Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?

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.

One Prompt is not Enough: Automated Construction of a Mixture-of-Expert Prompts

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

On Discrete Prompt Optimization for Diffusion Models

This paper introduces the first gradient-based framework for prompt optimization in text-to-image diffusion models. We formulate prompt engineering as a discrete optimization problem over the language space. Two major challenges arise in efficiently finding a solution to this problem: (1) Enormous Domain Space: Setting the domain to the entire language space poses significant difficulty to the optimization process. (2) Text Gradient: Efficiently computing the text gradient is challenging, as it requires backpropagating through the inference steps of the diffusion model and a non-differentiable embedding lookup table. Beyond the problem formulation, our main technical contributions lie in solving the above challenges. First, we design a family of dynamically generated compact subspaces comprised of only the most relevant words to user input, substantially restricting the domain space. Second, we introduce "Shortcut Text Gradient" -- an effective replacement for the text gradient that can be obtained with constant memory and runtime. Empirical evaluation on prompts collected from diverse sources (DiffusionDB, ChatGPT, COCO) suggests that our method can discover prompts that substantially improve (prompt enhancement) or destroy (adversarial attack) the faithfulness of images generated by the text-to-image diffusion model.

Large Language Models are Interpretable Learners

The trade-off between expressiveness and interpretability remains a core challenge when building human-centric predictive models for classification and decision-making. While symbolic rules offer interpretability, they often lack expressiveness, whereas neural networks excel in performance but are known for being black boxes. In this paper, we show a combination of Large Language Models (LLMs) and symbolic programs can bridge this gap. In the proposed LLM-based Symbolic Programs (LSPs), the pretrained LLM with natural language prompts provides a massive set of interpretable modules that can transform raw input into natural language concepts. Symbolic programs then integrate these modules into an interpretable decision rule. To train LSPs, we develop a divide-and-conquer approach to incrementally build the program from scratch, where the learning process of each step is guided by LLMs. To evaluate the effectiveness of LSPs in extracting interpretable and accurate knowledge from data, we introduce IL-Bench, a collection of diverse tasks, including both synthetic and real-world scenarios across different modalities. Empirical results demonstrate LSP's superior performance compared to traditional neurosymbolic programs and vanilla automatic prompt tuning methods. Moreover, as the knowledge learned by LSP is a combination of natural language descriptions and symbolic rules, it is easily transferable to humans (interpretable), and other LLMs, and generalizes well to out-of-distribution samples.

MOSSBench: Is Your Multimodal Language Model Oversensitive to Safe Queries?

Humans are prone to cognitive distortions -- biased thinking patterns that lead to exaggerated responses to specific stimuli, albeit in very different contexts. This paper demonstrates that advanced Multimodal Large Language Models (MLLMs) exhibit similar tendencies. While these models are designed to respond queries under safety mechanism, they sometimes reject harmless queries in the presence of certain visual stimuli, disregarding the benign nature of their contexts. As the initial step in investigating this behavior, we identify three types of stimuli that trigger the oversensitivity of existing MLLMs: Exaggerated Risk, Negated Harm, and Counterintuitive Interpretation. To systematically evaluate MLLMs' oversensitivity to these stimuli, we propose the Multimodal OverSenSitivity Benchmark (MOSSBench). This toolkit consists of 300 manually collected benign multimodal queries, cross-verified by third-party reviewers (AMT). Empirical studies using MOSSBench on 20 MLLMs reveal several insights: (1). Oversensitivity is prevalent among SOTA MLLMs, with refusal rates reaching up to 76% for harmless queries. (2). Safer models are more oversensitive: increasing safety may inadvertently raise caution and conservatism in the model's responses. (3). Different types of stimuli tend to cause errors at specific stages -- perception, intent reasoning, and safety judgement -- in the response process of MLLMs. These findings highlight the need for refined safety mechanisms that balance caution with contextually appropriate responses, improving the reliability of MLLMs in real-world applications. We make our project available at https://turningpoint-ai.github.io/MOSSBench/.

JIGMARK: A Black-Box Approach for Enhancing Image Watermarks against Diffusion Model Edits

In this study, we investigate the vulnerability of image watermarks to diffusion-model-based image editing, a challenge exacerbated by the computational cost of accessing gradient information and the closed-source nature of many diffusion models. To address this issue, we introduce JIGMARK. This first-of-its-kind watermarking technique enhances robustness through contrastive learning with pairs of images, processed and unprocessed by diffusion models, without needing a direct backpropagation of the diffusion process. Our evaluation reveals that JIGMARK significantly surpasses existing watermarking solutions in resilience to diffusion-model edits, demonstrating a True Positive Rate more than triple that of leading baselines at a 1% False Positive Rate while preserving image quality. At the same time, it consistently improves the robustness against other conventional perturbations (like JPEG, blurring, etc.) and malicious watermark attacks over the state-of-the-art, often by a large margin. Furthermore, we propose the Human Aligned Variation (HAV) score, a new metric that surpasses traditional similarity measures in quantifying the number of image derivatives from image editing.

