Daily Papers

World Action Models (WAMs) augment robot policies with action-conditioned predicted futures, but a plausible future alone does not justify changing the action that a bimanual policy would execute. We present CoWAM, a selective intervention layer that expresses synchronization, role compatibility, and collision convergence as coordination contracts. Each contract combines typed admissibility checks with event-conditioned verification and calibrated intervention gates. CoWAM preserves the nominal action unless an alternative satisfies every active obligation and provides a clear, low-risk improvement; when the nominal action is also inadmissible, it invokes a predefined abstention fallback. To separate selector quality from proposal quality, all methods operate on identical candidate pools and commit their decisions before shared oracle labeling. Across eight simulated bimanual tasks, CoWAM improves coordination-valid selection by 16.7 percentage points over the contract-only variant and raises closed-loop success by 9.6 percentage points over the strongest selective baseline, while keeping harmful interventions below 1%. Together, these results establish coordination contracts as an effective interface for conservative policy intervention with predicted world-action evidence across coordination-rich bimanual tasks.

In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence. This paper presents a novel GPU algorithm that achieves convergence rates comparable to fullspace Newton's method while maintaining good parallelizability just like the Jacobi method. Our approach is built on a key insight into the phenomenon of overshoot. Overshoot occurs when a local solver aggressively minimizes its local energy without accounting for the global context, resulting in a local update that undermines global convergence. To address this, we derive a theoretically second-order optimal solution to mitigate overshoot. Furthermore, we adapt this solution into a pre-computable form. Leveraging Cubature sampling, our runtime cost is only marginally higher than the Jacobi method, yet our algorithm converges nearly quadratically as Newton's method. We also introduce a novel full-coordinate formulation for more efficient pre-computation. Our method integrates seamlessly with the incremental potential contact method and achieves second-order convergence for both stiff and soft materials. Experimental results demonstrate that our approach delivers high-quality simulations and outperforms state-of-the-art GPU methods with 50 to 100 times better convergence.

Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an ADMM-Inspired Momentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem determines the acceleration form. Building on AIM, we propose Relativistic Adaptive gradient Descent with Accelerated Residual (RADAR), which combines relativistic adaptive geometry, decoupled residual correction, and second-order momentum filtering to improve the update direction and momentum estimation. We establish stochastic convergence through a variance-perturbed Lyapunov drift analysis. Experiments on supervised vision learning, language modeling, and reinforcement learning show that RADAR achieves consistent improvements over strong adaptive optimizer baselines.

Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, \ie the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth.

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds--the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n^{-1/d+ρ}), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of alpha-coherent function for which we provide convergence analysis. We show that for strictly alpha-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in alpha-coherent class of functions.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Optimisation-based parking planners usually impose collision constraints only at the time samples, so a vehicle corner can cut an obstacle between samples, and no executable trajectory exists until the solver converges. We present a planner for car-like vehicles with reverse gear in which every iterate of the optimisation phase satisfies the discretised dynamics exactly and keeps the whole vehicle rectangle clear of obstacles between the samples. Each time interval receives one convex corridor that holds all vehicle corners at both ends and is shrunk by a sweep margin bounding how far the corner paths leave their chords. Separating half-planes give the corridors a direction out of obstacles when the initial guess is in collision; later, heading-aligned boxes are grown from the speed, curvature and step of the current iterate and rebuilt after accepted steps. A feasibility-perturbed trust-region sequential quadratic programming method projects each step onto the dynamics by feedback and verifies it exactly; the cost decreases monotonically, and once the corridors stop changing, limit points are Karush-Kuhn-Tucker points of the corridor-constrained problem or violate a constraint qualification. On 820 benchmark cases the planner succeeds in 818 without penetration (797 from the first initial guess), none of the 7103 evaluated optimisation-phase iterates is unusable, and it succeeds in 96.5% of the cases when 99% of the initial guesses intersect an obstacle. Its maneuvers take 0.7% longer in the median than those of a similarly certified exact-collision baseline. The guarantees hold for the planning model, not for a physical vehicle.

Classical convergence guarantees for gradient-based learning in games require the pseudo-gradient to be (strongly) monotone in Euclidean geometry as shown by rosen(1965), a condition that often fails even in simple games with strong cross-player couplings. We introduce Small-Gain Nash (SGN), a block small-gain condition in a custom block-weighted geometry. SGN converts local curvature and cross-player Lipschitz coupling bounds into a tractable certificate of contraction. It constructs a weighted block metric in which the pseudo-gradient becomes strongly monotone on any region where these bounds hold, even when it is non-monotone in the Euclidean sense. The continuous flow is exponentially contracting in this designed geometry, and projected Euler and RK4 discretizations converge under explicit step-size bounds derived from the SGN margin and a local Lipschitz constant. Our analysis reveals a certified ``timescale band'', a non-asymptotic, metric-based certificate that plays a TTUR-like role: rather than forcing asymptotic timescale separation via vanishing, unequal step sizes, SGN identifies a finite band of relative metric weights for which a single-step-size dynamics is provably contractive. We validate the framework on quadratic games where Euclidean monotonicity analysis fails to predict convergence, but SGN successfully certifies it, and extend the construction to mirror/Fisher geometries for entropy-regularized policy gradient in Markov games. The result is an offline certification pipeline that estimates curvature, coupling, and Lipschitz parameters on compact regions, optimizes block weights to enlarge the SGN margin, and returns a structural, computable convergence certificate consisting of a metric, contraction rate, and safe step-sizes for non-monotone games.

In modern machine learning, parallelization of training is an important strategy for increasing scale. Asynchronous stochastic gradient descent (ASGD), which maximizes the utilization of available hardware by avoiding waiting for slow workers. However, with constant step sizes, the convergence of ASGD is nonetheless affected negatively by slow workers due to large delays in updates. At the same time, it has been empirically observed in asynchronous training of deep learning models that gradient clipping "stabilizes" training. In this work, we provide a theoretical justification for this behavior, as we show that clipping removes the dependence of the maximum delay in the oracle complexity. We employ a sub-Weibull model of gradient noise which generalizes sub-Gaussian and sub-exponential distributions to more heavy-tailed distributions, motivated by empirical observations in deep learning. We show convergence in expectation, and the first time in asynchronous optimization, convergence with high probability.

In this letter, an integrated task planning and reactive motion planning framework termed Multi-FLEX is presented that targets real-world, industrial multi-robot applications. Reactive motion planning has been attractive for the purposes of collision avoidance, particularly when there are sources of uncertainty and variation. Most industrial applications, though, typically require parts of motion to be at least partially non-reactive in order to achieve functional objectives. Multi-FLEX resolves this dissonance and enables such applications to take advantage of reactive motion planning. The Multi-FLEX framework achieves 1) coordination of motion requests to resolve task-level conflicts and overlaps, 2) incorporation of application-specific task constraints into online motion planning using the new concepts of task dependency accommodation, task decomposition, and task bundling, and 3) online generation of robot trajectories using a custom, online reactive motion planner. This planner combines fast-to-create, sparse dynamic roadmaps (to find a complete path to the goal) with fast-to-execute, short-horizon, online, optimization-based local planning (for collision avoidance and high performance). To demonstrate, we use two six-degree-of-freedom, high-speed industrial robots in a deburring application to show the ability of this approach to not just handle collision avoidance and task variations, but to also achieve industrial applications.

Performative Reinforcement Learning (PRL) refers to a scenario in which the deployed policy changes the reward and transition dynamics of the underlying environment. In this work, we study multi-agent PRL by incorporating performative effects into Markov Potential Games (MPGs). We introduce the notion of a performatively stable equilibrium (PSE) and show that it always exists under a reasonable sensitivity assumption. We then provide convergence results for state-of-the-art algorithms used to solve MPGs. Specifically, we show that independent policy gradient ascent (IPGA) and independent natural policy gradient (INPG) converge to an approximate PSE in the best-iterate sense, with an additional term that accounts for the performative effects. Furthermore, we show that INPG asymptotically converges to a PSE in the last-iterate sense. As the performative effects vanish, we recover the convergence rates from prior work. For a special case of our game, we provide finite-time last-iterate convergence results for a repeated retraining approach, in which agents independently optimize a surrogate objective. We conduct extensive experiments to validate our theoretical findings.

Physical principles are fundamental to realistic visual simulation, but remain a significant oversight in transformer-based video generation. This gap highlights a critical limitation in rendering rigid body motion, a core tenet of classical mechanics. While computer graphics and physics-based simulators can easily model such collisions using Newton formulas, modern pretrain-finetune paradigms discard the concept of object rigidity during pixel-level global denoising. Even perfectly correct mathematical constraints are treated as suboptimal solutions (i.e., conditions) during model optimization in post-training, fundamentally limiting the physical realism of generated videos. Motivated by these considerations, we introduce, for the first time, a physics-aware reinforcement learning paradigm for video generation models that enforces physical collision rules directly in high-dimensional spaces, ensuring the physics knowledge is strictly applied rather than treated as conditions. Subsequently, we extend this paradigm to a unified framework, termed Mimicry-Discovery Cycle (MDcycle), which allows substantial fine-tuning while fully preserving the model's ability to leverage physics-grounded feedback. To validate our approach, we construct new benchmark PhysRVGBench and perform extensive qualitative and quantitative experiments to thoroughly assess its effectiveness.

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be non-universal. These results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain boundary formation in two-dimensional materials is suggested.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdos-R\'enyi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

Dynamic scene reconstruction poses a persistent challenge in 3D vision. Deformable 3D Gaussian Splatting has emerged as an effective method for this task, offering real-time rendering and high visual fidelity. This approach decomposes a dynamic scene into a static representation in a canonical space and time-varying scene motion. Scene motion is defined as the collective movement of all Gaussian points, and for compactness, existing approaches commonly adopt implicit neural fields or sparse control points. However, these methods predominantly rely on gradient-based optimization for all motion information. Due to the high degree of freedom, they struggle to converge on real-world datasets exhibiting complex motion. To preserve the compactness of motion representation and address convergence challenges, this paper proposes heterogeneous 3D control points, termed H3D control points, whose attributes are obtained using a hybrid strategy combining optical flow back-projection and gradient-based methods. This design decouples directly observable motion components from those that are geometrically occluded. Specifically, components of 3D motion that project onto the image plane are directly acquired via optical flow back projection, while unobservable portions are refined through gradient-based optimization. Experiments on the Neu3DV and CMU-Panoptic datasets demonstrate that our method achieves superior performance over state-of-the-art deformable 3D Gaussian splatting techniques. Remarkably, our method converges within just 100 iterations and achieves a per-frame processing speed of 2 seconds on a single NVIDIA RTX 4070 GPU.

Modern distributed training relies heavily on communication compression to reduce the communication overhead. In this work, we study algorithms employing a popular class of contractive compressors in order to reduce communication overhead. However, the naive implementation often leads to unstable convergence or even exponential divergence due to the compression bias. Error Compensation (EC) is an extremely popular mechanism to mitigate the aforementioned issues during the training of models enhanced by contractive compression operators. Compared to the effectiveness of EC in the data homogeneous regime, the understanding of the practicality and theoretical foundations of EC in the data heterogeneous regime is limited. Existing convergence analyses typically rely on strong assumptions such as bounded gradients, bounded data heterogeneity, or large batch accesses, which are often infeasible in modern machine learning applications. We resolve the majority of current issues by proposing EControl, a novel mechanism that can regulate error compensation by controlling the strength of the feedback signal. We prove fast convergence for EControl in standard strongly convex, general convex, and nonconvex settings without any additional assumptions on the problem or data heterogeneity. We conduct extensive numerical evaluations to illustrate the efficacy of our method and support our theoretical findings.

Realtime perceptual and interaction capabilities in mixed reality require a range of 3D tracking problems to be solved at low latency on resource-constrained hardware such as head-mounted devices. Indeed, for devices such as HoloLens 2 where the CPU and GPU are left available for applications, multiple tracking subsystems are required to run on a continuous, real-time basis while sharing a single Digital Signal Processor. To solve model-fitting problems for HoloLens 2 hand tracking, where the computational budget is approximately 100 times smaller than an iPhone 7, we introduce a new surface model: the `Phong surface'. Using ideas from computer graphics, the Phong surface describes the same 3D shape as a triangulated mesh model, but with continuous surface normals which enable the use of lifting-based optimization, providing significant efficiency gains over ICP-based methods. We show that Phong surfaces retain the convergence benefits of smoother surface models, while triangle meshes do not.

We study the fine-grained uniform convergence behavior of halfspaces beyond worst-case VC bounds. For inhomogeneous halfspaces in R^d with dge 2, we show that standard first-order VC bounds are essentially tight: even consistent hypotheses can incur population error Θ(dln(n/d)/n), and in the agnostic setting the deviation scales as τln(1/τ) at true error τ. In contrast, homogeneous halfspaces in R^2 exhibit a markedly different behavior. In the realizable case, every hypothesis consistent with the sample has error O(1/n). In the agnostic case, we prove a bandwise, log-free deviation bound on each dyadic risk band via a critical-wedge localization argument. Unioning over bands incurs only a lnln n overhead, and we establish a matching lower bound showing this overhead is unavoidable. Together, these results give a fine-grained and nearly complete picture of uniform convergence for halfspaces, revealing sharp dimensional and structural thresholds.

In an asynchronous federated learning framework, the server updates the global model once it receives an update from a client instead of waiting for all the updates to arrive as in the synchronous setting. This allows heterogeneous devices with varied computing power to train the local models without pausing, thereby speeding up the training process. However, it introduces the stale model problem, where the newly arrived update was calculated based on a set of stale weights that are older than the current global model, which may hurt the convergence of the model. In this paper, we present an asynchronous federated learning framework with a proposed adaptive weight aggregation algorithm, referred to as AsyncFedED. To the best of our knowledge this aggregation method is the first to take the staleness of the arrived gradients, measured by the Euclidean distance between the stale model and the current global model, and the number of local epochs that have been performed, into account. Assuming general non-convex loss functions, we prove the convergence of the proposed method theoretically. Numerical results validate the effectiveness of the proposed AsyncFedED in terms of the convergence rate and model accuracy compared to the existing methods for three considered tasks.

A selector that allocates work across opaque components must evaluate them without being told how they performed. We study the least communication that suffices. Each parent maintains an allocation vector over its children and updates it from outcomes by proportional redistribution. Each child reads the sign of its own allocation change, one bit per round it is selected, so no evaluation message crosses the parent-child boundary. (1) The update preserves the simplex with strict positivity. (2) Conditional on being selected, a child's sign is exactly the root outcome at every depth, a sufficient statistic. The conditioning is necessary. (3) Under interiority a single selector has a unique interior equilibrium, exact and closed-form for N=2, with almost sure convergence under decreasing steps. For general N an equi-ratio condition gives an explicit affine equilibrium. (4) The linearised mean flow has real, strictly negative tangent eigenvalues with explicit bounds for all N >= 2. (5) The mean flow converges globally. An explicit potential, up to normalisation the KL divergence between the failure and slack distributions, decreases at a rate equal to the variance of the equi-ratio statistic. Without interiority the rule drops exactly the children below the surviving support's threshold. (6) The update law composes along a single active path, since ancestors select a node's active rounds but do not alter a realised signal. No joint convergence theorem for a hierarchy whose levels adapt simultaneously is claimed. (7) The one-bit interface admits exactly four deterministic memoryless distortions, and at a single selector passing the bit on unchanged delivers strictly higher mean quality upward than negation or constant transmission. Illustrations on synthetic hierarchies up to 16,384 leaves and three real datasets (3.4 billion comparisons, no mismatches) are consistent with the theory.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

This paper explores the problem of collision-free motion generation for manipulators by formulating it as a global motion optimization problem. We develop a parallel optimization technique to solve this problem and demonstrate its effectiveness on massively parallel GPUs. We show that combining simple optimization techniques with many parallel seeds leads to solving difficult motion generation problems within 50ms on average, 60x faster than state-of-the-art (SOTA) trajectory optimization methods. We achieve SOTA performance by combining L-BFGS step direction estimation with a novel parallel noisy line search scheme and a particle-based optimization solver. To further aid trajectory optimization, we develop a parallel geometric planner that plans within 20ms and also introduce a collision-free IK solver that can solve over 7000 queries/s. We package our contributions into a state of the art GPU accelerated motion generation library, cuRobo and release it to enrich the robotics community. Additional details are available at https://curobo.org

We study the problem of learning minimax policies in zero-sum matrix games. Fiegel et al. (2025) recently showed that achieving last-iterate convergence in this setting is harder when the players are uncoupled, by proving a lower bound on the exploitability gap of Omega(t^{-1/4}). Some online mirror descent algorithms were proposed in the literature for this problem, but none have truly attained this rate yet. We show that the use of a log-barrier regularization, along with a dual-focused analysis, allows this O-tilde(t^{-1/4}) convergence with high-probability. We additionally extend our idea to the setting of extensive-form games, proving a bound with the same rate.

Federated learning is an emerging distributed machine learning framework which jointly trains a global model via a large number of local devices with data privacy protections. Its performance suffers from the non-vanishing biases introduced by the local inconsistent optimal and the rugged client-drifts by the local over-fitting. In this paper, we propose a novel and practical method, FedSpeed, to alleviate the negative impacts posed by these problems. Concretely, FedSpeed applies the prox-correction term on the current local updates to efficiently reduce the biases introduced by the prox-term, a necessary regularizer to maintain the strong local consistency. Furthermore, FedSpeed merges the vanilla stochastic gradient with a perturbation computed from an extra gradient ascent step in the neighborhood, thereby alleviating the issue of local over-fitting. Our theoretical analysis indicates that the convergence rate is related to both the communication rounds T and local intervals K with a upper bound small O(1/T) if setting a proper local interval. Moreover, we conduct extensive experiments on the real-world dataset to demonstrate the efficiency of our proposed FedSpeed, which performs significantly faster and achieves the state-of-the-art (SOTA) performance on the general FL experimental settings than several baselines. Our code is available at https://github.com/woodenchild95/FL-Simulator.git.

Reliable dual-arm grasping is essential for manipulating large and complex objects but remains a challenging problem due to stability, collision, and generalization requirements. Prior methods typically decompose the task into two independent grasp proposals, relying on region priors or heuristics that limit generalization and provide no principled guarantee of stability. We propose DAGDiff, an end-to-end framework that directly denoises to grasp pairs in the SE(3) x SE(3) space. Our key insight is that stability and collision can be enforced more effectively by guiding the diffusion process with classifier signals, rather than relying on explicit region detection or object priors. To this end, DAGDiff integrates geometry-, stability-, and collision-aware guidance terms that steer the generative process toward grasps that are physically valid and force-closure compliant. We comprehensively evaluate DAGDiff through analytical force-closure checks, collision analysis, and large-scale physics-based simulations, showing consistent improvements over previous work on these metrics. Finally, we demonstrate that our framework generates dual-arm grasps directly on real-world point clouds of previously unseen objects, which are executed on a heterogeneous dual-arm setup where two manipulators reliably grasp and lift them.

Decentralized learning often involves a weighted global loss with heterogeneous node weights λ. We revisit two natural strategies for incorporating these weights: (i) embedding them into the local losses to retain a uniform weight (and thus a doubly stochastic matrix), and (ii) keeping the original losses while employing a λ-induced row-stochastic matrix. Although prior work shows that both strategies target the same λ-weighted global loss, it remains unclear whether the Euclidean-space guarantees are tight and what fundamentally differentiates their behaviors. To clarify this, we develop a weighted Hilbert-space framework L^2(λ;R^d) and obtain convergence rates that are strictly tighter than those from standard Euclidean analysis. In this geometry, the row-stochastic matrix becomes self-adjoint whereas the doubly stochastic one does not, creating additional penalty terms that amplify consensus error, thereby slowing convergence. Consequently, the difference in convergence arises not only from spectral gaps but also from these penalty terms. We then derive sufficient conditions under which the row-stochastic design converges faster even with a smaller spectral gap. Finally, by using a Rayleigh-quotient and Loewner-order eigenvalue comparison, we further obtain topology conditions that guarantee this advantage and yield practical topology-design guidelines.

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with O(n^2) cost. In this work, we replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at O(n) cost. We prove that the approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time relaxation to Maxwellian equilibrium where the blob method fails, and delivers 50% faster runtime with 4times lower peak memory.

Synthesizing realistic human-object interaction motions is a critical problem in VR/AR and human animation. Unlike the commonly studied scenarios involving a single human or hand interacting with one object, we address a more generic multi-body setting with arbitrary numbers of humans, hands, and objects. This complexity introduces significant challenges in synchronizing motions due to the high correlations and mutual influences among bodies. To address these challenges, we introduce SyncDiff, a novel method for multi-body interaction synthesis using a synchronized motion diffusion strategy. SyncDiff employs a single diffusion model to capture the joint distribution of multi-body motions. To enhance motion fidelity, we propose a frequency-domain motion decomposition scheme. Additionally, we introduce a new set of alignment scores to emphasize the synchronization of different body motions. SyncDiff jointly optimizes both data sample likelihood and alignment likelihood through an explicit synchronization strategy. Extensive experiments across four datasets with various multi-body configurations demonstrate the superiority of SyncDiff over existing state-of-the-art motion synthesis methods.

Sampling-based motion planning algorithms, like the Rapidly-Exploring Random Tree (RRT) and its widely used variant, RRT-Connect, provide efficient solutions for high-dimensional planning problems faced by real-world robots. However, these methods remain computationally intensive, particularly in complex environments that require many collision checks. To improve performance, recent efforts have explored parallelizing specific components of RRT such as collision checking, or running multiple planners independently. However, little has been done to develop an integrated parallelism approach, co-designed for large-scale parallelism. In this work we present pRRTC, a RRT-Connect based planner co-designed for GPU acceleration across the entire algorithm through parallel expansion and SIMT-optimized collision checking. We evaluate the effectiveness of pRRTC on the MotionBenchMaker dataset using robots with 7, 8, and 14 degrees of freedom (DoF). Compared to the state-of-the-art, pRRTC achieves as much as a 10x speedup on constrained reaching tasks with a 5.4x reduction in standard deviation. pRRTC also achieves a 1.4x reduction in average initial path cost. Finally, we deploy pRRTC on a 14-DoF dual Franka Panda arm setup and demonstrate real-time, collision-free motion planning with dynamic obstacles. We open-source our planner to support the wider community.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning and control literature, including Nash equilibrium seeking, composite minimization, Markov decision processes, and zero-sum games, and compare them to that of existing methods.

