Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains.We identify a core aspect of this issue as "invalid thinking"-models tend to repeatedly double-check their work after having derived the correct answer.To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved.Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO).LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process.Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression.Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs.

The visual world around us constantly evolves, from real-time news and social media trends to global infrastructure changes visible through satellite imagery and augmented reality enhancements. However, Multimodal Large Language Models (MLLMs), which automate many tasks, struggle to stay current, limited by the cutoff dates in their fixed training datasets.To quantify this stagnation, we introduce LiveVQA, the first-of-its-kind dataset featuring 107,143 samples and 12 categories data specifically designed to support research in both seeking and updating with live visual knowledge.Drawing from recent news articles, video platforms, and academic publications in April 2024-May 2025, LiveVQA enables evaluation of how models handle latest visual information beyond their knowledge boundaries and how current methods help to update them. Our comprehensive benchmarking of 17 state-of-the-art MLLMs reveals significant performance gaps on content beyond knowledge cutoff, and tool-use or agentic visual seeking framework drastically gain an average of 327% improvement. Furthermore, we explore parameter-efficient fine-tuning methods to update MLLMs with new visual knowledge.We dive deeply to the critical balance between adapter capacity and model capability when updating MLLMs with new visual knowledge. All the experimental dataset and source code are publicly available at: https://livevqa.github.io.

Opaque sales are a selling mechanism in which a seller offers multiple products but the buyer does not know which specific product they will receive until after the purchase. This mechanism is widely used in the tourism industry, such as staycation packages with undisclosed hotel options or tours to different destinations, and in e-commerce through mystery boxes. In many such settings, buyers operate under a unit demand constraint, meaning they derive benefit from only one item despite multiple options being available. In this paper, we formulate and solve a multi-item mechanism design problem for opaque sales. Our goal is to identify a distribution-free mechanism that maximizes the competitive ratio, defined as the ratio between the revenue generated by the mechanism and the maximum revenue attainable with full knowledge of the buyer's valuations. Despite the problem's infinite dimensionality, we show that the optimal mechanism admits a semi-analytical form, characterized by the solution of an auxiliary convex optimization problem whose size scales linearly with the number of items. Furthermore, we demonstrate that this mechanism can be equivalently implemented through a menu of infinite level-access lotteries, where the buyer pays an amount to access a randomly assigned subset of items, with higher payments granting access to a larger selection. We then analyze the impact of menu size limitations on the competitive ratio and conclude with a prototypical example illustrating our approach.