Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information

Geometry problem solving has garnered increasing attention due to its potential applications in intelligent education field. Inspired by the observation that text often introduces ambiguities that diagrams can clarify, this paper presents Pi-GPS, a novel framework that unleashes the power of diagrammatic information to resolve textual ambiguities, an aspect largely overlooked in prior research. Specifically, we design a micro module comprising a rectifier and verifier: the rectifier employs MLLMs to disambiguate text based on the diagrammatic context, while the verifier ensures the rectified output adherence to geometric rules, mitigating model hallucinations. Additionally, we explore the impact of LLMs in theorem predictor based on the disambiguated formal language. Empirical results demonstrate that Pi-GPS surpasses state-of-the-art models, achieving a nearly 10\% improvement on Geometry3K over prior neural-symbolic approaches. We hope this work highlights the significance of resolving textual ambiguity in multimodal mathematical reasoning, a crucial factor limiting performance.

HiGP: A high-performance Python package for Gaussian Process

Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification tasks due to their ability to capture complex data patterns and provide uncertainty quantification (UQ). Traditional GP implementations often face challenges in scalability and computational efficiency, especially with large datasets. To address these challenges, HiGP, a high-performance Python package, is designed for efficient Gaussian Process regression (GPR) and classification (GPC) across datasets of varying sizes. HiGP combines multiple new iterative methods to enhance the performance and efficiency of GP computations. It implements various effective matrix-vector (MatVec) and matrix-matrix (MatMul) multiplication strategies specifically tailored for kernel matrices. To improve the convergence of iterative methods, HiGP also integrates the recently developed Adaptive Factorized Nystrom (AFN) preconditioner and employs precise formulas for computing the gradients. With a user-friendly Python interface, HiGP seamlessly integrates with PyTorch and other Python packages, allowing easy incorporation into existing machine learning and data analysis workflows.

Problem-Solving Logic Guided Curriculum In-Context Learning for LLMs Complex Reasoning

In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple features to measure the relevance between examples. We argue that these features are not sufficient to reflect the intrinsic connections between examples. In this study, we propose a curriculum ICL strategy guided by problem-solving logic. We select demonstration examples by analyzing the problem-solving logic and order them based on curriculum learning. Specifically, we constructed a problem-solving logic instruction set based on the BREAK dataset and fine-tuned a language model to analyze the problem-solving logic of examples. Subsequently, we selected appropriate demonstration examples based on problem-solving logic and assessed their difficulty according to the number of problem-solving steps. In accordance with the principles of curriculum learning, we ordered the examples from easy to hard to serve as contextual prompts. Experimental results on multiple benchmarks indicate that our method outperforms previous ICL approaches in terms of performance and efficiency, effectively enhancing the complex reasoning capabilities of LLMs. Our project will be publicly available subsequently.

GNN-Coder: Boosting Semantic Code Retrieval with Combined GNNs and Transformer

Code retrieval is a crucial component in modern software development, particularly in large-scale projects. However, existing approaches relying on sequence-based models often fail to fully exploit the structural dependencies inherent in code, leading to suboptimal retrieval performance, particularly with structurally complex code fragments. In this paper, we introduce GNN-Coder, a novel framework based on Graph Neural Network (GNN) to utilize Abstract Syntax Tree (AST). We make the first attempt to study how GNN-integrated Transformer can promote the development of semantic retrieval tasks by capturing the structural and semantic features of code. We further propose an innovative graph pooling method tailored for AST, utilizing the number of child nodes as a key feature to highlight the intrinsic topological relationships within the AST. This design effectively integrates both sequential and hierarchical representations, enhancing the model's ability to capture code structure and semantics. Additionally, we introduce the Mean Angular Margin (MAM), a novel metric for quantifying the uniformity of code embedding distributions, providing a standardized measure of feature separability. The proposed method achieves a lower MAM, indicating a more discriminative feature representation. This underscores GNN-Coder's superior ability to distinguish between code snippets, thereby enhancing retrieval accuracy. Experimental results show that GNN-Coder significantly boosts retrieval performance, with a 1\%-10\% improvement in MRR on the CSN dataset, and a notable 20\% gain in zero-shot performance on the CosQA dataset.

MagicGeo: Training-Free Text-Guided Geometric Diagram Generation

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

Process-Supervised Reinforcement Learning for Code Generation

Existing reinforcement learning strategies based on outcome supervision have proven effective in enhancing the performance of large language models(LLMs) for code generation. While reinforcement learning based on process supervision has shown great promise in handling multi-step reasoning tasks, its effectiveness in code generation remains largely underexplored and underjustified. The primary obstacle stems from the resource-intensive nature of constructing high-quality process-supervised data, which demands substantial human expertise and computational resources. In response to this challenge, we propose a "statement mutation/refactoring-compile and execution verification" strategy: mutating and refactoring code line-by-line through a teacher model, and utilizing compiler execution results to automatically label each line, resulting in line-by-line process-supervised data, which is pivotal for training a process-supervised reward model. The trained reward model is then integrated into the PRLCoder framework, followed by experimental validation on several benchmarks. Experimental results demonstrate that process-supervised reinforcement learning significantly surpasses methods relying solely on outcome supervision. Notably, in tackling complex code generation tasks, process-supervised reinforcement learning shows a clear advantage, ensuring both the integrity of the code generation process and the correctness of the generation results.