Ameliorate Spurious Correlations in Dataset Condensation

Dataset Condensation has emerged as a technique for compressing large datasets into smaller synthetic counterparts, facilitating downstream training tasks. In this paper, we study the impact of bias inside the original dataset on the performance of dataset condensation. With a comprehensive empirical evaluation on canonical datasets with color, corruption and background biases, we found that color and background biases in the original dataset will be amplified through the condensation process, resulting in a notable decline in the performance of models trained on the condensed dataset, while corruption bias is suppressed through the condensation process. To reduce bias amplification in dataset condensation, we introduce a simple yet highly effective approach based on a sample reweighting scheme utilizing kernel density estimation. Empirical results on multiple real-world and synthetic datasets demonstrate the effectiveness of the proposed method. Notably, on CMNIST with 5% bias-conflict ratio and IPC 50, our method achieves 91.5% test accuracy compared to 23.8% from vanilla DM, boosting the performance by 67.7%, whereas applying state-of-the-art debiasing method on the same dataset only achieves 53.7% accuracy. Our findings highlight the importance of addressing biases in dataset condensation and provide a promising avenue to address bias amplification in the process.

Understanding the Impact of Negative Prompts: When and How Do They Take Effect?

The concept of negative prompts, emerging from conditional generation models like Stable Diffusion, allows users to specify what to exclude from the generated images.%, demonstrating significant practical efficacy. Despite the widespread use of negative prompts, their intrinsic mechanisms remain largely unexplored. This paper presents the first comprehensive study to uncover how and when negative prompts take effect. Our extensive empirical analysis identifies two primary behaviors of negative prompts. Delayed Effect: The impact of negative prompts is observed after positive prompts render corresponding content. Deletion Through Neutralization: Negative prompts delete concepts from the generated image through a mutual cancellation effect in latent space with positive prompts. These insights reveal significant potential real-world applications; for example, we demonstrate that negative prompts can facilitate object inpainting with minimal alterations to the background via a simple adaptive algorithm. We believe our findings will offer valuable insights for the community in capitalizing on the potential of negative prompts.

The Crystal Ball Hypothesis in diffusion models: Anticipating object positions from initial noise

Diffusion models have achieved remarkable success in text-to-image generation tasks; however, the role of initial noise has been rarely explored. In this study, we identify specific regions within the initial noise image, termed trigger patches, that play a key role for object generation in the resulting images. Notably, these patches are ``universal'' and can be generalized across various positions, seeds, and prompts. To be specific, extracting these patches from one noise and injecting them into another noise leads to object generation in targeted areas. We identify these patches by analyzing the dispersion of object bounding boxes across generated images, leading to the development of a posterior analysis technique. Furthermore, we create a dataset consisting of Gaussian noises labeled with bounding boxes corresponding to the objects appearing in the generated images and train a detector that identifies these patches from the initial noise. To explain the formation of these patches, we reveal that they are outliers in Gaussian noise, and follow distinct distributions through two-sample tests. Finally, we find the misalignment between prompts and the trigger patch patterns can result in unsuccessful image generations. The study proposes a reject-sampling strategy to obtain optimal noise, aiming to improve prompt adherence and positional diversity in image generation.

OR-Bench: An Over-Refusal Benchmark for Large Language Models

Large Language Models (LLMs) require careful safety alignment to prevent malicious outputs. While significant research focuses on mitigating harmful content generation, the enhanced safety often come with the side effect of over-refusal, where the LLMs may reject innocuous prompts and become less helpful. Although the issue of over-refusal has been empirically observed, a systematic measurement is challenging due to the difficulty of crafting prompts that appear harmful but are benign. This study proposes a novel method for automatically generating large-scale sets of ``seemingly toxic prompts'' (benign prompts likely rejected by LLMs). Leveraging this technique, we introduce OR-Bench, the first large-scale over-refusal benchmark. OR-Bench comprises 80,000 seemingly toxic prompts across 10 common rejection categories, a subset of around 1,000 hard prompts that are challenging even for state-of-the-art LLMs, and an additional 600 toxic prompts to prevent indiscriminate responses. We then conduct a comprehensive study to measure the over-refusal of 25 popular LLMs across 8 model families. Our datasets are available at https://huggingface.co/datasets/bench-llm/OR-Bench and the corresponding demo can be found at https://huggingface.co/spaces/bench-llm/or-bench. We hope this benchmark can help the community develop better safety aligned models.