We present a generic Branch-and-Bound procedure designed to solve L0-penalized optimization problems. Existing approaches primarily focus on quadratic losses and construct relaxations using "Big-M" constraints and/or L2-norm penalties. In contrast, our method accommodates a broader class of loss functions and allows greater flexibility in relaxation design through a general penalty term, encompassing existing techniques as special cases. We establish theoretical results ensuring that all key quantities required for the Branch-and-Bound implementation admit closed-form expressions under the general blanket assumptions considered in our work. Leveraging this framework, we introduce El0ps, an open-source Python solver with a plug-and-play workflow that enables user-defined losses and penalties in L0-penalized problems. Through extensive numerical experiments, we demonstrate that El0ps achieves state-of-the-art performance on classical instances and extends computational feasibility to previously intractable ones.

As the complexity of AI systems and their interactions with the world increases, generating explanations for their behaviour is important for safely deploying AI. For agents, the most natural abstractions for predicting behaviour attribute beliefs, intentions and goals to the system. If an agent behaves as if it has a certain goal or belief, then we can make reasonable predictions about how it will behave in novel situations, including those where comprehensive safety evaluations are untenable. How well can we infer an agent's beliefs from their behaviour, and how reliably can these inferred beliefs predict the agent's behaviour in novel situations? We provide a precise answer to this question under the assumption that the agent's behaviour is guided by a world model. Our contribution is the derivation of novel bounds on the agent's behaviour in new (unseen) deployment environments, which represent a theoretical limit for predicting intentional agents from behavioural data alone. We discuss the implications of these results for several research areas including fairness and safety.

With the rapid advancement of large reasoning models, long Chain-of-Thought (CoT) prompting has demonstrated strong performance on complex tasks. However, this often comes with a significant increase in token usage. In this paper, we conduct a comprehensive empirical analysis comparing long and short CoT strategies. Our findings reveal that while long CoT can lead to performance improvements, its benefits are often marginal relative to its significantly higher token consumption. Specifically, long CoT tends to outperform when ample generation budgets are available, whereas short CoT is more effective under tighter budget constraints. These insights underscore the need for a dynamic approach that selects the proper CoT strategy based on task context and resource availability. To address this, we propose SwitchCoT, an automatic framework that adaptively chooses between long and short CoT strategies to balance reasoning accuracy and computational efficiency. Moreover, SwitchCoT is designed to be budget-aware, making it broadly applicable across scenarios with varying resource constraints. Experimental results demonstrate that SwitchCoT can reduce inference costs by up to 50% while maintaining high accuracy. Notably, under limited token budgets, it achieves performance comparable to, or even exceeding, that of using either long or short CoT alone.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Memes have emerged as a popular form of multimodal online communication, where their interpretation heavily depends on the specific context in which they appear. Current approaches predominantly focus on isolated meme analysis, either for harmful content detection or standalone interpretation, overlooking a fundamental challenge: the same meme can express different intents depending on its conversational context. This oversight creates an evaluation gap: although humans intuitively recognize how context shapes meme interpretation, Large Vision Language Models (LVLMs) can hardly understand context-dependent meme intent. To address this critical limitation, we introduce MemeReaCon, a novel benchmark specifically designed to evaluate how LVLMs understand memes in their original context. We collected memes from five different Reddit communities, keeping each meme's image, the post text, and user comments together. We carefully labeled how the text and meme work together, what the poster intended, how the meme is structured, and how the community responded. Our tests with leading LVLMs show a clear weakness: models either fail to interpret critical information in the contexts, or overly focus on visual details while overlooking communicative purpose. MemeReaCon thus serves both as a diagnostic tool exposing current limitations and as a challenging benchmark to drive development toward more sophisticated LVLMs of the context-aware understanding.

Graph Retrieval Augmented Generation (GraphRAG) effectively enhances external knowledge integration capabilities by explicitly modeling knowledge relationships, thereby improving the factual accuracy and generation quality of Large Language Models (LLMs) in specialized domains. However, existing methods suffer from two inherent limitations: 1) Inefficient Information Aggregation: They rely on a single agent and fixed iterative patterns, making it difficult to adaptively capture multi-level textual, structural, and degree information within graph data. 2) Rigid Reasoning Mechanism: They employ preset reasoning schemes, which cannot dynamically adjust reasoning depth nor achieve precise semantic correction. To overcome these limitations, we propose Graph Counselor, an GraphRAG method based on multi-agent collaboration. This method uses the Adaptive Graph Information Extraction Module (AGIEM), where Planning, Thought, and Execution Agents work together to precisely model complex graph structures and dynamically adjust information extraction strategies, addressing the challenges of multi-level dependency modeling and adaptive reasoning depth. Additionally, the Self-Reflection with Multiple Perspectives (SR) module improves the accuracy and semantic consistency of reasoning results through self-reflection and backward reasoning mechanisms. Experiments demonstrate that Graph Counselor outperforms existing methods in multiple graph reasoning tasks, exhibiting higher reasoning accuracy and generalization ability. Our code is available at https://github.com/gjq100/Graph-Counselor.git.

Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a lack of automated methods to support this process. In this paper, we present Math2Visual, an automatic framework for generating pedagogically meaningful visuals from MWP text descriptions. Math2Visual leverages a pre-defined visual language and a design space grounded in interviews with math teachers, to illustrate the core mathematical relationships in MWPs. Using Math2Visual, we construct an annotated dataset of 1,903 visuals and evaluate Text-to-Image (TTI) models for their ability to generate visuals that align with our design. We further fine-tune several TTI models with our dataset, demonstrating improvements in educational visual generation. Our work establishes a new benchmark for automated generation of pedagogically meaningful visuals and offers insights into key challenges in producing multimodal educational content, such as the misrepresentation of mathematical relationships and the omission of essential visual elements.

It has been demonstrated that carefully designed reasoning paradigms, like Chain-of-Thought (CoT) and Tree-of-Thought (ToT), can enhance the reasoning capabilities of small language models by detailed thinking and extensive thought searching, unbounded branching factors in the searching space create prohibitive reasoning consumption. However these methods fall into the trap of local optimum reasoning, which means the model lacks a global perspective while solving problems. We propose a novel reasoning paradigm called Reason from Future (RFF), which generates reasoning paths by bidirectional reasoning that combines top-down planning with bottom-up reasoning accumulation. The essence of RFF lies in its reverse reasoning mechanism, which prioritizes core logical relationships and imposes goal-oriented constraints on intermediate steps, thereby reducing the searching space and mitigating error accumulation inherent in sequential forward reasoning. Empirical evaluations across diverse experiments demonstrate that RFF outperforms conventional paradigms with higher accuracy and less searching space to solve complex tasks.

Continual learning--the ability to acquire, retain, and refine knowledge over time--has always been fundamental to intelligence, both human and artificial. Historically, different AI paradigms have acknowledged this need, albeit with varying priorities: early expert and production systems focused on incremental knowledge consolidation, while reinforcement learning emphasised dynamic adaptation. With the rise of deep learning, deep continual learning has primarily focused on learning robust and reusable representations over time to solve sequences of increasingly complex tasks. However, the emergence of Large Language Models (LLMs) and foundation models has raised the question: Do we still need continual learning when centralised, monolithic models can tackle diverse tasks with access to internet-scale knowledge? We argue that continual learning remains essential for three key reasons: (i) continual pre-training is still necessary to ensure foundation models remain up to date, mitigating knowledge staleness and distribution shifts while integrating new information; (ii) continual fine-tuning enables models to specialise and personalise, adapting to domain-specific tasks, user preferences, and real-world constraints without full retraining, avoiding the need for computationally expensive long context-windows; (iii) continual compositionality offers a scalable and modular approach to intelligence, enabling the orchestration of foundation models and agents to be dynamically composed, recombined, and adapted. While continual pre-training and fine-tuning are explored as niche research directions, we argue it is continual compositionality that will mark the rebirth of continual learning. The future of AI will not be defined by a single static model but by an ecosystem of continually evolving and interacting models, making continual learning more relevant than ever.

As Large Language Models are increasingly deployed in high-stakes domains, their ability to detect false assumptions and reason critically is crucial for ensuring reliable outputs. False-premise questions (FPQs) serve as an important evaluation method by exposing cases where flawed assumptions lead to incorrect responses. While existing benchmarks focus on single-hop FPQs, real-world reasoning often requires multi-hop inference, where models must verify consistency across multiple reasoning steps rather than relying on surface-level cues. To address this gap, we introduce MultiHoax, a benchmark for evaluating LLMs' ability to handle false premises in complex, multi-step reasoning tasks. Our dataset spans seven countries and ten diverse knowledge categories, using Wikipedia as the primary knowledge source to enable factual reasoning across regions. Experiments reveal that state-of-the-art LLMs struggle to detect false premises across different countries, knowledge categories, and multi-hop reasoning types, highlighting the need for improved false premise detection and more robust multi-hop reasoning capabilities in LLMs.