Daily Papers

Multiple-choice QA benchmarks usually evaluate small language models (SLMs) as direct answerers, but deployed language-model systems increasingly rely on external scaffolds such as tools, code, and repeated model calls. We introduce Code-Guided Reasoning (CGR), an evaluation protocol and generated-program resource for measuring when executable reasoning scaffolds improve SLM performance on MCQA tasks. CGR standardizes six components: a normalized item interface, a direct solver prompt, a generator prompt, a Python scaffold, solver-call and extraction helpers, and a three-channel result record. On 20,498 retained result rows from a locally prepared MCQA bundle and six metadata-registered solver models, the observed non-zero-baseline partition shows 66.21% macro assisted accuracy versus 38.11% direct accuracy, a +28.10 percentage-point difference with a pair-bootstrap interval of [20.32, 36.43]. Under a stricter Ab > 30% direct-signal gate, the macro difference is +14.11 points. These estimates are descriptive. Assisted inference uses a larger solver-call budget, answer extraction is brittle, Time-MQA contains the observed regressions, and some generated programs violate the no-hard-coding instruction. CGR provides the trace package needed to interpret these results, including direct, assisted, and generator-side answers, partition definitions, generated programs, response metadata, and audits.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

Optimization is ubiquitous. While derivative-based algorithms have been powerful tools for various problems, the absence of gradient imposes challenges on many real-world applications. In this work, we propose Optimization by PROmpting (OPRO), a simple and effective approach to leverage large language models (LLMs) as optimizers, where the optimization task is described in natural language. In each optimization step, the LLM generates new solutions from the prompt that contains previously generated solutions with their values, then the new solutions are evaluated and added to the prompt for the next optimization step. We first showcase OPRO on linear regression and traveling salesman problems, then move on to prompt optimization where the goal is to find instructions that maximize the task accuracy. With a variety of LLMs, we demonstrate that the best prompts optimized by OPRO outperform human-designed prompts by up to 8% on GSM8K, and by up to 50% on Big-Bench Hard tasks.

Enabling large language models (LLMs) to perform tasks in zero-shot has been an appealing goal owing to its labor-saving (i.e., requiring no task-specific annotations); as such, zero-shot prompting approaches also enjoy better task generalizability. To improve LLMs' zero-shot performance, prior work has focused on devising more effective task instructions (e.g., ``let's think step by step'' ). However, we argue that, in order for an LLM to solve them correctly in zero-shot, individual test instances need more carefully designed and customized instructions. To this end, we propose PRoMPTd, an approach that rewrites the task prompt for each individual test input to be more specific, unambiguous, and complete, so as to provide better guidance to the task LLM. We evaluated PRoMPTd on eight datasets covering tasks including arithmetics, logical reasoning, and code generation, using GPT-4 as the task LLM. Notably, PRoMPTd achieves an absolute improvement of around 10% on the complex MATH dataset and 5% on the code generation task on HumanEval, outperforming conventional zero-shot methods. In addition, we also showed that the rewritten prompt can provide better interpretability of how the LLM resolves each test instance, which can potentially be leveraged as a defense mechanism against adversarial prompting. The source code and dataset can be obtained from https://github.com/salokr/PRoMPTd

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

Prompt engineering is critical for the development of LLM-based applications. However, it is usually done manually in a "trial and error" fashion. This manual procedure can be time consuming, ineffective, and the generated prompts are, in a lot of cases, sub-optimal. Even for the prompts which seemingly work well, there is always a lingering question: can the prompts be made better with further modifications? To address these questions, in this paper, we investigate prompt engineering automation. We consider a specific use case scenario in which developers/users have drafted initial prompts, but lack the time/expertise to optimize them. We propose PRewrite, an automated tool to rewrite these drafts and to generate highly effective new prompts. PRewrite is based on the Reinforcement Learning (RL) framework which allows for end-to-end optimization and our design allows the RL search to happen in a large action space. The automated tool leverages manually crafted prompts as starting points which makes the rewriting procedure more guided and efficient. The generated prompts are human readable, and self-explanatory, unlike some of those in previous works. We conducted extensive experiments on diverse datasets and found that the prompts generated with this new method not only outperform professionally crafted prompts, but also prompts generated with other previously proposed methods.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

We present DIRECT-3D, a diffusion-based 3D generative model for creating high-quality 3D assets (represented by Neural Radiance Fields) from text prompts. Unlike recent 3D generative models that rely on clean and well-aligned 3D data, limiting them to single or few-class generation, our model is directly trained on extensive noisy and unaligned `in-the-wild' 3D assets, mitigating the key challenge (i.e., data scarcity) in large-scale 3D generation. In particular, DIRECT-3D is a tri-plane diffusion model that integrates two innovations: 1) A novel learning framework where noisy data are filtered and aligned automatically during the training process. Specifically, after an initial warm-up phase using a small set of clean data, an iterative optimization is introduced in the diffusion process to explicitly estimate the 3D pose of objects and select beneficial data based on conditional density. 2) An efficient 3D representation that is achieved by disentangling object geometry and color features with two separate conditional diffusion models that are optimized hierarchically. Given a prompt input, our model generates high-quality, high-resolution, realistic, and complex 3D objects with accurate geometric details in seconds. We achieve state-of-the-art performance in both single-class generation and text-to-3D generation. We also demonstrate that DIRECT-3D can serve as a useful 3D geometric prior of objects, for example to alleviate the well-known Janus problem in 2D-lifting methods such as DreamFusion. The code and models are available for research purposes at: https://github.com/qihao067/direct3d.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

We propose a novel prompt design paradigm that challenges conventional wisdom in large language model (LLM) prompting. While conventional wisdom prioritizes well-crafted instructions and demonstrations for in-context learning (ICL), we show that pruning random demonstrations into seemingly incoherent "gibberish" can remarkably improve performance across diverse tasks. Notably, the "gibberish" always matches or surpasses state-of-the-art automatic prompt optimization techniques, achieving substantial gains regardless of LLM alignment. Nevertheless, discovering an effective pruning strategy is non-trivial, as existing attribution methods and prompt compression algorithms fail to deliver robust results, let alone human intuition. In terms of this, we propose a self-discover prompt optimization framework, PromptQuine, an evolutionary search framework that automatically searches for the pruning strategy by itself using only low-data regimes. Much like the emergent complexity in nature--such as symbiosis and self-organization--arising in response to resource constraints, our framework evolves and refines unconventional yet highly effective prompts by leveraging only the tokens present within the context. We demonstrate its effectiveness across classification, multi-choice question answering, generation and math reasoning tasks across LLMs, while achieving decent runtime efficiency. We hope our findings can guide mechanistic studies on in-context learning, and provide a call to action, to pave the way for more open-ended search algorithms for more effective LLM prompting.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

Prompting is a mainstream paradigm for adapting large language models to specific natural language processing tasks without modifying internal parameters. Therefore, detailed supplementary knowledge needs to be integrated into external prompts, which inevitably brings extra human efforts and computational burdens for practical applications. As an effective solution to mitigate resource consumption, Efficient Prompting Methods have attracted a wide range of attention. We provide mathematical expressions at a high level to deeply discuss Automatic Prompt Engineering for different prompt components and Prompt Compression in continuous and discrete spaces. Finally, we highlight promising future directions to inspire researchers interested in this field.

Prompt engineering has emerged as an indispensable technique for extending the capabilities of large language models (LLMs) and vision-language models (VLMs). This approach leverages task-specific instructions, known as prompts, to enhance model efficacy without modifying the core model parameters. Rather than updating the model parameters, prompts allow seamless integration of pre-trained models into downstream tasks by eliciting desired model behaviors solely based on the given prompt. Prompts can be natural language instructions that provide context to guide the model or learned vector representations that activate relevant knowledge. This burgeoning field has enabled success across various applications, from question-answering to commonsense reasoning. However, there remains a lack of systematic organization and understanding of the diverse prompt engineering methods and techniques. This survey paper addresses the gap by providing a structured overview of recent advancements in prompt engineering, categorized by application area. For each prompting approach, we provide a summary detailing the prompting methodology, its applications, the models involved, and the datasets utilized. We also delve into the strengths and limitations of each approach and include a taxonomy diagram and table summarizing datasets, models, and critical points of each prompting technique. This systematic analysis enables a better understanding of this rapidly developing field and facilitates future research by illuminating open challenges and opportunities for prompt engineering.

Large Language Models (LLMs) can perform various natural language processing tasks with suitable instruction prompts. However, designing effective prompts manually is challenging and time-consuming. Existing methods for automatic prompt optimization either lack flexibility or efficiency. In this paper, we propose an effective approach to automatically select the optimal prompt for a given input from a finite set of synthetic candidate prompts. Our approach consists of three steps: (1) clustering the training data and generating candidate prompts for each cluster using an LLM-based prompt generator; (2) synthesizing a dataset of input-prompt-output tuples for training a prompt evaluator to rank the prompts based on their relevance to the input; (3) using the prompt evaluator to select the best prompt for a new input at test time. Our approach balances prompt generality-specificity and eliminates the need for resource-intensive training and inference. It demonstrates competitive performance on zero-shot question-answering datasets: GSM8K, MultiArith, and AQuA.

Recent advances in large language models (LLMs), such as OpenAI-o1 and DeepSeek-R1, have demonstrated the effectiveness of test-time scaling, where extended reasoning processes substantially enhance model performance. Despite this, current models are constrained by limitations in handling long texts and reinforcement learning (RL) training efficiency. To address these issues, we propose a simple yet effective test-time scaling approach Multi-round Thinking. This method iteratively refines model reasoning by leveraging previous answers as prompts for subsequent rounds. Extensive experiments across multiple models, including QwQ-32B and DeepSeek-R1, consistently show performance improvements on various benchmarks such as AIME 2024, MATH-500, GPQA-diamond, and LiveCodeBench. For instance, the accuracy of QwQ-32B improved from 80.3% (Round 1) to 82.1% (Round 2) on the AIME 2024 dataset, while DeepSeek-R1 showed a similar increase from 79.7% to 82.0%. These results confirm that Multi-round Thinking is a broadly applicable, straightforward approach to achieving stable enhancements in model performance, underscoring its potential for future developments in test-time scaling techniques. The key prompt: {Original question prompt} The assistant's previous answer is: <answer> {last round answer} </answer>, and please re-answer.

