-level diagnostic profile that reflects how strongly an item depends on different forms of modality evidence, enabling fine-grained benchmark analysis beyond aggregate accuracy. SRCoD also provides interpretable attribution of the diagnosis results. Extensive experiments under two complementary protocols, i.e., benchmark-refinement oriented validation and human-labeled item validation, demonstrate that SRCoD outperforms state-of-the-art benchmark diagnosis methods.

Emerging strong Vision-Language Models (VLMs) have advanced navigation foundation models. However, these models still have unsatisfactory performance on goal-oriented navigation settings. In this paper, we first conduct a motivating study revealing that the key issue lies in the insufficient utilization of streaming observations and imprecise target localization. To tackle these challenges, we propose GG-Nav, a simple yet effective navigation framework that learns a structured chain-of-thought (CoT) mechanism via supervised fine-tuning to explicitly localize goal-relevant instances, accumulate grounding evidence, and support more reliable decision-making. Specifically, the structured CoT is designed with two key stages: (i) Observation-to-Evidence, which reasons over all intermediate frames between adjacent decision steps to retain useful goal-related evidence; and (ii) Evidence-to-Decision, which integrates the current observation with accumulated evidence to ground the target and support the generation of navigation actions or clarification questions. Extensive experiments show that GG-Nav outperforms the state-of-the-art methods in terms of success rates on the HM3D ObjectNav, VL-LN, and CoIN benchmarks by 3.1%, 16.6%, and 5.3%, respectively. Ablation studies further show that accumulating evidence from intermediate observations reduces evidence-missing failures by 11.6%, while explicit grounding reduces stopping errors by 49.4%. We also deploy GG-Nav on a Unitree Go2 robot, demonstrating its zero-shot generalization capability in unseen real-world environments.

We prove regularity for symmetric pairs of connected complex reductive groups by combining invariant theory with the analysis of Schwartz distributions. For the classical residual families, a Gaussian lifting argument reduces the required equivariant vanishing to invariant theory in quadratic moment quotients: contraction and supertrace identities settle DIII and balanced CII, while Gram-matrix invariants and volume tensors handle BDI/Spin. In the exceptional EVII case, transverse slices and explicit radial differential operators establish the vanishing of the full sign-equivariant Schwartz-distribution space. Together with the reduction to irreducible factors and finite-component assembly, these results establish regularity for all symmetric pairs of connected complex reductive groups. We further establish multiplicity one for irreducible Casselman-Wallach representations whenever the complex symmetric space is connected, allowing disconnected ambient groups. In particular, van Dijk's unitary Gelfand conjecture follows in this setting. Finally, we construct an invariant tempered distribution supported on an EVII nilpotent orbit closure whose Fourier transform also has nilpotent support, showing that the EVII isotropy representation is not special.

Real-world business requests often leave key requirements unstated because frontline practitioners struggle to articulate rules they know from experience. Forward-deployed engineers (FDEs) must elicit these requirements through dialogue and iteratively optimize solutions until they meet customer acceptance criteria. Existing optimization benchmarks typically start from explicit objectives, while clarification benchmarks often introduce information gaps into existing tasks. We introduce FDE-Bench, the first benchmark built from real customer projects to evaluate agents on end-to-end delivery tasks that require interactive requirement clarification and iterative optimization. Its 49 cases span combinatorial optimization and machine learning. Clarification targets are distilled from discussions between frontline practitioners and FDEs. Agents elicit missing requirements from a simulated customer, and case-specific evaluators assess final artifacts against acceptance criteria using customer-accepted FDE solutions as quality references. Across 18 agent configurations, the highest mean delivery score is only 0.5510, compared with an FDE reference of 1.0. The highest delivery success rate (DSR), defined as the fraction of planned runs reaching this reference, is only 6.12%. These results show that reliable FDE-level end-to-end delivery remains out of reach for the evaluated agents on underspecified real-world business tasks. The benchmark project page is available at https://baidubce.github.io/FM-Agent/FDE-Bench/.