Efficient Portrait Matte Creation With Layer Diffusion and Connectivity Priors

Learning effective deep portrait matting models requires training data of both high quality and large quantity. Neither quality nor quantity can be easily met for portrait matting, however. Since the most accurate ground-truth portrait mattes are acquired in front of the green screen, it is almost impossible to harvest a large-scale portrait matting dataset in reality. This work shows that one can leverage text prompts and the recent Layer Diffusion model to generate high-quality portrait foregrounds and extract latent portrait mattes. However, the portrait mattes cannot be readily in use due to significant generation artifacts. Inspired by the connectivity priors observed in portrait images, that is, the border of portrait foregrounds always appears connected, a connectivity-aware approach is introduced to refine portrait mattes. Building on this, a large-scale portrait matting dataset is created, termed LD-Portrait-20K, with $20,051$ portrait foregrounds and high-quality alpha mattes. Extensive experiments demonstrated the value of the LD-Portrait-20K dataset, with models trained on it significantly outperforming those trained on other datasets. In addition, comparisons with the chroma keying algorithm and an ablation study on dataset capacity further confirmed the effectiveness of the proposed matte creation approach. Further, the dataset also contributes to state-of-the-art video portrait matting, implemented by simple video segmentation and a trimap-based image matting model trained on this dataset.

Complementary Advantages: Exploiting Cross-Field Frequency Correlation for NIR-Assisted Image Denoising

Existing single-image denoising algorithms often struggle to restore details when dealing with complex noisy images. The introduction of near-infrared (NIR) images offers new possibilities for RGB image denoising. However, due to the inconsistency between NIR and RGB images, the existing works still struggle to balance the contributions of two fields in the process of image fusion. In response to this, in this paper, we develop a cross-field Frequency Correlation Exploiting Network (FCENet) for NIR-assisted image denoising. We first propose the frequency correlation prior based on an in-depth statistical frequency analysis of NIR-RGB image pairs. The prior reveals the complementary correlation of NIR and RGB images in the frequency domain. Leveraging frequency correlation prior, we then establish a frequency learning framework composed of Frequency Dynamic Selection Mechanism (FDSM) and Frequency Exhaustive Fusion Mechanism (FEFM). FDSM dynamically selects complementary information from NIR and RGB images in the frequency domain, and FEFM strengthens the control of common and differential features during the fusion of NIR and RGB features. Extensive experiments on simulated and real data validate that our method outperforms various state-of-the-art methods in terms of image quality and computational efficiency. The code will be released to the public.

Rethinking Model Redundancy for Low-light Image Enhancement

Low-light image enhancement (LLIE) is a fundamental task in computational photography, aiming to improve illumination, reduce noise, and enhance the image quality of low-light images. While recent advancements primarily focus on customizing complex neural network models, we have observed significant redundancy in these models, limiting further performance improvement. In this paper, we investigate and rethink the model redundancy for LLIE, identifying parameter harmfulness and parameter uselessness. Inspired by the rethinking, we propose two innovative techniques to mitigate model redundancy while improving the LLIE performance: Attention Dynamic Reallocation (ADR) and Parameter Orthogonal Generation (POG). ADR dynamically reallocates appropriate attention based on original attention, thereby mitigating parameter harmfulness. POG learns orthogonal basis embeddings of parameters and prevents degradation to static parameters, thereby mitigating parameter uselessness. Experiments validate the effectiveness of our techniques. We will release the code to the public.

Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoising

Image denoising enhances image quality, serving as a foundational technique across various computational photography applications. The obstacle to clean image acquisition in real scenarios necessitates the development of self-supervised image denoising methods only depending on noisy images, especially a single noisy image. Existing self-supervised image denoising paradigms (Noise2Noise and Noise2Void) rely heavily on information-lossy operations, such as downsampling and masking, culminating in low quality denoising performance. In this paper, we propose a novel self-supervised single image denoising paradigm, Positive2Negative, to break the information-lossy barrier. Our paradigm involves two key steps: Renoised Data Construction (RDC) and Denoised Consistency Supervision (DCS). RDC renoises the predicted denoised image by the predicted noise to construct multiple noisy images, preserving all the information of the original image. DCS ensures consistency across the multiple denoised images, supervising the network to learn robust denoising. Our Positive2Negative paradigm achieves state-of-the-art performance in self-supervised single image denoising with significant speed improvements. The code will be released to the public.