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

We introduce a novel framework that transforms the resource-intensive (adversarial) prompt optimization problem into an efficient, amortized inference task. Our core insight is that pretrained, non-autoregressive generative LLMs, such as Diffusion LLMs, which model the joint distribution over prompt-response pairs, can serve as powerful surrogates for prompt search. This approach enables the direct conditional generation of prompts, effectively replacing costly, per-instance discrete optimization with a small number of parallelizable samples. We provide a probabilistic analysis demonstrating that under mild fidelity assumptions, only a few conditional samples are required to recover high-reward (harmful) prompts. Empirically, we find that the generated prompts are low-perplexity, diverse jailbreaks that exhibit strong transferability to a wide range of black-box target models, including robustly trained and proprietary LLMs. Beyond adversarial prompting, our framework opens new directions for red teaming, automated prompt optimization, and leveraging emerging Flow- and Diffusion-based LLMs.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Chain-of-thought (CoT) prompting with large language models has proven effective in numerous natural language processing tasks, but designing prompts that generalize well to diverse problem types can be challenging, especially in the context of math word problem (MWP) solving. Additionally, it is common to have a large amount of training data that have a better diversity coverage but CoT annotations are not available, which limits the use of supervised learning techniques. To address these issues, we investigate two approaches to leverage the training data in a few-shot prompting scenario: dynamic program prompting and program distillation. Our approach is largely inspired by Gao et al., (2022), where they proposed to replace the CoT with the programs as the intermediate reasoning step. Such a prompting strategy allows us to accurately verify the answer correctness through program execution in MWP solving. Our dynamic program prompting involves annotating the training data by sampling correct programs from a large language model, while program distillation involves adapting a smaller model to the program-annotated training data. Our experiments on three standard MWP datasets demonstrate the effectiveness of these approaches, yielding significant improvements over previous baselines for prompting and fine-tuning. Our results suggest that leveraging a large amount of training data can improve the generalization ability of prompts and boost the performance of fine-tuned small models in MWP solving.

LLMs have demonstrated commendable performance across diverse domains. Nevertheless, formulating high-quality prompts to assist them in their work poses a challenge for non-AI experts. Existing research in prompt engineering suggests somewhat scattered optimization principles and designs empirically dependent prompt optimizers. Unfortunately, these endeavors lack a structural design, incurring high learning costs and it is not conducive to the iterative updating of prompts, especially for non-AI experts. Inspired by structured reusable programming languages, we propose LangGPT, a structural prompt design framework. Furthermore, we introduce Minstrel, a multi-generative agent system with reflection to automate the generation of structural prompts. Experiments and the case study illustrate that structural prompts generated by Minstrel or written manually significantly enhance the performance of LLMs. Furthermore, we analyze the ease of use of structural prompts through a user survey in our online community.

Large language models (LLMs) have transformed AI across diverse domains, with prompting being central to their success in guiding model outputs. However, manual prompt engineering is both labor-intensive and domain-specific, necessitating the need for automated solutions. We introduce PromptWizard, a novel, fully automated framework for discrete prompt optimization, utilizing a self-evolving, self-adapting mechanism. Through a feedback-driven critique and synthesis process, PromptWizard achieves an effective balance between exploration and exploitation, iteratively refining both prompt instructions and in-context examples to generate human-readable, task-specific prompts. This guided approach systematically improves prompt quality, resulting in superior performance across 45 tasks. PromptWizard excels even with limited training data, smaller LLMs, and various LLM architectures. Additionally, our cost analysis reveals a substantial reduction in API calls, token usage, and overall cost, demonstrating PromptWizard's efficiency, scalability, and advantages over existing prompt optimization strategies.

Recently, advanced large language models (LLMs) have emerged at an increasingly rapid pace. However, when faced with complex problems, most users are often unable to provide accurate and effective prompts to interact with LLMs, thus limiting the performance of LLMs. To address this challenge, we propose Prompt-R1, an end-to-end reinforcement learning framework that uses a small-scale LLM to collaborate with large-scale LLMs, replacing user interaction to solve problems better. This collaboration is cast as a multi-turn prompt interaction, where the small-scale LLM thinks and generates prompts, and the large-scale LLM performs complex reasoning. A dual-constrained reward is designed to optimize for correctness, generation quality, and reasoning accuracy. Prompt-R1 provides a plug-and-play framework that supports both inference and training with various large-scale LLMs. Experiments on multiple public datasets show that Prompt-R1 significantly outperforms baseline models across tasks. Our code is publicly available at https://github.com/QwenQKing/Prompt-R1.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve MILP problems from their natural language descriptions. OptiMUS is capable of developing mathematical models, writing and debugging solver code, developing tests, and checking the validity of generated solutions. To benchmark our agent, we present NLP4LP, a novel dataset of linear programming (LP) and mixed integer linear programming (MILP) problems. Our experiments demonstrate that OptiMUS solves nearly twice as many problems as a basic LLM prompting strategy. OptiMUS code and NLP4LP dataset are available at https://github.com/teshnizi/OptiMUS{https://github.com/teshnizi/OptiMUS}

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

Prompt engineering is a challenging yet crucial task for optimizing the performance of large language models (LLMs). It requires complex reasoning to examine the model's errors, hypothesize what is missing or misleading in the current prompt, and communicate the task with clarity. While recent works indicate that LLMs can be meta-prompted to perform automatic prompt engineering, their potentials may not be fully untapped due to the lack of sufficient guidance to elicit complex reasoning capabilities in LLMs in the meta-prompt. In this work, we investigate the problem of "prompt engineering a prompt engineer" -- constructing a meta-prompt that more effectively guides LLMs to perform automatic prompt engineering. We introduce and analyze key components, such as a step-by-step reasoning template and context specification, which lead to improved performance. In addition, inspired by common optimization concepts such as batch size, step size and momentum, we introduce their verbalized counterparts to the meta-prompt and investigate their effects. Our final method, named PE2, finds a prompt that outperforms "let's think step by step" by 6.3% on the MultiArith dataset and 3.1% on the GSM8K dataset. To demonstrate its versatility, we apply PE2 to the Instruction Induction benchmark, a suite of counterfactual tasks, and a lengthy, real-world industrial prompt. In these settings, PE2 achieves strong performance and outperforms prior automatic prompt engineering baselines. Further, we show that PE2 makes meaningful and targeted prompt edits, amends erroneous or incomplete prompts, and presents non-trivial counterfactual reasoning abilities.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

Highly effective, task-specific prompts are often heavily engineered by experts to integrate detailed instructions and domain insights based on a deep understanding of both instincts of large language models (LLMs) and the intricacies of the target task. However, automating the generation of such expert-level prompts remains elusive. Existing prompt optimization methods tend to overlook the depth of domain knowledge and struggle to efficiently explore the vast space of expert-level prompts. Addressing this, we present PromptAgent, an optimization method that autonomously crafts prompts equivalent in quality to those handcrafted by experts. At its core, PromptAgent views prompt optimization as a strategic planning problem and employs a principled planning algorithm, rooted in Monte Carlo tree search, to strategically navigate the expert-level prompt space. Inspired by human-like trial-and-error exploration, PromptAgent induces precise expert-level insights and in-depth instructions by reflecting on model errors and generating constructive error feedback. Such a novel framework allows the agent to iteratively examine intermediate prompts (states), refine them based on error feedbacks (actions), simulate future rewards, and search for high-reward paths leading to expert prompts. We apply PromptAgent to 12 tasks spanning three practical domains: BIG-Bench Hard (BBH), as well as domain-specific and general NLP tasks, showing it significantly outperforms strong Chain-of-Thought and recent prompt optimization baselines. Extensive analyses emphasize its capability to craft expert-level, detailed, and domain-insightful prompts with great efficiency and generalizability.

Large Language Models (LLMs) perform best with well-crafted prompts, yet prompt engineering remains manual, inconsistent, and inaccessible to non-experts. We introduce Promptomatix, an automatic prompt optimization framework that transforms natural language task descriptions into high-quality prompts without requiring manual tuning or domain expertise. Promptomatix supports both a lightweight meta-prompt-based optimizer and a DSPy-powered compiler, with modular design enabling future extension to more advanced frameworks. The system analyzes user intent, generates synthetic training data, selects prompting strategies, and refines prompts using cost-aware objectives. Evaluated across 5 task categories, Promptomatix achieves competitive or superior performance compared to existing libraries, while reducing prompt length and computational overhead making prompt optimization scalable and efficient.

Large Language Models (LLMs) have demonstrated significant capabilities, particularly in the domain of question answering (QA). However, their effectiveness in QA is often undermined by the vagueness of user questions. To address this issue, we introduce single-round instance-level prompt optimization, referred to as question rewriter. By enhancing the intelligibility of human questions for black-box LLMs, our question rewriter improves the quality of generated answers. The rewriter is optimized using direct preference optimization based on feedback collected from automatic criteria for evaluating generated answers; therefore, its training does not require costly human annotations. The experiments across multiple black-box LLMs and long-form question answering (LFQA) datasets demonstrate the efficacy of our method. This paper provides a practical framework for training question rewriters and sets a precedent for future explorations in prompt optimization within LFQA tasks. Code is available at https://github.com/3244we/Question-Rewriter.

Instruction-following made modern large language models (LLMs) helpful assistants. However, the key to taming LLMs on complex instructions remains mysterious, for that there are huge gaps between models trained by open-source community and those trained by leading companies. To bridge the gap, we propose a simple and scalable approach UltraIF for building LLMs that can follow complex instructions with open-source data. UltraIF first decomposes real-world user prompts into simpler queries, constraints, and corresponding evaluation questions for the constraints. Then, we train an UltraComposer to compose constraint-associated prompts with evaluation questions. This prompt composer allows us to synthesize complicated instructions as well as filter responses with evaluation questions. In our experiment, for the first time, we successfully align LLaMA-3.1-8B-Base to catch up with its instruct version on 5 instruction-following benchmarks without any benchmark information, using only 8B model as response generator and evaluator. The aligned model also achieved competitive scores on other benchmarks. Moreover, we also show that UltraIF could further improve LLaMA-3.1-8B-Instruct through self-alignment, motivating broader use cases for the method. Our code will be available at https://github.com/kkk-an/UltraIF.

Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset is available at https://github.com/yangzhch6/InterMWP.

Well-designed prompts are crucial for enhancing Large language models' (LLMs) reasoning capabilities while aligning their outputs with task requirements across diverse domains. However, manually designed prompts require expertise and iterative experimentation. While existing prompt optimization methods aim to automate this process, they rely heavily on external references such as ground truth or by humans, limiting their applicability in real-world scenarios where such data is unavailable or costly to obtain. To address this, we propose Self-Supervised Prompt Optimization (SPO), a cost-efficient framework that discovers effective prompts for both closed and open-ended tasks without requiring external reference. Motivated by the observations that prompt quality manifests directly in LLM outputs and LLMs can effectively assess adherence to task requirements, we derive evaluation and optimization signals purely from output comparisons. Specifically, SPO selects superior prompts through pairwise output comparisons evaluated by an LLM evaluator, followed by an LLM optimizer that aligns outputs with task requirements. Extensive experiments demonstrate that SPO outperforms state-of-the-art prompt optimization methods, achieving comparable or superior results with significantly lower costs (e.g., 1.1% to 5.6% of existing methods) and fewer samples (e.g., three samples). The code is available at https://github.com/geekan/MetaGPT.

Generative AI can now synthesize strikingly realistic images from text, yet output quality remains highly sensitive to how prompts are phrased. Direct Preference Optimization (DPO) offers a lightweight, off-policy alternative to RL for automatic prompt engineering, but its token-level regularization leaves semantic inconsistency unchecked as prompts that win higher preference scores can still drift away from the user's intended meaning. We introduce Sem-DPO, a variant of DPO that preserves semantic consistency yet retains its simplicity and efficiency. Sem-DPO adjusts the DPO loss using a weight based on how different the winning prompt is from the original, reducing the impact of training examples that are semantically misaligned. We provide the first analytical bound on semantic drift for preference-tuned prompt generators, showing that Sem-DPO keeps learned prompts within a provably bounded neighborhood of the original text. On three standard text-to-image prompt-optimization benchmarks and two language models, Sem-DPO achieves 8-12% higher CLIP similarity and 5-9% higher human-preference scores (HPSv2.1, PickScore) than DPO, while also outperforming state-of-the-art baselines. These findings suggest that strong flat baselines augmented with semantic weighting should become the new standard for prompt-optimization studies and lay the groundwork for broader, semantics-aware preference optimization in language models.

Direct Preference Optimization (DPO) has proven effective in complex reasoning tasks like math word problems and code generation. However, when applied to Text-to-SQL datasets, it often fails to improve performance and can even degrade it. Our investigation reveals the root cause: unlike math and code tasks, which naturally integrate Chain-of-Thought (CoT) reasoning with DPO, Text-to-SQL datasets typically include only final answers (gold SQL queries) without detailed CoT solutions. By augmenting Text-to-SQL datasets with synthetic CoT solutions, we achieve, for the first time, consistent and significant performance improvements using DPO. Our analysis shows that CoT reasoning is crucial for unlocking DPO's potential, as it mitigates reward hacking, strengthens discriminative capabilities, and improves scalability. These findings offer valuable insights for building more robust Text-to-SQL models. To support further research, we publicly release the code and CoT-enhanced datasets.

Language Model Programs, i.e. sophisticated pipelines of modular language model (LM) calls, are increasingly advancing NLP tasks, but they require crafting prompts that are jointly effective for all modules. We study prompt optimization for LM programs, i.e. how to update these prompts to maximize a downstream metric without access to module-level labels or gradients. To make this tractable, we factorize our problem into optimizing the free-form instructions and few-shot demonstrations of every module and introduce several strategies to craft task-grounded instructions and navigate credit assignment across modules. Our strategies include (i) program- and data-aware techniques for proposing effective instructions, (ii) a stochastic mini-batch evaluation function for learning a surrogate model of our objective, and (iii) a meta-optimization procedure in which we refine how LMs construct proposals over time. Using these insights we develop MIPRO, a novel algorithm for optimizing LM programs. MIPRO outperforms baseline optimizers on five of seven diverse multi-stage LM programs using a best-in-class open-source model (Llama-3-8B), by as high as 13% accuracy. We have released our new optimizers and benchmark in DSPy at http://dspy.ai

Large language models (LLMs) are evolving from conversational systems into strong reasoners for tasks such as Olympiad mathematics and competitive programming. While scaling parameters and test-time computation has driven progress, a key bottleneck is the lack of high-quality training problems: human-curated datasets are costly and limited, while existing synthetic corpora are often too easy or narrow. PromptCoT 1.0 showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptCoT 2.0, a scalable framework that replaces hand-crafted heuristics with an expectation-maximization (EM) loop, where rationales are iteratively refined to guide prompt construction. This produces problems that are both harder and more diverse than prior corpora. The synthetic prompts support two post-training regimes: (1) Self-Play, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) Supervised Fine-Tuning (SFT), where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptCoT 2.0 to Qwen3-30B-A3B-Thinking-2507 sets new state-of-the-art results at the 30B scale, with +4.4, +4.8, and +5.3 on AIME 24/25 and HMMT 25, +6.1 and +5.0 on LiveCodeBench v5/v6, and +35 Elo on Codeforces. In SFT, training Qwen2.5-7B-Instruct solely on synthetic prompts boosts accuracy to 73.1 (AIME 24), 65.6 (AIME 25), and 53.4 (LiveCodeBench v5), surpassing models trained on human or hybrid data. Analyses further confirm that PromptCoT 2.0 yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptCoT 2.0 as a scalable foundation for future open-source models. The implementation is available at https://github.com/inclusionAI/PromptCoT.

We explore the ability of large language models to solve and generate puzzles from the NPR Sunday Puzzle game show using PUZZLEQA, a dataset comprising 15 years of on-air puzzles. We evaluate four large language models using PUZZLEQA, in both multiple choice and free response formats, and explore two prompt engineering techniques to improve free response performance: chain-of-thought reasoning and prompt summarization. We find that state-of-the-art large language models can solve many PUZZLEQA puzzles: the best model, GPT-3.5, achieves 50.2% loose accuracy. However, in our few-shot puzzle generation experiment, we find no evidence that models can generate puzzles: GPT-3.5 generates puzzles with answers that do not conform to the generated rules. Puzzle generation remains a challenging task for future work.

Prompt engineering is very important to enhance the performance of large language models (LLMs). When dealing with complex issues, prompt engineers tend to distill multiple patterns from examples and inject relevant solutions to optimize the prompts, achieving satisfying results. However, existing automatic prompt optimization techniques are only limited to producing single flow instructions, struggling with handling diverse patterns. In this paper, we present AMPO, an automatic prompt optimization method that can iteratively develop a multi-branched prompt using failure cases as feedback. Our goal is to explore a novel way of structuring prompts with multi-branches to better handle multiple patterns in complex tasks, for which we introduce three modules: Pattern Recognition, Branch Adjustment, and Branch Pruning. In experiments across five tasks, AMPO consistently achieves the best results. Additionally, our approach demonstrates significant optimization efficiency due to our adoption of a minimal search strategy.

Recent studies have shown that large language models' (LLMs) mathematical problem-solving capabilities can be enhanced by integrating external tools, such as code interpreters, and employing multi-turn Chain-of-Thought (CoT) reasoning. While current methods focus on synthetic data generation and Supervised Fine-Tuning (SFT), this paper studies the complementary direct preference learning approach to further improve model performance. However, existing direct preference learning algorithms are originally designed for the single-turn chat task, and do not fully address the complexities of multi-turn reasoning and external tool integration required for tool-integrated mathematical reasoning tasks. To fill in this gap, we introduce a multi-turn direct preference learning framework, tailored for this context, that leverages feedback from code interpreters and optimizes trajectory-level preferences. This framework includes multi-turn DPO and multi-turn KTO as specific implementations. The effectiveness of our framework is validated through training of various language models using an augmented prompt set from the GSM8K and MATH datasets. Our results demonstrate substantial improvements: a supervised fine-tuned Gemma-1.1-it-7B model's performance increased from 77.5% to 83.9% on GSM8K and from 46.1% to 51.2% on MATH. Similarly, a Gemma-2-it-9B model improved from 84.1% to 86.3% on GSM8K and from 51.0% to 54.5% on MATH.

