On the Size and Width of the Decoder of a Boolean Threshold Autoencoder

Area of Science:

• Computer Science
• Artificial Intelligence
• Machine Learning

Background:

• Autoencoders are neural networks with encoder-decoder structures for data compression and reconstruction.
• Boolean threshold functions are fundamental units in constructing neural networks, particularly for binary data processing.

Purpose of the Study:

• To investigate the size and width of autoencoders composed of Boolean threshold functions.
• To analyze the complexity of the decoder component in reconstructing binary vectors.

Main Methods:

• Focusing on the decoder, the study derives theoretical bounds for the number of nodes required.
• Analysis involves transforming vectors between different dimensional binary spaces using Boolean threshold functions.

Main Results:

• The research establishes the exact number of nodes necessary for a decoder to map between n-dimensional and m-dimensional binary spaces.
• It demonstrates that the decoder's width can be decreased by permitting small reconstruction errors, quantified by average Hamming distance.

Conclusions:

• The findings provide insights into the structural requirements of Boolean autoencoders for binary data.
• Understanding the trade-off between decoder width and reconstruction accuracy is crucial for efficient autoencoder design.