Scalable driving simulators typically execute vehicle commands using prescribed behavioral or kinematic rules, overlooking the physics of tire-road interfaces, thereby limiting their ability to capture how adverse road and environmental conditions alter vehicle execution and propagate through traffic. To address this limitation, we present SceneFactory-3D, a GPU-batched, physics-grounded multi-agent driving simulator. Vehicles execute acceleration and steering commands via suspension- and friction-limited forces evaluated at each wheel-contact point. Spatially varying friction, per-world 3D heightfields, gravity, and rigid contact consistently govern wheel motion and chassis collisions. Per-world terrain isolation and GPU batching enable SceneFactory-3D to run matched physical counterfactuals in parallel: traffic scenario setup and vehicle controllers remain fixed while only the road condition changes, enabling the resulting closed-loop effects to be evaluated across parallel worlds. To demonstrate the advantage of the SceneFactory-3D-enabled counterfactual evaluation, we conduct an empirical study on vehicle controllers' sensitivity to road conditions. We study three learned-policy families on 1,024 matched 12-vehicle worlds per condition, and two classical planners on a shared 32-world subset, across 21 friction and grade conditions. When friction drops from 1.0 to 0.18, the share of vehicles that clear the work zone safely falls by 6 to 90 percentage points across learned policies (18-19 for classical planners), and near-collision situations become more frequent for every learned policy. Code: https://github.com/SmallWorldLab/SceneFactory_3D

Spacecraft collision avoidance procedures have become an essential part of satellite operations. Complex and constantly updated estimates of the collision risk between orbiting objects inform the various operators who can then plan risk mitigation measures. Such measures could be aided by the development of suitable machine learning models predicting, for example, the evolution of the collision risk in time. In an attempt to study this opportunity, the European Space Agency released, in October 2019, a large curated dataset containing information about close approach events, in the form of Conjunction Data Messages (CDMs), collected from 2015 to 2019. This dataset was used in the Spacecraft Collision Avoidance Challenge, a machine learning competition where participants had to build models to predict the final collision risk between orbiting objects. This paper describes the design and results of the competition and discusses the challenges and lessons learned when applying machine learning methods to this problem domain.

Realistic and diverse multi-agent driving scenes are crucial for evaluating autonomous vehicles, but safety-critical events which are essential for this task are rare and underrepresented in driving datasets. Data-driven scene generation offers a low-cost alternative by synthesizing complex traffic behaviors from existing driving logs. However, existing models often lack controllability or yield samples that violate physical or social constraints, limiting their usability. We present OMEGA, an optimization-guided, training-free framework that enforces structural consistency and interaction awareness during diffusion-based sampling from a scene generation model. OMEGA re-anchors each reverse diffusion step via constrained optimization, steering the generation towards physically plausible and behaviorally coherent trajectories. Building on this framework, we formulate ego-attacker interactions as a game-theoretic optimization in the distribution space, approximating Nash equilibria to generate realistic, safety-critical adversarial scenarios. Experiments on nuPlan and Waymo show that OMEGA improves generation realism, consistency, and controllability, increasing the ratio of physically and behaviorally valid scenes from 32.35% to 72.27% for free exploration capabilities, and from 11% to 80% for controllability-focused generation. Our approach can also generate 5times more near-collision frames with a time-to-collision under three seconds while maintaining the overall scene realism.

The increasing population of objects in geostationary orbit has raised concerns about the potential risks posed by debris clouds resulting from fragmentation. The short-term evolution and associated hazards of debris generated by collisions in the geostationary region is investigated in this study. The initial distribution of two debris clouds is modeled using a single probability density function.The combined distribution of the evolved clouds is determined by solving boundary value problems.The risks associated with these debris clouds are evaluated by calculating the instantaneous impact rate and cumulative collision probability.The probability of collisions with millimeter-sized fragments may increase to 1% within 36 hours, while the probability of collisions with fragments 5 cm or larger is approximately 10^{-5}.These findings underscore the vulnerability of the geostationary region to space traffic accidents.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo models hard contact and friction with a nonlinear complementarity problem with second-order cone constraints. We introduce a custom primal-dual interior-point method to solve the second order cone program for stable forward simulation over a broad range of sample rates. We obtain smooth gradient approximations with this solver through the implicit function theorem, giving gradients that are useful for downstream trajectory optimization, policy optimization, and system identification applications. Specifically, we propose to use the central path parameter threshold in the interior point solver as a user-tunable design parameter. A high value gives a smooth approximation to contact dynamics with smooth gradients for optimization and learning, while a low value gives precise simulation rollouts with hard contact. We demonstrate Dojo's differentiability in trajectory optimization, policy learning, and system identification examples. We also benchmark Dojo against MuJoCo, PyBullet, Drake, and Brax on a variety of robot models, and study the stability and simulation quality over a range of sample frequencies and accuracy tolerances. Finally, we evaluate the sim-to-real gap in hardware experiments with a Ufactory xArm 6 robot. Dojo is an open source project implemented in Julia with Python bindings, with code available at https://github.com/dojo-sim/Dojo.jl.

Expert demonstrations show how to complete contact-rich tasks, but provide limited coverage of how interaction forces respond to different actions. Task-agnostic play provides broader experience of contact dynamics without specifying task goals. To fully leverage these two types of data, we introduce ForceWAM, a force world action model that decouples knowledge of task-compatible interaction outcomes from knowledge of how local actions change contact. A world model learns from successful demonstrations to jointly predict future video and six-axis force/torque trajectories. Together, these futures describe the expected evolution of motion and contact during the task. A separate inverse dynamics model (IDM) learns from both task and play, mapping current observations and recorded visual-wrench futures to their associated robot actions. Play data thus provide knowledge of force responses for goal-directed execution. At deployment, the IDM reactively translates generated futures into actions, reusing them with fresh wrench feedback between world-model updates. Across real-robot force-regulated sliding, box flipping with and without disturbances, and ring placement, ForceWAM achieves 85-95% mean success, surpassing world-modeling and reactive baselines. Our experiments further show that adding task-agnostic play data improves success by 15-45 percentage points, demonstrating its value for learning contact-rich execution. Project page and code are available at https://force-wam.github.io/.

Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under the standard anisotropic gradient noise condition for quadratic regression problems. Although it is widely conjectured that heavy-ball momentum method can provide accelerated convergence and should work well in large batch settings, there is no rigorous theoretical analysis. In this paper, we fill this theoretical gap by establishing a non-asymptotic convergence bound for stochastic heavy-ball methods with step decay scheduler on quadratic objectives, under the anisotropic gradient noise condition. As a direct implication, we show that heavy-ball momentum can provide mathcal{O}(kappa) accelerated convergence of the bias term of SGD while still achieving near-optimal convergence rate with respect to the stochastic variance term. The combined effect implies an overall convergence rate within log factors from the statistical minimax rate. This means SGD with heavy-ball momentum is useful in the large-batch settings such as distributed machine learning or federated learning, where a smaller number of iterations can significantly reduce the number of communication rounds, leading to acceleration in practice.

When researchers ask whether two transformer layers are "equivalent" for compression, they often conflate distinct tests. Replacement asks whether one layer's map can substitute for another's in place; interchange asks whether two layers approximately commute when their positions are swapped. Both are output-grounded swap-KL probes, but they need not agree: on pretrained transformers the protocol gap can change which layers look safe to prune by several-fold under the same evaluator, especially when replacement distances are high. We measure both protocols across checkpoints and architectures. On a Pythia training trajectory (410M and 1.4B), the replacement-interchange gap grows from initialization to convergence. Under one matched WikiText-2 contract at 8B scale, Qwen3-8B enters a divergent regime: interchange-guided removal is several-fold safer than replacement-guided at the same layer budgets, while Llama-3.1-8B ties the two protocols for pruning cost even though interchange KL is lower, showing metric gaps need not map one-to-one to removal. Before layer removal or merging, score both swap-KLs on the target checkpoint; the diagnostic requires only unlabeled forward passes.

Alternating projections (AP) near a clean intersection of smooth manifolds can converge slowly when the Friedrichs angle is small. We develop the Fixed-Point Manifold Acceleration (FPMA) framework for {local convergence and polynomial acceleration of} smooth maps that fix a manifold pointwise. {Under suitable regularity and uniform normal spectral stability, FPMA establishes local R-linear convergence and a smooth limiting map inducing a local retraction. At fixed points, consistent polynomial acceleration with p(1)=1 preserves the selected limit's first-order response to normal initial perturbations whenever the transformed normal blocks are uniformly spectrally stable. Under sufficient smoothness, we give a curvature criterion for second-order induced retractions and show that stable consistent polynomial acceleration preserves both the quadratic retraction expansion and this criterion. {As a special case, we establish new local R-linear convergence guarantees for fixed-degree Chebyshev-accelerated exact AP and second-order induced retractions. For uniform Friedrichs angle θ_Fin(0,π/2), acceleration strictly improves the local convergence rate per AP evaluation. The large-degree limiting spectral factor at fixed θ_F predicts O(θ_F^{-1}) evaluations for fixed relative error reduction as θ_Fdownarrow0, versus O(θ_F^{-2}) for ordinary AP.}} {The framework also covers} inexact, relaxed, and generalized AP {under their respective regularity and stability conditions.}

Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliable only inside the Taylor convergence radius of the true loss along the update direction. That radius is set not by real-line curvature alone but by the nearest complex singularity. For cross-entropy, the softmax partition function F=sum_j exp(z_j) has complex zeros -- ``ghosts of softmax'' -- that induce logarithmic singularities in the loss and cap this radius. To make this geometry usable, we derive closed-form expressions under logit linearization along the proposed update direction. In the binary case, the exact radius is ρ^*=δ^2+ π^2/Δ_a. In the multiclass case, we obtain the lower bound ρ_a=π/Δ_a, where Δ_a=max_k a_k-min_k a_k is the spread of directional logit derivatives a_k=nabla z_kcdot v. This bound costs one Jacobian-vector product and reveals what makes a step fragile: samples that are both near a decision flip and highly sensitive to the proposed direction tighten the radius. The normalized step size r=τ/ρ_a separates safe from dangerous updates. Across six tested architectures and multiple step directions, no model fails for r<1, yet collapse appears once rge 1. Temperature scaling confirms the mechanism: normalizing by ρ_a shrinks the onset-threshold spread from standard deviation 0.992 to 0.164. A controller that enforces τleρ_a survives learning-rate spikes up to 10{,} 000times in our tests, where gradient clipping still collapses. Together, these results identify a geometric constraint on cross-entropy optimization that operates through Taylor convergence rather than Hessian curvature.

