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Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue distribution, and fall short of providing precise quantitative characterizations of the “spike” eigenvalues and eigenvectors that often capture the low-dimensional signal structure of the learning problem. In this work, we characterize these signal eigenvalues and eigenvectors for a nonlinear version of the spiked covariance model, including the CK as a special case. Using this general result, we give a quantitative description of how spiked eigenstructure in the input data propagates through the hidden layers of a neural network with random weights. As a second application, we study a simple regime of representation learning where the weight matrix develops a rank-one signal component over training and characterize the alignment of the target function with the spike eigenvector of the CK on test data. 

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Given a part design, the task of manufacturing process selection chooses an appropriate manufacturing process to fabricate it. Prior research has traditionally determined manufacturing processes through direct classification. However, an alternative approach to select a manufacturing process for a new design involves identifying previously produced parts with comparable shapes and materials and learning from them. Finding similar designs from a large dataset of previously manufactured parts is a challenging problem. To solve this problem, researchers have proposed different spatial and spectral shape descriptors to extract shape features including the D2 distribution, spherical harmonics (SH), and the Fast Fourier Transform (FFT), as well as the application of different machine learning methods on various representations of 3D part models like multi-view images, voxel, triangle mesh, and point cloud. However, there has not been a comprehensive analysis of these different shape descriptors, especially for part similarity search aimed at manufacturing process selection. To remedy this gap, this paper presents an in-depth comparative study of these shape descriptors for part similarity search. While we acknowledge the importance of factors like part size, tolerance, and cost in manufacturing process selection, this paper focuses on part shape and material properties only. Our findings show that SH performs the best among non-machine learning methods for manufacturing process selection, yielding 97.96% testing accuracy using the proposed quantitative evaluation metric. For machine learning methods, deep learning on multi-view image representations is best, yielding 99.85% testing accuracy when rotational invariance is not a primary concern. Deep learning on point cloud representations excels, yielding 99.44% testing accuracy when considering rotational invariance. 

Abstract Given a part design, the task of manufacturing process classification identifies an appropriate manufacturing process to fabricate it. Our previous research proposed a large dataset for manufacturing process classification and achieved accurate classification results based on a combination of a convolutional neural network (CNN) and the heat kernel signature for triangle meshes. In this paper, we constructed a classification method based on rotation invariant shape descriptors and a neural network, and it achieved better accuracy than all previous methods. This method uses a point cloud part representation, in contrast to the triangle mesh representation used in our previous work. The first step extracted rotation invariant features consisting of a set of distances between points in the point cloud. Then, the extracted shape descriptors were fed into a CNN for the classification of manufacturing processes. In addition, we provide two visualization methods for interpreting the intermediate layers of the neural network. Last, the performance of the method was tested on some ambiguous examples and their performances were consistent with expectations. In this paper, we have considered only shape information, while non-shape information like materials and tolerances were ignored. Additionally, only parts that require one manufacturing process were considered in this research. Our work demonstrates that part shape attributes alone are adequate for discriminating between different manufacturing processes considered. 

LLMs have demonstrated impressive proficiency in generating coherent and high-quality text, making them valuable across a range of text- generation tasks. However, rigorous evaluation of this generated content is crucial, as ensuring its quality remains a significant challenge due to persistent issues such as factual inaccuracies and hallucination. This paper introduces three fine-tuned general-purpose LLM auto-evaluators, REC-8B, REC-12B and REC-70B, specifically designed to evaluate generated text across sev- eral dimensions: faithfulness, instruction follow- ing, coherence, and completeness. These mod- els not only provide ratings for these metrics but also offer detailed explanation and verifiable citation, thereby enhancing trust in the content. Moreover, the models support various citation modes, accommodating different requirements for latency and granularity. Extensive evalua- tions on diverse benchmarks demonstrate that our general-purpose LLM auto-evaluator, REC-70B, outperforms state-of-the-art LLMs, excelling in content evaluation by delivering better quality ex- planation and citation with minimal bias. Our REC dataset and models are available at https: //github.com/adelaidehsu/REC. 

Abstract Generative design (GD) techniques have been proposed to generate numerous designs at early design stages for ideation and exploration purposes. Previous research on GD using deep neural networks required tedious iterations between the neural network and design optimization, as well as post-processing to generate functional designs. Additionally, design constraints such as volume fraction could not be enforced. In this paper, a two-stage non-iterative formulation is proposed to overcome these limitations. In the first stage, a conditional generative adversarial network (cGAN) is utilized to control design parameters. In the second stage, topology optimization (TO) is embedded into cGAN (cGAN + TO) to ensure that desired functionality is achieved. Tests on different combinations of loss terms and different parameter settings within topology optimization demonstrated the diversity of generated designs. Further study showed that cGAN + TO can be extended to different load and boundary conditions by modifying these parameters in the second stage of training without having to retrain the first stage. Results demonstrate that GD can be realized efficiently and robustly by cGAN+TO.