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Mikusiński's Operational Calculus for the Transmuted 1st‐Level General Fractional Derivatives
Mathematical methods in the applied sciencesThe transmuted ‐fold sequential 1st‐level general fractional derivatives are introduced within the framework of conjugation (transmutation) and Sonin kernels, providing a unified extension of general fractional derivatives that includes the Riemann ...
M. N. Dabhi, Krunal B. Kachhia
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On the fractional-in-time Keller-Segel model via Sonine kernels
Topological Methods in Nonlinear AnalysisIn this paper, we study the existence and asymptotic behavior to a diffusion system which is non-local in time. As consequence of our theorems we deduce new results for the fractional-in-time Keller-Segel model. Our approach is intimately related with the Sonine kernels.
Masterson Costa +3 more
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CMSIS-NN: Efficient Neural Network Kernels for Arm Cortex-M CPUs
arXiv.org, 2018Deep Neural Networks are becoming increasingly popular in always-on IoT edge devices performing data analytics right at the source, reducing latency as well as energy consumption for data communication.
Liangzhen Lai, Naveen Suda, V. Chandra
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MixConv: Mixed Depthwise Convolutional Kernels
British Machine Vision Conference, 2019Depthwise convolution is becoming increasingly popular in modern efficient ConvNets, but its kernel size is often overlooked. In this paper, we systematically study the impact of different kernel sizes, and observe that combining the benefits of multiple
Ming-Xing Tan, Quoc V. Le
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Journal of Applied Mathematics and Mechanics, 1984
Generalized potential theory methods are used to re-establish the spectral relationship for the integral operators generated by a symmetric kernel in the form of the Weber-Sonin integral in the finite interval (0,a), the kernel containing Jacobi polynomials.
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Generalized potential theory methods are used to re-establish the spectral relationship for the integral operators generated by a symmetric kernel in the form of the Weber-Sonin integral in the finite interval (0,a), the kernel containing Jacobi polynomials.
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KernelBench: Can LLMs Write Efficient GPU Kernels?
International Conference on Machine LearningEfficient GPU kernels are crucial for building performant machine learning architectures, but writing them is a time-consuming challenge that requires significant expertise; therefore, we explore using language models (LMs) to automate kernel generation.
Anne Ouyang +6 more
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On the Inductive Bias of Neural Tangent Kernels
Neural Information Processing Systems, 2019State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties.
A. Bietti, Julien Mairal
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Liger Kernel: Efficient Triton Kernels for LLM Training
arXiv.orgTraining Large Language Models (LLMs) efficiently at scale presents a formidable challenge, driven by their ever-increasing computational demands and the need for enhanced performance.
Pin-Lun Hsu +9 more
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Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels
Neural Information Processing Systems, 2019While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs.
S. Du +5 more
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Wasserstein Weisfeiler-Lehman Graph Kernels
Neural Information Processing Systems, 2019Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures.
Matteo Togninalli +4 more
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