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

Non-cooperative game theory provides a robust framework for analyzing distributed resource allocation in multi-user wireless networks, with Iterative Water-Filling (IWF) emerging as a canonical solution for power control problems. Although classical fixed-point theorems guarantee the existence of a Nash Equilibrium (NE) under mild concavity and compactness conditions, the convergence of practical iterative algorithms to that equilibrium remains a challenging endeavor. This challenge intensifies under varying update schedules, interference regimes, and imperfections such as channel estimation errors or feedback delay. In this paper, we present an in-depth examination of IWF in multi-user systems under three different update schemes: (1) synchronous sequential updates, (2) synchronous simultaneous updates, and (3) totally asynchronous updates. We first formulate the water-filling operator in a multi-carrier environment, then recast the iterative process as a fixed-point problem. Using contraction mapping principles, we demonstrate sufficient conditions under which IWF converges to a unique NE and highlight how spectral radius constraints, diagonal dominance, and careful step-size selection are pivotal for guaranteeing convergence. We further discuss robustness to measurement noise, partial updates, and network scaling to emphasize the practical viability of these schemes. This comprehensive analysis unifies diverse threads in the literature while offering novel insights into asynchronous implementations. Our findings enable network designers to ascertain system parameters that foster both stable convergence and efficient spectrum usage.

Safety-aligned LLMs can exhibit emergent misalignment (EM): narrow domain adaptation unexpectedly triggers catastrophic safety failures across unrelated domains. Prior static analyses leave training dynamics unmapped, while existing defenses rely on heuristics that degrade utility. We present a dynamic, second-order geometric study of EM. Tracking training trajectories reveals that directional Hessian curvature concentrates sharply on semantic pivot tokens. Grassmannian projections show that, in most settings, harmful-safe gap widens mainly because safe-gradient overlap declines. Leveraging these insights, we introduce a parameter-level Geometric Mitigation Framework that orthogonally projects empirical harmful gradient subspace out of parameter updates. On Qwen2.5-14B-IT, our defense suppresses free-generation EM by up to 80.0%; across the other three of four open-weight instruction-based model families (3B--20B), where single-layer behavioral EM is already near zero, teacher-forced evaluation shows same harmful subspace controls the conditional support of frozen EM responses. Crucially, these diagnostics unmask the illusion of behavioral safety: the same subspace remains measurable and steerable in models where behavioral EM is near zero. Code: https://github.com/WeiqiaoQUE/mechanistic-emergent-misalignment.

In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data u_0in B^{s}_{p,r} and for some T>0, the solutions of the Navier--Stokes equations converge strongly in L^infty_TB^{s}_{p,r} to the Euler equations as the viscosity parameter tends to zero. We furthermore prove the failure of the uniform (with respect to the initial data) B^{s}_{p,r} convergence in the inviscid limit of a family of solutions of the Navier-Stokes equations towards a solution of the Euler equations.

Sampling-based motion planners (SBMPs) are effective for planning with complex kinodynamic constraints in high-dimensional spaces, but they still struggle to achieve real-time performance, which is mainly due to their serial computation design. We present Kinodynamic Parallel Accelerated eXpansion (Kino-PAX), a novel highly parallel kinodynamic SBMP designed for parallel devices such as GPUs. Kino-PAX grows a tree of trajectory segments directly in parallel. Our key insight is how to decompose the iterative tree growth process into three massively parallel subroutines. Kino-PAX is designed to align with the parallel device execution hierarchies, through ensuring that threads are largely independent, share equal workloads, and take advantage of low-latency resources while minimizing high-latency data transfers and process synchronization. This design results in a very efficient GPU implementation. We prove that Kino-PAX is probabilistically complete and analyze its scalability with compute hardware improvements. Empirical evaluations demonstrate solutions in the order of 10 ms on a desktop GPU and in the order of 100 ms on an embedded GPU, representing up to 1000 times improvement compared to coarse-grained CPU parallelization of state-of-the-art sequential algorithms over a range of complex environments and systems.

We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cyclically among prescribed velocity fields V_1,dots,V_p with random run times and evolves according to either a flight dynamics, consisting of piecewise-linear motion, or a gliding dynamics, in which the particle follows the corresponding velocity flow. Under a Kac-type scaling that couples vanishing run times with diverging particle speed, we prove weak convergence of both processes to multidimensional diffusions. It turns out that the order of successive cyclic motions affects the diffusion limit. In addition to the second-order term generated by fluctuations of the random run times, the limiting drift contains directional derivatives DV_i[V_j] of the underlying vector fields. In Stratonovich form, part of this drift is expressed through their Lie brackets [V_i,V_j]. Thus, the generic non-commutativity of the microscopic motions survives the diffusive scaling and generates a macroscopic drift which depends on the cyclic order. The limiting drift also distinguishes the flight and gliding dynamics, despite their being driven by the same vector fields and run times. Several examples, including run-and-reverse motion and cyclic dynamics generated by multiple vector fields, illustrate how the cyclic switching protocol and the geometry of the underlying velocity fields shape the limiting diffusions.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Recent advancements in human motion synthesis have focused on specific types of motions, such as human-scene interaction, locomotion or human-human interaction, however, there is a lack of a unified system capable of generating a diverse combination of motion types. In response, we introduce Sitcom-Crafter, a comprehensive and extendable system for human motion generation in 3D space, which can be guided by extensive plot contexts to enhance workflow efficiency for anime and game designers. The system is comprised of eight modules, three of which are dedicated to motion generation, while the remaining five are augmentation modules that ensure consistent fusion of motion sequences and system functionality. Central to the generation modules is our novel 3D scene-aware human-human interaction module, which addresses collision issues by synthesizing implicit 3D Signed Distance Function (SDF) points around motion spaces, thereby minimizing human-scene collisions without additional data collection costs. Complementing this, our locomotion and human-scene interaction modules leverage existing methods to enrich the system's motion generation capabilities. Augmentation modules encompass plot comprehension for command generation, motion synchronization for seamless integration of different motion types, hand pose retrieval to enhance motion realism, motion collision revision to prevent human collisions, and 3D retargeting to ensure visual fidelity. Experimental evaluations validate the system's ability to generate high-quality, diverse, and physically realistic motions, underscoring its potential for advancing creative workflows. Project page: https://windvchen.github.io/Sitcom-Crafter.

Structural survival of offshore structures is crucial for the growing marine economy. Calculating the added mass, radiation damping, and excitation coefficients to quantify wave loads with the traditional boundary element method (BEM) presents a computational bottleneck. The matched eigenfunction expansion method (MEEM), a long-known but rarely-used alternative, offers computational benefits due to its semi-analytical nature. However, previous work fails to directly compare its accuracy and computational performance with BEM, leaving the extent of its utility unknown. Furthermore, the geometry-dependent convergence for cylindrical and slanted geometries has not yet been documented, making the method's practicality for general geometries unclear. This paper presents a unifying MEEM framework for modeling an arbitrary number of fixed or heaving surface-piercing annular cylinders with continuous and radially-monotonic body profiles, and explores the method's block matrix structure, convergence behavior, ability to accurately approximate slanted geometries, and computational advantages over the BEM solver Capytaine. The numerical experiments show that MEEM can compute hydrodynamic coefficients of slanted geometries within 5% of Capytaine, even for angles as steep as 15 degrees from vertical. Finally, MEEM can achieve 2% convergence of its hydrodynamic coefficients an order of magnitude faster than Capytaine with a matrix size two orders of magnitude smaller, making it a computationally effective alternative to traditional BEM solvers. These contributions enable hydrodynamic analysis of a broad range of shapes with increased speed and confidence, paving the way for future optimization studies to yield improved designs.

End-to-end (E2E) autonomous driving presents a promising approach for translating perceptual inputs directly into driving actions. However, prohibitive annotation costs and temporal data quality degradation hinder long-term real-world deployment. While combining imitation learning (IL) and reinforcement learning (RL) is a common strategy for policy improvement, conventional RL training relies on delayed, event-based rewards-policies learn only from catastrophic outcomes such as collisions, leading to premature convergence to suboptimal behaviors. To address these limitations, we introduce GSDrive, a framework that exploits 3D Gaussian Splatting (3DGS) for differentiable, physics-based reward shaping in E2E driving policy improvement. Our method incorporates a flow matching-based trajectory predictor within the 3DGS simulator, enabling multi-mode trajectory probing where candidate trajectories are rolled out to assess prospective rewards. This establishes a bidirectional knowledge exchange between IL and RL by grounding reward functions in physically simulated interaction signals, offering immediate dense feedback instead of sparse catastrophic events. Evaluated on the reconstructed nuScenes dataset, our method surpasses existing simulation-based RL driving approaches in closed-loop experiments. Code is available at https://github.com/ZionGo6/GSDrive.

In order for agents in multi-agent systems (MAS) to be safe, they need to take into account the risks posed by the actions of other agents. However, the dominant paradigm in game theory (GT) assumes that agents are not affected by risk from other agents and only strive to maximise their expected utility. For example, in hybrid human-AI driving systems, it is necessary to limit large deviations in reward resulting from car crashes. Although there are equilibrium concepts in game theory that take into account risk aversion, they either assume that agents are risk-neutral with respect to the uncertainty caused by the actions of other agents, or they are not guaranteed to exist. We introduce a new GT-based Risk-Averse Equilibrium (RAE) that always produces a solution that minimises the potential variance in reward accounting for the strategy of other agents. Theoretically and empirically, we show RAE shares many properties with a Nash Equilibrium (NE), establishing convergence properties and generalising to risk-dominant NE in certain cases. To tackle large-scale problems, we extend RAE to the PSRO multi-agent reinforcement learning (MARL) framework. We empirically demonstrate the minimum reward variance benefits of RAE in matrix games with high-risk outcomes. Results on MARL experiments show RAE generalises to risk-dominant NE in a trust dilemma game and that it reduces instances of crashing by 7x in an autonomous driving setting versus the best performing baseline.

The fundamental success of large language models hinges upon the efficacious implementation of large-scale distributed training techniques. Nevertheless, building a vast, high-performance cluster featuring high-speed communication interconnectivity is prohibitively costly, and accessible only to prominent entities. In this work, we aim to lower this barrier and democratize large-scale training with limited bandwidth clusters. We propose a new approach called CO2 that introduces local-updating and asynchronous communication to the distributed data-parallel training, thereby facilitating the full overlap of COmunication with COmputation. CO2 is able to attain a high scalability even on extensive multi-node clusters constrained by very limited communication bandwidth. We further propose the staleness gap penalty and outer momentum clipping techniques together with CO2 to bolster its convergence and training stability. Besides, CO2 exhibits seamless integration with well-established ZeRO-series optimizers which mitigate memory consumption of model states with large model training. We also provide a mathematical proof of convergence, accompanied by the establishment of a stringent upper bound. Furthermore, we validate our findings through an extensive set of practical experiments encompassing a wide range of tasks in the fields of computer vision and natural language processing. These experiments serve to demonstrate the capabilities of CO2 in terms of convergence, generalization, and scalability when deployed across configurations comprising up to 128 A100 GPUs. The outcomes emphasize the outstanding capacity of CO2 to hugely improve scalability, no matter on clusters with 800Gbps RDMA or 80Gbps TCP/IP inter-node connections.

