医学人工智能AIM(Artificial Intelligence in Medicine)杂志发表了多学科领域的原创文章,涉及医学中的人工智能理论和实践,以医学为导向的人类生物学和卫生保健。医学中的人工智能可以被描述为与研究、项目和应用相关的科学学科,旨在通过基于知识或数据密集型的计算机解决方案支持基于决策的医疗任务,最终支持和改善人类护理提供者的性能。 官网地址:http://dblp.uni-trier.de/db/journals/artmed/

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Propelled by new designs that permit to circumvent the spectral bias, implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still lack a proper theoretical characterization of how INRs represent signals. In this work, we aim to fill this gap, and we propose a novel unified perspective to theoretically analyse INRs. Leveraging results from harmonic analysis and deep learning theory, we show that most INR families are analogous to structured signal dictionaries whose atoms are integer harmonics of the set of initial mapping frequencies. This structure allows INRs to express signals with an exponentially increasing frequency support using a number of parameters that only grows linearly with depth. Afterwards, we explore the inductive bias of INRs exploiting recent results about the empirical neural tangent kernel (NTK). Specifically, we show that the eigenfunctions of the NTK can be seen as dictionary atoms whose inner product with the target signal determines the final performance of their reconstruction. In this regard, we reveal that meta-learning the initialization has a reshaping effect of the NTK analogous to dictionary learning, building dictionary atoms as a combination of the examples seen during meta-training. Our results permit to design and tune novel INR architectures, but can also be of interest for the wider deep learning theory community.

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