Local training of neural networks

A method for performing learning, comprising:

• performing, using a learning network, a free inference for a plurality of input signals, the plurality of input signals corresponding to a plurality of target output signals, the learning network including a plurality of inputs receiving the plurality of input signals, a plurality of weights corresponding to a plurality of programmable impedances, a plurality of neurons, and a plurality of outputs, the plurality of weights interconnecting the plurality of neurons, the learning network being described by an energy for the free inference, the energy including an interaction term corresponding to interactions between the plurality of neurons, the interactions consisting of neuron pair interactions, the free inference resulting in a plurality of output signals for the plurality of outputs, at least a first portion of the plurality of weights corresponding to data flow for the free inference;
• providing the plurality of input signals to the plurality of inputs and a plurality of bias signals to the plurality of outputs to perform a biased inference, the plurality of bias signals being based on the plurality of target output signals and the plurality of output signals, the plurality of bias signals being fed back to the learning network in a path corresponding to a transpose of the at least the first portion of the plurality of weights;
• determining, at a plurality of locations in the learning network, learning network equilibrium states for the biased inference;
• and
• updating the plurality of weights based on the learning network equilibrium states.

A learning network comprising:

• a weight layer including a plurality of weights corresponding to a weight matrix, the plurality of weights corresponding to a plurality of programmable impedances;
• and
• a neuron layer including a plurality of inputs, a plurality of outputs, and a plurality of neurons coupled between the plurality inputs and the plurality of outputs, the neuron layer being coupled with the weight layer such the plurality of inputs receive a plurality of weighted input signals from at least a portion of the plurality of weights and such that the plurality of outputs provide a plurality of neuron output signals to the the weight layer in a path corresponding to a transpose of the weight matrix, the plurality of weights connecting a plurality of neuron pairs in the plurality of neurons;
• and
• wherein the learning network is configured to receive a plurality of input signals corresponding to a plurality of target outputs, to provide a plurality of learning network output signals in response to the plurality of input signals, to receive a plurality of bias signals based on the plurality of target outputs and the plurality of learning network output signals, and to update the plurality of weights based on the plurality of bias signals, the plurality of target outputs, and the plurality of learning network output signals.

A learning network, comprising:

• a plurality of system inputs configured to receive a plurality of input signals;
• at least one weight layer coupled with the plurality of system inputs, the at least one weight layer including a plurality of weights, at least a portion of the plurality of weights corresponding to a weight matrix;
• a plurality of neuron layers, the weight layer being interleaved and coupled with the plurality of neuron layers, each of the plurality of neuron layers including a plurality of inputs, a plurality of outputs, and a plurality of neurons coupled between the plurality inputs and the plurality of outputs, each of at least a portion of the plurality of neuron layers being coupled such that the plurality of inputs receive a plurality of weighted input signals from the at least the portion of the plurality of weights of the at least one weight layer and such that the plurality of outputs provide a plurality of neuron output signals to the weight layer in a configuration corresponding to a transpose of the weight matrix;
• and
• a plurality of system outputs coupled with a final neuron layer of the plurality of neuron layers, the plurality of system outputs configured to provide a plurality of output signals based on the input signals and to receive a plurality of bias signals;
• wherein the plurality of input signals corresponds to a plurality of target outputs, the plurality of bias signals is based on the plurality of target outputs and the plurality of output signals, and the plurality of weights are configured to be updated based on the plurality of bias signals, the plurality of target outputs, and the plurality of output signals.