Characterizing a large language model's (LLM's) knowledge of a given question is challenging. As a result, prior work has primarily examined LLM behavior under knowledge conflicts, where the model's internal parametric memory contradicts information in the external context. However, this does not fully reflect how well the model knows the answer to the question. In this paper, we first introduce a taxonomy of five knowledge statuses based on the consistency and correctness of LLM knowledge modes. We then propose KScope, a hierarchical framework of statistical tests that progressively refines hypotheses about knowledge modes and characterizes LLM knowledge into one of these five statuses. We apply KScope to nine LLMs across four datasets and systematically establish: (1) Supporting context narrows knowledge gaps across models.

Recent efforts to apply Large Language Models (LLMs) to time-series anomaly detection (TSAD) have yielded limited success, often performing worse than even simple methods. While prior work has focused solely on downstream performance evaluation, the fundamental question--why do LLMs struggle with TSAD?--has remained largely unexplored. In this paper, we present an in-depth analysis that identifies two core challenges in understanding complex temporal dynamics and accurately localizing anomalies. To address these challenges, we propose a simple yet effective method that combines statistical decomposition with index-aware prompting. Our method outperforms 21 existing prompting strategies on the AnomLLM benchmark, achieving up to a 66.6\% improvement in F1 score. We further compare LLMs with 16 non-LLM baselines on the TSB-AD benchmark, highlighting scenarios where LLMs offer unique advantages via contextual reasoning. Our findings provide empirical insights into how and when LLMs can be effective for TSAD.

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 25.6% to 27.3% for Qwen2.5-1.5B, and from 45.9% to 51.0% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 25.2% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training. Additionally, we have open-sourced both the trained models and the source code.

Large language models (LLMs) have achieved notable progress. Despite their success, next-token prediction (NTP), the dominant method for LLM training and inference, is constrained in both contextual coverage and inference efficiency due to its inherently sequential process. To overcome these challenges, we propose leap multi-token prediction~(L-MTP), an innovative token prediction method that extends the capabilities of multi-token prediction (MTP) by introducing a leap-based mechanism. Unlike conventional MTP, which generates multiple tokens at adjacent positions, L-MTP strategically skips over intermediate tokens, predicting non-sequential ones in a single forward pass. This structured leap not only enhances the model's ability to capture long-range dependencies but also enables a decoding strategy specially optimized for non-sequential leap token generation, effectively accelerating inference. We theoretically demonstrate the benefit of L-MTP in improving inference efficiency.

Large Language Models (LLMs) have emerged with many intellectual capacities. While numerous benchmarks assess their intelligence, limited attention has been given to their ability to explore--an essential capacity for discovering new information and adapting to novel environments in both natural and artificial systems. The extent to which LLMs can effectively explore, particularly in open-ended tasks, remains unclear. This study investigates whether LLMs can surpass humans in exploration during an open-ended task, using Little Alchemy 2 as a paradigm, where agents combine elements to discover new ones. Results show most LLMs underperform compared to humans, except for the o1 model, with those traditional LLMs relying primarily on uncertainty-driven strategies, unlike humans who balance uncertainty and empowerment. Results indicate that traditional reasoning-focused LLMs, such as GPT-4o, exhibit a significantly faster and less detailed reasoning process, limiting their exploratory performance. In contrast, the DeepSeek reasoning model demonstrates prolonged, iterative thought processes marked by repetitive analysis of combinations and past trials, reflecting a more thorough and human-like exploration strategy. Representational analysis of the models with Sparse Autoencoders (SAE) revealed that uncertainty and choices are represented at earlier transformer blocks, while empowerment values are processed later, causing LLMs to think too fast and make premature decisions, hindering effective exploration. These findings shed light on the limitations of LLM exploration and suggest directions for improving their adaptability.

Recent advances in large language models (LLMs) and audio language models have significantly improved music generation, particularly in lyrics-to-song generation.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA's effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.

Large language models have been widely applied, but can inadvertently encode sensitive or harmful information, raising significant safety concerns. Machine unlearning has emerged to alleviate this concern; however, existing training-time unlearning approaches, relying on coarse-grained loss combinations, have limitations in precisely separating knowledge and balancing removal effectiveness with model utility. In contrast, we propose $\textbf{F}$ine-grained $\textbf{A}$ctivation manipu$\textbf{L}$ation by $\textbf{C}$ontrastive $\textbf{O}$rthogonal u$\textbf{N}$alignment (FALCON), a novel representation-guided unlearning approach that leverages information-theoretic guidance for efficient parameter selection, employs contrastive mechanisms to enhance representation separation, and projects conflict gradients onto orthogonal subspaces to resolve conflicts between forgetting and retention objectives. Extensive experiments demonstrate that FALCON achieves superior unlearning effectiveness while maintaining model utility, exhibiting robust resistance against knowledge recovery attempts.

Human-AI conversation frequently relies on quoting earlier text--"check it with the formula I just highlighted"--yet today's large language models (LLMs) lack an explicit mechanism for locating and exploiting such spans.

Multi-Agent Debate (MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components-Majority Voting and inter-agent Debate-and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings.