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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

At least 127 records · Page 7Linked to original sources
arXiv2026

Allometric Scaling Laws for Bipedal Robots

Legged robots operate across a wide range of physical scales, but how their designs should be adapted as size changes remains unclear. Here, we tackle this question in two ways. First, we survey existing legged robots to provide a broad context for the key scaling variables, robot mass m and leg length L. We find the surprising result that bipedal robot mass generally scales with the length squared, L^2, rather than the isometric prediction L^3. Then, to reduce the variance in design choices, we focus on a pair of previously developed bipeds that share the same quasi-passive morphology but differ by a factor of six in leg length, use different feet and controllers, and achieve different relative speeds. We reconstruct both robots in a common 3-D simulation environment and scale each design over leg lengths from 0.02 to 1.2 meters under both mass models (mass is proportional to L^2 and is proportional to L^). The controlled comparison shows that velocity follows dynamic similarity, velocity is proportional to L^{1/2}, across designs and mass models, while the torque needed to sustain walking follows that tau is proportional to mL. Consequently, torque scales approximately with L^3 when m is proportional to L^2 and L^4 when mass is proportional to L^3. A 3-D foot-shape sweep further shows that foot dimensions that permit walking scale approximately linearly with leg length, but the speed-maximizing shape and the mechanism by which each robot moves do not transfer by scaling alone. Overall, the results provide practical insights for rescaling legged systems that leverage natural body dynamics.

cs.RO↗
arXiv2026

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY↗
arXiv2026

Rectify, Don't Regret: On-Policy Closed-Loop Training for Multimodal Trajectory Prediction

Current trajectory prediction models are primarily trained in an open-loop manner, which often leads to covariate shift and compounding errors when deployed in real-world, closed-loop settings. In this work, we propose a closed-loop training paradigm for receding-horizon ego prediction and identify two design choices that are critical for it to succeed. First, closed-loop supervision must be on-policy: each predicted mode is rolled out and supervised only from the states its own execution produced, preserving the prediction accuracy that cross-mode supervision would otherwise degrade. Second, gradients must not flow across the executed state transition, as backpropagating through these transitions allows the model to retroactively adjust an earlier prediction so that the resulting state is easier to predict from, mathematically regretting a mistake rather than learning to recover from it. We show empirically that this shortcut couples the learned policy to the specific replanning rate used during training and degrades at other rates, whereas detaching the gradient forces the model to rectify drift instead, allowing it to generalize across replanning rates unseen during training. Evaluated across three benchmarks (nuScenes, DeepScenario, and Argoverse 2) and two architectures, a decoder-only adaptation of LMFormer and an unmodified implementation of QCNet, our approach matches open-loop baselines under single-shot evaluation and improves with higher replanning rates, reducing collisions by up to 35% and off-road rates by up to 67%.

cs.RO↗
arXiv2026

Goal-Oriented Reactive Simulation for Closed-Loop Trajectory Prediction

Current trajectory prediction models are primarily trained in an open-loop manner, which often leads to covariate shift and compounding errors when deployed in real-world, closed-loop settings. Furthermore, relying on static datasets or non-reactive log-replay simulators severs the interactive loop, preventing the ego agent from learning to actively negotiate surrounding traffic. In this work, we propose an on-policy closed-loop training paradigm optimized for high-frequency, receding horizon ego prediction. To ground the ego prediction in a realistic representation of traffic interactions and to achieve reactive consistency, we introduce a goal-oriented, transformer-based scene decoder, resulting in an inherently reactive training simulation. By exposing the ego agent to a mixture of open-loop data and simulated, self-induced states, the model learns recovery behaviors to correct its own execution errors. Extensive evaluation demonstrates that closed-loop training significantly enhances collision avoidance capabilities at high replanning frequencies, yielding relative collision rate reductions of up to 27.0% on nuScenes and 79.5% in dense DeepScenario intersections compared to open-loop baselines. Additionally, we show that a hybrid simulation combining reactive with non-reactive surrounding agents achieves optimal balance between immediate interactivity and long-term behavioral stability.

