To fill this gap, we introduce a nonparametric causal inference framework for analyzing "closed-loop" designs, which use

Verifying closed-loop vision-based control systems remains a fundamental challenge due to the high dimensionality of images and the difficulty of modeling visual environments. While generative models are increasingly used as camera surrogates in verification, their reliance on stochastic latent variables introduces unnecessary overapproximation error. To address this bottleneck, we propose a Deterministic World Model (DWM) that maps system states directly to generative images, effectively eliminating uninterpretable latent variables to ensure precise input bounds. The DWM is trained with a dual-objective loss function that combines pixel-level reconstruction accuracy with a control difference loss to maintain behavioral consistency with the real system. We integrate DWM into a verification pipeline utilizing Star-based reachabil-ity analysis (StarV) and employ conformal prediction to derive rigorous statistical bounds on the trajectory deviation between the world model and the actual vision-based system. Experiments on standard benchmarks show that our approach yields significantly tighter reachable sets and better verification performance than a latent-variable baseline.

Diffusion-based planners have shown great promise for autonomous driving due to their ability to capture multi-modal driving behaviors. However, guiding these models effectively in reactive, closed-loop environments remains a significant challenge. Simple conditioning often fails to provide sufficient guidance in complex and dynamic driving scenarios. Recent work attempts to use typical expert driving behaviors (i.e., anchors) to guide diffusion models but relies on a truncated schedule, which introduces theoretical inconsistencies and can compromise performance. To address this, we introduce BridgeDrive, a novel anchor-guided diffusion bridge policy for closed-loop trajectory planning. Our approach provides a principled diffusion framework that effectively translates anchors into fine-grained trajectory plans, appropriately responding to varying traffic conditions. Our planner is compatible with efficient ODE solvers, a critical factor for real-time autonomous driving deployment. We achieve state-of-the-art performance on the Bench2Drive benchmark, improving the success rate by 7.72% over prior arts. Closed-loop planning with reactive agents is a critical challenge in autonomous driving, which requires effective interaction with complex and dynamic traffic environments (Jia et al., 2024).

Self-driving laboratories (SDLs) have accelerated the throughput and automation capabilities for discovering and improving chemistries and materials. Although these SDLs have automated many of the steps required to conduct chemical and materials experiments, a commonly overlooked step in the automation pipeline is the handling and reloading of substrates used to transfer or deposit materials onto for downstream characterization. Here, we develop a closed-loop method of Automated Substrate Handling and Exchange (ASHE) using robotics, dual-actuated dispensers, and deep learning-driven computer vision to detect and correct errors in the manipulation of fragile and transparent substrates for SDLs. Using ASHE, we demonstrate a 98.5% first-time placement accuracy across 130 independent trials of reloading transparent glass substrates into an SDL, where only two substrate misplacements occurred and were successfully detected as errors and automatically corrected. Through the development of more accurate and reliable methods for handling various types of substrates, we move toward an improvement in the automation capabilities of self-driving laboratories, furthering the acceleration of novel chemical and materials discoveries.

Recent efficient sequence modeling methods such as Gated DeltaNet, TTT, and RWKV-7 have achieved performance improvements by supervising the recurrent memory management through Delta learning rule. Unlike previous state-space models (e.g., Mamba) and gated linear attentions (e.g., GLA), these models introduce interactions between the recurrent state and the key vector, structurally resembling bilinear systems. In this paper, we first introduce the concept of Bilinear RNNs with a comprehensive analysis on the advantages and limitations of these models. Then, based on closed-loop control theory, we propose a novel Bilinear RNN variant named Comba, which adopts a scalar-plus-low-rank state transition, with both state feedback and output feedback corrections. We also implement a hardware-efficient chunk-wise parallel kernel in Triton and train models with 340M/1.3B parameters on large-scale corpus. Comba demonstrates superior performance and computation efficiency in both language and vision modeling.

We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks. By leveraging interval analysis and interval bound propagation, we derive a tractable and scalable sufficient condition for closed-loop contractivity that reduces to checking that the dominant eigenvalue of a symmetric Metzler matrix is nonpositive. We combine this sufficient condition with a domain partitioning strategy to integrate this sufficient condition into training. The proposed approach is validated on an inverted pendulum system, demonstrating the ability to learn neural network controllers and contraction metrics that provably satisfy the contraction condition.

