The rapid advancement of large language model (LLM) technology has led to diverse applications, many of which inherently require randomness, such as stochastic decision-making, gaming, scheduling, AI agents, and cryptography-related tasks. However, the capabilities of LLMs in handling randomness, particularly in generating and utilizing random numbers effectively, remain unclear. This paper investigates the capacity of LLMs for handling tasks that involve randomness through a series of experiments. We designed a set of experiments that consider various factors that can influence an LLM's performance in tasks involving randomness, such as accessibility to external tools, types of tasks, model states (fresh vs. non-fresh), and prompting strategies. The experiments cover a range of tasks, including generating random numbers, generating random strings such as passwords, shuffling items, and evaluating the quality of randomness using entropy and the NIST randomness test-suite. Our findings reveal that while LLMs can generate outputs that exhibit some degree of randomness, their performance is inconsistent and often deviates significantly from the expected behavior. The analysis of the experimental results highlights key limitations and areas where improvement is needed for the LLMs to effectively handle tasks involving randomness

Fine-tuning (FT) large language models (LLMs) is crucial for adapting general-purpose models to specific tasks, enhancing accuracy and relevance with minimal resources. To further enhance generalization ability while reducing training costs, this paper proposes Federated LoRA with Dropout (FedLoDrop), a new framework that applies dropout to the rows and columns of the trainable matrix in Federated LoRA. A generalization error bound and convergence analysis under sparsity regularization are obtained, which elucidate the fundamental trade-off between underfitting and overfitting. The error bound reveals that a higher dropout rate increases model sparsity, thereby lowering the upper bound of pointwise hypothesis stability (PHS). While this reduces the gap between empirical and generalization errors, it also incurs a higher empirical error, which, together with the gap, determines the overall generalization error. On the other hand, though dropout reduces communication costs, deploying FedLoDrop at the network edge still faces challenges due to limited network resources. To address this issue, an optimization problem is formulated to minimize the upper bound of the generalization error, by jointly optimizing the dropout rate and resource allocation subject to the latency and per-device energy consumption constraints. To solve this problem, a branch-and-bound (B\&B)-based method is proposed to obtain its globally optimal solution. Moreover, to reduce the high computational complexity of the B\&B-based method, a penalized successive convex approximation (P-SCA)-based algorithm is proposed to efficiently obtain its high-quality suboptimal solution. Finally, numerical results demonstrate the effectiveness of the proposed approach in mitigating overfitting and improving the generalization capability.

Embodied decision-making enables agents to translate high-level goals into executable actions through continuous interactions within the physical world, forming a cornerstone of general-purpose embodied intelligence. Large language models (LLMs), with their general decision-making capabilities, offer a promising path to realize this potential; however, LLMs trained solely on language lack exposure to physical environments, limiting their true embodied understanding. To bridge this gap, we propose the concept of a training ground: a comprehensive infrastructure that provides task and scene simulation, embodied interaction, and feedback signals, offering a one-stop solution for LLM acquire genuine embodied decision-making skills. In this work, we present EmboMatrix, the first training ground of its kind, providing massive and diverse tasks with efficient simulation and precise rewards. EmboMatrix incorporates a series of novel techniques: a multi-agent data engine for large-scale task and scene generation, a distributed heterogeneous-hardware system for scalable simulation, and a multi-level reward architecture for precise supervision. Leveraging EmboMatrix, we cultivate EmboBrain, an LLM whose embodied decision-making abilities emerge from extensive embodied interactions. Experiments show that EmboBrain-7B surpasses the 671B DeepSeek-R1 baseline by 9.5\% on two challenging embodied decision-making benchmarks, demonstrating the power of interactive, environment-grounded learning for building truly intelligent embodied agents.

