Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for efficiently solving mixed-integer MPC motion planning problems using a hybrid zonotope representation of the obstacle-free space. The MPC optimization problem is formulated as a multi-stage mixed-integer quadratic program (MIQP) using a hybrid zonotope representation of the non-convex constraints. Risk-aware planning is supported by assigning costs to different regions of the obstacle-free space within the MPC cost function. A multi-stage MIQP solver is presented that exploits the structure of the hybrid zonotope constraints. For some hybrid zonotope representations, it is shown that the convex relaxation is tight, i.e., equal to the convex hull. In conjunction with logical constraints derived from the AV motion planning context, this property is leveraged to generate tight quadratic program (QP) sub-problems within a branch-and-bound mixed-integer solver. The hybrid zonotope structure is further leveraged to reduce the number of matrix factorizations that need to be computed within the QP sub-problems. Simulation studies are presented for obstacle-avoidance and risk-aware motion planning problems using polytopic maps and occupancy grids. In most cases, the proposed solver finds the optimal solution an order of magnitude faster than a state-of-the-art commercial solver. Processor-in-the-loop studies demonstrate the utility of the solver for real-time implementations on embedded hardware.

We introduce forward-backward stochastic differential equations, highlighting the connection between solutions of these and solutions of partial differential equations, related by the Feynman-Kac theorem. We review the technique of approximating solutions to high dimensional partial differential equations using neural networks, and similarly approximate solutions of stochastic differential equations using multilevel Monte Carlo. Connecting the multilevel Monte Carlo method with the neural network framework using the setup established by E et al. and Raissi, we replicate many of their empirical results, and provide novel numerical analyses to produce strong error bounds for the specific framework of Raissi. Our results bound the overall strong error in terms of the maximum of the discretisation error and the neural network's approximation error. Our analyses are pivotal for applications of multilevel Monte Carlo, for which we propose suitable frameworks to exploit the variance structures of the multilevel estimators we elucidate. Also, focusing on the loss function advocated by Raissi, we expose the limitations of this, highlighting and quantifying its bias and variance. Lastly, we propose various avenues of further research which we anticipate should offer significant insight and speed improvements.

In this work, we introduce a framework that enables highly maneuverable locomotion using non-periodic contacts. This task is challenging for traditional optimization and planning methods to handle due to difficulties in specifying contact mode sequences in real-time. To address this, we use a bi-level contact-implicit planner and hybrid model predictive controller to draft and execute a motion plan. We investigate how this method allows us to plan arm contact events on the shmoobot, a smaller ballbot, which uses an inverse mouse-ball drive to achieve dynamic balancing with a low number of actuators. Through multiple experiments we show how the arms allow for acceleration, deceleration and dynamic obstacle avoidance that are not achievable with the mouse-ball drive alone. This demonstrates how a holistic approach to locomotion can increase the control authority of unique robot morpohologies without additional hardware by leveraging robot arms that are typically used only for manipulation. Project website: https://cmushmoobot.github.io/Wallbounce

As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem dimensions grow. In this paper, we introduce an end-to-end quantum algorithm for linear-quadratic control with provable speedups. Our algorithm, based on a policy gradient method, incorporates a novel quantum subroutine for solving the matrix Lyapunov equation. Specifically, we build a quantum-assisted differentiable simulator for efficient gradient estimation that is more accurate and robust than classical methods relying on stochastic approximation. Compared to the classical approaches, our method achieves a super-quadratic speedup. To the best of our knowledge, this is the first end-to-end quantum application to linear control problems with provable quantum advantage.

In-context learning (ICL) is a powerful technique for getting language models to perform complex tasks with no training updates. Prior work has established strong correlations between the number of in-context examples provided and the accuracy of the model's predictions. In this paper, we seek to explain this correlation by showing that ICL approximates a Bayesian learner. This perspective gives rise to a family of novel Bayesian scaling laws for ICL. In experiments with \mbox{GPT-2} models of different sizes, our scaling laws exceed or match existing scaling laws in accuracy while also offering interpretable terms for task priors, learning efficiency, and per-example probabilities. To illustrate the analytic power that such interpretable scaling laws provide, we report on controlled synthetic dataset experiments designed to inform real-world studies of safety alignment. In our experimental protocol, we use SFT to suppress an unwanted existing model capability and then use ICL to try to bring that capability back (many-shot jailbreaking). We then experiment on real-world instruction-tuned LLMs using capabilities benchmarks as well as a new many-shot jailbreaking dataset. In all cases, Bayesian scaling laws accurately predict the conditions under which ICL will cause the suppressed behavior to reemerge, which sheds light on the ineffectiveness of post-training at increasing LLM safety.

