Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem proving, and optimization techniques. This survey explores the evolution of mathematical problem-solving in AI, from early statistical learning approaches to modern deep learning and transformer-based methodologies. We review the capabilities of pretrained language models and LLMs in performing arithmetic operations, complex reasoning, theorem proving, and structured symbolic computation. A key focus is on how LLMs integrate with optimization and control frameworks, including mixed-integer programming, linear quadratic control, and multi-agent optimization strategies. We examine how LLMs assist in problem formulation, constraint generation, and heuristic search, bridging theoretical reasoning with practical applications. We also discuss enhancement techniques such as Chain-of-Thought reasoning, instruction tuning, and tool-augmented methods that improve LLM's problem-solving performance. Despite their progress, LLMs face challenges in numerical precision, logical consistency, and proof verification. Emerging trends such as hybrid neural-symbolic reasoning, structured prompt engineering, and multi-step self-correction aim to overcome these limitations. Future research should focus on interpretability, integration with domain-specific solvers, and improving the robustness of AI-driven decision-making. This survey offers a comprehensive review of the current landscape and future directions of mathematical reasoning and optimization with LLMs, with applications across engineering, finance, and scientific research.
The rapid growth of AI-generated content (AIGC) services has created an urgent need for effective prompt pricing strategies, yet current approaches overlook users' strategic two-step decision-making process in selecting and utilizing generative AI models. This oversight creates two key technical challenges: quantifying the relationship between user prompt capabilities and generation outcomes, and optimizing platform payoff while accounting for heterogeneous user behaviors. We address these challenges by introducing prompt ambiguity, a theoretical framework that captures users' varying abilities in prompt engineering, and developing an Optimal Prompt Pricing (OPP) algorithm. Our analysis reveals a counterintuitive insight: users with higher prompt ambiguity (i.e., lower capability) exhibit non-monotonic prompt usage patterns, first increasing then decreasing with ambiguity levels, reflecting complex changes in marginal utility. Experimental evaluation using a character-level GPT-like model demonstrates that our OPP algorithm achieves up to 31.72% improvement in platform payoff compared to existing pricing mechanisms, validating the importance of user-centric prompt pricing in AIGC services.
Medical Question Answering systems based on Retrieval Augmented Generation is promising for clinical decision support because they can integrate external knowledge, thus reducing inaccuracies inherent in standalone large language models (LLMs). However, these systems may unintentionally propagate or amplify biases associated with sensitive demographic attributes like race, gender, and socioeconomic factors. This study systematically evaluates demographic biases within medical RAG pipelines across multiple QA benchmarks, including MedQA, MedMCQA, MMLU, and EquityMedQA. We quantify disparities in retrieval consistency and answer correctness by generating and analyzing queries sensitive to demographic variations. We further implement and compare several bias mitigation strategies to address identified biases, including Chain of Thought reasoning, Counterfactual filtering, Adversarial prompt refinement, and Majority Vote aggregation. Experimental results reveal significant demographic disparities, highlighting that Majority Vote aggregation notably improves accuracy and fairness metrics. Our findings underscore the critical need for explicitly fairness-aware retrieval methods and prompt engineering strategies to develop truly equitable medical QA systems.
In zero-shot image recognition tasks, humans demonstrate remarkable flexibility in classifying unseen categories by composing known simpler concepts. However, existing vision-language models (VLMs), despite achieving significant progress through large-scale natural language supervision, often underperform in real-world applications because of sub-optimal prompt engineering and the inability to adapt effectively to target classes. To address these issues, we propose a Concept-guided Human-like Bayesian Reasoning (CHBR) framework. Grounded in Bayes' theorem, CHBR models the concept used in human image recognition as latent variables and formulates this task by summing across potential concepts, weighted by a prior distribution and a likelihood function. To tackle the intractable computation over an infinite concept space, we introduce an importance sampling algorithm that iteratively prompts large language models (LLMs) to generate discriminative concepts, emphasizing inter-class differences. We further propose three heuristic approaches involving Average Likelihood, Confidence Likelihood, and Test Time Augmentation (TTA) Likelihood, which dynamically refine the combination of concepts based on the test image. Extensive evaluations across fifteen datasets demonstrate that CHBR consistently outperforms existing state-of-the-art zero-shot generalization methods.