Self-play (SP) is a popular multi-agent reinforcement learning (MARL) framework for solving competitive games, where each agent optimizes policy by treating others as part of the environment. Despite the empirical successes, the theoretical properties of SP-based methods are limited to two-player zero-sum games. However, for mixed cooperative-competitive games where agents on the same team need to cooperate with each other, we can show a simple counter-example where SP-based methods cannot converge to a global Nash equilibrium (NE) with high probability. Alternatively, Policy-Space Response Oracles (PSRO) is an iterative framework for learning NE, where the best responses w.r.t. previous policies are learned in each iteration. PSRO can be directly extended to mixed cooperative-competitive settings by jointly learning team best responses with all convergence properties unchanged. However, PSRO requires repeatedly training joint policies from scratch till convergence, which makes it hard to scale to complex games. In this work, we develop a novel algorithm, Fictitious Cross-Play (FXP), which inherits the benefits from both frameworks. FXP simultaneously trains an SP-based main policy and a counter population of best response policies. The main policy is trained by fictitious self-play and cross-play against the counter population, while the counter policies are trained as the best responses to the main policy's past versions. We validate our method in matrix games and show that FXP converges to global NEs while SP methods fail. We also conduct experiments in a gridworld domain, where FXP achieves higher Elo ratings and lower exploitabilities than baselines, and a more challenging football game, where FXP defeats SOTA models with over 94% win rate.

The entropic fictitious play (EFP) is a recently proposed algorithm that minimizes the sum of a convex functional and entropy in the space of measures -- such an objective naturally arises in the optimization of a two-layer neural network in the mean-field regime. In this work, we provide a concise primal-dual analysis of EFP in the setting where the learning problem exhibits a finite-sum structure. We establish quantitative global convergence guarantees for both the continuous-time and discrete-time dynamics based on properties of a proximal Gibbs measure introduced in Nitanda et al. (2022). Furthermore, our primal-dual framework entails a memory-efficient particle-based implementation of the EFP update, and also suggests a connection to gradient boosting methods. We illustrate the efficiency of our novel implementation in experiments including neural network optimization and image synthesis.

Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley-Terry model, which may not accurately capture the complexities of real human preferences (e.g., intransitivity). Nash Learning from Human Feedback (NLHF) offers a more direct alternative by framing the problem as finding a Nash equilibrium of a game defined by these preferences. In this work, we introduce Nash Mirror Prox (Nash-MP), an online NLHF algorithm that leverages the Mirror Prox optimization scheme to achieve fast and stable convergence to the Nash equilibrium. Our theoretical analysis establishes that Nash-MP exhibits last-iterate linear convergence towards the beta-regularized Nash equilibrium. Specifically, we prove that the KL-divergence to the optimal policy decreases at a rate of order (1+2beta)^{-N/2}, where N is a number of preference queries. We further demonstrate last-iterate linear convergence for the exploitability gap and uniformly for the span semi-norm of log-probabilities, with all these rates being independent of the size of the action space. Furthermore, we propose and analyze an approximate version of Nash-MP where proximal steps are estimated using stochastic policy gradients, making the algorithm closer to applications. Finally, we detail a practical implementation strategy for fine-tuning large language models and present experiments that demonstrate its competitive performance and compatibility with existing methods.

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

In an effort to better understand the different ways in which the discount factor affects the optimization process in reinforcement learning, we designed a set of experiments to study each effect in isolation. Our analysis reveals that the common perception that poor performance of low discount factors is caused by (too) small action-gaps requires revision. We propose an alternative hypothesis that identifies the size-difference of the action-gap across the state-space as the primary cause. We then introduce a new method that enables more homogeneous action-gaps by mapping value estimates to a logarithmic space. We prove convergence for this method under standard assumptions and demonstrate empirically that it indeed enables lower discount factors for approximate reinforcement-learning methods. This in turn allows tackling a class of reinforcement-learning problems that are challenging to solve with traditional methods.

Reinforcement Learning from Human Feedback (RLHF) has been highly successful in aligning large language models with human preferences. While prevalent methods like DPO have demonstrated strong performance, they frame interactions with the language model as a bandit problem, which limits their applicability in real-world scenarios where multi-turn conversations are common. Additionally, DPO relies on the Bradley-Terry model assumption, which does not adequately capture the non-transitive nature of human preferences. In this paper, we address these challenges by modeling the alignment problem as a two-player constant-sum Markov game, where each player seeks to maximize their winning rate against the other across all steps of the conversation. Our approach Optimistic Multi-step Preference Optimization (OMPO) is built upon the optimistic online mirror descent algorithm~rakhlin2013online,joulani17a. Theoretically, we provide a rigorous analysis for the convergence of OMPO and show that OMPO requires O(ε^{-1}) policy updates to converge to an ε-approximate Nash equilibrium. We also validate the effectiveness of our method on multi-turn conversations dataset and math reasoning dataset.

Collaborative perception, fusing information from multiple agents, can extend perception range so as to improve perception performance. However, temporal asynchrony in real-world environments, caused by communication delays, clock misalignment, or sampling configuration differences, can lead to information mismatches. If this is not well handled, then the collaborative performance is patchy, and what's worse safety accidents may occur. To tackle this challenge, we propose CoDynTrust, an uncertainty-encoded asynchronous fusion perception framework that is robust to the information mismatches caused by temporal asynchrony. CoDynTrust generates dynamic feature trust modulus (DFTM) for each region of interest by modeling aleatoric and epistemic uncertainty as well as selectively suppressing or retaining single-vehicle features, thereby mitigating information mismatches. We then design a multi-scale fusion module to handle multi-scale feature maps processed by DFTM. Compared to existing works that also consider asynchronous collaborative perception, CoDynTrust combats various low-quality information in temporally asynchronous scenarios and allows uncertainty to be propagated to downstream tasks such as planning and control. Experimental results demonstrate that CoDynTrust significantly reduces performance degradation caused by temporal asynchrony across multiple datasets, achieving state-of-the-art detection performance even with temporal asynchrony. The code is available at https://github.com/CrazyShout/CoDynTrust.

Finding high-quality solutions quickly is an important objective in motion planning. This is especially true for high-degree-of-freedom robots. Satisficing planners have traditionally found feasible solutions quickly but provide no guarantees on their optimality, while almost-surely asymptotically optimal (a.s.a.o.) planners have probabilistic guarantees on their convergence towards an optimal solution but are more computationally expensive. This paper uses the AO-x meta-algorithm to extend the satisficing RRT-Connect planner to optimal planning. The resulting Asymptotically Optimal RRT-Connect (AORRTC) finds initial solutions in similar times as RRT-Connect and uses any additional planning time to converge towards the optimal solution in an anytime manner. It is proven to be probabilistically complete and a.s.a.o. AORRTC was tested with the Panda (7 DoF) and Fetch (8 DoF) robotic arms on the MotionBenchMaker dataset. These experiments show that AORRTC finds initial solutions as fast as RRT-Connect and faster than the tested state-of-the-art a.s.a.o. algorithms while converging to better solutions faster. AORRTC finds solutions to difficult high-DoF planning problems in milliseconds where the other a.s.a.o. planners could not consistently find solutions in seconds. This performance was demonstrated both with and without single instruction/multiple data (SIMD) acceleration.

In this paper we consider a particular class of solutions of the Rayleigh-Boltzmann equation, known in the nonlinear setting as homoenergetic solutions, which have the form gleft( x,v,t right) =fleft( v-Lleft( tright)x,tright) where the matrix L(t) describes a shear flow deformation. We began this analysis in [22] where we rigorously proved the existence of a stationary non-equilibrium solution and established the different behaviour of the solutions for small and large values of the shear parameter, for cut-off collision kernels with homogeneity parameter 0leq gamma <1, including Maxwell molecules and hard potentials. In this paper, we concentrate in the case where the deformation term dominates the collision term for large times (hyperbolic-dominated regime). This occurs for collision kernels with gamma < 0 and in particular we focus on gamma in (-1,0). In such a hyperbolic-dominated regime, it appears challenging to provide a clear description of the long-term asymptotics of the solutions. Here we present a formal analysis of the long-time asymptotics for the distribution of velocities and provide the explicit form for the asymptotic profile. Additionally, we discuss the different asymptotic behaviour expected in the case of homogeneity gamma < -1. Furthermore, we provide a probabilistic interpretation describing a stochastic process consisting in a combination of collisions and shear flows. The tagged particle velocity {v(t)}_{tgeq 0} is a Markov process that arises from the combination of free flights in a shear flow along with random jumps caused by collisions.

We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update their strategies (actors) using feedback from two distinct critics: a fast critic that intuitively responds to observed payoffs under limited information, and a slow critic that deliberatively approximates the solution to the underlying dynamic programming problem. Crucially, the learning process relies on non-equilibrium adaptation through smoothed best responses to observed payoffs. We establish convergence to (approximate) equilibria in two-agent zero-sum and multi-agent identical-interest stochastic games over an infinite horizon. This provides one of the first payoff-based and fully decentralized learning algorithms with theoretical guarantees in both settings. Empirical results further validate the robustness and effectiveness of the proposed approach across both classes of games.

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed.

Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient descent with a finite number of particles and establishes its theoretical guarantees to optimize functions that are displacement convex in measures. Concretely, for Lipschitz displacement convex functions defined on probability over R^d, we prove that O(1/epsilon^2) particles and O(d/epsilon^4) computations are sufficient to find the epsilon-optimal solutions. We further provide improved complexity bounds for optimizing smooth displacement convex functions. We demonstrate the application of our results for function approximation with specific neural architectures with two-dimensional inputs.

Asynchronous reinforcement learning improves throughput by decoupling rollout generation from optimization, but staleness is an inevitable byproduct compounded by policy lag, engine delays, and mixture-of-experts routing. From a trust-region perspective, this mismatch is critical: training-inference divergence governs approximation error in finite-horizon bounds, whereas PPO clipping only gates sampled outward updates, acting as a sampled surrogate rather than a full-policy constraint. As a result, high-staleness updates remain weakly controlled in the asynchronous regime where stale rollouts matter most. We introduce the Staleness-Adaptive Trust Region (SAT), which uses the detached sampled log-ratio as a practical staleness proxy, identifies high-mismatch tails within each batch via staleness-based kernel scaling, and contracts only the sign-selected endpoint of the nominal PPO interval. This preserves baseline behavior on ordinary tokens while enforcing more conservative updates on newly intercepted outward bands. We prove local interval containment and pointwise pessimism relative to PPO, showing how the adaptive rule reshapes update geometry under heterogeneous staleness. We evaluate SAT in a decoupled asynchronous RL setup built on Qwen3-30B-A3B-Base, using SGLang as the inference engine and Megatron for training. In this setting, SAT-GSPO w/ R3 achieves the best observed AIME24 avg@8, reaching 35.83 at lag 1 and 34.79 at lag 8, while SAT-GSPO reaches 34.17 at lag 1. Adaptive clipping and routing replay act as complementary stabilizers targeting mismatch tails and routing inconsistency, respectively. Overall, aligning clip intervals with staleness heterogeneity effectively stabilizes asynchronous RL.

