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This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a complete and compatible formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at //github.com/BitSecret/FGPS.

相關內容

Automator是蘋果公司為他們的Mac OS X系統開發的一款軟件。 只要通過點擊拖拽鼠標等操作就可以將一系列動作組合成一個工作流,從而幫助你自動的(可重復的)完成一些復雜的工作。Automator還能橫跨很多不同種類的程序,包括:查找器、Safari網絡瀏覽器、iCal、地址簿或者其他的一些程序。它還能和一些第三方的程序一起工作,如微軟的Office、Adobe公司的Photoshop或者Pixelmator等。

In this paper, we introduce the Volumetric Relightable Morphable Model (VRMM), a novel volumetric and parametric facial prior for 3D face modeling. While recent volumetric prior models offer improvements over traditional methods like 3D Morphable Models (3DMMs), they face challenges in model learning and personalized reconstructions. Our VRMM overcomes these by employing a novel training framework that efficiently disentangles and encodes latent spaces of identity, expression, and lighting into low-dimensional representations. This framework, designed with self-supervised learning, significantly reduces the constraints for training data, making it more feasible in practice. The learned VRMM offers relighting capabilities and encompasses a comprehensive range of expressions. We demonstrate the versatility and effectiveness of VRMM through various applications like avatar generation, facial reconstruction, and animation. Additionally, we address the common issue of overfitting in generative volumetric models with a novel prior-preserving personalization framework based on VRMM. Such an approach enables accurate 3D face reconstruction from even a single portrait input. Our experiments showcase the potential of VRMM to significantly enhance the field of 3D face modeling.

In this paper, we extend our prior research named DKIC and propose the perceptual-oriented learned image compression method, PO-DKIC. Specifically, DKIC adopts a dynamic kernel-based dynamic residual block group to enhance the transform coding and an asymmetric space-channel context entropy model to facilitate the estimation of gaussian parameters. Based on DKIC, PO-DKIC introduces PatchGAN and LPIPS loss to enhance visual quality. Furthermore, to maximize the overall perceptual quality under a rate constraint, we formulate this challenge into a constrained programming problem and use the Linear Integer Programming method for resolution. The experiments demonstrate that our proposed method can generate realistic images with richer textures and finer details when compared to state-of-the-art image compression techniques.

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance five times better than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

In this paper, we introduce HoughToRadon Transform layer, a novel layer designed to improve the speed of neural networks incorporated with Hough Transform to solve semantic image segmentation problems. By placing it after a Hough Transform layer, "inner" convolutions receive modified feature maps with new beneficial properties, such as a smaller area of processed images and parameter space linearity by angle and shift. These properties were not presented in Hough Transform alone. Furthermore, HoughToRadon Transform layer allows us to adjust the size of intermediate feature maps using two new parameters, thus allowing us to balance the speed and quality of the resulting neural network. Our experiments on the open MIDV-500 dataset show that this new approach leads to time savings in document segmentation tasks and achieves state-of-the-art 97.7% accuracy, outperforming HoughEncoder with larger computational complexity.

In this paper, we propose a continuous-time lidar-inertial odometry (CT-LIO) system named SLICT2, which promotes two main insights. One, contrary to conventional wisdom, CT-LIO algorithm can be optimized by linear solvers in only a few iterations, which is more efficient than commonly used nonlinear solvers. Two, CT-LIO benefits more from the correct association than the number of iterations. Based on these ideas, we implement our method with a customized solver where the feature association process is performed immediately after each incremental step, and the solution can converge within a few iterations. Our implementation can achieve real-time performance with a high density of control points while yielding competitive performance in highly dynamical motion scenarios. We demonstrate the advantages of our method by comparing with other existing state-of-the-art CT-LIO methods. The source code will be released for the benefit of the community.

In this paper, we introduce a new class of parameterized controllers, drawing inspiration from Model Predictive Control (MPC). The controller resembles a Quadratic Programming (QP) solver of a linear MPC problem, with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. This approach addresses the limitations of common controllers with Multi-Layer Perceptron (MLP) or other general neural network architecture used in DRL, in terms of verifiability and performance guarantees, and the learned controllers possess verifiable properties like persistent feasibility and asymptotic stability akin to MPC. On the other hand, numerical examples illustrate that the proposed controller empirically matches MPC and MLP controllers in terms of control performance and has superior robustness against modeling uncertainty and noises. Furthermore, the proposed controller is significantly more computationally efficient compared to MPC and requires fewer parameters to learn than MLP controllers. Real-world experiments on vehicle drift maneuvering task demonstrate the potential of these controllers for robotics and other demanding control tasks.

Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.

In this paper, we introduce a two-level attention schema, Poolingformer, for long document modeling. Its first level uses a smaller sliding window pattern to aggregate information from neighbors. Its second level employs a larger window to increase receptive fields with pooling attention to reduce both computational cost and memory consumption. We first evaluate Poolingformer on two long sequence QA tasks: the monolingual NQ and the multilingual TyDi QA. Experimental results show that Poolingformer sits atop three official leaderboards measured by F1, outperforming previous state-of-the-art models by 1.9 points (79.8 vs. 77.9) on NQ long answer, 1.9 points (79.5 vs. 77.6) on TyDi QA passage answer, and 1.6 points (67.6 vs. 66.0) on TyDi QA minimal answer. We further evaluate Poolingformer on a long sequence summarization task. Experimental results on the arXiv benchmark continue to demonstrate its superior performance.

In this paper, we present a comprehensive review of the imbalance problems in object detection. To analyze the problems in a systematic manner, we introduce a problem-based taxonomy. Following this taxonomy, we discuss each problem in depth and present a unifying yet critical perspective on the solutions in the literature. In addition, we identify major open issues regarding the existing imbalance problems as well as imbalance problems that have not been discussed before. Moreover, in order to keep our review up to date, we provide an accompanying webpage which catalogs papers addressing imbalance problems, according to our problem-based taxonomy. Researchers can track newer studies on this webpage available at: //github.com/kemaloksuz/ObjectDetectionImbalance .

We consider an interesting problem-salient instance segmentation in this paper. Other than producing bounding boxes, our network also outputs high-quality instance-level segments. Taking into account the category-independent property of each target, we design a single stage salient instance segmentation framework, with a novel segmentation branch. Our new branch regards not only local context inside each detection window but also its surrounding context, enabling us to distinguish the instances in the same scope even with obstruction. Our network is end-to-end trainable and runs at a fast speed (40 fps when processing an image with resolution 320x320). We evaluate our approach on a publicly available benchmark and show that it outperforms other alternative solutions. We also provide a thorough analysis of the design choices to help readers better understand the functions of each part of our network. The source code can be found at \url{//github.com/RuochenFan/S4Net}.

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