Autonomous driving policies are typically trained via open-loop behavior cloning of human demonstrations. However, such policies suffer from covariate shift when deployed in closed loop, leading to compounding errors. W e introduce Rollouts as Demonstrations (RoaD), a simple and efficient method to mitigate covariate shift by leveraging the policy's own closed-loop rollouts as additional training data. During rollout generation, RoaD incorporates expert guidance to bias trajectories toward high-quality behavior, producing informative yet realistic demonstrations for fine-tuning. This approach enables robust closed-loop adaptation with orders of magnitude less data than reinforcement learning, and avoids restrictive assumptions of prior closed-loop supervised fine-tuning (CL-SFT) methods, allowing broader applications domains including end-to-end driving. W e demonstrate the effectiveness of RoaD on WOSAC, a large-scale traffic simulation benchmark, where it performs similar or better than the prior CL-SFT method; and in AlpaSim, a high-fidelity neural reconstruction-based simulator for end-to-end driving, where it improves driving score by 41% and reduces collisions by 54%.

Contemporary autoregressive transformers operate in open loop: each hidden state is computed in a single forward pass and never revised, causing errors to propagate uncorrected through the sequence. We identify this open-loop bottleneck as a fundamental architectural limitation underlying well-documented failures in long-range reasoning, factual consistency, and multi-step planning. To address this limitation, we introduce the closed-loop prediction principle, which requires that models iteratively refine latent representations until reaching a self-consistent equilibrium before committing to each token. We instantiate this principle as Equilibrium Transformers (EqT), which augment standard transformer layers with an Equilibrium Refinement Module that minimizes a learned energy function via gradient descent in latent space. The energy function enforces bidirectional prediction consistency, episodic memory coherence, and output confidence, all computed without external supervision. Theoretically, we prove that EqT performs approximate MAP inference in a latent energy-based model, establish linear convergence guarantees, and show that refinement improves predictions precisely on hard instances where one-shot inference is suboptimal. The framework unifies deep equilibrium models, diffusion language models, and test-time training as special cases. Preliminary experiments on the binary parity task demonstrate +3.28% average improvement on challenging sequences, with gains reaching +8.07% where standard transformers approach random performance, validating that the benefit of deliberation scales with task difficulty. Just as attention mechanisms resolved the sequential bottleneck of recurrent networks, we propose that closed-loop equilibrium may resolve the commitment bottleneck of open-loop autoregression, representing a foundational step toward language models.

End-to-end (E2E) autonomous driving models have demonstrated strong performance in open-loop evaluations but often suffer from cascading errors and poor generalization in closed-loop settings. To address this gap, we propose Model-based Policy Adaptation (MPA), a general framework that enhances the robustness and safety of pretrained E2E driving agents during deployment. MPA first generates diverse counterfactual trajectories using a geometry-consistent simulation engine, exposing the agent to scenarios beyond the original dataset. Based on this generated data, MPA trains a diffusion-based policy adapter to refine the base policy's predictions and a multi-step Q value model to evaluate long-term outcomes. At inference time, the adapter proposes multiple trajectory candidates, and the Q value model selects the one with the highest expected utility. Experiments on the nuScenes benchmark using a photorealistic closed-loop simulator demonstrate that MPA significantly improves performance across in-domain, out-of-domain, and safety-critical scenarios. We further investigate how the scale of counterfactual data and inference-time guidance strategies affect overall effectiveness.

Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time diffusion (denoising) process, for action inference, makes it challenging to use for real-time applications where quick decision-making is mandatory. This work studies the possibility of conducting the denoising process only partially before executing an action, allowing the plant to evolve according to its dynamics in parallel to the reverse-time diffusion dynamics ongoing on the computer. In a classical diffusion policy setting, the plant dynamics are usually slow and the two dynamical processes are uncoupled. Here, we investigate theoretical bounds on the stability of closed-loop systems using diffusion policies when the plant dynamics and the denoising dynamics are coupled. The contribution of this work gives a framework for faster imitation learning and a metric that yields if a controller will be stable based on the variance of the demonstrations.