While `jailbreaks' have been central to research on the safety and reliability of LLMs (large language models), the underlying mechanisms behind these attacks are not well understood. Some prior works have used linear methods to analyze jailbreak prompts or model refusal. Here, however, we compare linear and nonlinear methods to study the features in prompts that contribute to successful jailbreaks. We do this by probing for jailbreak success based only on the portions of the latent representations corresponding to prompt tokens. First, we introduce a dataset of 10,800 jailbreak attempts from 35 attack methods. We then show that different jailbreaking methods work via different nonlinear features in prompts. Specifically, we find that while probes can distinguish between successful and unsuccessful jailbreaking prompts with a high degree of accuracy, they often transfer poorly to held-out attack methods. We also show that nonlinear probes can be used to mechanistically jailbreak the LLM by guiding the design of adversarial latent perturbations. These mechanistic jailbreaks are able to jailbreak Gemma-7B-IT more reliably than 34 of the 35 techniques that it was trained on. Ultimately, our results suggest that jailbreaks cannot be thoroughly understood in terms of universal or linear prompt features alone.

Scientists have discovered a technique whereby light can be bent around corners, inspired by the way clouds scatter sunlight. This type of light-bending could lead to advances in medical imaging, electronics cooling and even nuclear reactor design. Daniele Faccio at the University of Glasgow, UK, and his colleagues say they are shocked this type of light scattering wasn't noticed before. It works on the same basis as clouds, snow and other white materials that absorb light: once photons hit the surface of such a material, they are scattered in all directions, barely penetrating at all and getting reflected out the way they came. For instance, when sunlight hits a tall cumulonimbus cloud, it bounces off the top, making this part of the cloud appear bright white.

Warm-starting neural network training by initializing networks with previously learned weights is appealing, as practical neural networks are often deployed under a continuous influx of new data. However, it often leads to loss of plasticity, where the network loses its ability to learn new information, resulting in worse generalization than training from scratch. This occurs even under stationary data distributions, and its underlying mechanism is poorly understood. We develop a framework emulating real-world neural network training and identify noise memorization as the primary cause of plasticity loss when warm-starting on stationary data. Motivated by this, we propose Direction-Aware SHrinking (DASH), a method aiming to mitigate plasticity loss by selectively forgetting memorized noise while preserving learned features.

Tiny aerial robots show promise for applications like environmental monitoring and search-and-rescue but face challenges in control due to their limited computing power and complex dynamics. Model Predictive Control (MPC) can achieve agile trajectory tracking and handle constraints. Although current learning-based MPC methods, such as Gaussian Process (GP) MPC, improve control performance by learning residual dynamics, they are computationally demanding, limiting their onboard application on tiny robots. This paper introduces Tiny Learning-Based Model Predictive Control (LB MPC), a novel framework for resource-constrained micro multirotor platforms. By exploiting multirotor dynamics' structure and developing an efficient solver, our approach enables high-rate control at 100 Hz on a Crazyflie 2.1 with a Teensy 4.0 microcontroller. We demonstrate a 23% average improvement in tracking performance over existing embedded MPC methods, achieving the first onboard implementation of learning-based MPC on a tiny multirotor (53 g).

Autonomous cooperative planning (ACP) is a promising technique to improve the efficiency and safety of multi-vehicle interactions for future intelligent transportation systems. However, realizing robust ACP is a challenge due to the aggregation of perception, motion, and communication uncertainties. This paper proposes a novel multi-uncertainty aware ACP (MUACP) framework that simultaneously accounts for multiple types of uncertainties via regularized cooperative model predictive control (RC-MPC). The regularizers and constraints for perception, motion, and communication are constructed according to the confidence levels, weather conditions, and outage probabilities, respectively. The effectiveness of the proposed method is evaluated in the Car Learning to Act (CARLA) simulation platform. Results demonstrate that the proposed MUACP efficiently performs cooperative formation in real time and outperforms other benchmark approaches in various scenarios under imperfect knowledge of the environment.