The ML community is rapidly exploring techniques for prompting language models (LMs) and for stacking them into pipelines that solve complex tasks. Unfortunately, existing LM pipelines are typically implemented using hard-coded "prompt templates", i.e. lengthy strings discovered via trial and error. Toward a more systematic approach for developing and optimizing LM pipelines, we introduce DSPy, a programming model that abstracts LM pipelines as text transformation graphs, i.e. imperative computational graphs where LMs are invoked through declarative modules. DSPy modules are parameterized, meaning they can learn (by creating and collecting demonstrations) how to apply compositions of prompting, finetuning, augmentation, and reasoning techniques. We design a compiler that will optimize any DSPy pipeline to maximize a given metric. We conduct two case studies, showing that succinct DSPy programs can express and optimize sophisticated LM pipelines that reason about math word problems, tackle multi-hop retrieval, answer complex questions, and control agent loops. Within minutes of compiling, a few lines of DSPy allow GPT-3.5 and llama2-13b-chat to self-bootstrap pipelines that outperform standard few-shot prompting (generally by over 25% and 65%, respectively) and pipelines with expert-created demonstrations (by up to 5-46% and 16-40%, respectively). On top of that, DSPy programs compiled to open and relatively small LMs like 770M-parameter T5 and llama2-13b-chat are competitive with approaches that rely on expert-written prompt chains for proprietary GPT-3.5. DSPy is available at https://github.com/stanfordnlp/dspy

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

Prompt optimization (PO) offers a practical alternative to fine-tuning large language models (LLMs), enabling performance improvements without altering model weights. Existing methods typically rely on advanced, large-scale LLMs like GPT-4 to generate optimized prompts. However, due to limited downward compatibility, verbose, instruction-heavy prompts from advanced LLMs can overwhelm lightweight inference models and degrade response quality. In this work, we rethink prompt optimization through the lens of interpretable design. We first identify a set of model-agnostic prompt quality merits and empirically validate their effectiveness in enhancing prompt and response quality. We then introduce MePO, a merit-guided, lightweight, and locally deployable prompt optimizer trained on our preference dataset built from merit-aligned prompts generated by a lightweight LLM. Unlike prior work, MePO avoids online optimization reliance, reduces cost and privacy concerns, and, by learning clear, interpretable merits, generalizes effectively to both large-scale and lightweight inference models. Experiments demonstrate that MePO achieves better results across diverse tasks and model types, offering a scalable and robust solution for real-world deployment. Our model and dataset are available at: https://github.com/MidiyaZhu/MePO

In the quest to facilitate the deep intelligence of Large Language Models (LLMs) accessible in final-end user-bot interactions, the art of prompt crafting emerges as a critical yet complex task for the average user. Contrast to previous model-oriented yet instruction-agnostic Automatic Prompt Optimization methodologies, yielding polished results for predefined target models while suffering rapid degradation with out-of-box models, we present Free-form Instruction-oriented Prompt Optimization (FIPO). This approach is supported by our large-scale prompt preference dataset and employs a modular fine-tuning schema. The FIPO schema reimagines the optimization process into manageable modules, anchored by a meta prompt that dynamically adapts content. This allows for the flexible integration of the raw task instruction, the optional instruction response, and the optional ground truth to produce finely optimized task prompts. The FIPO preference dataset is meticulously constructed using the optimal and suboptimal LLMs, undergoing rigorous cross-verification by human experts and analytical models. Applying the insights from the data with Tulu2 models and fine-tuning strategies, we validate the efficacy of FIPO schema across five public benchmarks. Codes, data and scripts are here: https://github.com/LuJunru/FIPO_Project.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities. However, these approaches overlook crucial requirements for prior knowledge of specific concepts, theorems, and tricks to tackle most arithmetic reasoning problems successfully. To address this issue, we propose a novel and effective Teaching-Inspired Integrated Framework, which emulates the instructional process of a teacher guiding students. This method equips LLMs with essential concepts, relevant theorems, and similar problems with analogous solution approaches, facilitating the enhancement of reasoning abilities. Additionally, we introduce two new Chinese datasets, MathMC and MathToF, both with detailed explanations and answers. Experiments are conducted on nine benchmarks which demonstrates that our approach improves the reasoning accuracy of LLMs. With GPT-4 and our framework, we achieve new state-of-the-art performance on four math benchmarks (AddSub, SVAMP, Math23K and AQuA) with accuracies of 98.2% (+3.3%), 93.9% (+0.2%), 94.3% (+7.2%) and 81.1% (+1.2%). Our data and code are available at https://github.com/SallyTan13/Teaching-Inspired-Prompting.

We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.

Solving an NP-hard optimization problem often requires reformulating it for a specific solver -- quantum hardware, a commercial optimizer, or a domain heuristic. A tool for polynomial-time reductions between hard problems would let practitioners route any supported problem to any supported solver through a single interface. Building such a library at scale, however, has remained out of reach. We show that harness engineering, the practice of designing constraints, verification systems, and feedback loops that channel AI coding agents, can overcome this barrier. Our harness combines a no-code contribution route for domain experts, a multilayer verification stack ranging from type-level checks to agentic feature tests (AI agents role-playing as end users), and a fully automated implementation-review-integration pipeline. In about three months, we built a command-line tool backed by a library of 100+ problem types and 200+~reduction rules in over 170k lines of Rust. The result suggests that a well-engineered harness lets agents build well-tested software at a scale and pace beyond prior reduction-library efforts. Because the reduction graph composes transitively, a new solver registered for any single problem type instantly becomes available to every problem connected by a reduction path. The source code is available at https://github.com/CodingThrust/problem-reductions.

Artificial Intelligence (AI) advancement is heavily dependent on access to large-scale, high-quality training data. However, in specialized domains such as healthcare, data acquisition faces significant constraints due to privacy regulations, ethical considerations, and limited availability. While synthetic data generation offers a promising solution, conventional approaches typically require substantial real data for training generative models. The emergence of large-scale prompt-based models presents new opportunities for synthetic data generation without direct access to protected data. However, crafting effective prompts for domain-specific data generation remains challenging, and manual prompt engineering proves insufficient for achieving output with sufficient precision and authenticity. We review recent developments in automatic prompt optimization, following PRISMA guidelines. We analyze six peer-reviewed studies published between 2020 and 2024 that focus on automatic data-free prompt optimization methods. Our analysis reveals three approaches: feedback-driven, error-based, and control-theoretic. Although all approaches demonstrate promising capabilities in prompt refinement and adaptation, our findings suggest the need for an integrated framework that combines complementary optimization techniques to enhance synthetic data generation while minimizing manual intervention. We propose future research directions toward developing robust, iterative prompt optimization frameworks capable of improving the quality of synthetic data. This advancement can be particularly crucial for sensitive fields and in specialized domains where data access is restricted, potentially transforming how we approach synthetic data generation for AI development.

Prompt engineering is an increasingly important skill set needed to converse effectively with large language models (LLMs), such as ChatGPT. Prompts are instructions given to an LLM to enforce rules, automate processes, and ensure specific qualities (and quantities) of generated output. Prompts are also a form of programming that can customize the outputs and interactions with an LLM. This paper describes a catalog of prompt engineering techniques presented in pattern form that have been applied to solve common problems when conversing with LLMs. Prompt patterns are a knowledge transfer method analogous to software patterns since they provide reusable solutions to common problems faced in a particular context, i.e., output generation and interaction when working with LLMs. This paper provides the following contributions to research on prompt engineering that apply LLMs to automate software development tasks. First, it provides a framework for documenting patterns for structuring prompts to solve a range of problems so that they can be adapted to different domains. Second, it presents a catalog of patterns that have been applied successfully to improve the outputs of LLM conversations. Third, it explains how prompts can be built from multiple patterns and illustrates prompt patterns that benefit from combination with other prompt patterns.

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt Mixer, is tested on the AIMO 3 competition: 3 models, 23+ experiments, 50 IMO-level problems, one H100 80 GB, 5-hour limit. Every prompt-level intervention fails. High-temperature sampling already decorrelates errors; weaker strategies reduce accuracy more than they reduce correlation. Across an 8-point capability gap at equal N=8 and every optimization tested, model capability dominates. The gap between the best majority-vote score (42/50) and pass@20 (~45.5) is selection loss, not prompt loss. A verifier-based selector could close it. Prompt engineering cannot.

The shift toward interacting with frozen, "black-box" Large Language Models (LLMs) has transformed prompt engineering from a heuristic exercise into a critical optimization challenge. We propose a Reinforcement Learning (RL) framework for training learned prompting policies via iterative distillation of experience. In this architecture, a lightweight prompter model is optimized to maximize task-specific rewards for a larger, frozen worker LLM. By utilizing a contrastive experience buffer that couples scalar rewards with dense textual critiques, our approach effectively amortizes iterative prompt refinement into single-shot policy weights. Our experimental analysis focuses on the Big Bench Extra Hard (BBEH) and Tau-bench suites, covering a diverse range of multi-step reasoning and tool-use tasks. We demonstrate significant gains, improving performance from 55% to 90% in logic-intensive reasoning and 74% to 91% in tool-use tasks. Furthermore, we analyze the structural evolution of prompts, demonstrating how the policy discovers specialized algorithmic heuristics. We provide comprehensive comparisons against state-of-the-art evolutionary baselines like GEPA, showing that iterative distillation achieves superior performance with higher sample efficiency.

LLMs have demonstrated commendable performance across diverse domains. Nevertheless, formulating high-quality prompts to instruct LLMs proficiently poses a challenge for non-AI experts. Existing research in prompt engineering suggests somewhat scattered optimization principles and designs empirically dependent prompt optimizers. Unfortunately, these endeavors lack a structured design template, incurring high learning costs and resulting in low reusability. In addition, it is not conducive to the iterative updating of prompts. Inspired by structured reusable programming languages, we propose LangGPT, a dual-layer prompt design framework as the programming language for LLMs. LangGPT has an easy-to-learn normative structure and provides an extended structure for migration and reuse. Experiments illustrate that LangGPT significantly enhances the performance of LLMs. Moreover, the case study shows that LangGPT leads LLMs to generate higher-quality responses. Furthermore, we analyzed the ease of use and reusability of LangGPT through a user survey in our online community.

Prompt engineering for LLMs remains complex, with existing frameworks either hiding complexity behind restrictive APIs or providing inflexible canned patterns that resist customization -- making sophisticated agentic programming challenging. We present the Prompt Declaration Language (PDL), a novel approach to prompt representation that tackles this fundamental complexity by bringing prompts to the forefront, enabling manual and automatic prompt tuning while capturing the composition of LLM calls together with rule-based code and external tools. By abstracting away the plumbing for such compositions, PDL aims at improving programmer productivity while providing a declarative representation that is amenable to optimization. This paper demonstrates PDL's utility through a real-world case study of a compliance agent. Tuning the prompting pattern of this agent yielded up to 4x performance improvement compared to using a canned agent and prompt pattern.

Large Language Models (LLMs) have already been widely adopted for automated algorithm design, demonstrating strong abilities in generating and evolving algorithms across various fields. Existing work has largely focused on examining their effectiveness in solving specific problems, with search strategies primarily guided by adaptive prompt designs. In this paper, through investigating the token-wise attribution of the prompts to LLM-generated algorithmic codes, we show that providing high-quality algorithmic code examples can substantially improve the performance of the LLM-driven optimization. Building upon this insight, we propose leveraging prior benchmark algorithms to guide LLM-driven optimization and demonstrate superior performance on two black-box optimization benchmarks: the pseudo-Boolean optimization suite (pbo) and the black-box optimization suite (bbob). Our findings highlight the value of integrating benchmarking studies to enhance both efficiency and robustness of the LLM-driven black-box optimization methods.

The International Mathematical Olympiad (IMO) is widely regarded as the world championship of high-school mathematics. IMO problems are renowned for their difficulty and novelty, demanding deep insight, creativity, and rigor. Although large language models perform well on many mathematical benchmarks, they often struggle with Olympiad-level problems. Using carefully designed prompts, we construct a model-agnostic, verification-and-refinement pipeline. We demonstrate its effectiveness on the recent IMO 2025, avoiding data contamination for models released before the competition. Equipped with any of the three leading models -- Gemini 2.5 Pro, Grok-4, or GPT-5 -- our pipeline correctly solved 5 out of the 6 problems (approx85.7% accuracy). This is in sharp contrast to their baseline accuracies: 31.6% (Gemini 2.5 Pro), 21.4% (Grok-4), and 38.1% (GPT-5), obtained by selecting the best of 32 candidate solutions. The substantial improvement underscores that the path to advanced AI reasoning requires not only developing more powerful base models but also designing effective methodologies to harness their full potential for complex tasks.

We introduce a large language model (LLM) based approach to answer complex questions requiring multi-hop numerical reasoning over financial reports. While LLMs have exhibited remarkable performance on various natural language and reasoning tasks, complex reasoning problems often rely on few-shot prompts that require carefully crafted examples. In contrast, our approach uses novel zero-shot prompts that guide the LLM to encode the required reasoning into a Python program or a domain specific language. The generated program is then executed by a program interpreter, thus mitigating the limitations of LLM in performing accurate arithmetic calculations. We evaluate the proposed approach on three financial datasets using some of the recently developed generative pretrained transformer (GPT) models and perform comparisons with various zero-shot baselines. The experimental results demonstrate that our approach significantly improves the accuracy for all the LLMs over their respective baselines. We provide a detailed analysis of the results, generating insights to support our findings. The success of our approach demonstrates the enormous potential to extract complex domain specific numerical reasoning by designing zero-shot prompts to effectively exploit the knowledge embedded in LLMs.

Large Language Models (LLMs) have shown impressive capabilities in many scenarios, but their performance depends, in part, on the choice of prompt. Past research has focused on optimizing prompts specific to a task. However, much less attention has been given to optimizing the general instructions included in a prompt, known as a system prompt. To address this gap, we propose SPRIG, an edit-based genetic algorithm that iteratively constructs prompts from prespecified components to maximize the model's performance in general scenarios. We evaluate the performance of system prompts on a collection of 47 different types of tasks to ensure generalizability. Our study finds that a single optimized system prompt performs on par with task prompts optimized for each individual task. Moreover, combining system and task-level optimizations leads to further improvement, which showcases their complementary nature. Experiments also reveal that the optimized system prompts generalize effectively across model families, parameter sizes, and languages. This study provides insights into the role of system-level instructions in maximizing LLM potential.

Many recent prompting strategies for large language models (LLMs) query the model multiple times sequentially -- first to produce intermediate results and then the final answer. However, using these methods, both decoder and model are unaware of potential follow-up prompts, leading to disconnected and undesirably wordy intermediate responses. In this work, we address this issue by proposing prompt sketching, a new prompting paradigm in which an LLM does not only respond by completing a prompt, but by predicting values for multiple variables in a template. This way, sketching grants users more control over the generation process, e.g., by providing a reasoning framework via intermediate instructions, leading to better overall results. The key idea enabling sketching with existing, autoregressive models is to adapt the decoding procedure to also score follow-up instructions during text generation, thus optimizing overall template likelihood in inference. Our experiments show that in a zero-shot setting, prompt sketching outperforms existing, sequential prompting schemes such as direct asking or chain-of-thought on 7 out of 8 LLM benchmarking tasks, including state tracking, arithmetic reasoning, and general question answering. To facilitate future use, we release a number of generic, yet effective sketches applicable to many tasks, and an open source library called dclib, powering our sketch-aware decoders.

We propose a diffusion-based framework for prompt optimization that leverages Diffusion Language Models (DLMs) to iteratively refine system prompts through masked denoising. By conditioning on interaction traces, including user queries, model responses, and optional feedback, our method enables flexible, span-level prompt updates without requiring gradient access or modifying the downstream language model. Across diverse benchmarks (e.g., τ-bench, SST-2, SST-5), DLM-optimized prompts consistently improve the performance of a frozen target LLM (e.g., GPT-4o-mini). We further show that moderate diffusion step counts provide the best balance between refinement quality and stability. These results highlight diffusion-based prompt optimization as a general, model-agnostic, and scalable approach for enhancing LLM performance through iterative prompt refinement.

Large Language Models (LLMs) are nowadays extensively used for various types of software engineering tasks, primarily code generation. Previous research has shown how suitable prompt engineering could help developers in improving their code generation prompts. However, so far, there do not exist specific guidelines driving developers towards writing suitable prompts for code generation. In this work, we derive and evaluate development-specific prompt optimization guidelines. First, we use an iterative, test-driven approach to automatically refine code generation prompts, and we analyze the outcome of this process to identify prompt improvement items that lead to test passes. We use such elements to elicit 10 guidelines for prompt improvement, related to better specifying I/O, pre-post conditions, providing examples, various types of details, or clarifying ambiguities. We conduct an assessment with 50 practitioners, who report their usage of the elicited prompt improvement patterns, as well as their perceived usefulness, which does not always correspond to the actual usage before knowing our guidelines. Our results lead to implications not only for practitioners and educators, but also for those aimed at creating better LLM-aided software development tools.

Large Language Models (LLMs) enable a new ecosystem with many downstream applications, called LLM applications, with different natural language processing tasks. The functionality and performance of an LLM application highly depend on its system prompt, which instructs the backend LLM on what task to perform. Therefore, an LLM application developer often keeps a system prompt confidential to protect its intellectual property. As a result, a natural attack, called prompt leaking, is to steal the system prompt from an LLM application, which compromises the developer's intellectual property. Existing prompt leaking attacks primarily rely on manually crafted queries, and thus achieve limited effectiveness. In this paper, we design a novel, closed-box prompt leaking attack framework, called PLeak, to optimize an adversarial query such that when the attacker sends it to a target LLM application, its response reveals its own system prompt. We formulate finding such an adversarial query as an optimization problem and solve it with a gradient-based method approximately. Our key idea is to break down the optimization goal by optimizing adversary queries for system prompts incrementally, i.e., starting from the first few tokens of each system prompt step by step until the entire length of the system prompt. We evaluate PLeak in both offline settings and for real-world LLM applications, e.g., those on Poe, a popular platform hosting such applications. Our results show that PLeak can effectively leak system prompts and significantly outperforms not only baselines that manually curate queries but also baselines with optimized queries that are modified and adapted from existing jailbreaking attacks. We responsibly reported the issues to Poe and are still waiting for their response. Our implementation is available at this repository: https://github.com/BHui97/PLeak.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

The generations of large language models are commonly controlled through prompting techniques, where a user's query to the model is prefixed with a prompt that aims to guide the model's behaviour on the query. The prompts used by companies to guide their models are often treated as secrets, to be hidden from the user making the query. They have even been treated as commodities to be bought and sold. However, there has been anecdotal evidence showing that the prompts can be extracted by a user even when they are kept secret. In this paper, we present a framework for systematically measuring the success of prompt extraction attacks. In experiments with multiple sources of prompts and multiple underlying language models, we find that simple text-based attacks can in fact reveal prompts with high probability.

Large language models (LLMs) are increasingly adept at following instructions containing task descriptions to solve complex problems, such as mathematical reasoning and automatic evaluation (LLM-as-a-Judge). However, as prompts grow more complex, models often struggle to adhere to all instructions. This difficulty is especially common when instructive prompts intertwine reasoning directives -- specifying what the model should solve -- with rigid formatting requirements that dictate how the solution must be presented. The entanglement creates competing goals for the model, suggesting that more explicit separation of these two aspects could lead to improved performance. To this front, we introduce Deco-G, a decoding framework that explicitly decouples format adherence from task solving. Deco-G handles format compliance with a separate tractable probabilistic model (TPM), while prompts LLMs with only task instructions. At each decoding step, Deco-G combines next token probabilities from the LLM with the TPM calculated format compliance likelihood to form the output probability. To make this approach both practical and scalable for modern instruction-tuned LLMs, we introduce three key innovations: instruction-aware distillation, a flexible trie-building algorithm, and HMM state pruning for computational efficiency. We demonstrate the effectiveness of Deco-G across a wide range of tasks with diverse format requirements, including mathematical reasoning, LLM-as-a-judge, and event argument extraction. Overall, our approach yields 1.0% to 6.0% relative gain over regular prompting practice with guaranteed format compliance.

Recent advancements in large language models (LLMs) have enabled a wide range of natural language processing (NLP) tasks to be performed through simple prompt-based interactions. Consequently, several approaches have been proposed to engineer prompts that most effectively enable LLMs to perform a given task (e.g., chain-of-thought prompting). In settings with a well-defined metric to optimize model performance, automatic prompt optimization (APO) methods have been developed to refine a seed prompt. Advancing this line of research, we propose APIO, a simple but effective prompt induction and optimization approach for the tasks of Grammatical Error Correction (GEC) and Text Simplification, without relying on manually specified seed prompts. APIO achieves a new state-of-the-art performance for purely LLM-based prompting methods on these tasks. We make our data, code, prompts, and outputs publicly available.

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

The efficacy of large language models (LLMs) in understanding and generating natural language has aroused a wide interest in developing prompt-based methods to harness the power of black-box LLMs. Existing methodologies usually prioritize a global optimization for finding the global optimum, which however will perform poorly in certain tasks. This thus motivates us to re-think the necessity of finding a global optimum in prompt optimization. To answer this, we conduct a thorough empirical study on prompt optimization and draw two major insights. Contrasting with the rarity of global optimum, local optima are usually prevalent and well-performed, which can be more worthwhile for efficient prompt optimization (Insight I). The choice of the input domain, covering both the generation and the representation of prompts, affects the identification of well-performing local optima (Insight II). Inspired by these insights, we propose a novel algorithm, namely localized zeroth-order prompt optimization (ZOPO), which incorporates a Neural Tangent Kernel-based derived Gaussian process into standard zeroth-order optimization for an efficient search of well-performing local optima in prompt optimization. Remarkably, ZOPO outperforms existing baselines in terms of both the optimization performance and the query efficiency, which we demonstrate through extensive experiments.

In recent years, Large Language Models have garnered significant attention for their strong performance in various natural language tasks, such as machine translation and question answering. These models demonstrate an impressive ability to generalize across diverse tasks. However, their effectiveness in tackling domain-specific tasks, such as financial sentiment analysis and monetary policy understanding, remains a topic of debate, as these tasks often require specialized knowledge and precise reasoning. To address such challenges, researchers design various prompts to unlock the models' abilities. By carefully crafting input prompts, researchers can guide these models to produce more accurate responses. Consequently, prompt engineering has become a key focus of study. Despite the advancements in both models and prompt engineering, the relationship between the two-specifically, how prompt design impacts models' ability to perform domain-specific tasks-remains underexplored. This paper aims to bridge this research gap.

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decision-making problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

Large Language Models (LLMs) have shown impressive performance as general purpose agents, but their abilities remain highly dependent on prompts which are hand written with onerous trial-and-error effort. We propose a simple and nonparametric solution to this problem, Automatic Prompt Optimization (APO), which is inspired by numerical gradient descent to automatically improve prompts, assuming access to training data and an LLM API. The algorithm uses minibatches of data to form natural language ``gradients'' that criticize the current prompt. The gradients are then ``propagated'' into the prompt by editing the prompt in the opposite semantic direction of the gradient. These gradient descent steps are guided by a beam search and bandit selection procedure which significantly improves algorithmic efficiency. Preliminary results across three benchmark NLP tasks and the novel problem of LLM jailbreak detection suggest that Automatic Prompt Optimization can outperform prior prompt editing techniques and improve an initial prompt's performance by up to 31\%, by using data to rewrite vague task descriptions into more precise annotation instructions.

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves are hard to learn, especially when embedded in more complex tasks. To address this, we propose Decomposed Prompting, a new approach to solve complex tasks by decomposing them (via prompting) into simpler sub-tasks that can be delegated to a library of prompting-based LLMs dedicated to these sub-tasks. This modular structure allows each prompt to be optimized for its specific sub-task, further decomposed if necessary, and even easily replaced with more effective prompts, trained models, or symbolic functions if desired. We show that the flexibility and modularity of Decomposed Prompting allows it to outperform prior work on few-shot prompting using GPT3. On symbolic reasoning tasks, we can further decompose sub-tasks that are hard for LLMs into even simpler solvable sub-tasks. When the complexity comes from the input length, we can recursively decompose the task into the same task but with smaller inputs. We also evaluate our approach on textual multi-step reasoning tasks: on long-context multi-hop QA task, we can more effectively teach the sub-tasks via our separate sub-tasks prompts; and on open-domain multi-hop QA, we can incorporate a symbolic information retrieval within our decomposition framework, leading to improved performance on both tasks. Datasets, Code and Prompts available at https://github.com/allenai/DecomP.

The basic question-answering format of large language models involves inputting a prompt and receiving a response, and the quality of the prompt directly impacts the effectiveness of the response. Automated Prompt Optimization (APO) aims to break free from the cognitive biases of manually designed prompts and explores a broader design space for prompts. However, existing APO methods suffer from limited flexibility of fixed templates and inefficient search in prompt spaces as key issues. To this end, we propose a Multi-Agent framework Incorporating Socratic guidance (MARS), which utilizes multi-agent fusion technology for automatic planning, with gradual continuous optimization and evaluation. Specifically, MARS comprises seven agents, each with distinct functionalities, which autonomously use the Planner to devise an optimization path that ensures flexibility. Additionally, it employs a Teacher-Critic-Student Socratic dialogue pattern to iteratively optimize the prompts while conducting effective search. We conduct extensive experiments on various datasets to validate the effectiveness of our method, and perform additional analytical experiments to assess the model's advancement as well as the interpretability.

Prompting ChatGPT to achieve complex goals (e.g., creating a customer support chatbot) often demands meticulous prompt engineering, including aspects like fluent writing and chain-of-thought techniques. While emerging prompt optimizers can automatically refine many of these aspects, we argue that clearly conveying customized requirements (e.g., how to handle diverse inputs) remains a human-centric challenge. In this work, we introduce Requirement-Oriented Prompt Engineering (ROPE), a paradigm that focuses human attention on generating clear, complete requirements during prompting. We implement ROPE through an assessment and training suite that provides deliberate practice with LLM-generated feedback. In a study with 30 novices, we show that requirement-focused training doubles novices' prompting performance, significantly outperforming conventional prompt engineering training and prompt optimization. We also demonstrate that high-quality LLM outputs are directly tied to the quality of input requirements. Our work paves the way for more effective task delegation in human-LLM collaborative prompting.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

This paper presents the first ChatGPT4PCG Competition at the 2023 IEEE Conference on Games. The objective of this competition is for participants to create effective prompts for ChatGPT--enabling it to generate Science Birds levels with high stability and character-like qualities--fully using their creativity as well as prompt engineering skills. ChatGPT is a conversational agent developed by OpenAI. Science Birds is selected as the competition platform because designing an Angry Birds-like level is not a trivial task due to the in-game gravity; the quality of the levels is determined by their stability. To lower the entry barrier to the competition, we limit the task to the generation of capitalized English alphabetical characters. We also allow only a single prompt to be used for generating all the characters. Here, the quality of the generated levels is determined by their stability and similarity to the given characters. A sample prompt is provided to participants for their reference. An experiment is conducted to determine the effectiveness of several modified versions of this sample prompt on level stability and similarity by testing them on several characters. To the best of our knowledge, we believe that ChatGPT4PCG is the first competition of its kind and hope to inspire enthusiasm for prompt engineering in procedural content generation.

Prompt engineering has emerged as a powerful technique for optimizing large language models (LLMs) for specific applications, enabling faster prototyping and improved performance, and giving rise to the interest of the community in protecting proprietary system prompts. In this work, we explore a novel perspective on prompt privacy through the lens of membership inference. We develop Prompt Detective, a statistical method to reliably determine whether a given system prompt was used by a third-party language model. Our approach relies on a statistical test comparing the distributions of two groups of model outputs corresponding to different system prompts. Through extensive experiments with a variety of language models, we demonstrate the effectiveness of Prompt Detective for prompt membership inference. Our work reveals that even minor changes in system prompts manifest in distinct response distributions, enabling us to verify prompt usage with statistical significance.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

Various human-designed prompt engineering techniques have been proposed to improve problem solvers based on Large Language Models (LLMs), yielding many disparate code bases. We unify these approaches by describing LLM-based agents as computational graphs. The nodes implement functions to process multimodal data or query LLMs, and the edges describe the information flow between operations. Graphs can be recursively combined into larger composite graphs representing hierarchies of inter-agent collaboration (where edges connect operations of different agents). Our novel automatic graph optimizers (1) refine node-level LLM prompts (node optimization) and (2) improve agent orchestration by changing graph connectivity (edge optimization). Experiments demonstrate that our framework can be used to efficiently develop, integrate, and automatically improve various LLM agents. The code can be found at https://github.com/metauto-ai/gptswarm.

The recent advances in the development of Large Language Models (LLMs) like ChatGPT have achieved remarkable performance by leveraging human expertise. Yet, fully eliciting LLMs' potential for complex tasks requires navigating the vast search space of natural language prompts. While prompt engineering has shown promise, the requisite human-crafted prompts in trial-and-error attempts and the associated costs pose significant challenges. Crucially, the efficiency of prompt optimization hinges on the costly procedure of prompt evaluation. This work introduces Prompt-OIRL, an approach rooted in offline inverse reinforcement learning that seeks to bridge the gap between effective prompt evaluation and affordability. Our method draws on offline datasets from expert evaluations, employing Inverse-RL to derive a reward model for offline, query-dependent prompt evaluations. The advantages of Prompt-OIRL are manifold: it predicts prompt performance, is cost-efficient, produces human-readable results, and efficiently navigates the prompt space. We validate our method across four LLMs and three arithmetic datasets, highlighting its potential as a robust and effective tool for offline prompt evaluation and optimization. Our code as well as the offline datasets are released, and we highlight the Prompt-OIRL can be reproduced within a few hours using a single laptop using CPU

We discover that DALLE-2 seems to have a hidden vocabulary that can be used to generate images with absurd prompts. For example, it seems that Apoploe vesrreaitais means birds and Contarra ccetnxniams luryca tanniounons (sometimes) means bugs or pests. We find that these prompts are often consistent in isolation but also sometimes in combinations. We present our black-box method to discover words that seem random but have some correspondence to visual concepts. This creates important security and interpretability challenges.

Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic solvers: the model directly generates a formal program that a geometry solver can execute. However, this direct program generation lacks intermediate reasoning, making the decision process opaque and prone to errors. In this work, we explore a new approach that integrates Chain-of-Thought (CoT) with formal language. The model interleaves natural language reasoning with incremental emission of solver-executable code, producing a hybrid reasoning trace in which critical derivations are expressed in formal language. To teach this behavior at scale, we combine (1) supervised fine-tuning on an 11K newly developed synthetic dataset with interleaved natural language reasoning and automatic formalization, and (2) solver-in-the-loop reinforcement learning that jointly optimizes both the CoT narrative and the resulting program through outcome-based rewards. Built on Qwen2.5-VL-7B, our new model, named GF-Reasoner, achieves up to 15% accuracy improvements on standard GPS benchmarks, surpassing both 7B-scale peers and the much larger model Qwen2.5-VL-72B. By exploiting high-order geometric knowledge and offloading symbolic computation to the solver, the generated reasoning traces are noticeably shorter and cleaner. Furthermore, we present a comprehensive analysis of method design choices (e.g., reasoning paradigms, data synthesis, training epochs, etc.), providing actionable insights for future research.

Text entry is an essential task in our day-to-day digital interactions. Numerous intelligent features have been developed to streamline this process, making text entry more effective, efficient, and fluid. These improvements include sentence prediction and user personalization. However, as deep learning-based language models become the norm for these advanced features, the necessity for data collection and model fine-tuning increases. These challenges can be mitigated by harnessing the in-context learning capability of large language models such as GPT-3.5. This unique feature allows the language model to acquire new skills through prompts, eliminating the need for data collection and fine-tuning. Consequently, large language models can learn various text prediction techniques. We initially showed that, for a sentence prediction task, merely prompting GPT-3.5 surpassed a GPT-2 backed system and is comparable with a fine-tuned GPT-3.5 model, with the latter two methods requiring costly data collection, fine-tuning and post-processing. However, the task of prompting large language models to specialize in specific text prediction tasks can be challenging, particularly for designers without expertise in prompt engineering. To address this, we introduce Promptor, a conversational prompt generation agent designed to engage proactively with designers. Promptor can automatically generate complex prompts tailored to meet specific needs, thus offering a solution to this challenge. We conducted a user study involving 24 participants creating prompts for three intelligent text entry tasks, half of the participants used Promptor while the other half designed prompts themselves. The results show that Promptor-designed prompts result in a 35% increase in similarity and 22% in coherence over those by designers.

Direct Preference Optimization (DPO) is an effective technique that leverages pairwise preference data (usually one chosen and rejected response pair per user prompt) to align LLMs to human preferences. In practice, multiple responses can exist for a given prompt with varying quality relative to each other. With availability of such quality ratings for multiple responses, we propose utilizing these responses to create multiple preference pairs for a given prompt. Our work focuses on systematically using the constructed multiple preference pair in DPO training via curriculum learning methodology. In particular, we order these multiple pairs of preference data from easy to hard (emulating curriculum training) according to various criteria. We show detailed comparisons of our proposed approach to the standard single-pair DPO setting. Our method, which we call Curry-DPO consistently shows increased performance gains on MTbench, Vicuna, WizardLM, and the UltraFeedback test set, highlighting its effectiveness. More specifically, Curry-DPO achieves a score of 7.43 on MT-bench with Zephy-7B model outperforming majority of existing LLMs with similar parameter size. Curry-DPO also achieves the highest adjusted win rates on Vicuna, WizardLM, and UltraFeedback test datasets (90.7%, 87.1%, and 87.9% respectively) in our experiments, with notable gains of upto 7.5% when compared to standard DPO technique.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

With the success of large language models (LLMs) of code and their use as code assistants (e.g. Codex used in GitHub Copilot), techniques for introducing domain-specific knowledge in the prompt design process become important. In this work, we propose a framework called Repo-Level Prompt Generator that learns to generate example-specific prompts using prompt proposals. The prompt proposals take context from the entire repository, thereby incorporating both the structure of the repository and the context from other relevant files (e.g. imports, parent class files). Our technique doesn't require any access to the weights of the LLM, making it applicable in cases where we only have black-box access to the LLM. We conduct experiments on the task of single-line code-autocompletion using code repositories taken from Google Code archives. We demonstrate that an oracle constructed from our prompt proposals gives a remarkably high relative improvement of 36% over Codex, showing the quality of these proposals. Further, we show that when we train a model to predict a prompt proposal, we can achieve significant performance gains over Codex and other baselines. We release our code, data, and trained checkpoints at: https://github.com/shrivastavadisha/repo_level_prompt_generation.

Large language models (LLMs) have played a fundamental role in various natural language processing tasks with powerful prompt techniques. However, in real-world applications, there are often similar prompt components for repeated queries, which causes significant computational burdens during inference. Existing prompt compression and direct fine-tuning methods aim to tackle these challenges, yet they frequently struggle to strike an optimal balance between cost-efficiency and performance effectiveness, especially in complex tasks such as NL2Code. In this paper, we propose a novel method namely PromptIntern to internalize the prompt knowledge into model parameters via progressive fine-tuning. Our method enables LLMs to emulate the human learning process for a new task, where detailed templates and examples in a prompt are gradually internalized and phased out progressively as the model grows accustomed to the task. Extensive experiments demonstrate that our method reduces inference tokens over 90%, speedups inference by 4.2 times, and saves 88.3% monetary cost.

Large Language Models (LLMs) are increasingly being integrated into various applications. The functionalities of recent LLMs can be flexibly modulated via natural language prompts. This renders them susceptible to targeted adversarial prompting, e.g., Prompt Injection (PI) attacks enable attackers to override original instructions and employed controls. So far, it was assumed that the user is directly prompting the LLM. But, what if it is not the user prompting? We argue that LLM-Integrated Applications blur the line between data and instructions. We reveal new attack vectors, using Indirect Prompt Injection, that enable adversaries to remotely (without a direct interface) exploit LLM-integrated applications by strategically injecting prompts into data likely to be retrieved. We derive a comprehensive taxonomy from a computer security perspective to systematically investigate impacts and vulnerabilities, including data theft, worming, information ecosystem contamination, and other novel security risks. We demonstrate our attacks' practical viability against both real-world systems, such as Bing's GPT-4 powered Chat and code-completion engines, and synthetic applications built on GPT-4. We show how processing retrieved prompts can act as arbitrary code execution, manipulate the application's functionality, and control how and if other APIs are called. Despite the increasing integration and reliance on LLMs, effective mitigations of these emerging threats are currently lacking. By raising awareness of these vulnerabilities and providing key insights into their implications, we aim to promote the safe and responsible deployment of these powerful models and the development of robust defenses that protect users and systems from potential attacks.

Pre-trained vision-language models like CLIP have remarkably adapted to various downstream tasks. Nonetheless, their performance heavily depends on the specificity of the input text prompts, which requires skillful prompt template engineering. Instead, current approaches to prompt optimization learn the prompts through gradient descent, where the prompts are treated as adjustable parameters. However, these methods tend to lead to overfitting of the base classes seen during training and produce prompts that are no longer understandable by humans. This paper introduces a simple but interpretable prompt optimizer (IPO), that utilizes large language models (LLMs) to generate textual prompts dynamically. We introduce a Prompt Optimization Prompt that not only guides LLMs in creating effective prompts but also stores past prompts with their performance metrics, providing rich in-context information. Additionally, we incorporate a large multimodal model (LMM) to condition on visual content by generating image descriptions, which enhance the interaction between textual and visual modalities. This allows for thae creation of dataset-specific prompts that improve generalization performance, while maintaining human comprehension. Extensive testing across 11 datasets reveals that IPO not only improves the accuracy of existing gradient-descent-based prompt learning methods but also considerably enhances the interpretability of the generated prompts. By leveraging the strengths of LLMs, our approach ensures that the prompts remain human-understandable, thereby facilitating better transparency and oversight for vision-language models.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Mathematics is often perceived as a complex subject by students, leading to high failure rates in exams. To improve Mathematics skills, it is important to provide sample questions for students to practice problem-solving. Manually creating Math Word Problems (MWPs) is time consuming for tutors, because they have to type in natural language while adhering to grammar and spelling rules of the language. Existing Deep Learning techniques for MWP generation either require a tutor to provide the initial portion of the MWP, and/or additional information such as an equation. In this paper, we present an MWP generation system based on Large Language Models (LLMs) that overcome the need for additional input - the only input to our system is the number of MWPs needed, the grade and the type of question (e.g. addition, subtraction). Unlike the existing LLM-based solutions for MWP generation, we carried out an extensive set of experiments involving different LLMs, prompting strategies, techniques to improve the diversity of questions, as well as techniques that employ human feedback to improve LLM performance. Human and automated evaluations confirmed that the generated MWPs are high in quality, with minimal spelling and grammar issues. However, LLMs still struggle to generate questions that adhere to the specified grade and question type requirements.

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose p1, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that p1 substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.

Prompt learning has emerged as an efficient alternative for fine-tuning foundational models, such as CLIP, for various downstream tasks. Conventionally trained using the task-specific objective, i.e., cross-entropy loss, prompts tend to overfit downstream data distributions and find it challenging to capture task-agnostic general features from the frozen CLIP. This leads to the loss of the model's original generalization capability. To address this issue, our work introduces a self-regularization framework for prompting called PromptSRC (Prompting with Self-regulating Constraints). PromptSRC guides the prompts to optimize for both task-specific and task-agnostic general representations using a three-pronged approach by: (a) regulating prompted representations via mutual agreement maximization with the frozen model, (b) regulating with self-ensemble of prompts over the training trajectory to encode their complementary strengths, and (c) regulating with textual diversity to mitigate sample diversity imbalance with the visual branch. To the best of our knowledge, this is the first regularization framework for prompt learning that avoids overfitting by jointly attending to pre-trained model features, the training trajectory during prompting, and the textual diversity. PromptSRC explicitly steers the prompts to learn a representation space that maximizes performance on downstream tasks without compromising CLIP generalization. We perform extensive experiments on 4 benchmarks where PromptSRC overall performs favorably well compared to the existing methods. Our code and pre-trained models are publicly available at: https://github.com/muzairkhattak/PromptSRC.

PromptSource is a system for creating, sharing, and using natural language prompts. Prompts are functions that map an example from a dataset to a natural language input and target output. Using prompts to train and query language models is an emerging area in NLP that requires new tools that let users develop and refine these prompts collaboratively. PromptSource addresses the emergent challenges in this new setting with (1) a templating language for defining data-linked prompts, (2) an interface that lets users quickly iterate on prompt development by observing outputs of their prompts on many examples, and (3) a community-driven set of guidelines for contributing new prompts to a common pool. Over 2,000 prompts for roughly 170 datasets are already available in PromptSource. PromptSource is available at https://github.com/bigscience-workshop/promptsource.

