Optimizations for analog hardware realization of trained neural networks
Systems and methods are provided for analog hardware realization of neural networks. The method includes obtaining a neural network topology and weights of a trained neural network. The method also includes transforming the neural network topology to an equivalent analog network of analog components including operational amplifiers and resistors. Each operational amplifier represents an analog neuron of the equivalent analog network, and each resistor represents a connection between two analog neurons. The method also includes computing a weight matrix based on the weights of the trained neural network. The method also includes generating a resistance matrix for the weight matrix. The method also includes pruning the equivalent analog network to reduce the number of operational amplifiers or the resistors, based on the resistance matrix, to obtain an optimized analog network of analog components.
1. A method for hardware realization of neural networks, comprising:
obtaining a neural network topology and weights of a trained neural network;
transforming the neural network topology to an equivalent analog network of analog components including a plurality of operational amplifiers and a plurality of resistors, wherein each operational amplifier represents an analog neuron of the equivalent analog network and each resistor represents a connection between two analog neurons;
computing a weight matrix for the equivalent analog network based on the weights of the trained neural network, wherein each element of the weight matrix represents a respective connection;
generating a resistance matrix for the weight matrix, wherein each element of the resistance matrix corresponds to a respective weight of the weight matrix;
pruning the equivalent analog network to reduce number of the plurality of operational amplifiers or the plurality of resistors, based on the resistance matrix, to obtain an optimized analog network of analog components; and
generating a schematic model for implementing the optimized analog network as electronic circuitry based on the resistance matrix, including:
selecting component values for each individual operational amplifier and each individual resistor, and
for each analog neuron of the equivalent analog network:
computing a respective bias value for the respective analog neuron based on the weights of the trained neural network, while computing the weight matrix;
in accordance with a determination that the respective bias value is above a predetermined maximum bias threshold, removing the respective analog neuron from the equivalent analog network; and
in accordance with a determination that the respective bias value is below a predetermined minimum bias threshold, replacing the respective analog neuron with a linear junction in the equivalent analog network.
2. The method of claim 1 , wherein pruning the equivalent analog network comprises:
substituting, with conductors, resistors corresponding to one or more elements of the resistance matrix that have resistance values below a predetermined minimum threshold resistance value.
3. The method of claim 1 , wherein pruning the equivalent analog network comprises:
removing one or more connections of the equivalent analog network corresponding to one or more elements of the resistance matrix that are above a predetermined maximum threshold resistance value.
4. The method of claim 1 , wherein pruning the equivalent analog network comprises:
removing one or more connections of the equivalent analog network corresponding to one or more elements of the weight matrix that are approximately zero.
5. The method of claim 4 , wherein pruning the equivalent analog network further comprises:
removing one or more analog neurons of the equivalent analog network without any input connections.
6. The method of claim 1 , wherein pruning the equivalent analog network comprises:
ranking analog neurons of the equivalent analog network based on detecting use of the analog neurons when making calculations for one or more data sets;
selecting one or more analog neurons of the equivalent analog network based on the ranking; and
removing the one or more analog neurons from the equivalent analog network.
7. The method of claim 6 , wherein detecting use of the analog neurons comprises:
building a model of the equivalent analog network using a modelling software; and
measuring propagation of analog signals by using the model to generate calculations for the one or more data sets.
8. The method of claim 6 , wherein detecting use of the analog neurons comprises:
building a model of the equivalent analog network using a modelling software; and
measuring output signals of the model by using the model to generate calculations for the one or more data sets.
9. The method of claim 6 , wherein detecting use of the analog neurons comprises:
building a model of the equivalent analog network using a modelling software; and
measuring power consumed by the analog neurons by using the model to generate calculations for the one or more data sets.
10. The method of claim 1 , further comprising:
subsequent to pruning the equivalent analog network and prior to generating one or more lithographic masks for fabricating a circuit implementing the equivalent analog network, recomputing the weight matrix for the equivalent analog network and updating the resistance matrix based on the recomputed weight matrix.
11. The method of claim 1 , further comprising reducing number of neurons of the equivalent analog network, prior to generating the weight matrix, by increasing number of connections from one or more analog neurons of the equivalent analog network.
12. The method of claim 1 , further comprising:
prior to transforming the neural network topology, pruning the trained neural network to update the neural network topology and the weights of the trained neural network, using pruning techniques for neural networks, so that the equivalent analog network includes less than a predetermined number of analog components.
13. The method of claim 12 , wherein the pruning is performed iteratively taking into account accuracy or a level of match in output between the trained neural network and the equivalent analog network.
14. The method of claim 1 , further comprising:
prior to transforming the neural network topology to the equivalent analog network, performing network knowledge extraction.
15. A system for hardware realization of neural networks, comprising:
one or more processors; and
memory;
wherein the memory stores one or more programs configured for execution by the one or more processors, and the one or more programs comprise instructions for:
obtaining a neural network topology and weights of a trained neural network;
transforming the neural network topology to an equivalent analog network of analog components including a plurality of operational amplifiers and a plurality of resistors, wherein each operational amplifier represents an analog neuron of the equivalent analog network and each resistor represents a connection between two analog neurons;
computing a weight matrix for the equivalent analog network based on the weights of the trained neural network, wherein each element of the weight matrix represents a respective connection;
generating a resistance matrix for the weight matrix, wherein each element of the resistance matrix corresponds to a respective weight of the weight matrix;
pruning the equivalent analog network to reduce number of the plurality of operational amplifiers or the plurality of resistors, based on the resistance matrix, to obtain an optimized analog network of analog components; and
generating a schematic model for implementing the optimized analog network as electronic circuitry based on the resistance matrix, including:
selecting component values for each individual operational amplifier and each individual resistor; and
for each analog neuron of the equivalent analog network:
computing a respective bias value for the respective analog neuron based on the weights of the trained neural network, while computing the weight matrix;
in accordance with a determination that the respective bias value is above a predetermined maximum bias threshold, removing the respective analog neuron from the equivalent analog network; and
in accordance with a determination that the respective bias value is below a predetermined minimum bias threshold, replacing the respective analog neuron with a linear junction in the equivalent analog network.
16. The system of claim 15 , wherein pruning the equivalent analog network comprises:
substituting, with conductors, resistors corresponding to one or more elements of the resistance matrix that have resistance values below a predetermined minimum threshold resistance value.
17. The system of claim 15 , wherein pruning the equivalent analog network comprises:
removing one or more connections of the equivalent analog network corresponding to one or more elements of the resistance matrix that are above a predetermined maximum threshold resistance value.
18. The system of claim 15 , wherein pruning the equivalent analog network comprises:
removing one or more connections of the equivalent analog network corresponding to one or more elements of the weight matrix that are approximately zero.
19. A non-transitory computer readable storage medium storing one or more programs configured for execution by a computer system having one or more processors, the one or more programs comprising instructions for:
obtaining a neural network topology and weights of a trained neural network;
transforming the neural network topology to an equivalent analog network of analog components including a plurality of operational amplifiers and a plurality of resistors, wherein each operational amplifier represents an analog neuron of the equivalent analog network and each resistor represents a connection between two analog neurons;
computing a weight matrix for the equivalent analog network based on the weights of the trained neural network, wherein each element of the weight matrix represents a respective connection;
generating a resistance matrix for the weight matrix, wherein each element of the resistance matrix corresponds to a respective weight of the weight matrix;
pruning the equivalent analog network to reduce number of the plurality of operational amplifiers or the plurality of resistors, based on the resistance matrix, to obtain an optimized analog network of analog components; and
generating a schematic model for implementing the optimized analog network as electronic circuitry based on the resistance matrix, including:
selecting component values for each individual operational amplifier and each individual resistor; and
for each analog neuron of the equivalent analog network:
computing a respective bias value for the respective analog neuron based on the weights of the trained neural network, while computing the weight matrix;
in accordance with a determination that the respective bias value is above a predetermined maximum bias threshold, removing the respective analog neuron from the equivalent analog network; and
in accordance with a determination that the respective bias value is below a predetermined minimum bias threshold, replacing the respective analog neuron with a linear junction in the equivalent analog network.