The rise of foundation models has shifted focus from resource-intensive fine-tuning to prompt engineering, a paradigm that steers model behavior through input design rather than weight updates. While manual prompt engineering faces limitations in scalability, adaptability, and cross-modal alignment, automated methods, spanning foundation model (FM) based optimization, evolutionary methods, gradient-based optimization, and reinforcement learning, offer promising solutions. Existing surveys, however, remain fragmented across modalities and methodologies. This paper presents the first comprehensive survey on automated prompt engineering through a unified optimization-theoretic lens. We formalize prompt optimization as a maximization problem over discrete, continuous, and hybrid prompt spaces, systematically organizing methods by their optimization variables (instructions, soft prompts, exemplars), task-specific objectives, and computational frameworks. By bridging theoretical formulation with practical implementations across text, vision, and multimodal domains, this survey establishes a foundational framework for both researchers and practitioners, while highlighting underexplored frontiers in constrained optimization and agent-oriented prompt design.

While retrieval techniques are widely used in practice, they still face significant challenges in cross-domain scenarios. Recently, generation-augmented methods have emerged as a promising solution to this problem. These methods enhance raw queries by incorporating additional information from an LLM-based generator, facilitating more direct retrieval of relevant documents. However, existing methods struggle with highly specialized situations that require extensive domain expertise. To address this problem, we present \textbf{Reinforced-IR}, a novel approach that jointly adapts a pre-trained retriever and generator for precise cross-domain retrieval. A key innovation of Reinforced-IR is its \textbf{Self-Boosting} framework, which enables retriever and generator to learn from each other's feedback. Specifically, the generator is reinforced to generate query augmentations that enhance the retriever's performance, while the retriever is trained to better discriminate the relevant documents identified by the generator. This iterative process allows the end-to-end retrieval performance to be progressively optimized using an unlabeled corpus from the target domain. In our experiment, Reinforced-IR outperforms existing domain adaptation methods by a large margin, leading to substantial improvements in retrieval quality across a wide range of application scenarios.

Reasoning has long been viewed as an emergent property of large language models (LLMs), appearing at or above a certain scale ($\sim$100B parameters). However, recent studies challenge this assumption, showing that small language models (SLMs) can also achieve competitive reasoning performance. SLMs are increasingly favored for their efficiency and deployability. However, there is a lack of systematic study on the reasoning abilities of diverse SLMs, including those trained from scratch or derived from LLMs through quantization, pruning, and distillation. This raises a critical question: Can SLMs achieve reasoning abilities comparable to LLMs? In this work, we systematically survey, benchmark, and analyze 72 SLMs from six model families across 14 reasoning benchmarks. For reliable evaluation, we examine four evaluation methods and compare four LLM judges against human evaluations on 800 data points. We repeat all experiments three times to ensure a robust performance assessment. Additionally, we analyze the impact of different prompting strategies in small models. Beyond accuracy, we also evaluate model robustness under adversarial conditions and intermediate reasoning steps. Our findings challenge the assumption that scaling is the only way to achieve strong reasoning. Instead, we foresee a future where SLMs with strong reasoning capabilities can be developed through structured training or post-training compression. They can serve as efficient alternatives to LLMs for reasoning-intensive tasks.

Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) have made significant advancements in reasoning capabilities. However, they still face challenges such as high computational demands and privacy concerns. This paper focuses on developing efficient Small Language Models (SLMs) and Multimodal Small Language Models (MSLMs) that retain competitive reasoning abilities. We introduce a novel training pipeline that enhances reasoning capabilities and facilitates deployment on edge devices, achieving state-of-the-art performance while minimizing development costs. \InfR~ aims to advance AI systems by improving reasoning, reducing adoption barriers, and addressing privacy concerns through smaller model sizes. Resources are available at https://github. com/Reallm-Labs/InfiR.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Large Language Models (LLMs) have made significant strides in natural language generation but often face challenges in tasks requiring precise calculations and structural analysis. This paper investigates the performance of state-of-the-art LLMs on language complexity measurement tasks, through the computation of the LIX readability metric and Average Dependency Distance (ADD). Using Swedish high school and university-level essays, we evaluate the models' abilities to compute LIX scores and perform dependency parsing, comparing their results to established ground truths. Our findings reveal that while all models demonstrate some capacity for these tasks, ChatGPT-o1-mini performs most consistently, achieving the highest accuracy in both LIX computation and dependency parsing. Additionally, we observe a strong significant correlation -0.875 p 0.026 (N=6) between the models' accuracy in computing LIX and their overall performance on the Massive Multitask Language Understanding (MMLU) benchmark. These results suggest that language complexity measurement abilities can serve as a noisy zero-shot proxies for assessing the general capabilities of LLMs, providing a practical method for model evaluation without the need for extensive benchmarking datasets.