Recent studies have shown LLMs possess some ability to improve their responses when given external feedback. However, it remains unclear how effectively and thoroughly these models can incorporate extrinsic feedback. In an ideal scenario, if LLMs receive near-perfect and complete feedback, we would expect them to fully integrate the feedback and change their incorrect answers to correct ones. In this paper, we systematically investigate LLMs' ability to incorporate feedback by designing a controlled experimental environment. For each problem, a solver model attempts a solution, then a feedback generator with access to near-complete ground-truth answers produces targeted feedback, after which the solver tries again. We evaluate this pipeline across a diverse range of tasks, including math reasoning, knowledge reasoning, scientific reasoning, and general multi-domain evaluations with state-of-the-art language models including Claude 3.7 (with and without extended thinking). Surprisingly, even under these near-ideal conditions, solver models consistently show resistance to feedback, a limitation that we term FEEDBACK FRICTION. To mitigate this limitation, we experiment with sampling-based strategies like progressive temperature increases and explicit rejection of previously attempted incorrect answers, which yield improvements but still fail to help models achieve target performance. We also perform a rigorous exploration of potential causes of FEEDBACK FRICTION, ruling out factors such as model overconfidence and data familiarity. We hope that highlighting this issue in LLMs and ruling out several apparent causes will help future research in self-improvement.

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

Can large language models improve without external data -- by generating their own questions and answers? We hypothesize that a pre-trained language model can improve its reasoning skills given only a single prompt specifying the topic (e.g., algebra word problems) and asking the model to generate its own questions. To do this, we propose Self-Questioning Language Models (SQLM): an asymmetric self-play framework where a proposer is given the topic and generates a question for a solver, who tries to answer it. Both the proposer and solver are trained via reinforcement learning. The proposer receives a reward if the problem is not too easy or too difficult, and the solver receives a reward based on majority voting, a proxy for correctness in the absence of ground-truth answers. For coding, the proposer can instead generate unit tests which are used for verification. We study this asymmetric self-play framework on three benchmarks: three-digit multiplication, algebra problems from the OMEGA benchmark, and programming problems from Codeforces. By continually generating more interesting problems and attempting to solve them, language models can improve on downstream benchmarks without access to any curated training datasets.

The strength of modern generative models lies in their ability to be controlled through text-based prompts. Typical "hard" prompts are made from interpretable words and tokens, and must be hand-crafted by humans. There are also "soft" prompts, which consist of continuous feature vectors. These can be discovered using powerful optimization methods, but they cannot be easily interpreted, re-used across models, or plugged into a text-based interface. We describe an approach to robustly optimize hard text prompts through efficient gradient-based optimization. Our approach automatically generates hard text-based prompts for both text-to-image and text-to-text applications. In the text-to-image setting, the method creates hard prompts for diffusion models, allowing API users to easily generate, discover, and mix and match image concepts without prior knowledge on how to prompt the model. In the text-to-text setting, we show that hard prompts can be automatically discovered that are effective in tuning LMs for classification.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

The performance of Large Language Models (LLMs) in reasoning tasks depends heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency being critical methods that enhance this ability. However, these methods do not fully exploit the answers generated by the LLM to guide subsequent responses. This paper proposes a new prompting method, named Progressive-Hint Prompting (PHP), that enables automatic multiple interactions between users and LLMs by using previously generated answers as hints to progressively guide toward the correct answers. PHP is orthogonal to CoT and self-consistency, making it easy to combine with state-of-the-art techniques to further improve performance. We conducted extensive and comprehensive experiments on seven benchmarks. The results show that PHP significantly improves accuracy while remaining highly efficient. For instance, with text-davinci-003, we observed a 4.2% improvement on GSM8K with greedy decoding compared to Complex CoT, and a 46.17% reduction in sample paths with self-consistency. With GPT-4 and PHP, we achieve state-of-the-art performances on SVAMP (89.1% -> 91.9%), GSM8K (92% -> 95.5%), AQuA (76.4% -> 79.9%) and MATH (50.3% -> 53.9%).

Popular prompt strategies like Chain-of-Thought Prompting can dramatically improve the reasoning abilities of Large Language Models (LLMs) in various domains. However, such hand-crafted prompt-strategies are often sub-optimal. In this paper, we present Promptbreeder, a general-purpose self-referential self-improvement mechanism that evolves and adapts prompts for a given domain. Driven by an LLM, Promptbreeder mutates a population of task-prompts, and subsequently evaluates them for fitness on a training set. Crucially, the mutation of these task-prompts is governed by mutation-prompts that the LLM generates and improves throughout evolution in a self-referential way. That is, Promptbreeder is not just improving task-prompts, but it is also improving the mutationprompts that improve these task-prompts. Promptbreeder outperforms state-of-the-art prompt strategies such as Chain-of-Thought and Plan-and-Solve Prompting on commonly used arithmetic and commonsense reasoning benchmarks. Furthermore, Promptbreeder is able to evolve intricate task-prompts for the challenging problem of hate speech classification.

This research explores the integration of large language models (LLMs) into scientific data assimilation, focusing on combustion science as a case study. Leveraging foundational models integrated with Retrieval-Augmented Generation (RAG) framework, the study introduces an approach to process diverse combustion research data, spanning experimental studies, simulations, and literature. The multifaceted nature of combustion research emphasizes the critical role of knowledge processing in navigating and extracting valuable information from a vast and diverse pool of sources. The developed approach minimizes computational and economic expenses while optimizing data privacy and accuracy. It incorporates prompt engineering and offline open-source LLMs, offering user autonomy in selecting base models. The study provides a thorough examination of text segmentation strategies, conducts comparative studies between LLMs, and explores various optimized prompts to demonstrate the effectiveness of the framework. By incorporating an external database, the framework outperforms a conventional LLM in generating accurate responses and constructing robust arguments. Additionally, the study delves into the investigation of optimized prompt templates for the purpose of efficient extraction of scientific literature. The research addresses concerns related to hallucinations and false research articles by introducing a custom workflow developed with a detection algorithm to filter out inaccuracies. Despite identified areas for improvement, the framework consistently delivers accurate domain-specific responses with minimal human oversight. The prompt-agnostic approach introduced holds promise for future deliberations. The study underscores the significance of integrating LLMs and knowledge processing techniques in scientific research, providing a foundation for advancements in data assimilation and utilization.

Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

This paper presents the second ChatGPT4PCG competition at the 2024 IEEE Conference on Games. In this edition of the competition, we follow the first edition, but make several improvements and changes. We introduce a new evaluation metric along with allowing a more flexible format for participants' submissions and making several improvements to the evaluation pipeline. Continuing from the first edition, we aim to foster and explore the realm of prompt engineering (PE) for procedural content generation (PCG). While the first competition saw success, it was hindered by various limitations; we aim to mitigate these limitations in this edition. We introduce diversity as a new metric to discourage submissions aimed at producing repetitive structures. Furthermore, we allow submission of a Python program instead of a prompt text file for greater flexibility in implementing advanced PE approaches, which may require control flow, including conditions and iterations. We also make several improvements to the evaluation pipeline with a better classifier for similarity evaluation and better-performing function signatures. We thoroughly evaluate the effectiveness of the new metric and the improved classifier. Additionally, we perform an ablation study to select a function signature to instruct ChatGPT for level generation. Finally, we provide implementation examples of various PE techniques in Python and evaluate their preliminary performance. We hope this competition serves as a resource and platform for learning about PE and PCG in general.

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset (78.7%rightarrow92.5%) evaluated using 175B parameter GPT-based LLM.

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

Large Language Models (LLMs) have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical reasoning processes. To mitigate this problem, we introduced Hint-before-Solving Prompting (HSP), which guides the model to generate hints (e.g., specific knowledge or key ideas) for solving the problem and then generate solutions containing intermediate reasoning steps. Since HSP is orthogonal to prompting methods (e.g., Chain-of-Thought (CoT)), we applied HSP to CoT, Least-to-Most, Plan-and-Solve, and Standard promptings. The results of extensive experiments on 6 reasoning benchmarks and 4 open-source LLMs demonstrate that HSP can effectively improve the accuracy of reasoning tasks: (1) By applying high-quality hint-enhanced HSP to CoT prompting, Llama2-70B-Chat shows an improvement of 9.7. (2) Beyond exploring training-free LLM capabilities, we built the HSPMATH dataset based on HSP and fine-tuned Llemma-7B, reaching 64.3 accuracy, surpassing GPT-3.5 and WizardMath-13B. We make our code and dataset publicly available at https://github.com/jinlanfu/HSP.

Evaluating LLMs with a single prompt has proven unreliable, with small changes leading to significant performance differences. However, generating the prompt variations needed for a more robust multi-prompt evaluation is challenging, limiting its adoption in practice. To address this, we introduce PromptSuite, a framework that enables the automatic generation of various prompts. PromptSuite is flexible - working out of the box on a wide range of tasks and benchmarks. It follows a modular prompt design, allowing controlled perturbations to each component, and is extensible, supporting the addition of new components and perturbation types. Through a series of case studies, we show that PromptSuite provides meaningful variations to support strong evaluation practices. It is available through both a Python API: https://github.com/eliyahabba/PromptSuite, and a user-friendly web interface: https://promptsuite.streamlit.app/

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

The progression from traditional prompt engineering to a more rigorous discipline of prompt design marks a pivotal shift in human-LLM interaction. As Large Language Models (LLMs) become increasingly embedded in mission-critical applications, there emerges a pressing need for frameworks that are not only explicit and systematic but also minimal enough to remain practical and broadly accessible. While many existing approaches address prompt structuring through elaborate Domain-Specific Languages (DSLs) or multi-layered templates, such methods can impose significant token and cognitive overhead, potentially constraining the model's creative capacity. In this context, we propose the 5C Prompt Contract, a framework that distills prompt design into five intuitive components: Character, Cause, Constraint, Contingency, and Calibration. This minimal cognitive schema explicitly integrates fallback and output optimization directives, fostering reliable, interpretable, and creatively flexible AI interactions. Experimental results demonstrate that the 5C framework consistently achieves superior input token efficiency while maintaining rich and consistent outputs across diverse LLM architectures (OpenAI, Anthropic, DeepSeek, and Gemini), making it particularly suited for individuals and Small-to-Medium Enterprises (SMEs) with limited AI engineering resources.