cs.RO↗
arXiv2026

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY↗
arXiv2026

On a minimal Andô dilation for a pair of strict contractions

The isometric dilation of a pair of commuting contractions due to Andô is not minimal. We modify Andô's dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a commuting pair of strict contractions on a Hilbert space $\mathcal H$. In the same spirit, we construct under certain conditions a minimal Andô dilation for a commuting pair of strict Banach space contractions. Further, we show that an Andô dilation is possible even for a more general pair of commuting contractions $(T_1,T_2)$ on a normed space $\mathbb X$ provided that the function $A_{T_i}: \mathbb X \rightarrow \mathbb R$ given by $A_{T_i}(x)=(\|x\|^2-\|T_ix\|^2)^{\frac{1}{2}}$ defines a norm on $\mathbb X$ for $i=1,2$.

math.FA↗
arXiv2026

MPC-Based Trajectory Tracking for a Quadrotor UAV with Uniform Semi-Global Asymptotic Stability Guarantees

This paper proposes a model predictive trajectory tracking approach for quadrotor UAVs subject to input constraints. Our proposed approach relies on a hierarchical control strategy with an outer-loop feedback generating the required thrust and desired attitude, and an inner-loop feedback regulating the actual attitude to the desired one. For the outer-loop translational dynamics, the generation of the virtual control input is formulated as a constrained model predictive control problem with time-varying input constraints and a control strategy, endowed with uniform global asymptotic stability guarantees, is proposed. For the inner-loop rotational dynamics, a hybrid geometric controller is adopted, achieving semi-global exponential tracking of the desired attitude. Finally, we prove that the overall cascaded system is semi-globally asymptotically stable. Simulation results illustrate the effectiveness of the proposed approach.

eess.SY↗
arXiv2026

Near-Optimal Primal-Dual Algorithm for Learning Linear Mixture CMDPs with Adversarial Rewards

We study safe reinforcement learning in finite-horizon linear mixture constrained Markov decision processes (CMDPs) with adversarial rewards under full-information feedback and an unknown transition kernel. We propose a primal-dual policy optimization algorithm that achieves regret and constraint violation bounds of $\widetilde{O}(\sqrt{d^2 H^3 K})$ under mild conditions, where $d$ is the feature dimension, $H$ is the horizon, and $K$ is the number of episodes. To the best of our knowledge, this is the first provably efficient algorithm for linear mixture CMDPs with adversarial rewards. In particular, our regret bound is near-optimal, matching the known minimax lower bound up to logarithmic factors. The key idea is to introduce a regularized dual update that enables a drift-based analysis. This step is essential, as strong duality-based analysis cannot be directly applied when reward functions change across episodes. In addition, we extend weighted ridge regression-based parameter estimation to the constrained setting, allowing us to construct tighter confidence intervals that are crucial for deriving the near-optimal regret bound.

cs.LG↗
arXiv2026

Transferable knowledge graphs with executable learned operators for algorithm design

Procedural knowledge in algorithm design is embedded in source code and rebuilt for each new domain. We introduce Generative Executable Algorithm Knowledge Graphs (GEAKG), a representation in which this knowledge is stored as a generative, executable, transferable graph: typed nodes hold validated operators, edges encode admissible compositions, and learned edge weights record effective sequences. The same engine instantiates the structure across domains by changing only a role ontology (RoleSchema) and a binding. We study GEAKG as a representation mechanism rather than a state-of-the-art optimizer, asking what transfers and when. Layer ablations localize transfer by granularity: within a neural-architecture-search family the learned snapshot transfers across 70 dataset pairs - its weights stay correlated across datasets and one frozen snapshot remains competitive with Regularized Evolution at zero deployment-token cost; across combinatorial domains only the ontology-constrained executable structure transfers, not the learned weights. That structure pays off where target-side search is expensive - a Traveling Salesman snapshot beats an equally untuned from-scratch search on large scheduling instances even at one-fifth its budget - but does not improve on an effective local search where one is cheap, as in assignment and linear ordering. Executable procedural knowledge can thus be acquired offline, compacted, inspected, and reused without runtime language-model calls.