Large language models (LLMs) have unlocked new possibilities for generating synthetic training data in both natural language and code. By producing artificial but task-relevant examples, these models can significantly augment or even replace real-world datasets, especially when labeled data is scarce or sensitive. This paper surveys recent advances in using LLMs to create synthetic text and code, emphasizing prompt-based generation, retrieval-augmented pipelines, and iterative self-refinement. We show how these methods enrich low-resource tasks such as classification and question answering, as well as code-centric applications such as instruction tuning, code translation, and bug repair, by enabling automated verification of functional correctness. Alongside potential benefits like cost-effectiveness, broad coverage, and controllable diversity, we address challenges such as factual inaccuracies in generated text, lack of stylistic realism, and the risk of bias amplification. Proposed mitigations include filtering and weighting outputs and reinforcement learning with execution feedback for code. We conclude with open research directions like automated prompt engineering, cross-modal data synthesis, and robust evaluation frameworks, highlighting the importance of LLM-generated synthetic data in advancing AI while emphasizing ethical and quality safeguards.
Multimodal Large Language Models (MLLMs) exhibit impressive capabilities across a variety of tasks, especially when equipped with carefully designed visual prompts. However, existing studies primarily focus on logical reasoning and visual understanding, while the capability of MLLMs to operate effectively in 3D vision remains an ongoing area of exploration. In this paper, we introduce a novel visual prompting method, called 3DAxisPrompt, to elicit the 3D understanding capabilities of MLLMs in real-world scenes. More specifically, our method leverages the 3D coordinate axis and masks generated from the Segment Anything Model (SAM) to provide explicit geometric priors to MLLMs and then extend their impressive 2D grounding and reasoning ability to real-world 3D scenarios. Besides, we first provide a thorough investigation of the potential visual prompting formats and conclude our findings to reveal the potential and limits of 3D understanding capabilities in GPT-4o, as a representative of MLLMs. Finally, we build evaluation environments with four datasets, i.e., ScanRefer, ScanNet, FMB, and nuScene datasets, covering various 3D tasks. Based on this, we conduct extensive quantitative and qualitative experiments, which demonstrate the effectiveness of the proposed method. Overall, our study reveals that MLLMs, with the help of 3DAxisPrompt, can effectively perceive an object's 3D position in real-world scenarios. Nevertheless, a single prompt engineering approach does not consistently achieve the best outcomes for all 3D tasks. This study highlights the feasibility of leveraging MLLMs for 3D vision grounding/reasoning with prompt engineering techniques.
With the rapid development of Large Language Models (LLMs), LLM-based agents have been widely adopted in various fields, becoming essential for autonomous decision-making and interactive tasks. However, current work typically relies on prompt design or fine-tuning strategies applied to vanilla LLMs, which often leads to limited effectiveness or suboptimal performance in complex agent-related environments. Although LLM optimization techniques can improve model performance across many general tasks, they lack specialized optimization towards critical agent functionalities such as long-term planning, dynamic environmental interaction, and complex decision-making. Although numerous recent studies have explored various strategies to optimize LLM-based agents for complex agent tasks, a systematic review summarizing and comparing these methods from a holistic perspective is still lacking. In this survey, we provide a comprehensive review of LLM-based agent optimization approaches, categorizing them into parameter-driven and parameter-free methods. We first focus on parameter-driven optimization, covering fine-tuning-based optimization, reinforcement learning-based optimization, and hybrid strategies, analyzing key aspects such as trajectory data construction, fine-tuning techniques, reward function design, and optimization algorithms. Additionally, we briefly discuss parameter-free strategies that optimize agent behavior through prompt engineering and external knowledge retrieval. Finally, we summarize the datasets and benchmarks used for evaluation and tuning, review key applications of LLM-based agents, and discuss major challenges and promising future directions. Our repository for related references is available at https://github.com/YoungDubbyDu/LLM-Agent-Optimization.
Prompting LLMs offers an efficient way to guide output generation without explicit model training. In the e-commerce domain, prompting-based applications are widely used for tasks such as query understanding, recommender systems, and customer support. However, adapting LLMs to different tasks often requires extensive prompt engineering by domain experts, along with frequent updates to align with evolving business needs. Additionally, crafting fully unbiased natural language prompts remains a challenge for humans. To address these challenges, we propose a novel framework, Examples as the Prompt (EaP) which leverages labeled data to enhance prompts. Specifically, EaP automatically selects the most representative examples to maximize the few-shot capability of LLMs. It is efficient due to its unsupervised example selection and adaptive to potential data distribution shifts. We validate EaP on four real-world production use cases, demonstrating that it achieves comparable or even superior performance comparing to hand-crafted prompts designed by domain experts. Additionally, we introduce EaP_lite, which entirely replaces the natural language components of prompts with labeled examples. EaP_lite improves LLM inference speed by up to 70% without compromising performance. Latest online A/B test shows that using EaP and EaP_lite for data labeling can bring significant composite revenue gain by 0.06%.
