At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit (14; 11), thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f θ (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinitewidth limit, the network function f θ follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

use of traditional and emerging techniques to identifying suspected myocarditis patients. Consolidating our understanding of myocarditis may aid in new research that can spearhead challenging questions and overcome obstacles in the field, especially in better defining the wide range of causative agents and clinical presentations of myocarditis.

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Viral infection triggers the activation of antiviral innate immune responses in mammalian cells. Viral RNA in the cytoplasm activates signaling pathways that result in the production of interferons (IFNs) and IFN-stimulated genes. Some viral infections have been shown to induce cytoplasmic granular aggregates similar to the dynamic ribonucleoprotein aggregates termed stress granules (SGs), suggesting that these viruses may utilize this stress response for their own benefit. By contrast, some viruses actively inhibit SG formation, suggesting an antiviral function for these structures. We review here the relationship between different viral infections and SG formation. We examine the evidence for antiviral functions for SGs and highlight important areas of inquiry towards understanding cellular stress responses to viral infection.