Rediscovering Deep Neural Networks Through Finite-State Distributions
We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models constructed in our framework assign probabilities to uncertain realiza...
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Zusammenfassung: | We propose a new way of thinking about deep neural networks, in which the
linear and non-linear components of the network are naturally derived and
justified in terms of principles in probability theory. In particular, the
models constructed in our framework assign probabilities to uncertain
realizations, leading to Kullback-Leibler Divergence (KLD) as the linear layer.
In our model construction, we also arrive at a structure similar to ReLU
activation supported with Bayes' theorem. The non-linearities in our framework
are normalization layers with ReLU and Sigmoid as element-wise approximations.
Additionally, the pooling function is derived as a marginalization of spatial
random variables according to the mechanics of the framework. As such, Max
Pooling is an approximation to the aforementioned marginalization process.
Since our models are comprised of finite state distributions (FSD) as variables
and parameters, exact computation of information-theoretic quantities such as
entropy and KLD is possible, thereby providing more objective measures to
analyze networks. Unlike existing designs that rely on heuristics, the proposed
framework restricts subjective interpretations of CNNs and sheds light on the
functionality of neural networks from a completely new perspective. |
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DOI: | 10.48550/arxiv.1809.10073 |