cs.AI↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗
arXiv2026

Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper

This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.

cs.RO↗
arXiv2026

Why is Regularization Underused? An Empirical Study on Trust and Adoption of Statistical Methods

Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by data analysts. We investigate this implementation gap in a large-scale empirical study of trust in, and acceptance of, regularization techniques, based on $N = 606$ data analysts. Drawing on measurement frameworks from technology acceptance research, we survey practitioners and embed a randomized experiment to test whether written recommendation of regularization methods increases trust or intended use. We find no evidence of such an effect. Instead, adoption intentions are strongly associated with analysts' perceptions of ease of implementation and practical benefit, such as improved bias control or interpretability. Perceived social norms also emerge as a central driver. These results indicate that uptake of statistical methodology depends less on formal recommendations than on usability, perceived utility, and community practice.

stat.OT↗
arXiv2026

Transcriptomic Models for Immunotherapy Response Prediction Show Limited Cross-cohort Generalisability

Immune checkpoint inhibitors (ICIs) have transformed cancer therapy; yet substantial proportion of patients exhibit intrinsic or acquired resistance, making accurate pre-treatment response prediction a critical unmet need. Transcriptomics-based biomarkers derived from bulk and single-cell RNA sequencing (scRNA-seq) offer a promising avenue for capturing tumour-immune interactions, yet the cross-cohort generalisability of existing prediction models remains unclear.We systematically benchmark nine state-of-the-art transcriptomic ICI response predictors, five bulk RNA-seq-based models (COMPASS, IRNet, NetBio, IKCScore, and TNBC-ICI) and four scRNA-seq-based models (PRECISE, DeepGeneX, Tres and scCURE), using publicly available independent datasets unseen during model development. Overall, predictive performance was modest: bulk RNA-seq models performed at or near chance level across most cohorts, while scRNA-seq models showed only marginal improvements. Pathway-level analyses revealed sparse and inconsistent biomarker signals across models. Although scRNA-seq-based predictors converged on immune-related programs such as allograft rejection, bulk RNA-seq-based models exhibited little reproducible overlap. PRECISE and NetBio identified the most coherent immune-related themes, whereas IRNet predominantly captured metabolic pathways weakly aligned with ICI biology. Together, these findings demonstrate the limited cross-cohort robustness and biological consistency of current transcriptomic ICI prediction models, underscoring the need for improved domain adaptation, standardised preprocessing, and biologically grounded model design.

q-bio.GN↗
arXiv2026

Kinetics of Salt Creeping on a Free Surface: From Nucleation to Saturation

The phenomenon of salt creeping along a free surface remains only partially understood, particularly with respect to its dynamics. In this work, combining a theoretical model with controlled experiments, we identify three distinct kinetic regimes: an initial exponential growth of the height of the crystallized salt deposit on vertical walls, followed by a linear regime, and a final stage where the height saturates while the crystal deposit thickens logarithmically. This unified description makes it possible to follow the macroscopic kinetics of salt growth on a free surface from its nucleation to saturation. In addition, we complement this macroscopic analysis with numerical simulations that shed light on the evolution of the microscopic crystal structure under varying external conditions (humidity and temperature).

cond-mat.soft↗
arXiv2026

Evolving Skill Modules under a Fixed Planner: Versioning, Rollback, and Runtime Governance for Long-Lived Robot Systems