The rise of large language models (LLMs) has revolutionized natural language processing (NLP), yet the influence of prompt sentiment, a latent affective characteristic of input text, remains underexplored. This study systematically examines how sentiment variations in prompts affect LLM-generated outputs in terms of coherence, factuality, and bias. Leveraging both lexicon-based and transformer-based sentiment analysis methods, we categorize prompts and evaluate responses from five leading LLMs: Claude, DeepSeek, GPT-4, Gemini, and LLaMA. Our analysis spans six AI-driven applications, including content generation, conversational AI, legal and financial analysis, healthcare AI, creative writing, and technical documentation. By transforming prompts, we assess their impact on output quality. Our findings reveal that prompt sentiment significantly influences model responses, with negative prompts often reducing factual accuracy and amplifying bias, while positive prompts tend to increase verbosity and sentiment propagation. These results highlight the importance of sentiment-aware prompt engineering for ensuring fair and reliable AI-generated content.
Accurate segmentation is essential for effective treatment planning and disease monitoring. Existing medical image segmentation methods predominantly rely on uni-modal visual inputs, such as images or videos, requiring labor-intensive manual annotations. Additionally, medical imaging techniques capture multiple intertwined organs within a single scan, further complicating segmentation accuracy. To address these challenges, MedSAM, a large-scale medical segmentation model based on the Segment Anything Model (SAM), was developed to enhance segmentation accuracy by integrating image features with user-provided prompts. While MedSAM has demonstrated strong performance across various medical segmentation tasks, it primarily relies on geometric prompts (e.g., points and bounding boxes) and lacks support for text-based prompts, which could help specify subtle or ambiguous anatomical structures. To overcome these limitations, we propose the Organ-aware Multi-scale Text-guided Medical Image Segmentation Model (OMT-SAM) for multi-organ segmentation. Our approach introduces CLIP encoders as a novel image-text prompt encoder, operating with the geometric prompt encoder to provide informative contextual guidance. We pair descriptive textual prompts with corresponding images, processing them through pre-trained CLIP encoders and a cross-attention mechanism to generate fused image-text embeddings. Additionally, we extract multi-scale visual features from MedSAM, capturing fine-grained anatomical details at different levels of granularity. We evaluate OMT-SAM on the FLARE 2021 dataset, benchmarking its performance against existing segmentation methods. Empirical results demonstrate that OMT-SAM achieves a mean Dice Similarity Coefficient of 0.937, outperforming MedSAM (0.893) and other segmentation models, highlighting its superior capability in handling complex medical image segmentation tasks.
Scientific names of organisms consist of a genus name and a species epithet, with the latter often reflecting aspects such as morphology, ecology, distribution, and cultural background. Traditionally, researchers have manually labeled species names by carefully examining taxonomic descriptions, a process that demands substantial time and effort when dealing with large datasets. This study evaluates the feasibility of automatic species name labeling using large language model (LLM) by leveraging their text classification and semantic extraction capabilities. Using the spider name dataset compiled by Mammola et al., we compared LLM-based labeling results-enhanced through prompt engineering-with human annotations. The results indicate that LLM-based classification achieved high accuracy in Morphology, Geography, and People categories. However, classification accuracy was lower in Ecology & Behavior and Modern & Past Culture, revealing challenges in interpreting animal behavior and cultural contexts. Future research will focus on improving accuracy through optimized few-shot learning and retrieval-augmented generation techniques, while also expanding the applicability of LLM-based labeling to diverse biological taxa.
