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Register a new userNeural networks behave as hash encoders: An empirical study
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Fengxiang He
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition exhibits the following encoding properties across a variety of deep learning models: (1) {it determinism}: almost every linear region contains at most one training example. We can therefore represent almost every training example by a unique activation pattern, which is parameterized by a {it neural code}; and (2) {it categorization}: according to the neural code, simple algorithms, such as $K$-Means, $K$-NN, and logistic regression, can achieve fairly good performance on both training and test data. These encoding properties surprisingly suggest that {it normal neural networks well-trained for classification behave as hash encoders without any extra efforts.} In addition, the encoding properties exhibit variability in different scenarios. {Further experiments demonstrate that {it model size}, {it training time}, {it training sample size}, {it regularization}, and {it label noise} contribute in shaping the encoding properties, while the impacts of the first three are dominant.} We then define an {it activation hash phase chart} to represent the space expanded by {model size}, training time, training sample size, and the encoding properties, which is divided into three canonical regions: {it under-expressive regime}, {it critically-expressive regime}, and {it sufficiently-expressive regime}. The source code package is available at url{https://github.com/LeavesLei/activation-code}.
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