Multi-dimensional logarithmic number system processor for inner product computations

A method for implementing training and inference of deep neural networks, comprising:

• (a) receiving a set of training data;
• (b) representing the set of training data in a multidimensional logarithmic number system (MDLNS), the MDLNS representation using a first exponent associated with a first base and a second exponent associated with a second base;
• (c) conducting deep neural network training on the set of training data, using a predetermined first base and a predetermined second base, to determine a set of neural network weight coefficients;
• (d) based on the determined set of neural network weight coefficients and for the predetermined first base, optimizing the second base for multi-dimensional logarithmic data representation;
• and
• (e) conducting deep neural network inference on a set of network inputs to obtain a set of network outputs, using the optimized multi-dimensional logarithmic data representation determined in step (d).