Artificial intelligence (AI) is being applied to an expanding range of scientific activities, including literature analysis, hypothesis generation, software development and automated experimentation. Yet these capabilities rely on a more fundamental condition: scientific information must remain identifiable and traceable across systems and over time. In practice, different versions of a work and their associated records and files are often scattered across services and local directories. This fragmentation forces researchers to identify and contextualize the same work repeatedly, disrupting continuity from discovery to interpretation and reuse. Here we present Gewu Insight, a research information infrastructure that addresses this discontinuity by organizing scientific works as persistent, stateful research objects. It unifies venue-, topic- and author-based discovery records through a shared paper identity. Within a local library, metadata, versioned resources and research context can then accumulate around the same work. These capabilities are integrated into an iterative workflow for scientist-led, AI-assisted research, allowing earlier interpretations to be revisited and refined. A bounded evaluation showed high candidate precision across the three discovery modes, with paper identity, resource distinctions and research state preserved in controlled workflows. By making continuity an explicit property of research infrastructure, Gewu Insight can serve as an inspectable scientific memory layer shared by researchers and AI assistants, supporting human judgment and providing a foundation for future, more epistemically grounded scientific AI.

Particle-in-cell (PIC) simulation is indispensable for modeling beam dynamics in particle accelerators, but its computational cost limits many-query workflows, such as configuration exploration, virtual diagnostics, and controller design. We introduce GLOBE, a physics-constrained Generative Latent Operator for Beam Evolution, modeling the nonlinear, control-dependent, multiscale evolution of 3D beam–field dynamics covering $10^7$ spatial cells. GLOBE compresses beam–field states into a compact latent space and factors their evolution into two components. A control-conditioned neural operator learns the dominant dynamics, while an amplitude-normalized generative model captures the residual distribution, recovering fine-scale structures and conditional variations. GLOBE enforces field constraints by regime-specific, parameter-free operators: a Poisson solve reconstructs the electric field in the electrostatic regime, and a spectral projection imposes Gauss's law and a divergence-free magnetic field in the electromagnetic regime. On two high-resolution 3D particle-accelerator benchmarks, bunched-beam transport and plasma-wakefield acceleration, GLOBE lowers relative-$L_2$ error by 9% and 13%, low-frequency spectral error by 69% and 51%, and mid-frequency spectral error by 54% and 20% relative to the strongest baseline (DPOT), satisfies field constraints, and reduces hours of PIC simulation to a minute per rollout.

Twisted equations in free groups are equations in which a finite group of symmetries acts on the free group by automorphisms and anti-automorphisms, such as inversion and reversal; moreover, the variables may be subject to rational constraints. Algorithms from the theory of equations in virtually free groups solve such equations in PSPACE, but they are intricate. Our main result is an elementary algorithm for quadratic twisted equations, which extends the algorithm of Comerford and Edmunds (1981) for quadratic equations in free groups to the twisted setting and to rational constraints. Besides deciding solvability in PSPACE and yielding EDT0L descriptions of solution sets, our algorithm computes, for every quadratic expression, finitely many parametric forms describing its values as freely reduced words. As an application, we study the palindrome length of elements of free groups, that is, the least number of palindromes whose product they are. Guided by the parametric forms that our algorithm computes for products of palindromes, we found, and then proved directly, a characterization of the freely reduced words of palindrome length at most $n$ in terms of patterns describing how palindromes are nested by twisted conjugations, thereby confirming a Catalan structure conjectured by the second author. Consequently, these words form a context-free language, and palindrome length is computable in cubic time as well as in LOGCFL, answering a question of Bardakov, Shpilrain, and Tolstykh (2005).

Let $P = \sum_{\omega} a_\omega x^\omega$ be a degree $d$ homogeneous polynomial in $x_0, \dots, x_n$ with real coefficients. Pólya showed that, if $P$ is strictly positive on the standard $n$-simplex, then $(x_0 + \cdots + x_n)^M P$ has strictly positive coefficients for all $M \gg 0$. The least such $M$ is known as the Pólya exponent of $P$. de Klerk-Laurent-Parrilo showed that the Pólya exponent is $O(d^2) P^{(0)}_{\max}/\lambda(P)$, where $P^{(0)}_{\max} := \max_\omega a_\omega/\binom{d}{\omega}$ and $\lambda(P)$ is the infimum of $P$ on the standard simplex. Pólya's Positivstellensatz is a consequence of the classical approximation of the multivariate hypergeometric distribution by the multinomial distribution, as was already implicitly known to de Klerk-Laurent-Sun. By applying known estimates of this approximation from probability theory, we obtain a different $O_n(d) L(P)/\lambda(P)$ upper bound of the Pólya exponent, where $L(P) := \max |a_\omega|/\binom{d}{\omega}$. An example shows that $O_n(d)$ is tight.