Deep reinforcement policy learning directly in physical robots (on-robot learning) remains bottlenecked by slow wall-clock training times. We present SymmGrid, a trajectory level augmentation framework inspired by parallelized symmetries that super-scales group transformations to significantly accelerate on-robot learning in both egocentric and exocentric visual setups. We model a Markov Decision Process (MDP) under a symmetry tree, in which state-action pairs have admissible parallelized invariant transformations that yield a geometric grid structure. The state is modelled with ego- or exocentric images and proprioception information. The latter require special treatment, in the form of homographies, to warp visual scenes in line with their corresponding spatial transformations. These parallelized transformations produce a large set of unique symmetric equivalences that populate the replay buffer with diverse and consistent experiences that speed up learning and improve performance. We present extensive training and evaluations performed directly on real robot manipulation contact tasks including peg-insertions, cable routing, and object relocations. Relative to SOTA, SymmGrid achieved wall-clock training convergence speed-ups of 1.37-2.17x, evaluation success rate improvements of 1.09x-1.27x, fastest training convergence times of 16.6, 10.9, and 79.3 minutes respectively. For trajectory wide assessments, we used normalized area under the curve (nAUC) ratios. SymmGrid achieved improvements of up to 2.59x. These results confirm that simple branch symmetries can have an outsized result due to super-scaling and bring us closer to sub-10 minute on-robot learning training in manipulation tasks suitable for arms and humanoids. The project page is available at symmgrid-robot.github.io

Quadruped robots are increasingly expected to navigate through narrow passages, cluttered indoor scenes, and large-scale 3D unstructured environments. Existing local planners commonly approximate the robot using isotropic geometric inflation or rely on planar and elevation-map representations, leading to conservative motion in tight spaces and limited reasoning about overhanging structures. This letter presents SCAN-Planner, a spatial collision-aware local planning framework for long-range quadruped navigation. A yaw-aware twin-cylinder footprint is used to model the elongated robot body, enabling whole-body collision evaluation through sparse queries in an inflated 3D occupancy map. We further introduce a projected A* search that generates collision-free guidance on an interpolated ground-following surface, with z-gradient suppression to avoid obstacles horizontally while maintaining vertical stability. For large-scale deployment, a robot-centric sliding map with boundary fallback provides high-resolution local collision checking and recovery from local dead ends. Simulation and real-world experiments demonstrate that SCAN-Planner generates safe, smooth, and efficient trajectories in dense clutter, 3D unstructured scenes, stair traversal, and long-range navigation tasks.

We propose a delay-agnostic asynchronous coordinate update algorithm (DEGAS) for computing operator fixed points, with applications to asynchronous optimization. DEGAS includes novel asynchronous variants of ADMM and block-coordinate descent as special cases. We prove that DEGAS converges under both bounded and unbounded delays under delay-free parameter conditions. We also validate by theory and experiments that DEGAS adapts well to the actual delays. The effectiveness of DEGAS is demonstrated by numerical experiments on classification problems.

Ensuring safety and driving consistency is a significant challenge for autonomous vehicles operating in partially observed environments. This work introduces a consistent parallel trajectory optimization (CPTO) approach to enable safe and consistent driving in dense obstacle environments with perception uncertainties. Utilizing discrete-time barrier function theory, we develop a consensus safety barrier module that ensures reliable safety coverage within the spatiotemporal trajectory space across potential obstacle configurations. Following this, a bi-convex parallel trajectory optimization problem is derived that facilitates decomposition into a series of low-dimensional quadratic programming problems to accelerate computation. By leveraging the consensus alternating direction method of multipliers (ADMM) for parallel optimization, each generated candidate trajectory corresponds to a possible environment configuration while sharing a common consensus trajectory segment. This ensures driving safety and consistency when executing the consensus trajectory segment for the ego vehicle in real time. We validate our CPTO framework through extensive comparisons with state-of-the-art baselines across multiple driving tasks in partially observable environments. Our results demonstrate improved safety and consistency using both synthetic and real-world traffic datasets.

Shared autonomy blends operator intent with autonomous assistance. In cluttered environments, linear blending can produce unsafe commands even when each source is individually collision-free. Many existing approaches model obstacle avoidance through potentials or cost terms, which only enforce safety as a soft constraint. In contrast, safety-critical control requires hard guarantees. We investigate the use of control barrier functions (CBFs) at the inverse kinematics (IK) layer of shared autonomy, targeting post-blend safety while preserving task performance. Our approach is evaluated in simulation on representative cluttered environments and in a VR teleoperation study comparing pure teleoperation with shared autonomy. Across conditions, employing CBFs at the IK layer reduces violation time and increases minimum clearance while maintaining task performance. In the user study, participants reported higher perceived safety and trust, lower interference, and an overall preference for shared autonomy with our safety filter. Additional materials available at https://berkguler.github.io/barrierik.

In many real-world multi-agent cooperative tasks, due to high cost and risk, agents cannot continuously interact with the environment and collect experiences during learning, but have to learn from offline datasets. However, the transition dynamics in the dataset of each agent can be much different from the ones induced by the learned policies of other agents in execution, creating large errors in value estimates. Consequently, agents learn uncoordinated low-performing policies. In this paper, we propose a framework for offline decentralized multi-agent reinforcement learning, which exploits value deviation and transition normalization to deliberately modify the transition probabilities. Value deviation optimistically increases the transition probabilities of high-value next states, and transition normalization normalizes the transition probabilities of next states. They together enable agents to learn high-performing and coordinated policies. Theoretically, we prove the convergence of Q-learning under the altered non-stationary transition dynamics. Empirically, we show that the framework can be easily built on many existing offline reinforcement learning algorithms and achieve substantial improvement in a variety of multi-agent tasks.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

We address the task of generating physically accurate and visually faithful 4D Human-Object Interaction (HOI). Given a static 3D human and target object represented as 3D Gaussian Splats (3DGS), our goal is to synthesize dynamic scenes where the human actively engages with the object through actions, such as punching or kicking, in accordance with a given input text. To this end, we introduce PhyGenHOI, a novel framework that couples generative human motion with an explicit physical object simulation. We model the human as a semantic agent driven by a Motion Diffusion Model (MDM) and the object as a physical agent simulated via the Material Point Method (MPM), utilizing 3D Gaussians as a unified, differentiable representation. We supervise their interaction through three coupled mechanisms: (1) A Windowed Attraction Loss that temporally synchronizes generative motion to intercept the object; (2) A Contact-Driven Re-simulation step that triggers physically consistent momentum transfer upon impact; and (3) A Masked Video-SDS objective that injects video-based priors to enhance contact fidelity. Experiments show PhyGenHOI generates physically consistent 4D HOI across diverse actions, humans, and objects, outperforming baselines. Project page and videos: https://omerbenishu.github.io/PhyGenHOI/

The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite stream, and name three resource walls: a Shannon wall barring any o(Nb)-state architecture, a horizon wall barring any fixed window, and a circuit wall barring fixed-depth attention-only composition (conditional on TC0 != NC1). Under an explicit separability assumption a hybrid crosses all three by paying each wall's price, so capability is strictly super-additive under composition. We separate what we prove from what we conjecture: the access-completeness principle rests on information-theoretic lower bounds and pre-registered experiments, while the field-level convergence trend is an economics-motivated conjecture. We report the first pre-registered small-scale tests under criteria frozen before the data: the predicted scissors gap is measured (exact-retrieval error 0.994 vs. 0.000 once a 64-scalar state gains one global-attention layer), the state-tracking bifurcation lands at the registered boundary, and a conjunction witness shows an irreducibly two-channel solution; one prediction failed with its direction reversed and is reported as such. Representational convergence is given freely by scale; capability convergence must be purchased by access structure.

Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Fr\'echet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.

Soft Actor-Critic (SAC) is widely used for entropy-regularised reinforcement learning with continuous action spaces, and practical implementations perform only a few actor steps towards an evolving target. In this work, we prove convergence guarantees when the target policy arises from policy mirror descent and compare it with the classical Gibbs target. We derive sufficient conditions for the strong convexity and smoothness of the actor objective, characterised by the curvature of the Q-function estimate through the Legendre differential operator, and establish an O!left(N^{-1{5}}right) best-iterate finite-time convergence rate up to actor and critic approximation errors. Moreover, the mirror-descent step size λ directly controls the target drift and hence actor tracking error, whereas the analogous Gibbs bound contains a non-vanishing tracking term.

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem is the local analogue of Hilbert's 18th problem, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry, dimensional structure variability, and combinatorial explosion beyond Go limit the scalability and generality of existing methods. Here we model the problem as a two-player matrix completion game and train the reinforcement learning system, PackingStar, to play the games. The matrix entries represent pairwise cosines of sphere center vectors. One player fills entries while another corrects suboptimal ones to improve exploration quality, cooperatively maximizing the matrix size, corresponding to the kissing number. These matrices are decomposed into representative substructures, providing diverse bases and structural constraints that steer subsequent games and make extremely large spaces tractable. PackingStar surpasses records from dimensions 25 to 31 and sets new lower bounds for generalized kissing numbers under various angular constraints. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in other dimensions. Notably, some configurations challenge long-held antipodal paradigms, revealing algebraic correspondences with finite simple groups as well as geometric relationships across dimensions. Inspired by these patterns, humans devised further improved constructions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition via extreme-scale reinforcement learning and open new pathways for the Kissing Number Problem and broader geometry research.

Occlusion-aware prediction remains a critical challenge in autonomous driving due to the inherent uncertainty of unobserved regions. Existing approaches either overestimate risk based on reachable states or struggle to predict accurate trajectories under high occlusion uncertainty. To address these limitations, we propose a unified risk map modeling and learning framework for partially observable environments. Our method integrates traffic flow risk and collision risk through spatiotemporal modeling, enabling fine-grained assessment of occlusion-induced hazards. To address the scarcity of scenarios involving occluded interactions, we introduce a diffusion-based scenario generation framework that produces realistic yet adversarial scenarios. We integrate the modeling and learning of a unified risk map into a framework that supports risk-aware planning under partial observability. Experiments on the Waymo Open Motion Dataset show that our method significantly outperforms the state-of-the-art occlusion-aware baseline, improving minimum time-to-collision by 0.78 times and average time-to-collision by 1.67 times. The proposed framework offers a comprehensive and practical solution for risk-aware planning in partially observable environments.

