Reply to "Emergent LLM behaviors are observationally equivalent to data leakage" Abstract A potential concern when simulating populations of large language models (LLMs) is data contamination, i.e. the possibility that training data may shape outcomes in unintended ways. While this concern is important and may hinder certain experiments with multi-agent models, it does not preclude the study of genuinely emergent dynamics in LLM populations. The recent critique by Barrie and T ornberg [1] of the results of Flint Ashery et al. [2] offers an opportunity to clarify that self-organisation and model-dependent emergent dynamics can be studied in LLM populations, highlighting how such dynamics have been empirically observed in the specific case of social conventions. Barrie & T ornberg [1] question whether the emergence of conventions observed in our recent study of interacting large language models (LLMs) [2] can be attributed to genuine collective dynamics, or instead result from data leakage from the models' training data. In this note, we respond to their main points and argue that the observed dynamics cannot be explained by data contamination alone.

Large Language Models (LLMs) increasingly rely on automatic prompt engineering in graphical user interfaces (GUIs) to refine user inputs and enhance response accuracy. However, the diversity of user requirements often leads to unintended misinterpretations, where automated optimizations distort original intentions and produce erroneous outputs. To address this challenge, we propose the Adaptive Greedy Binary Search (AGBS) method, which simulates common prompt optimization mechanisms while preserving semantic stability. Our approach dynamically evaluates the impact of such strategies on LLM performance, enabling robust adversarial sample generation. Through extensive experiments on open and closed-source LLMs, we demonstrate AGBS's effectiveness in balancing semantic consistency and attack efficacy. Our findings offer actionable insights for designing more reliable prompt optimization systems. Code is available at: https://github.com/franz-chang/DOBS

Vector representations of contextual embeddings learned by pre-trained large language models (LLMs) are effective in various downstream tasks in numerical domains such as time series forecasting. Despite their significant benefits, the tendency of LLMs to hallucinate in such domains can have severe consequences in applications such as energy, nature, finance, healthcare, retail and transportation, among others. To guarantee prediction reliability and accuracy in numerical domains, it is necessary to open the black box behind the LLM and provide performance guarantees through explanation. However, there is little theoretical understanding of when pre-trained language models help solve numerical downstream tasks. This paper seeks to bridge this gap by understanding when the next-word prediction capability of LLMs can be adapted to numerical domains through a novel analysis based on the concept of isotropy in the contextual embedding space. Specifically, a log-linear model for LLMs is considered in which numerical data can be predicted from its context through a network with softmax in the output layer of LLMs (i.e., language model head in self-attention). For this model, it is demonstrated that, in order to achieve state-of-the-art performance in numerical domains, the hidden representations of the LLM embeddings must possess a structure that accounts for the shift-invariance of the softmax function. By formulating a gradient structure of self-attention in pre-trained models, it is shown how the isotropic property of LLM embeddings in contextual embedding space preserves the underlying structure of representations, thereby resolving the shift-invariance problem and providing a performance guarantee. Experiments show that different characteristics of numerical data and model architectures have different impacts on isotropy, and this variability directly affects the performances.

Reinforcement Learning (RL)-based post-training has significantly advanced the complex reasoning capabilities of language models, fostering sophisticated self-reflection processes. However, this ``slow thinking'' paradigm presents a critical challenge to reasoning efficiency: models may expend excessive computation on simple questions and shift reasoning prematurely for complex ones. Previous mechanisms typically rely on static length budgets or predefined rules, lacking the adaptability for varying question complexities and models' evolving capabilities. To this end, we propose AdapThink, an adaptive post-training framework designed to induce more efficient thinking while maintaining the performance of reasoning language models. Specifically, AdapThink incorporates two key mechanisms: 1) A group-relative reward function that leverages model confidence and response's characteristic to dynamically adjust the preference of reflection-related transition words without resorting to a fixed length preference. 2) A diversity-aware sampling mechanism that balances the training group's solution accuracy with reasoning diversity via an entropy-guided score. Experiments on several mathematical reasoning datasets with DeepSeek-distilled models demonstrate AdapThink's advantages in enabling adaptive reasoning patterns and mitigating the inefficiencies.

We study an iterative selection problem over N i.i.d. discrete-time stochastic processes with independent increments. At each stage, a fixed number of processes are retained based on their observed values. Under this simple model, we prove that the optimal strategy for selecting the final maximum-value process is to apply greedy selection at each stage. While the result relies on strong independence assumptions, it offers a clean justification for greedy heuristics in multi-stage elimination settings and may serve as a toy example for understanding related algorithms in high-dimensional applications.

