frax: Fast Robot Kinematics and Dynamics in JAX

In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU execution or high-throughput GPU workloads, few provide a unified framework that targets multiple architectures without compromising performance or ease-of-use. To address this, we introduce frax, a JAX-based library for robot kinematics and dynamics, providing a high-performance, pure-Python interface across CPU, GPU, and TPU. Via a fully-vectorized approach to robot dynamics, frax enables efficient real-time control and parallelization, while supporting automatic differentiation for optimization-based methods. On CPU, frax achieves low-microsecond computation times suitable for kilohertz control rates, outperforming common libraries in Python and approaching optimized C++ implementations. On GPU, the same code scales to thousands of instances, reaching upwards of 100 million dynamics evaluations per second. We validate performance on a Franka Panda manipulator and a Unitree G1 humanoid, and release frax as an open-source library.

Learning Actuator-Aware Spectral Submanifolds for Precise Control of Continuum Robots

Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical systems to low-dimensional invariant manifolds. Our proposed control-augmented SSMs (caSSMs) extend this methodology by explicitly incorporating control inputs into the state representation, enabling these models to capture nonlinear state-input couplings. Training these models relies solely on controlled decay trajectories of the actuator-augmented state, thereby removing the additional actuation-calibration step commonly needed by prior SSM-for-control methods. We learn a compact caSSM model for a tendon-driven trunk robot, enabling real-time control and reducing open-loop prediction error by 40% compared to existing methods. In closed-loop experiments with model predictive control (MPC), caSSM reduces tracking error by 52%, demonstrating improved performance against Koopman and SSM based MPC and practical deployability on hardware continuum robots.

$Ψ_0$: An Open Foundation Model Towards Universal Humanoid Loco-Manipulation

We introduce $Ψ_0$ (Psi-Zero), an open foundation model to address challenging humanoid loco-manipulation tasks. While existing approaches often attempt to address this fundamental problem by co-training on large and diverse human and humanoid data, we argue that this strategy is suboptimal due to the fundamental kinematic and motion disparities between humans and humanoid robots. Therefore, data efficiency and model performance remain unsatisfactory despite the considerable data volume. To address this challenge, \ours\;decouples the learning process to maximize the utility of heterogeneous data sources. Specifically, we propose a staged training paradigm with different learning objectives: First, we autoregressively pre-train a VLM backbone on large-scale egocentric human videos to acquire generalizable visual-action representations. Then, we post-train a flow-based action expert on high-quality humanoid robot data to learn precise robot joint control. Our research further identifies a critical yet often overlooked data recipe: in contrast to approaches that scale with noisy Internet clips or heterogeneous cross-embodiment robot datasets, we demonstrate that pre-training on high-quality egocentric human manipulation data followed by post-training on domain-specific real-world humanoid trajectories yields superior performance. Extensive real-world experiments demonstrate that \ours\ achieves the best performance using only about 800 hours of human video data and 30 hours of real-world robot data, outperforming baselines pre-trained on more than 10$\times$ as much data by over 40\% in overall success rate across multiple tasks. We will open-source the entire ecosystem to the community, including a data processing and training pipeline, a humanoid foundation model, and a real-time action inference engine.

Observing and Controlling Features in Vision-Language-Action Models

Vision-Language-Action Models (VLAs) have shown remarkable progress towards embodied intelligence. While their architecture partially resembles that of Large Language Models (LLMs), VLAs exhibit higher complexity due to their multi-modal inputs/outputs and often hybrid nature of transformer and diffusion heads. This is part of the reason why insights from mechanistic interpretability in LLMs, which explain how the internal model representations relate to their output behavior, do not trivially transfer to VLA counterparts. In this work, we propose to close this gap by introducing and analyzing two main concepts: feature-observability and feature-controllability. In particular, we first study features that are linearly encoded in representation space, and show how they can be observed by means of a linear classifier. Then, we use a minimal linear intervention grounded in optimal control to accurately place internal representations and steer the VLA's output towards a desired region. Our results show that targeted, lightweight interventions can reliably steer a robot's behavior while preserving closed-loop capabilities. We demonstrate on different VLA architectures ($π_{0.5}$ and OpenVLA) through simulation experiments that VLAs possess interpretable internal structure amenable to online adaptation without fine-tuning, enabling real-time alignment with user preferences and task requirements.

Graph Neural Model Predictive Control for High-Dimensional Systems

The control of high-dimensional systems, such as soft robots, requires models that faithfully capture complex dynamics while remaining computationally tractable. This work presents a framework that integrates Graph Neural Network (GNN)-based dynamics models with structure-exploiting Model Predictive Control to enable real-time control of high-dimensional systems. By representing the system as a graph with localized interactions, the GNN preserves sparsity, while a tailored condensing algorithm eliminates state variables from the control problem, ensuring efficient computation. The complexity of our condensing algorithm scales linearly with the number of system nodes, and leverages Graphics Processing Unit (GPU) parallelization to achieve real-time performance. The proposed approach is validated in simulation and experimentally on a physical soft robotic trunk. Results show that our method scales to systems with up to 1,000 nodes at 100 Hz in closed-loop, and demonstrates real-time reference tracking on hardware with sub-centimeter accuracy, outperforming baselines by 63.6%. Finally, we show the capability of our method to achieve effective full-body obstacle avoidance.