After the recent groundbreaking results of AlphaGo and AlphaZero, we have seen strong interests in deep reinforcement learning and artificial general intelligence (AGI) in game playing. However, deep learning is resource-intensive and the theory is not yet well developed. For small games, simple classical table-based Q-learning might still be the algorithm of choice. General Game Playing (GGP) provides a good testbed for reinforcement learning to research AGI. Q-learning is one of the canonical reinforcement learning methods, and has been used by (Banerjee & Stone, IJCAI 2007) in GGP. In this paper we implement Q-learning in GGP for three small-board games (Tic-Tac-Toe, Connect Four, Hex)source code: https://github.com/wh1992v/ggp-rl, to allow comparison to Banerjee et al.. We find that Q-learning converges to a high win rate in GGP. For the ε-greedy strategy, we propose a first enhancement, the dynamic ε algorithm. In addition, inspired by (Gelly & Silver, ICML 2007) we combine online search (Monte Carlo Search) to enhance offline learning, and propose QM-learning for GGP. Both enhancements improve the performance of classical Q-learning. In this work, GGP allows us to show, if augmented by appropriate enhancements, that classical table-based Q-learning can perform well in small games.

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset (γp to ρ^0 p to π^+π^- p), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

Computing stable partitions in hedonic games is a challenging task because there exist games in which stable outcomes do not exist. Even more, these No-instances can often be leveraged to prove computational hardness results. We make this impression rigorous in a dynamic model of cardinal hedonic games by providing meta theorems. These imply hardness of deciding about the possible or necessary convergence of deviation dynamics based on the mere existence of No-instances. Our results hold for additively separable, fractional, and modified fractional hedonic games (ASHGs, FHGs, and MFHGs). Moreover, they encompass essentially all reasonable stability notions based on single-agent deviations. In addition, we propose dynamics as a method to find individually rational and contractually individual stable (CIS) partitions in ASHGs. In particular, we find that CIS dynamics from the singleton partition possibly converge after a linear number of deviations but may require an exponential number of deviations in the worst case.

Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.

Collisions between cyclists and pedestrians at urban intersections remain a persistent source of injuries, yet few systems attempt real-time warnings to unequipped road users using commodity hardware. We present a prototype collision warning system that runs on a single edge device with a wide-angle fisheye camera, producing audible and visual alerts at 30\,fps. The system makes four contributions. First, we develop a calibration pipeline for ultra-wide fisheye lenses that overcomes corner-detection failure and optimizer divergence through perspective remapping and direct bundle adjustment. Second, we combine fisheye-aware object detection with a closed-form ground-plane projection via a precomputed lookup table. Third, we introduce a design-time conformance simulation with 24 scripted hazard scenarios, stochastic size-aware detection failures, and a latency sweep showing that a first-order kinematic predictor maintains the mean warning budget above the distracted-pedestrian reaction time across realistic camera latencies. Fourth, we formalize the decision layer as a separable, auditable testbench with explicit deployment gates, contestability mechanisms, and a residual risk register. Under conformance testing with fisheye localization error, the selected pipeline configuration achieves 93.3\% sensitivity and 92.3\% specificity, with a mean warning budget of 3.3\,s. The system design was informed by community-aided design workshops. Code and replication scripts are available at https://github.com/mkturkcan/bikeped.

Despite the rapid development of safety alignment techniques for LLMs, defending against multi-turn jailbreaks is still a challenging task. In this paper, we conduct a comprehensive comparison, revealing that some existing defense methods can improve the robustness of LLMs against multi-turn jailbreaks but compromise usability, i.e., reducing general capabilities or causing the over-refusal problem. From the perspective of mechanism interpretability of LLMs, we discover that these methods fail to establish a boundary that exactly distinguishes safe and harmful feature representations. Therefore, boundary-safe representations close to harmful representations are inevitably disrupted, leading to a decline in usability. To address this issue, we propose X-Boundary to push harmful representations away from boundary-safe representations and obtain an exact distinction boundary. In this way, harmful representations can be precisely erased without disrupting safe ones. Experimental results show that X-Boundary achieves state-of-the-art defense performance against multi-turn jailbreaks, while reducing the over-refusal rate by about 20% and maintaining nearly complete general capability. Furthermore, we theoretically prove and empirically verify that X-Boundary can accelerate the convergence process during training. Please see our code at: https://github.com/AI45Lab/X-Boundary.

Neural networks increasingly embed non-differentiable components (spiking neurons, quantized layers, discrete routing, blackbox simulators, etc.) where backpropagation is inapplicable and surrogate gradients introduce bias. We present PolyStep, a gradient-free optimizer that updates parameters using only forward passes. Each step evaluates the loss at structured polytope vertices in a compressed subspace, computes softmax-weighted assignments over the resulting cost matrix, and displaces particles toward low-cost vertices via barycentric projection. This update corresponds to the one-sided limit of a regularized optimal-transport problem, inheriting its geometric structure without Sinkhorn iterations. PolyStep trains genuinely non-differentiable models where existing gradient-free methods collapse to near-random accuracy. On hard-LIF spiking networks we reach 93.4% test accuracy, outperforming all gradient-free baselines by over 60~pp and closing to within 4.4~pp of a surrogate-gradient Adam ceiling. Across four additional non-differentiable architectures (int8 quantization, argmax attention, staircase activations, hard MoE routing) we lead every gradient-free competitor. On MAX-SAT scaling from 100 to 1M variables, we sustain above 92% clause satisfaction while evolution strategies drop 8--12~pp. On RL policy search, we match OpenAI-ES on classical control and retain performance under integer and binary quantization that collapses gradient-based methods. We prove convergence to conservative-stationary points at rate O(log T/T) on piecewise-smooth losses, upgraded to Clarke-stationary on the headline architectures and extended to the piecewise-constant regime via a hitting-time bound. These rates match the known zeroth-order query-complexity lower bounds that all forward-only methods inherit. Code is available at https://github.com/anindex/polystep.

Reinforcement learning (RL) has emerged as the predominant paradigm for training large language model (LLM)-based AI agents. However, existing backbone RL algorithms lack verified convergence guarantees in agentic scenarios, especially in multi-turn settings, which can lead to training instability and failure to converge to optimal policies. In this paper, we systematically analyze how different combinations of policy update mechanisms and advantage estimation methods affect convergence properties in single/multi-turn scenarios. We find that REINFORCE with Group Relative Advantage Estimation (GRAE) can converge to the globally optimal under undiscounted conditions, but the combination of PPO & GRAE breaks PPO's original monotonic improvement property. Furthermore, we demonstrate that mainstream backbone RL algorithms cannot simultaneously achieve both critic-free and convergence guarantees in multi-turn scenarios. To address this, we propose SeeUPO (Sequence-level Sequential Update Policy Optimization), a critic-free approach with convergence guarantees for multi-turn interactions. SeeUPO models multi-turn interaction as sequentially executed multi-agent bandit problems. Through turn-by-turn sequential policy updates in reverse execution order, it ensures monotonic improvement and convergence to global optimal solution via backward induction. Experiments on AppWorld and BFCL v4 demonstrate SeeUPO's substantial improvements over existing backbone algorithms: relative gains of 43.3%-54.6% on Qwen3-14B and 24.1%-41.9% on Qwen2.5-14B (averaged across benchmarks), along with superior training stability.

Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

Self-collision remains a persistent challenge in SMPL-based human pose estimation and motion generation. Under extreme articulations or stochastic motion synthesis, generated meshes frequently exhibit self-penetrations, leading to physically implausible results. We propose PoseShield, a neural collision constraint defined directly in SMPL pose space. We formulate collision correction as a constrained optimization problem and connect the learned constraint with the Eikonal equation. Enforcing Eikonal regularization ensures non-vanishing gradients near the collision boundary, improving numerical stability and robustness of the optimization process. Unlike prior methods that operate in the mesh space or rely on heuristic penalties, our approach operates directly in the low-dimensional space of human poses and is theoretically grounded. The same learned constraint extends to human motion sequences, providing a generator-agnostic post-hoc collision corrector without retraining the underlying motion model. Experiments on a newly constructed SMPL pose benchmark show that our method achieves a 95.8% success rate and outperforms state-of-the-art baselines.

Recent video diffusion models can synthesize visually compelling clips, yet often violate basic physical laws-objects float, accelerations drift, and collisions behave inconsistently-revealing a persistent gap between visual realism and physical realism. We propose NewtonRewards, the first physics-grounded post-training framework for video generation based on verifiable rewards. Instead of relying on human or VLM feedback, NewtonRewards extracts measurable proxies from generated videos using frozen utility models: optical flow serves as a proxy for velocity, while high-level appearance features serve as a proxy for mass. These proxies enable explicit enforcement of Newtonian structure through two complementary rewards: a Newtonian kinematic constraint enforcing constant-acceleration dynamics, and a mass conservation reward preventing trivial, degenerate solutions. We evaluate NewtonRewards on five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, and ramp sliding down/up) using our newly constructed large-scale benchmark, NewtonBench-60K. Across all primitives in visual and physics metrics, NewtonRewards consistently improves physical plausibility, motion smoothness, and temporal coherence over prior post-training methods. It further maintains strong performance under out-of-distribution shifts in height, speed, and friction. Our results show that physics-grounded verifiable rewards offer a scalable path toward physics-aware video generation.

We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in realistic adversarial games - like generative adversarial networks - by showing we can find better solutions with an almost identical computational cost. We also show a practical generalization to a complex-valued Adam variant, which we use to train BigGAN to better inception scores on CIFAR-10.

Accurate 3D tracking in highly deformable scenes with occlusions and shadows can facilitate new applications in robotics, augmented reality, and generative AI. However, tracking under these conditions is extremely challenging due to the ambiguity that arises with large deformations, shadows, and occlusions. We introduce MD-Splatting, an approach for simultaneous 3D tracking and novel view synthesis, using video captures of a dynamic scene from various camera poses. MD-Splatting builds on recent advances in Gaussian splatting, a method that learns the properties of a large number of Gaussians for state-of-the-art and fast novel view synthesis. MD-Splatting learns a deformation function to project a set of Gaussians with non-metric, thus canonical, properties into metric space. The deformation function uses a neural-voxel encoding and a multilayer perceptron (MLP) to infer Gaussian position, rotation, and a shadow scalar. We enforce physics-inspired regularization terms based on local rigidity, conservation of momentum, and isometry, which leads to trajectories with smaller trajectory errors. MD-Splatting achieves high-quality 3D tracking on highly deformable scenes with shadows and occlusions. Compared to state-of-the-art, we improve 3D tracking by an average of 23.9 %, while simultaneously achieving high-quality novel view synthesis. With sufficient texture such as in scene 6, MD-Splatting achieves a median tracking error of 3.39 mm on a cloth of 1 x 1 meters in size. Project website: https://md-splatting.github.io/.