As Large Language Models (LLMs) are integrated into safety-critical applications involving sequential decision-making in the real world, it is essential to know when to trust LLM decisions. Existing LLM Uncertainty Quantification (UQ) methods are primarily designed for single-turn question-answering formats, resulting in multi-step decision-making scenarios, e.g., LLM agentic system, being underexplored. In this paper, we introduce a principled, information-theoretic framework that decomposes LLM sequential decision uncertainty into two parts: (i) internal uncertainty intrinsic to the current decision, which is focused on existing UQ methods, and (ii) extrinsic uncertainty, a Mutual-Information (MI) quantity describing how much uncertainty should be inherited from preceding decisions. We then propose UProp, an efficient and effective extrinsic uncertainty estimator that converts the direct estimation of MI to the estimation of Pointwise Mutual Information (PMI) over multiple Trajectory-Dependent Decision Processes (TDPs). UProp is evaluated over extensive multi-step decision-making benchmarks, e.g., AgentBench and HotpotQA, with state-of-the-art LLMs, e.g., GPT-4.1 and DeepSeek-V3. Experimental results demonstrate that UProp significantly outperforms existing single-turn UQ baselines equipped with thoughtful aggregation strategies. Moreover, we provide a comprehensive analysis of UProp, including sampling efficiency, potential applications, and intermediate uncertainty propagation, to demonstrate its effectiveness. Codes will be available at https://github.com/jinhaoduan/UProp.

Attention mechanisms have revolutionized machine learning (ML) by enabling efficient modeling of global dependencies across inputs. Their inherently parallelizable structures allow for efficient scaling with the exponentially increasing size of both pretrained data and model parameters. Yet, despite their central role as the computational backbone of modern large language models (LLMs), the theoretical understanding of Attentions, especially in the nonlinear setting, remains limited. In this paper, we provide a precise characterization of the \emph{in-context memorization error} of \emph{nonlinear Attention}, in the high-dimensional proportional regime where the number of input tokens $n$ and their embedding dimension $p$ are both large and comparable. Leveraging recent advances in the theory of large kernel random matrices, we show that nonlinear Attention typically incurs higher memorization error than linear ridge regression on random inputs. However, this gap vanishes, and can even be reversed, when the input exhibits statistical structure, particularly when the Attention weights align with the input signal direction. Our results reveal how nonlinearity and input structure interact with each other to govern the memorization performance of nonlinear Attention. The theoretical insights are supported by numerical experiments.

Large Language Models (LLMs) are increasingly integrated into everyday applications. As their influence grows, understanding their decision making and underlying personality becomes essential. In this work, we interpret model personality using our proposed Supernova Event Dataset, a novel dataset with diverse articles spanning biographies, historical events, news, and scientific discoveries. We use this dataset to benchmark LLMs on extracting and ranking key events from text, a subjective and complex challenge that requires reasoning over long-range context and modeling causal chains. We evaluate small models like Phi-4, Orca 2, and Qwen 2.5, and large, stronger models such as Claude 3.7, Gemini 2.5, and OpenAI o3, and propose a framework where another LLM acts as a judge to infer each model's personality based on its selection and classification of events. Our analysis shows distinct personality traits: for instance, Orca 2 demonstrates emotional reasoning focusing on interpersonal dynamics, while Qwen 2.5 displays a more strategic, analytical style. When analyzing scientific discovery events, Claude Sonnet 3.7 emphasizes conceptual framing, Gemini 2.5 Pro prioritizes empirical validation, and o3 favors step-by-step causal reasoning. This analysis improves model interpretability, making them user-friendly for a wide range of diverse applications. Project Page - https://www.supernova-event.ai/

Effective multimodal reasoning depends on the alignment of visual and linguistic representations, yet the mechanisms by which vision-language models (VLMs) achieve this alignment remain poorly understood. Following the LiMBeR framework, we deliberately maintain a frozen large language model (LLM) and a frozen vision transformer (ViT), connected solely by training a linear adapter during visual instruction tuning. By keeping the language model frozen, we ensure it maintains its original language representations without adaptation to visual data. Consequently, the linear adapter must map visual features directly into the LLM's existing representational space rather than allowing the language model to develop specialized visual understanding through fine-tuning. Our experimental design uniquely enables the use of pre-trained sparse autoencoders (SAEs) of the LLM as analytical probes. These SAEs remain perfectly aligned with the unchanged language model and serve as a snapshot of the learned language feature-representations. Through systematic analysis of SAE reconstruction error, sparsity patterns, and feature SAE descriptions, we reveal the layer-wise progression through which visual representations gradually align with language feature representations, converging in middle-to-later layers. This suggests a fundamental misalignment between ViT outputs and early LLM layers, raising important questions about whether current adapter-based architectures optimally facilitate cross-modal representation learning.

Cognitive impairment (CI) is of growing public health concern, and early detection is vital for effective intervention. Speech has gained attention as a non-invasive and easily collectible biomarker for assessing cognitive decline. Traditional CI detection methods typically rely on supervised models trained on acoustic and linguistic features extracted from speech, which often require manual annotation and may not generalise well across datasets and languages. In this work, we propose the first zero-shot speech-based CI detection method using the Qwen2- Audio AudioLLM, a model capable of processing both audio and text inputs. By designing prompt-based instructions, we guide the model in classifying speech samples as indicative of normal cognition or cognitive impairment. We evaluate our approach on two datasets: one in English and another multilingual, spanning different cognitive assessment tasks. Our results show that the zero-shot AudioLLM approach achieves performance comparable to supervised methods and exhibits promising generalizability and consistency across languages, tasks, and datasets.