Reduced Implication-bias Logic Loss for Neuro-Symbolic Learning

Integrating logical reasoning and machine learning by approximating logical inference with differentiable operators is a widely used technique in Neuro-Symbolic systems. However, some differentiable operators could bring a significant bias during backpropagation and degrade the performance of Neuro-Symbolic learning. In this paper, we reveal that this bias, named \textit{Implication Bias} is common in loss functions derived from fuzzy logic operators. Furthermore, we propose a simple yet effective method to transform the biased loss functions into \textit{Reduced Implication-bias Logic Loss (RILL)} to address the above problem. Empirical study shows that RILL can achieve significant improvements compared with the biased logic loss functions, especially when the knowledge base is incomplete, and keeps more robust than the compared methods when labelled data is insufficient.Comment: ACML'2023 Journal Track(Accepted by Machine Learning Journal

SASMU: boost the performance of generalized recognition model using synthetic face dataset

Nowadays, deploying a robust face recognition product becomes easy with the development of face recognition techniques for decades. Not only profile image verification but also the state-of-the-art method can handle the in-the-wild image almost perfectly. However, the concern of privacy issues raise rapidly since mainstream research results are powered by tons of web-crawled data, which faces the privacy invasion issue. The community tries to escape this predicament completely by training the face recognition model with synthetic data but faces severe domain gap issues, which still need to access real images and identity labels to fine-tune the model. In this paper, we propose SASMU, a simple, novel, and effective method for face recognition using a synthetic dataset. Our proposed method consists of spatial data augmentation (SA) and spectrum mixup (SMU). We first analyze the existing synthetic datasets for developing a face recognition system. Then, we reveal that heavy data augmentation is helpful for boosting performance when using synthetic data. By analyzing the previous frequency mixup studies, we proposed a novel method for domain generalization. Extensive experimental results have demonstrated the effectiveness of SASMU, achieving state-of-the-art performance on several common benchmarks, such as LFW, AgeDB-30, CA-LFW, CFP-FP, and CP-LFW.Comment: under revie

ChatEDA: A Large Language Model Powered Autonomous Agent for EDA

The integration of a complex set of Electronic Design Automation (EDA) tools to enhance interoperability is a critical concern for circuit designers. Recent advancements in large language models (LLMs) have showcased their exceptional capabilities in natural language processing and comprehension, offering a novel approach to interfacing with EDA tools. This research paper introduces ChatEDA, an autonomous agent for EDA empowered by a large language model, AutoMage, complemented by EDA tools serving as executors. ChatEDA streamlines the design flow from the Register-Transfer Level (RTL) to the Graphic Data System Version II (GDSII) by effectively managing task planning, script generation, and task execution. Through comprehensive experimental evaluations, ChatEDA has demonstrated its proficiency in handling diverse requirements, and our fine-tuned AutoMage model has exhibited superior performance compared to GPT-4 and other similar LLMs

G2PTL: A Pre-trained Model for Delivery Address and its Applications in Logistics System

Text-based delivery addresses, as the data foundation for logistics systems, contain abundant and crucial location information. How to effectively encode the delivery address is a core task to boost the performance of downstream tasks in the logistics system. Pre-trained Models (PTMs) designed for Natural Language Process (NLP) have emerged as the dominant tools for encoding semantic information in text. Though promising, those NLP-based PTMs fall short of encoding geographic knowledge in the delivery address, which considerably trims down the performance of delivery-related tasks in logistic systems such as Cainiao. To tackle the above problem, we propose a domain-specific pre-trained model, named G2PTL, a Geography-Graph Pre-trained model for delivery address in Logistics field. G2PTL combines the semantic learning capabilities of text pre-training with the geographical-relationship encoding abilities of graph modeling. Specifically, we first utilize real-world logistics delivery data to construct a large-scale heterogeneous graph of delivery addresses, which contains abundant geographic knowledge and delivery information. Then, G2PTL is pre-trained with subgraphs sampled from the heterogeneous graph. Comprehensive experiments are conducted to demonstrate the effectiveness of G2PTL through four downstream tasks in logistics systems on real-world datasets. G2PTL has been deployed in production in Cainiao's logistics system, which significantly improves the performance of delivery-related tasks

Joint Inversion of 3D Gravity and Magnetic Data under Undulating Terrain Based on Combined Hexahedral Grid

