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Learning to Relax: Setting Solver Parameters Across a Sequence of Linear System Instances

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm -- using only the number of iterations as feedback -- can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

GUI Action Narrator: Where and When Did That Action Take Place?

The advent of Multimodal LLMs has significantly enhanced image OCR recognition capabilities, making GUI automation a viable reality for increasing efficiency in digital tasks. One fundamental aspect of developing a GUI automation system is understanding primitive GUI actions. This comprehension is crucial as it enables agents to learn from user demonstrations, an essential element of automation. To rigorously evaluate such capabilities, we developed a video captioning benchmark for GUI actions, comprising 4,189 diverse video captioning samples. This task presents unique challenges compared to natural scene video captioning: 1) GUI screenshots typically contain denser information than natural scenes, and 2) events within GUIs are subtler and occur more rapidly, requiring precise attention to the appropriate time span and spatial region for accurate understanding. To address these challenges, we introduce our GUI action dataset Act2Cap as well as a simple yet effective framework, GUI Narrator, for GUI video captioning that utilizes the cursor as a visual prompt to enhance the interpretation of high-resolution screenshots. Specifically, a cursor detector is trained on our dataset, and a multimodal LLM model with mechanisms for selecting keyframes and key regions generates the captions. Experimental results indicate that even for today's most advanced multimodal models, such as GPT-4o, the task remains highly challenging. Additionally, our evaluations show that our strategy effectively enhances model performance, whether integrated into the fine-tuning of open-source models or employed as a prompting strategy in closed-source models.

ShortcutsBench: A Large-Scale Real-world Benchmark for API-based Agents

Recent advancements in integrating large language models (LLMs) with application programming interfaces (APIs) have gained significant interest in both academia and industry. These API-based agents, leveraging the strong autonomy and planning capabilities of LLMs, can efficiently solve problems requiring multi-step actions. However, their ability to handle multi-dimensional difficulty levels, diverse task types, and real-world demands through APIs remains unknown. In this paper, we introduce ShortcutsBench, a large-scale benchmark for the comprehensive evaluation of API-based agents in solving tasks with varying levels of difficulty, diverse task types, and real-world demands. ShortcutsBench includes a wealth of real APIs from Apple Inc.'s operating systems, refined user queries from shortcuts, human-annotated high-quality action sequences from shortcut developers, and accurate parameter filling values about primitive parameter types, enum parameter types, outputs from previous actions, and parameters that need to request necessary information from the system or user. Our extensive evaluation of agents built with 5 leading open-source (size >= 57B) and 4 closed-source LLMs (e.g. Gemini-1.5-Pro and GPT-3.5) reveals significant limitations in handling complex queries related to API selection, parameter filling, and requesting necessary information from systems and users. These findings highlight the challenges that API-based agents face in effectively fulfilling real and complex user queries. All datasets, code, and experimental results will be available at https://github.com/eachsheep/shortcutsbench.

Programmable Heisenberg interactions between Floquet qubits

The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emerging quantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model is on one hand the basis for many-body quantum simulation of spin systems, and on the other hand the primitive for an expressive quantum gate set. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%, 99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is applicable to various fixed-frequency high-coherence platforms, thereby unlocking a suite of essential interactions for high-performance quantum information processing. From a broader perspective, our work provides compelling avenues for future exploration of quantum electrodynamics and optimal control using the Floquet framework.

OmniManip: Towards General Robotic Manipulation via Object-Centric Interaction Primitives as Spatial Constraints

The development of general robotic systems capable of manipulating in unstructured environments is a significant challenge. While Vision-Language Models(VLM) excel in high-level commonsense reasoning, they lack the fine-grained 3D spatial understanding required for precise manipulation tasks. Fine-tuning VLM on robotic datasets to create Vision-Language-Action Models(VLA) is a potential solution, but it is hindered by high data collection costs and generalization issues. To address these challenges, we propose a novel object-centric representation that bridges the gap between VLM's high-level reasoning and the low-level precision required for manipulation. Our key insight is that an object's canonical space, defined by its functional affordances, provides a structured and semantically meaningful way to describe interaction primitives, such as points and directions. These primitives act as a bridge, translating VLM's commonsense reasoning into actionable 3D spatial constraints. In this context, we introduce a dual closed-loop, open-vocabulary robotic manipulation system: one loop for high-level planning through primitive resampling, interaction rendering and VLM checking, and another for low-level execution via 6D pose tracking. This design ensures robust, real-time control without requiring VLM fine-tuning. Extensive experiments demonstrate strong zero-shot generalization across diverse robotic manipulation tasks, highlighting the potential of this approach for automating large-scale simulation data generation.