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.

Self-Supervised Learning for User Localization

Machine learning techniques have shown remarkable accuracy in localization tasks, but their dependency on vast amounts of labeled data, particularly Channel State Information (CSI) and corresponding coordinates, remains a bottleneck. Self-supervised learning techniques alleviate the need for labeled data, a potential that remains largely untapped and underexplored in existing research. Addressing this gap, we propose a pioneering approach that leverages self-supervised pretraining on unlabeled data to boost the performance of supervised learning for user localization based on CSI. We introduce two pretraining Auto Encoder (AE) models employing Multi Layer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs) to glean representations from unlabeled data via self-supervised learning. Following this, we utilize the encoder portion of the AE models to extract relevant features from labeled data, and finetune an MLP-based Position Estimation Model to accurately deduce user locations. Our experimentation on the CTW-2020 dataset, which features a substantial volume of unlabeled data but limited labeled samples, demonstrates the viability of our approach. Notably, the dataset covers a vast area spanning over 646x943x41 meters, and our approach demonstrates promising results even for such expansive localization tasks.

RAGIC: Risk-Aware Generative Adversarial Model for Stock Interval Construction

Efforts to predict stock market outcomes have yielded limited success due to the inherently stochastic nature of the market, influenced by numerous unpredictable factors. Many existing prediction approaches focus on single-point predictions, lacking the depth needed for effective decision-making and often overlooking market risk. To bridge this gap, we propose a novel model, RAGIC, which introduces sequence generation for stock interval prediction to quantify uncertainty more effectively. Our approach leverages a Generative Adversarial Network (GAN) to produce future price sequences infused with randomness inherent in financial markets. RAGIC's generator includes a risk module, capturing the risk perception of informed investors, and a temporal module, accounting for historical price trends and seasonality. This multi-faceted generator informs the creation of risk-sensitive intervals through statistical inference, incorporating horizon-wise insights. The interval's width is carefully adjusted to reflect market volatility. Importantly, our approach relies solely on publicly available data and incurs only low computational overhead. RAGIC's evaluation across globally recognized broad-based indices demonstrates its balanced performance, offering both accuracy and informativeness. Achieving a consistent 95% coverage, RAGIC maintains a narrow interval width. This promising outcome suggests that our approach effectively addresses the challenges of stock market prediction while incorporating vital risk considerations.

HI-GAN: Hierarchical Inpainting GAN with Auxiliary Inputs for Combined RGB and Depth Inpainting

Inpainting involves filling in missing pixels or areas in an image, a crucial technique employed in Mixed Reality environments for various applications, particularly in Diminished Reality (DR) where content is removed from a user's visual environment. Existing methods rely on digital replacement techniques which necessitate multiple cameras and incur high costs. AR devices and smartphones use ToF depth sensors to capture scene depth maps aligned with RGB images. Despite speed and affordability, ToF cameras create imperfect depth maps with missing pixels. To address the above challenges, we propose Hierarchical Inpainting GAN (HI-GAN), a novel approach comprising three GANs in a hierarchical fashion for RGBD inpainting. EdgeGAN and LabelGAN inpaint masked edge and segmentation label images respectively, while CombinedRGBD-GAN combines their latent representation outputs and performs RGB and Depth inpainting. Edge images and particularly segmentation label images as auxiliary inputs significantly enhance inpainting performance by complementary context and hierarchical optimization. We believe we make the first attempt to incorporate label images into inpainting process.Unlike previous approaches requiring multiple sequential models and separate outputs, our work operates in an end-to-end manner, training all three models simultaneously and hierarchically. Specifically, EdgeGAN and LabelGAN are first optimized separately and further optimized inside CombinedRGBD-GAN to enhance inpainting quality. Experiments demonstrate that HI-GAN works seamlessly and achieves overall superior performance compared with existing approaches.

Stock Broad-Index Trend Patterns Learning via Domain Knowledge Informed Generative Network

Predicting the Stock movement attracts much attention from both industry and academia. Despite such significant efforts, the results remain unsatisfactory due to the inherently complicated nature of the stock market driven by factors including supply and demand, the state of the economy, the political climate, and even irrational human behavior. Recently, Generative Adversarial Networks (GAN) have been extended for time series data; however, robust methods are primarily for synthetic series generation, which fall short for appropriate stock prediction. This is because existing GANs for stock applications suffer from mode collapse and only consider one-step prediction, thus underutilizing the potential of GAN. Furthermore, merging news and market volatility are neglected in current GANs. To address these issues, we exploit expert domain knowledge in finance and, for the first time, attempt to formulate stock movement prediction into a Wasserstein GAN framework for multi-step prediction. We propose IndexGAN, which includes deliberate designs for the inherent characteristics of the stock market, leverages news context learning to thoroughly investigate textual information and develop an attentive seq2seq learning network that captures the temporal dependency among stock prices, news, and market sentiment. We also utilize the critic to approximate the Wasserstein distance between actual and predicted sequences and develop a rolling strategy for deployment that mitigates noise from the financial market. Extensive experiments are conducted on real-world broad-based indices, demonstrating the superior performance of our architecture over other state-of-the-art baselines, also validating all its contributing components.

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.