Scaling Verification Can Be More Effective than Scaling Policy Learning for Vision-Language-Action Alignment

The long-standing vision of general-purpose robots hinges on their ability to understand and act upon natural language instructions. Vision-Language-Action (VLA) models have made remarkable progress toward this goal, yet their generated actions can still misalign with the given instructions. In this paper, we investigate test-time verification as a means to shrink the "intention-action gap.'' We first characterize the test-time scaling law for embodied instruction following and demonstrate that jointly scaling the number of rephrased instructions and generated actions greatly increases test-time sample diversity, often recovering correct actions more efficiently than scaling each dimension independently. To capitalize on these scaling laws, we present CoVer, a contrastive verifier for vision-language-action alignment, and show that our architecture scales gracefully with additional computational resources and data. We then introduce "boot-time compute" and a hierarchical verification inference pipeline for VLAs. At deployment, our framework precomputes a diverse set of rephrased instructions from a Vision-Language-Model (VLM), repeatedly generates action candidates for each instruction, and then uses a verifier to select the optimal high-level prompt and low-level action chunks. Compared to scaling policy pre-training on the same data, our verification approach yields 22% gains in-distribution and 13% out-of-distribution on the SIMPLER benchmark, with a further 45% improvement in real-world experiments. On the PolaRiS benchmark, CoVer achieves 14% gains in task progress and 9% in success rate.

Self-Supervised Bootstrapping of Action-Predictive Embodied Reasoning

Embodied Chain-of-Thought (CoT) reasoning has significantly enhanced Vision-Language-Action (VLA) models, yet current methods rely on rigid templates to specify reasoning primitives (e.g., objects in the scene, high-level plans, structural affordances). These templates can force policies to process irrelevant information that distracts from critical action-prediction signals. This creates a bottleneck: without successful policies, we cannot verify reasoning quality; without quality reasoning, we cannot build robust policies. We introduce R&B-EnCoRe, which enables models to bootstrap embodied reasoning from internet-scale knowledge through self-supervised refinement. By treating reasoning as a latent variable within importance-weighted variational inference, models can generate and distill a refined reasoning training dataset of embodiment-specific strategies without external rewards, verifiers, or human annotation. We validate R&B-EnCoRe across manipulation (Franka Panda in simulation, WidowX in hardware), legged navigation (bipedal, wheeled, bicycle, quadruped), and autonomous driving embodiments using various VLA architectures with 1B, 4B, 7B, and 30B parameters. Our approach achieves 28% gains in manipulation success, 101% improvement in navigation scores, and 21% reduction in collision-rate metric over models that indiscriminately reason about all available primitives. R&B-EnCoRe enables models to distill reasoning that is predictive of successful control, bypassing manual annotation engineering while grounding internet-scale knowledge in physical execution.

Accelerating Structured Chain-of-Thought in Autonomous Vehicles

Chain-of-Thought (CoT) reasoning enhances the decision-making capabilities of vision-language-action models in autonomous driving, but its autoregressive nature introduces significant inference latency, making it impractical for real-time applications. To address this, we introduce FastDriveCoT, a novel parallel decoding method that accelerates template-structured CoT. Our approach decomposes the reasoning process into a dependency graph of distinct sub-tasks, such as identifying critical objects and summarizing traffic rules, some of which can be generated in parallel. By generating multiple independent reasoning steps concurrently within a single forward pass, we significantly reduce the number of sequential computations. Experiments demonstrate a 3-4$\times$ speedup in CoT generation and a substantial reduction in end-to-end latency across various model architectures, all while preserving the original downstream task improvements brought by incorporating CoT reasoning.

Text-Guided Layer Fusion Mitigates Hallucination in Multimodal LLMs

Multimodal large language models (MLLMs) typically rely on a single late-layer feature from a frozen vision encoder, leaving the encoder's rich hierarchy of visual cues under-utilized. MLLMs still suffer from visually ungrounded hallucinations, often relying on language priors rather than image evidence. While many prior mitigation strategies operate on the text side, they leave the visual representation unchanged and do not exploit the rich hierarchy of features encoded across vision layers. Existing multi-layer fusion methods partially address this limitation but remain static, applying the same layer mixture regardless of the query. In this work, we introduce TGIF (Text-Guided Inter-layer Fusion), a lightweight module that treats encoder layers as depth-wise "experts" and predicts a prompt-dependent fusion of visual features. TGIF follows the principle of direct external fusion, requires no vision-encoder updates, and adds minimal overhead. Integrated into LLaVA-1.5-7B, TGIF provides consistent improvements across hallucination, OCR, and VQA benchmarks, while preserving or improving performance on ScienceQA, GQA, and MMBench. These results suggest that query-conditioned, hierarchy-aware fusion is an effective way to strengthen visual grounding and reduce hallucination in modern MLLMs.

Counterfactual VLA: Self-Reflective Vision-Language-Action Model with Adaptive Reasoning

Recent reasoning-augmented Vision-Language-Action (VLA) models have improved the interpretability of end-to-end autonomous driving by generating intermediate reasoning traces. Yet these models primarily describe what they perceive and intend to do, rarely questioning whether their planned actions are safe or appropriate. This work introduces Counterfactual VLA (CF-VLA), a self-reflective VLA framework that enables the model to reason about and revise its planned actions before execution. CF-VLA first generates time-segmented meta-actions that summarize driving intent, and then performs counterfactual reasoning conditioned on both the meta-actions and the visual context. This step simulates potential outcomes, identifies unsafe behaviors, and outputs corrected meta-actions that guide the final trajectory generation. To efficiently obtain such self-reflective capabilities, we propose a rollout-filter-label pipeline that mines high-value scenes from a base (non-counterfactual) VLA's rollouts and labels counterfactual reasoning traces for subsequent training rounds. Experiments on large-scale driving datasets show that CF-VLA improves trajectory accuracy by up to 17.6%, enhances safety metrics by 20.5%, and exhibits adaptive thinking: it only enables counterfactual reasoning in challenging scenarios. By transforming reasoning traces from one-shot descriptions to causal self-correction signals, CF-VLA takes a step toward self-reflective autonomous driving agents that learn to think before they act.