Crash simulation is a cornerstone of modern vehicle development because it reduces the need for costly physical prototypes, accelerates safety-driven design iteration, and increasingly supports virtual testing workflows. At the same time, modeling structural crash mechanics remains exceptionally challenging: the response is governed by nonlinear contact, large deformation, material plasticity, failure, and complex multi-body interactions evolving over space and time on high-resolution finite-element meshes. In this work, we introduce CarCrashNet, a public high-fidelity open-source benchmark for data-driven structural crash simulation. CarCrashNet combines component-scale and full-vehicle simulations in a multi-modal format, including more than 14{,}000 bumper-beam pole-impact simulations with varying geometry, materials, and boundary conditions, together with 825 full-vehicle crash simulations built from three industry-standard vehicle models of increasing structural complexity: Dodge Neon, Toyota Yaris, and Chevrolet Silverado. To establish the reliability of the benchmark, we validate our open-source finite-element workflow based on OpenRadioss against both experimental crash data and the commercial solver Ansys LS-DYNA. We also introduce CrashSolver, a machine-learning model designed for full-vehicle crash prediction from high-resolution finite-element crash data. We further perform extensive benchmarking across the released datasets and evaluate CrashSolver against state-of-the-art geometric deep learning and transformer-based neural solvers. Our results position CarCrashNet as a foundation for reproducible research in structural simulation, crashworthiness modeling, and AI-driven virtual crash testing. The dataset is available at https://github.com/Mohamedelrefaie/CarCrashNet.

Short-recurrence Krylov methods that are equivalent in exact arithmetic often diverge in floating-point arithmetic. To illustrate this, we provide an exactly representable two-cycle for steepest descent with a recursively updated residual. A complementary convergence theorem gives a sufficient condition under which the stored residual decreases geometrically. We then show that a second positive definite family yields different outcomes for a Hestenes--Stiefel Conjugate Gradient (CG) implementation and a direct Lanczos--Galerkin approach. CG finds the exact solution after four updates, whereas the two-step projected system becomes inconsistent. Under stated perturbation and transfer hypotheses, a common spectral enclosure gives comparable convergence bounds. For a dense, left-to-right evaluation order, we prove a sufficient precision bound for a prescribed backward error within n updates for an ntimes n matrix, together with a computable stopping test and specified exponent-range assumptions. We use polynomial estimates and numerical experiments to examine the trade-off between working precision and the number of CG iterations needed to achieve a prescribed backward error. We also compare results on inexact matrix-vector products and preconditioning with the frameworks of Paige and Greenbaum. For block Lanczos, we analyze Householder orthogonalization and singular-value truncation as the block size changes. Under componentwise and normwise error bounds, the computed coefficients satisfy a controlled local recurrence and an exact block Lanczos relation for a nearby symmetric problem in a larger space. A block form of Paige's identity bounds the overlap with a Ritz vector along its residual coordinate direction. An inter-block recurrence describes the evolution of overlap, and a Gram-matrix argument gives a count of additional nearby Ritz values.

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy gamma_t = 2/(t+2), obtaining a O(1/t) convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where t is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.

Autonomous driving requires safe planning, but most learning-based planners lack explicit self-correction ability: once an unsafe action is proposed, there is no mechanism to correct it. Thus, we propose CorrectionPlanner, an autoregressive planner with self-correction that models planning as motion-token generation within a propose, evaluate, and correct loop. At each planning step, the policy proposes an action, namely a motion token, and a learned collision critic predicts whether it will induce a collision within a short horizon. If the critic predicts a collision, we retain the sequence of historical unsafe motion tokens as a self-correction trace, generate the next motion token conditioned on it, and repeat this process until a safe motion token is proposed or the safety criterion is met. This self-correction trace, consisting of all unsafe motion tokens, represents the planner's correction process in motion-token space, analogous to a reasoning trace in language models. We train the planner with imitation learning followed by model-based reinforcement learning using rollouts from a pretrained world model that realistically models agents' reactive behaviors. Closed-loop evaluations show that CorrectionPlanner reduces collision rate by over 20% on Waymax and achieves state-of-the-art planning scores on nuPlan.

When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments have implicit constraints that are difficult to specify and transfer to a learning agent. To address this challenge, we propose a novel method that utilizes the principle of maximum causal entropy to learn constraints and an optimal policy that adheres to these constraints, using demonstrations of agents that abide by the constraints. We prove convergence in a tabular setting and provide an approximation which scales to complex environments. We evaluate the effectiveness of the learned policy by assessing the reward received and the number of constraint violations, and we evaluate the learned cost function based on its transferability to other agents. Our method has been shown to outperform state-of-the-art approaches across a variety of tasks and environments, and it is able to handle problems with stochastic dynamics and a continuous state-action space.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical constraints. Existing methods excel at semantic alignment, however, they struggle to maintain precise object contact. We reveal a key finding termed Geometric Forgetting: as diffusion model depth increases, semantic feature tend to overshadow object geometry feature, causing the model to lose its perception to object geometry. To address this, we propose MaMi-HOI, a hierarchical framework reconciling Macro-level kinematic fluidity with Micro-level spatial precision. First, to counteract geometric forgetting, we introduce the Geometry-Aware Proximity Adapter (GAPA), which explicitly re-injects dense object details to perform residual snapping corrections for precise contact. Nevertheless, such aggressive local enforcement can disrupt global dynamics, leading to robotic stiffness. In response, we introduce the Kinematic Harmony Adapter (KHA), which proactively aligns whole-body posture with spatial objectives, ensuring the skeleton actively accommodates constraints without compromising naturalness. Extensive experiments validate that MaMi-HOI simultaneously achieves natural motion and precise contact. Crucially, it extends generation capabilities to long-term tasks with complex trajectories, effectively bridging the gap between global navigation and high-fidelity manipulation in 3D scenes. Code is available at https://github.com/DON738110198/MaMi-HOI.git

This paper presents methods for dramatically improving the performance of sampling-based kinodynamic planners. The key component is the first-known complete, exact steering method that produces a time-optimal trajectory between any states for a vector of synchronized double integrators. This method is applied in three ways: 1) to generate RRT edges that quickly solve the two-point boundary-value problems, 2) to produce a (quasi)metric for more accurate Voronoi bias in RRTs, and 3) to iteratively time-optimize a given collision-free trajectory. Experiments are performed for state spaces with up to 2000 dimensions, resulting in improved computed trajectories and orders of magnitude computation time improvements over using ordinary metrics and constant controls.

We introduce Gradient Descent with Adaptive Momentum Scaling (Grams), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

Effective robot autonomy requires motion generation that is safe, feasible, and reactive. Current methods are fragmented: fast planners output physically unexecutable trajectories, reactive controllers struggle with high-fidelity perception, and existing solvers fail on high-DoF systems. We present cuRoboV2, a unified framework with three key innovations: (1) B-spline trajectory optimization that enforces smoothness and torque limits; (2) a GPU-native TSDF/ESDF perception pipeline that generates dense signed distance fields covering the full workspace, unlike existing methods that only provide distances within sparsely allocated blocks, up to 10x faster and in 8x less memory than the state-of-the-art at manipulation scale, with up to 99% collision recall; and (3) scalable GPU-native whole-body computation, namely topology-aware kinematics, differentiable inverse dynamics, and map-reduce self-collision, that achieves up to 61x speedup while also extending to high-DoF humanoids (where previous GPU implementations fail). On benchmarks, cuRoboV2 achieves 99.7% success under 3kg payload (where baselines achieve only 72--77%), 99.6% collision-free IK on a 48-DoF humanoid (where prior methods fail entirely), and 89.5% retargeting constraint satisfaction (vs. 61% for PyRoki); these collision-free motions yield locomotion policies with 21% lower tracking error than PyRoki and 12x lower cross-seed variance than GMR. A ground-up codebase redesign for discoverability enabled LLM coding assistants to author up to 73% of new modules, including hand-optimized CUDA kernels, demonstrating that well-structured robotics code can unlock productive human-LLM collaboration. Together, these advances provide a unified, dynamics-aware motion generation stack that scales from single-arm manipulators to full humanoids. Code is available at https://github.com/NVlabs/curobo.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

Low-rank adaptation (LoRA) has become a standard tool for efficiently fine-tuning large language models (LLMs). Yet, even minor LoRA updates can induce alignment drift, weakening safety and behavioral constraints through entangled parameter changes. To address this, we propose AlignGuard-LoRA (AGL), a principled framework for preserving alignment during finetuning. AGL introduces several key components: a primary task loss for supervision, Fisher Information Matrix-based regularization to restrict updates in alignment-sensitive subspaces, and task-specific regularization to stabilize the integration of new knowledge. We further introduce collision-aware regularization, blending Riemannian overlap -- which penalizes coordinate-wise interference -- and geodesic separation -- which encourages disjoint update geometry. We curate DriftCaps, a targeted diagnostic benchmark of safe and unsafe prompts designed to quantify alignment drift and safety degradation. Empirical evaluations show that AGL mitigates alignment drift by up to 50% on safety-critical benchmarks without degrading downstream task performance. Comprehensive ablation confirms that each component contributes distinctly to preserving latent safety behaviors. Finally, we derive and validate a scaling law for catastrophic forgetting, revealing that AGL flattens post-finetuning loss escalation while preserving adaptation dynamics. AGL is a structurally grounded refinement of LoRA, ensuring alignment preservation with minimal trade-offs. To encourage further exploration and development, we open-source our implementation.

The ability to forecast human-environment collisions from egocentric observations is vital to enable collision avoidance in applications such as VR, AR, and wearable assistive robotics. In this work, we introduce the challenging problem of predicting collisions in diverse environments from multi-view egocentric videos captured from body-mounted cameras. Solving this problem requires a generalizable perception system that can classify which human body joints will collide and estimate a collision region heatmap to localize collisions in the environment. To achieve this, we propose a transformer-based model called COPILOT to perform collision prediction and localization simultaneously, which accumulates information across multi-view inputs through a novel 4D space-time-viewpoint attention mechanism. To train our model and enable future research on this task, we develop a synthetic data generation framework that produces egocentric videos of virtual humans moving and colliding within diverse 3D environments. This framework is then used to establish a large-scale dataset consisting of 8.6M egocentric RGBD frames. Extensive experiments show that COPILOT generalizes to unseen synthetic as well as real-world scenes. We further demonstrate COPILOT outputs are useful for downstream collision avoidance through simple closed-loop control. Please visit our project webpage at https://sites.google.com/stanford.edu/copilot.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

Training large models with distributed data parallelism (DDP) requires frequent communication of gradients across workers, which can saturate bandwidth. Infrequent communication strategies (e.g., Local SGD) reduce this overhead but, when applied to adaptive optimizers, often suffer a performance gap relative to fully synchronous DDP. We trace this gap to a time-scale mismatch: the optimizer's fast-moving momentum, tuned for frequent updates, decays too quickly to smooth gradients over long intervals, leading to noise-dominated optimization. To address this, we propose MT-DAO, a family of optimizers that employs multiple slow- and fast-moving first momenta or the gradient to track update dynamics across different time scales, for which we provide the first convergence guarantees. Empirically, for language-model pre-training, this eliminates the performance gap with DDP, outperforming infrequent-communication baselines in perplexity and reducing iso-token wall-clock time by 6-27% on Ethernet interconnects. At the 720M scale, MT-DAO reaches a target perplexity in 24% fewer steps and 35% less time than the single-momentum DDP baseline. MT-DAO enables effective cross-datacenter training and training over wide geographic areas.