Inferring demographic attributes such as age, sex, or income level from human mobility patterns enables critical applications such as targeted public health interventions, equitable urban planning, and personalized transportation services. Existing mobility-based demographic inference studies heavily rely on large-scale trajectory data with demographic labels, leading to limited interpretability and poor generalizability across different datasets and user groups. We propose HiCoTraj (Zero-Shot Demographic Reasoning via Hierarchical Chain-of-Thought Prompting from Trajectory), a framework that leverages LLMs' zero-shot learning and semantic understanding capabilities to perform demographic inference without labeled training data. HiCoTraj transforms trajectories into semantically rich, natural language representations by creating detailed activity chronicles and multi-scale visiting summaries. Then HiCoTraj uses a novel hierarchical chain of thought reasoning to systematically guide LLMs through three cognitive stages: factual feature extraction, behavioral pattern analysis, and demographic inference with structured output. This approach addresses the scarcity challenge of labeled demographic data while providing transparent reasoning chains. Experimental evaluation on real-world trajectory data demonstrates that HiCoTraj achieves competitive performance across multiple demographic attributes in zero-shot scenarios.

AI reasoning agents are already able to solve a variety of tasks by deploying tools, simulating outcomes of multiple hypotheses and reflecting on them. In doing so, they perform computation, although not in the classical sense -- there is no program being executed. Still, if they perform computation, can AI agents be universal? Can chain-of-thought reasoning solve any computable task? How does an AI Agent learn to reason? Is it a matter of model size? Or training dataset size? In this work, we reinterpret the role of learning in the context of AI Agents, viewing them as compute-capable stochastic dynamical systems, and highlight the role of time in a foundational principle for learning to reason. In doing so, we propose a shift from classical inductive learning to transductive learning -- where the objective is not to approximate the distribution of past data, but to capture their algorithmic structure to reduce the time needed to find solutions to new tasks. Transductive learning suggests that, counter to Shannon's theory, a key role of information in learning is about reduction of time rather than reconstruction error. In particular, we show that the optimal speed-up that a universal solver can achieve using past data is tightly related to their algorithmic information. Using this, we show a theoretical derivation for the observed power-law scaling of inference time versus training time. We then show that scaling model size can lead to behaviors that, while improving accuracy on benchmarks, fail any reasonable test of intelligence, let alone super-intelligence: In the limit of infinite space and time, large models can behave as savants, able to brute-force through any task without any insight. Instead, we argue that the key quantity to optimize when scaling reasoning models is time, whose critical role in learning has so far only been indirectly considered.

Large Reasoning Models (LRMs) are powerful, but they still suffer from inefficient and off-target reasoning. Currently, training-free methods are limited to either rigid heuristics or descriptive, non-actionable analyses. In this paper, we introduce ThinkPilot, a training-free framework that automatically optimizes LRMs reasoning. It uses an evolutionary process to generate think-prefixes, which are instructions that evolve driven by a taxonomy of reasoning behaviors to guide models toward superior performance. Extensive experiments demonstrate ThinkPilot's broad effectiveness: it significantly improves the accuracy-length trade-off for efficient reasoning, drastically improves safety (for example, cutting the StrongREJECT score of DeepSeek-R1-Distill-Qwen-32B from 27.0% to 0.7), and enhances instruction following. It also synergizes with existing training-based methods. Our analysis reveals that think-prefixes can reliably control LRMs' reasoning behaviors, and that different tasks have strong preferences for specific behavioral distributions. By automatically identifying and eliciting these behaviors, ThinkPilot provides a generalizable framework for aligning LRMs reasoning with task demands. Data and code are available at https://github.com/teqkilla/ThinkPilot

Deploying useful Long-Context Transformer Models (LCTMs) requires addressing two key challenges: (1) A growing memory footprint due to quadratic self-attention and linear KV-cache scaling in memory as sequence length increases; (2) the ContextRot phenomena where empirical evidence suggests that transformer architecture's performance degrades with increasing context length. Given the shared dependency on the input, a natural question arises: Can we surgically select the most important input chunks for processing to synergistically (a) reduce the memory footprint, and (b) mitigate the ContextRot effects? In this paper, we answer this question in the affirmative for long-context summarization tasks. We propose APCE as a context-aware solution to select the most important input chunks through low-dimensional semantic similarity matching with the current query. By directly operating on the input, APCE decouples from strict dependency on underlying hardware or CUDA environments, promising a compatible solution scalable to different deployment systems. Our empirical evaluations have demonstrated superior or on-par summarization performance for APCE compared to the full dense baseline using a fraction (50%-70%) of the input sequence resulting in KV-cache and self-attention memory efficiency improvements. We hope our findings inspire further research on context-aware efficiency solutions for LCTMs geared towards other relevant long-context tasks.