As an effective underground imaging method, the joint inversion of the gravity and magnetic data has an important application in the comprehensive interpretation of mineral exploration, and unstructured modeling is the key to accurately solving its topographic problem. However, the traditional tetrahedral grid can only impose the gradient-based constraints approximately, owing to its poor arrangement regularity. To address the difficulty of applying a cross-gradient constraint in an unstructured grid, we propose a joint inversion based on a combined hexahedral grid, which regularly divides the shallow part into curved hexahedrons and the deep part into regular hexahedrons. Instead of a cross-gradient in the spatial sense, we construct a geometric sense “cross-gradient” for a structural constraint to reduce the influence of approximation. In addition, we further correct the traditional sensitivity-based weighting function according to element volume, to make it suitable for an unstructured grid. Model tests indicate that the new grid can impose the cross-gradient constraint more strongly, and the proposed correction can effectively solve the false anomaly caused by the element volume difference. Finally, we apply our method to the measured data from a mining area in Huzhong, Heilongjiang Province, China, and successfully invert out the specific location of a known skarn deposit, which further proves its practicability

Joint Inversion of 3D Gravity and Magnetic Data under Undulating Terrain Based on Combined Hexahedral Grid

As an effective underground imaging method, the joint inversion of the gravity and magnetic data has an important application in the comprehensive interpretation of mineral exploration, and unstructured modeling is the key to accurately solving its topographic problem. However, the traditional tetrahedral grid can only impose the gradient-based constraints approximately, owing to its poor arrangement regularity. To address the difficulty of applying a cross-gradient constraint in an unstructured grid, we propose a joint inversion based on a combined hexahedral grid, which regularly divides the shallow part into curved hexahedrons and the deep part into regular hexahedrons. Instead of a cross-gradient in the spatial sense, we construct a geometric sense “cross-gradient” for a structural constraint to reduce the influence of approximation. In addition, we further correct the traditional sensitivity-based weighting function according to element volume, to make it suitable for an unstructured grid. Model tests indicate that the new grid can impose the cross-gradient constraint more strongly, and the proposed correction can effectively solve the false anomaly caused by the element volume difference. Finally, we apply our method to the measured data from a mining area in Huzhong, Heilongjiang Province, China, and successfully invert out the specific location of a known skarn deposit, which further proves its practicability

Multiple positive solutions for nonlinear coupled fractional Laplacian system with critical exponent

Abstract In this paper, we study the following critical system with fractional Laplacian: {(−Δ)su+λ1u=μ1|u|2∗−2u+αγ2∗|u|α−2u|v|βin Ω,(−Δ)sv+λ2v=μ2|v|2∗−2v+βγ2∗|u|α|v|β−2vin Ω,u=v=0in RN∖Ω, $$\textstyle\begin{cases} (-\Delta)^{s}u+\lambda_{1}u=\mu_{1}|u|^{2^{\ast}-2}u+\frac{\alpha \gamma}{2^{\ast}}|u|^{\alpha-2}u|v|^{\beta} & \text{in } \Omega, \\ (-\Delta)^{s}v+\lambda_{2}v= \mu_{2}|v|^{2^{\ast}-2}v+\frac{\beta \gamma}{2^{\ast}}|u|^{\alpha}|v|^{\beta-2}v & \text{in } \Omega, \\ u=v=0 & \text{in } \mathbb{R}^{N}\setminus\Omega, \end{cases}$$ where (−Δ)s $(-\Delta)^{s}$ is the fractional Laplacian, 00 $\mu_{1},\mu_{2}>0$, 2∗=2NN−2s $2^{\ast}=\frac{2N}{N-2s}$ is a fractional critical Sobolev exponent, N>2s $N>2s$, 1−λ1,s(Ω) $\lambda_{1},\lambda_{2}>-\lambda_{1,s}(\Omega)$, λ1,s(Ω) $\lambda_{1,s}(\Omega)$ is the first eigenvalue of the non-local operator (−Δ)s $(-\Delta)^{s}$ with homogeneous Dirichlet boundary datum. By using the Nehari manifold, we prove the existence of a positive ground state solution of the system for all γ>0 $\gamma>0$. Via a perturbation argument and using the topological degree and a pseudo-gradient vector field, we show that this system has a positive higher energy solution. Then the asymptotic behaviors of the positive ground state solutions are analyzed when γ→0 $\gamma\rightarrow0$