From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems

Consider the math problem: "Lily received 3 cookies from her best friend yesterday and ate 5 for breakfast. Today, her friend gave her 3 more cookies. How many cookies does Lily have now?" Many large language models (LLMs) in previous research approach this problem by calculating the answer "1" using the equation "3 - 5 + 3." However, from a human perspective, we recognize the inherent flaw in this problem: Lily cannot eat 5 cookies if she initially only had 3. This discrepancy prompts a key question: Are current LLMs merely Blind Solver that apply mathematical operations without deeper reasoning, or can they function as Logical Thinker capable of identifying logical inconsistencies? To explore this question, we propose a benchmark dataset, FaultyMath, which includes faulty math problems of rich diversity: i) multiple mathematical categories, e.g., algebra, geometry, number theory, etc., ii) varying levels of difficulty, and iii) different origins of faultiness -- ranging from violations of common sense and ambiguous statements to mathematical contradictions and more. We evaluate a broad spectrum of LLMs, including open-source, closed-source, and math-specialized models, using FaultyMath across three dimensions: (i) How accurately can the models detect faulty math problems without being explicitly prompted to do so? (ii) When provided with hints -- either correct or misleading -- about the validity of the problems, to what extent do LLMs adapt to become reliable Logical Thinker? (iii) How trustworthy are the explanations generated by LLMs when they recognize a math problem as flawed? Through extensive experimentation and detailed analysis, our results demonstrate that existing LLMs largely function as Blind Solver and fall short of the reasoning capabilities required to perform as Logical Thinker.

Assessing the Creativity of LLMs in Proposing Novel Solutions to Mathematical Problems

The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing correct answers, AI systems should also be capable of, or assist humans in, developing novel solutions to mathematical challenges. This study explores the creative potential of Large Language Models (LLMs) in mathematical reasoning, an aspect that has received limited attention in prior research. We introduce a novel framework and benchmark, CreativeMath, which encompasses problems ranging from middle school curricula to Olympic-level competitions, designed to assess LLMs' ability to propose innovative solutions after some known solutions have been provided. Our experiments demonstrate that, while LLMs perform well on standard mathematical tasks, their capacity for creative problem-solving varies considerably. Notably, the Gemini-1.5-Pro model outperformed other LLMs in generating novel solutions. This research opens a new frontier in evaluating AI creativity, shedding light on both the strengths and limitations of LLMs in fostering mathematical innovation, and setting the stage for future developments in AI-assisted mathematical discovery.

DataFrame QA: A Universal LLM Framework on DataFrame Question Answering Without Data Exposure

This paper introduces DataFrame question answering (QA), a novel task that utilizes large language models (LLMs) to generate Pandas queries for information retrieval and data analysis on dataframes, emphasizing safe and non-revealing data handling. Our method, which solely relies on dataframe column names, not only ensures data privacy but also significantly reduces the context window in the prompt, streamlining information processing and addressing major challenges in LLM-based data analysis. We propose DataFrame QA as a comprehensive framework that includes safe Pandas query generation and code execution. Various LLMs, notably GPT-4, are evaluated using the pass@1 metric on the renowned WikiSQL and our newly developed 'UCI-DataFrameQA', tailored for complex data analysis queries. Our findings indicate that GPT-4 achieves pass@1 rates of 86% on WikiSQL and 97% on UCI-DataFrameQA, underscoring its capability in securely retrieving and aggregating dataframe values and conducting sophisticated data analyses. This approach, deployable in a zero-shot manner without prior training or adjustments, proves to be highly adaptable and secure for diverse applications.

SafeLight: A Reinforcement Learning Method toward Collision-free Traffic Signal Control

Traffic signal control is safety-critical for our daily life. Roughly one-quarter of road accidents in the U.S. happen at intersections due to problematic signal timing, urging the development of safety-oriented intersection control. However, existing studies on adaptive traffic signal control using reinforcement learning technologies have focused mainly on minimizing traffic delay but neglecting the potential exposure to unsafe conditions. We, for the first time, incorporate road safety standards as enforcement to ensure the safety of existing reinforcement learning methods, aiming toward operating intersections with zero collisions. We have proposed a safety-enhanced residual reinforcement learning method (SafeLight) and employed multiple optimization techniques, such as multi-objective loss function and reward shaping for better knowledge integration. Extensive experiments are conducted using both synthetic and real-world benchmark datasets. Results show that our method can significantly reduce collisions while increasing traffic mobility.

A review of Generative Adversarial Networks and its applications in a wide variety of disciplines -- From Medical to Remote Sensing

We look into Generative Adversarial Network (GAN), its prevalent variants and applications in a number of sectors. GANs combine two neural networks that compete against one another using zero-sum game theory, allowing them to create much crisper and discrete outputs. GANs can be used to perform image processing, video generation and prediction, among other computer vision applications. GANs can also be utilised for a variety of science-related activities, including protein engineering, astronomical data processing, remote sensing image dehazing, and crystal structure synthesis. Other notable fields where GANs have made gains include finance, marketing, fashion design, sports, and music. Therefore in this article we provide a comprehensive overview of the applications of GANs in a wide variety of disciplines. We first cover the theory supporting GAN, GAN variants, and the metrics to evaluate GANs. Then we present how GAN and its variants can be applied in twelve domains, ranging from STEM fields, such as astronomy and biology, to business fields, such as marketing and finance, and to arts, such as music. As a result, researchers from other fields may grasp how GANs work and apply them to their own study. To the best of our knowledge, this article provides the most comprehensive survey of GAN's applications in different fields.

High Resolution Solar Image Generation using Generative Adversarial Networks

We applied Deep Learning algorithm known as Generative Adversarial Networks (GANs) to perform solar image-to-image translation. That is, from Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager(HMI) line of sight magnetogram images to SDO/Atmospheric Imaging Assembly(AIA) 0304-{\AA} images. The Ultraviolet(UV)/Extreme Ultraviolet(EUV) observations like the SDO/AIA0304-{\AA} images were only made available to scientists in the late 1990s even though the magenetic field observations like the SDO/HMI have been available since the 1970s. Therefore by leveraging Deep Learning algorithms like GANs we can give scientists access to complete datasets for analysis. For generating high resolution solar images we use the Pix2PixHD and Pix2Pix algorithms. The Pix2PixHD algorithm was specifically designed for high resolution image generation tasks, and the Pix2Pix algorithm is by far the most widely used image to image translation algorithm. For training and testing we used the data for the year 2012, 2013 and 2014. The results show that our deep learning models are capable of generating high resolution(1024 x 1024 pixels) AIA0304 images from HMI magnetograms. Specifically, the pixel-to-pixel Pearson Correlation Coefficient of the images generated by Pix2PixHD and original images is as high as 0.99. The number is 0.962 if Pix2Pix is used to generate images. The results we get for our Pix2PixHD model is better than the results obtained by previous works done by others to generate AIA0304 images. Thus, we can use these models to generate AIA0304 images when the AIA0304 data is not available which can be used for understanding space weather and giving researchers the capability to predict solar events such as Solar Flares and Coronal Mass Ejections. As far as we know, our work is the first attempt to leverage Pix2PixHD algorithm for SDO/HMI to SDO/AIA0304 image-to-image translation.