Robots deployed for long periods keep improving their skills, and each update changes a released system. We treat this as a software-lifecycle problem: a fixed decision layer dispatches versioned skill modules and a runtime layer was built to screen each action. On six robosuite tasks we report three negative results and two measurements. First, peak task success is unstable across random seeds (within one method it spans 23.3 to 73.3%), so single-run peaks cannot rank these methods. Second, the system's four modules are whole-task policies with different labels, rotated on a clock, not the phase decomposition its documentation describes. At a matched budget one such policy holds the geometry at the final step in 0.734 of episodes reaching it, averaged over seeds, against 0.023 for the rotation, with no seed overlap at four seeds per arm (exact p=0.029). An intervention isolates why: restoring the termination condition the clock replaced raises retention on every seed. Third, our shield cut violations 98 to 100% on five single-arm tasks (34.9% on the sixth) by discarding whole actions, leaving success at zero: its acceptance criterion omitted completions, so a shield that stopped the robot scored perfectly. What survives is release machinery: a promotion gate kept all twelve injected regressions out, a rate its calibration nearly guarantees, at a 22.5% clean-candidate rejection cost; a dip detector caught nine of twelve, missing all three on one seed.

cs.RO↗
arXiv2026

Einstein connection of a weak almost contact metric manifold

Advances in modern physics since Einstein have made the nonsymmetric metric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, more attractive than ever. Einstein considered a linear connection $\nabla$ with torsion $T$ such that $(\nabla_X\,G)(Y,Z)=G(T(Y,X),Z)$. In this paper, we explicitly present the Einstein connection of $G=g+F$ using a weak almost contact structure $(f,ξ,η)$ with $g(X,fY)=F(X,Y)$ with a natural condition (trivial in the almost contact case). We discuss special Einstein connections, and give an example in terms of the weighted product of almost Hermitian manifold and a real line.

math.DG↗
arXiv2026

Incentive Design without Hypergradients: A Social-Gradient Method

In incentive design problems, a system planner seeks to steer self-interested agents toward a socially optimal Nash equilibrium by issuing incentives in the presence of information asymmetry, that is, uncertainty about the agents' cost functions. A common approach formulates the problem as a Mathematical Program with Equilibrium Constraints and optimizes incentives using hypergradients-the total derivatives of the planner's objective with respect to incentives. However, computing the hypergradient typically requires full or partial knowledge of equilibrium sensitivities to incentives, which is generally unavailable under information asymmetry. In this paper, we propose a hypergradient-free incentive law, called the social-gradient flow, for incentive design when the social cost depends on the agents' joint action. We prove that the social cost gradient is a descent direction for the planner's objective, irrespective of the agent cost landscape. In the idealized setting where equilibrium responses are observable, the social-gradient flow converges to the unique socially optimal incentive. When equilibria are not directly observable, the social-gradient flow emerges as the slow-timescale limit of a two-timescale interaction, in which agents' strategies evolve on a faster timescale. We establish that the joint strategy-incentive dynamics converge to the social optimum for any agent learning rule that asymptotically tracks the equilibrium. Finally, we validate theoretical results via numerical experiments.

math.OC↗
arXiv2026

Semidefinite relaxations for nonlinear elasticity with energies convex in the Cauchy-Green strain tensor

In nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have minimizers: the energy optimal material forms infinitely fine microstructures (wrinkles) rather than deforming smoothly. In the case where the energy function is non-convex but frame indifferent and convex with respect to the Cauchy-Green strain tensor, we use the standard Le Dret-Raoult semidefinite projection formula for the quasiconvex envelope of the energy function together with a recent no gap result for convex calculus of variation problems to prove that there is no relaxation gap between the original non-convex calculus of variations problem and its linear moment formulation based on occupation measures. This implies convergence of the Lasserre moment-sum-of-squares (SOS) hierarchy and provides a computationally efficient, mesh-free numerical method that, unlike the finite element method, avoids undesirable mesh-dependent artifacts. Under the additional condition that the boundary condition is linear and the function is SOS convex in the strain tensor, we show that the first relaxation of the Lasserre hierarchy is exact. In other words, computing the quasiconvex envelope at a point boils down to solving a small convex semidefinite optimization problem.

math.OC↗