Large-scale pre-training of deep models, followed by fine-tuning them, has become the cornerstone of natural language processing (NLP). The prevalence of data coupled with computational resources has led to large models with a considerable number of parameters. While the massive size of these models has led to remarkable success in many NLP tasks, a detriment is the expense required to retrain all the base model's parameters for the adaptation to each task or domain. Parameter Efficient Fine-Tuning (PEFT) provides an effective solution for this challenge by minimizing the number of parameters required to be fine-tuned while maintaining the quality of the model. While existing methods have achieved impressive results, they mainly focus on adapting a subset of parameters, weight reparameterization, and prompt engineering. In this paper, we study layers as extractors of different types of linguistic information that are valuable when used in conjunction. We then propose the Mixture of Layer Experts (MoLEx), a novel sparse mixture of experts (SMoE) whose experts are layers in the pre-trained model. It performs a conditional computation of a mixture of layers during fine-tuning to provide the model with more structural knowledge about the data. By providing an avenue for information exchange between layers, MoLEx enables the model to make a more well-informed prediction for the downstream task, leading to better fine-tuning results with the same number of effective parameters. As experts can be processed in parallel, MoLEx introduces minimal additional computational overhead. We empirically corroborate the advantages of MoLEx when combined with popular PEFT baseline methods on a variety of downstream fine-tuning tasks, including the popular GLUE benchmark as well as the End-to-End Challenge (E2E). The code is publicly available at https://github.com/rachtsy/molex.
Large-scale vision-language models (VLMs), trained on extensive datasets of image-text pairs, exhibit strong multimodal understanding capabilities by implicitly learning associations between textual descriptions and image regions. This emergent ability enables zero-shot object detection and segmentation, using techniques that rely on text-image attention maps, without necessarily training on abundant labeled segmentation datasets. However, performance of such methods depends heavily on prompt engineering and manually selected layers or head choices for the attention layers. In this work, we demonstrate that, rather than relying solely on textual prompts, providing a single visual example for each category and fine-tuning the text-to-image attention layers and embeddings significantly improves the performance. Additionally, we propose learning an ensemble through few-shot fine-tuning across multiple layers and/or prompts. An entropy-based ranking and selection mechanism for text-to-image attention layers is proposed to identify the top-performing layers without the need for segmentation labels. This eliminates the need for hyper-parameter selection of text-to-image attention layers, providing a more flexible and scalable solution for open-vocabulary segmentation. We show that this approach yields strong zero-shot performance, further enhanced through fine-tuning with a single visual example. Moreover, we demonstrate that our method and findings are general and can be applied across various vision-language models (VLMs).
Phishing is a persistent cybersecurity threat in today's digital landscape. This paper introduces Phishsense-1B, a refined version of the Llama-Guard-3-1B model, specifically tailored for phishing detection and reasoning. This adaptation utilizes Low-Rank Adaptation (LoRA) and the GuardReasoner finetuning methodology. We outline our LoRA-based fine-tuning process, describe the balanced dataset comprising phishing and benign emails, and highlight significant performance improvements over the original model. Our findings indicate that Phishsense-1B achieves an impressive 97.5% accuracy on a custom dataset and maintains strong performance with 70% accuracy on a challenging real-world dataset. This performance notably surpasses both unadapted models and BERT-based detectors. Additionally, we examine current state-of-the-art detection methods, compare prompt-engineering with fine-tuning strategies, and explore potential deployment scenarios.
The limitations sections of scientific articles play a crucial role in highlighting the boundaries and shortcomings of research, thereby guiding future studies and improving research methods. Analyzing these limitations benefits researchers, reviewers, funding agencies, and the broader academic community. We introduce LimTopic, a strategy where Topic generation in Limitation sections in scientific articles with Large Language Models (LLMs). Here, each topic contains the title and Topic Summary. This study focuses on effectively extracting and understanding these limitations through topic modeling and text summarization, utilizing the capabilities of LLMs. We extracted limitations from research articles and applied an LLM-based topic modeling integrated with the BERtopic approach to generate a title for each topic and Topic Sentences. To enhance comprehension and accessibility, we employed LLM-based text summarization to create concise and generalizable summaries for each topic Topic Sentences and produce a Topic Summary. Our experimentation involved prompt engineering, fine-tuning LLM and BERTopic, and integrating BERTopic with LLM to generate topics, titles, and a topic summary. We also experimented with various LLMs with BERTopic for topic modeling and various LLMs for text summarization tasks. Our results showed that the combination of BERTopic and GPT 4 performed the best in terms of silhouette and coherence scores in topic modeling, and the GPT4 summary outperformed other LLM tasks as a text summarizer.
Large language models (LLMs) exhibit strong reasoning abilities, often attributed to few-shot or zero-shot chain-of-thought (CoT) prompting. While effective, these methods require labor-intensive prompt engineering, raising the question of whether reasoning can be induced without reliance on explicit prompts. In this work, we unlock the reasoning capabilities of LLMs without explicit prompting. Inspired by zero-shot CoT and CoT-decoding, we propose a novel decoding strategy that systematically nudges LLMs to continue reasoning, thereby preventing immature reasoning processes. Specifically, we monitor the model's generation and inject a designated phrase whenever it is likely to conclude its response prematurely, before completing the reasoning process. Our experimental evaluations on diverse reasoning benchmarks demonstrate that our proposed strategy substantially improves LLM reasoning capabilities, highlighting the potential of decoding-based interventions as an alternative to traditional prompting techniques.
