Can the Hebbian theory apply to Inhibitory Neurons If I understand the basic Hebbian theory, when a neuron fires a pulse to another neuron and this pulse causes the target neuron to fire then the delta energy sent from the initial neuron to the target is increased. (Making it easier to trigger the target cell) With this in mind is there a way for an inhibitory neuron to increase the delta energy it applies to a target neuron (reducing the excitation level of a target neuron). If the inhibitory neuron never triggers the target then I would assume it would never increase the decrease in energy it sends to the target.

≈Yes, it's easy to conceptualize at a simple ganglionic circuit. A really good example is (I believe from Kandel's lab)demonstrated by Aplysia's gill withdrawal reflex. Repeated stimulation causes reduced EPSPs in motor neurons that innervate muscles that cause the withdrawal reflex. However when you apply a electric shock to the tail, the snail will immediately regain withdrawal reflex sensitivity. The tail sensory neuron response activates the serotonergic facilatory interneurons which have multiple IO with sensory and motor neurons.

And don't forget, interneurons can inhibit other interneurons leading to disinhibition.

For most LTP work you're probably ok using Hebbian models. Make sure to keep in mind that in more complex systems like cortical circuits. there are some modes of communication that don't always play well with Hebb's Laws: gliotransmission, retrograde transmission, neuropeptides/GPCRs, and activation of perisynaptic receptors/receptors on adjacent cells.