The radioactive nature of Large Language Model (LLM) watermarking enables the detection of watermarks inherited by student models when trained on the outputs of watermarked teacher models, making it a promising tool for preventing unauthorized knowledge distillation. However, the robustness of watermark radioactivity against adversarial actors remains largely unexplored. In this paper, we investigate whether student models can acquire the capabilities of teacher models through knowledge distillation while avoiding watermark inheritance. We propose two categories of watermark removal approaches: pre-distillation removal through untargeted and targeted training data paraphrasing (UP and TP), and post-distillation removal through inference-time watermark neutralization (WN). Extensive experiments across multiple model pairs, watermarking schemes and hyper-parameter settings demonstrate that both TP and WN thoroughly eliminate inherited watermarks, with WN achieving this while maintaining knowledge transfer efficiency and low computational overhead. Given the ongoing deployment of watermarking techniques in production LLMs, these findings emphasize the urgent need for more robust defense strategies. Our code is available at https://github.com/THU-BPM/Watermark-Radioactivity-Attack.

Large Language Models (LLMs) exhibit strong natural language processing capabilities but also inherit and amplify societal biases, including gender bias, raising fairness concerns. Existing debiasing methods face significant limitations: parameter tuning requires access to model weights, prompt-based approaches often degrade model utility, and optimization-based techniques lack generalizability. To address these challenges, we propose DR.GAP (Demonstration and Reasoning for Gender-Aware Prompting), an automated and model-agnostic approach that mitigates gender bias while preserving model performance. DR.GAP selects bias-revealing examples and generates structured reasoning to guide models toward more impartial responses. Extensive experiments on coreference resolution and QA tasks across multiple LLMs (GPT-3.5, Llama3, and Llama2-Alpaca) demonstrate its effectiveness, generalization ability, and robustness. DR.GAP can generalize to vision-language models (VLMs), achieving significant bias reduction.

Large language models (LLMs) have demonstrated remarkable capabilities across various domains, especially in text processing and generative tasks. Recent advancements in the reasoning capabilities of state-of-the-art LLMs, such as OpenAI-o1, have significantly broadened their applicability, particularly in complex problem-solving and logical inference. However, most existing LLMs struggle with notable limitations in handling graph combinatorial optimization (GCO) problems. To bridge this gap, we formally define the Optimal Thoughts Design (OTD) problem, including its state and action thought space. We then introduce a novel framework, GraphThought, designed to generate high-quality thought datasets for GCO problems. Leveraging these datasets, we fine-tune the Llama-3-8B-Instruct model to develop Llama-GT. Notably, despite its compact 8B-parameter architecture, Llama-GT matches the performance of state-of-the-art LLMs on the GraphArena benchmark. Experimental results show that our approach outperforms both proprietary and open-source models, even rivaling specialized models like o1-mini. This work sets a new state-of-the-art benchmark while challenging the prevailing notion that model scale is the primary driver of reasoning capability.

Prior studies have shown that distinguishing text generated by large language models (LLMs) from human-written one is highly challenging, and often no better than random guessing. To verify the generalizability of this finding across languages and domains, we perform an extensive case study to identify the upper bound of human detection accuracy. Across 16 datasets covering 9 languages and 9 domains, 19 annotators achieved an average detection accuracy of 87.6%, thus challenging previous conclusions. We find that major gaps between human and machine text lie in concreteness, cultural nuances, and diversity. Prompting by explicitly explaining the distinctions in the prompts can partially bridge the gaps in over 50% of the cases. However, we also find that humans do not always prefer human-written text, particularly when they cannot clearly identify its source.