Neural Network Layer Algebra: A Framework to Measure Capacity and
Compression in Deep Learning
- URL: http://arxiv.org/abs/2107.01081v1
- Date: Fri, 2 Jul 2021 13:43:53 GMT
- Title: Neural Network Layer Algebra: A Framework to Measure Capacity and
Compression in Deep Learning
- Authors: Alberto Badias and Ashis Banerjee
- Abstract summary: We present a new framework to measure the intrinsic properties of (deep) neural networks.
While we focus on convolutional networks, our framework can be extrapolated to any network architecture.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We present a new framework to measure the intrinsic properties of (deep)
neural networks. While we focus on convolutional networks, our framework can be
extrapolated to any network architecture. In particular, we evaluate two
network properties, namely, capacity (related to expressivity) and compression,
both of which depend only on the network structure and are independent of the
training and test data. To this end, we propose two metrics: the first one,
called layer complexity, captures the architectural complexity of any network
layer; and, the second one, called layer intrinsic power, encodes how data is
compressed along the network. The metrics are based on the concept of layer
algebra, which is also introduced in this paper. This concept is based on the
idea that the global properties depend on the network topology, and the leaf
nodes of any neural network can be approximated using local transfer functions,
thereby, allowing a simple computation of the global metrics. We also compare
the properties of the state-of-the art architectures using our metrics and use
the properties to analyze the classification accuracy on benchmark datasets.
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