Existing alignment techniques for Large Language Models (LLMs), such as Direct Preference Optimization (DPO), typically treat the model as a monolithic entity, applying uniform optimization pressure across all layers. This approach overlooks the functional specialization within the Transformer architecture, where different layers are known to handle distinct tasks from syntax to abstract reasoning. In this paper, we challenge this one-size-fits-all paradigm by introducing Hierarchical Alignment, a novel method that applies targeted DPO to distinct functional blocks of a model's layers: local (syntax), intermediate (logic), and global (factuality). Through a series of controlled experiments on state-of-the-art models like Llama-3.1-8B and Qwen1.5-7B using LoRA for surgical fine-tuning, our results, evaluated by a powerful LLM-as-Judge, demonstrate significant and predictable improvements. Specifically, aligning the local layers (Local-Align) enhances grammatical fluency. More importantly, aligning the global layers (Global-Align) not only improves factual consistency as hypothesized but also proves to be the most effective strategy for enhancing logical coherence, outperforming all baselines. Critically, all hierarchical strategies successfully avoid the "alignment tax" observed in standard DPO, where gains in fluency come at the cost of degraded logical reasoning. These findings establish a more resource-efficient, controllable, and interpretable path for model alignment, highlighting the immense potential of shifting from monolithic optimization to structure-aware surgical fine-tuning to build more advanced and reliable LLMs.

The rapid advancement of large language models (LLMs) has transformed the landscape of natural language processing, enabling breakthroughs across a wide range of areas including question answering, machine translation, and text summarization. Yet, their deployment in real-world applications has raised concerns over reliability and trustworthiness, as LLMs remain prone to hallucinations that produce plausible but factually incorrect outputs. Uncertainty quantification (UQ) has emerged as a central research direction to address this issue, offering principled measures for assessing the trustworthiness of model generations. We begin by introducing the foundations of UQ, from its formal definition to the traditional distinction between epistemic and aleatoric uncertainty, and then highlight how these concepts have been adapted to the context of LLMs. Building on this, we examine the role of UQ in hallucination detection, where quantifying uncertainty provides a mechanism for identifying unreliable generations and improving reliability. We systematically categorize a wide spectrum of existing methods along multiple dimensions and present empirical results for several representative approaches. Finally, we discuss current limitations and outline promising future research directions, providing a clearer picture of the current landscape of LLM UQ for hallucination detection.

Recent advancements in large language models (LLMs) have shown strong performance in natural language understanding and generation tasks. However, LLMs continue to encounter challenges with hallucinations, where models generate plausible but incorrect information. While several factors contribute to hallucinations, the impact of ill-formed prompts, prompts with ambiguous wording, incorrect grammar, or incomplete information, was relatively under explored. To address this, we introduce Multi-stage Prompt Refinement (MPR), a framework designed to systematically improve these ill-formed prompts across multiple stages. Each stage addresses specific errors such as punctuation, typographical mistakes, and misuse of key terms, using small language models (SLMs) fine-tuned for these tasks. MPR iteratively enhances the clarity of prompts with additional context and employs a self-reflection mechanism with ranking to prioritize the most relevant input. Experimental results on hallucination benchmarks show that prompts refined by MPR achieve over an 85 % win rate compared to their original forms, demonstrating its effectiveness in reducing hallucinations and improving LLM output accuracy. Interestingly, we reveal that MPR can be combined with existing post-hoc hallucination mitigation frameworks, further enhancing its versatility. MPR provides a lightweight and adaptable solution for enhancing LLM reliability across various domains. Introduction Advancements in artificial intelligence have significantly improved large language models (LLMs), enabling them to excel in tasks like contextual understanding and human-like text generation [1, 2, 3, 4, 5].