Webthe network polynomial has size exponential in the number of variables, but we may be able to represent and evaluate it in polynomial space and time using a sum-product network. … WebCorollary (Informal) A depth-3 ReLU network with width d_1 = d_2 = O (\sqrt {N}) d1 = d2 = O( N) is sufficient to memorize N N points. This indicates a concrete separation in terms of memorization capacity between depth-2 and depth-3 networks. Suppose we focus on the regime where d \ll N d ≪ N. For this case, we have achieved a polynomial ...

On the Sample Complexity of Learning Sum-Product Networks

Web(2011) that a deep sum-product network may require exponentially less units to represent the same function compared to a shallow sum-product network. Furthermore, there is a wealth of empirical evidences supporting this hypothesis (see, e.g., Goodfellow et al., 2013; Hinton et al., 2012b,a). WebFeb 16, 2024 · We introduce Convolutional Sum-Product Networks (ConvSPNs) which exploit the inherent structure of images in a way similar to deep convolutional neural networks, optionally with weight sharing. ConvSPNs encode spatial relationships through local products and local sum operations. the mary louis academy - jamaica

Poisson Sum-Product Networks: A Deep Architecture for …

WebJun 16, 2013 · Sum-product networks (SPNs) are a new class of deep probabilistic models. SPNs can have unbounded treewidth but inference in them is always tractable. An SPN is either a univariate distribution, a product of SPNs over disjoint variables, or a weighted sum of SPNs over the same variables. Web2 days ago · 0:38. Due to global warming, a deep ocean current around Antarctica that has been relatively stable for thousands of years could head for "collapse" over the next few decades. Such a sudden shift ... WebApr 12, 2024 · Deep work. As students and busy professionals, we are all saturated with so many minor tasks like checking emails and social networks – watch the reel, get a snack, make the bed, etc. In Deep Work, Newport is trying to instill the idea of working in blocks of time when you are most productive, away from all the distractions. This means ... the mary louis academy ny