Investigating bias in large language models (LLMs) is crucial for developing trustworthy AI. While prompt-based through prompt engineering is common, its effectiveness relies on the assumption that models inherently understand biases. Our study systematically analyzed this assumption using the BBQ and StereoSet benchmarks on both open-source models as well as commercial GPT model. Experimental results indicate that prompt-based is often superficial; for instance, the Llama2-7B-Chat model misclassified over 90% of unbiased content as biased, despite achieving high accuracy in identifying bias issues on the BBQ dataset. Additionally, specific evaluation and question settings in bias benchmarks often lead LLMs to choose "evasive answers", disregarding the core of the question and the relevance of the response to the context. Moreover, the apparent success of previous methods may stem from flawed evaluation metrics. Our research highlights a potential "false prosperity" in prompt-base efforts and emphasizes the need to rethink bias metrics to ensure truly trustworthy AI.
Large pre-trained vision-language models (VLMs) offer a promising approach to leveraging human language for enhancing downstream tasks. However, VLMs such as CLIP face significant limitation: its performance is highly sensitive to prompt template design. Although prompt learning methods can address the sensitivity issue by replacing natural language prompts with learnable ones, they are incomprehensible to humans. Ensuring consistent performance across various prompt templates enables models to adapt seamlessly to diverse phrasings, enhancing their ability to handle downstream tasks without requiring extensive prompt engineering. In this work, we introduce the RobustPrompt Benchmark, a systematic benchmark to evaluate robustness to different prompt templates for VLMs. It includes a dataset with hundreds of carefully designed prompt templates, divided into six types, covering a wide variety of commonly used templates. Beside the benchmark, we propose Modeling Variants of Prompts (MVP), a simple yet effective method that mitigates sensitivity by modeling variants of prompt structures. The innovation of MVP lies in decoupling prompts into templates and class names, and using Variational Autoencoders (VAE) to model the distribution of diverse prompt structures. Experiments across 11 datasets demonstrate that MVP can greatly enhance model robustness to variations in input prompts without a drop in performance. The code is available at https://github.com/liaolea/MVP.
LLM-based automated program repair methods have attracted significant attention for their state-of-the-art performance. However, they were primarily evaluated on a few well known datasets like Defects4J, raising questions about their effectiveness on new datasets. In this study, we evaluate 11 top-performing LLMs on DEFECTS4J-TRANS, a new dataset derived from transforming Defects4J while maintaining the original semantics. Results from experiments on both Defects4J and DEFECTS4J-TRANS show that all studied LLMs have limited generalizability in APR tasks, with the average number of correct and plausible patches decreasing by 49.48% and 42.90%, respectively, on DEFECTS4J-TRANS. Further investigation into incorporating additional repair-relevant information in repair prompts reveals that, although this information significantly enhances the LLMs' capabilities (increasing the number of correct and plausible patches by up to 136.67% and 121.82%, respectively), performance still falls short of their original results. This indicates that prompt engineering alone is insufficient to substantially enhance LLMs' repair capabilities. Based on our study, we also offer several recommendations for future research.
Enabling humanoid robots to perform long-horizon mobile manipulation planning in real-world environments based on embodied perception and comprehension abilities has been a longstanding challenge. With the recent rise of large language models (LLMs), there has been a notable increase in the development of LLM-based planners. These approaches either utilize human-provided textual representations of the real world or heavily depend on prompt engineering to extract such representations, lacking the capability to quantitatively understand the environment, such as determining the feasibility of manipulating objects. To address these limitations, we present the Instruction-Augmented Long-Horizon Planning (IALP) system, a novel framework that employs LLMs to generate feasible and optimal actions based on real-time sensor feedback, including grounded knowledge of the environment, in a closed-loop interaction. Distinct from prior works, our approach augments user instructions into PDDL problems by leveraging both the abstract reasoning capabilities of LLMs and grounding mechanisms. By conducting various real-world long-horizon tasks, each consisting of seven distinct manipulatory skills, our results demonstrate that the IALP system can efficiently solve these tasks with an average success rate exceeding 80%. Our proposed method can operate as a high-level planner, equipping robots with substantial autonomy in unstructured environments through the utilization of multi-modal sensor inputs.