Physical neural network systems and methods are disclosed. A physical neural network can be configured utilizing molecular technology, wherein said physical neural network comprises a plurality of molecular conductors, which form neural network connections thereof. A training mechanism can be provided for training said physical neural network to accomplish a particular neural network task based on a neural network training rule. The neural network connections are formed between pre-synaptic and post-synaptic components of said physical neural network. The neural network generally includes dynamic and modifiable connections for adaptive signal processing. The neural network training mechanism can be based, for example, on the Anti-Hebbian and Hebbian (AHAH) rule and/or other plasticity rules.