We present a counterexample-guided approach for synthesizing convex piecewise affine control Lyapunov functions, obtained as the maximum over a finite number of affine functions, for stabilizing switched linear systems. Our approach considers systems whose dynamics are defined by a set of affine ODEs over different regions of the state-space. The goal is to synthesize a control feedback function that uses state-based switching by assigning a dynamical mode to each state from the set of available dynamics. This is achieved by synthesizing a piecewise affine control Lyapunov function that guarantees that for each state variable, the appropriate choice of a control input can cause an instantaneous decrease in the value of the Lyapunov function. Since piecewise affine functions are not smooth, we use a non-smooth analytic characterization of piecewise affine Lyapunov functions. The key contribution of our approach is a counterexample driven algorithm that alternates between verification that a given convex PWA function is a control Lyapunov function or generating a counterexample point where the Lyapunov conditions fail, and synthesis from a finite set of counterexamples generated in the past. We demonstrate that the two steps can be performed using mixed integer linear programming problems (MILP) although no termination guarantees are possible. We show that the branch and cut approach used inside a MILP solver can be adapted to yield a termination guarantee. Although the resulting approach is computationally expensive, it has the advantage of not requiring a "demonstrator" or a pre-existing controller. We provide an empirical evaluation that explores the results of this approach over a set of numerical examples.

Despite the latest remarkable advances in generative modeling, efficient generation of high-quality 3D objects from textual prompts remains a difficult task. A key chal-lenge lies in data scarcity: the most extensive 3D datasets encompass merely millions of samples, while their 2D coun-terparts contain billions of text-image pairs. To address this, we propose a novel approach which harnesses the power of large, pretrained 2D diffusion models. More specifically, our approach, HexaGen3D, fine-tunes a pre-trained text-to-image model to jointly predict 6 orthographic projections and the corresponding 3D latent. We then decode these latents to generate a textured mesh. Hex-aGen3D does not require per-sample optimization, and can infer high-quality and diverse objects from textual prompts in 7 seconds, offering significantly better quality-to-latency trade-offs than existing approaches. Furthermore, Hexa-Gen3D demonstrates strong generalization to new objects or compositions.

Vision-language models have shown impressive progress in recent years. However, existing models are largely limited to turn-based interactions, where each turn must be stepped (i.e., prompted) by the user. Open-ended, asynchronous interactions, where an AI model may proactively deliver timely responses or feedback based on the unfolding situation in real-time, are an open challenge. In this work, we present the QEVD benchmark and dataset, which explores human-AI interaction in the challenging, yet controlled, real-world domain of fitness coaching – a task which intrinsically requires monitoring live user activity and providing immediate feedback. The benchmark requires vision-language models to recognize complex human actions, identify possible mistakes, and provide appropriate feedback in real-time. Our experiments reveal the limitations of existing state-of-the-art vision-language models for such asynchronous situated interactions. Motivated by this, we propose a simple end-to-end streaming baseline that can respond asynchronously to human actions with appropriate feedback at the appropriate time.

Real-time rendering for video games has become increasingly challenging due to the need for higher resolutions, framerates and photorealism. Supersampling has emerged as an effective solution to address this challenge. Our work introduces a novel neural algorithm for super-sampling rendered content that is 4× more efficient than existing methods while maintaining the same level of accuracy. Additionally, we introduce a new dataset which provides auxiliary modalities such as motion vectors and depth generated using graphics rendering features like viewport jittering and mipmap biasing at different resolutions. We believe that this dataset fills a gap in the current dataset landscape and can serve as a valuable resource to help measure progress in the field and advance the state-of-the-art in super-resolution techniques for gaming content.