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I'm reading Bio Inspired Artificial Intelligence which cites this passage about neuron plasticity:

"Spike time-dependent plasticity. The percentage of synaptic modification depends on the difference between presynaptic and postsynaptic spikes (tpre −tpost). The temporal difference in the figure ranges between -100 ms and +100 ms. When the postsynaptic neuron fires after arrival of the presynaptic pulse (positive difference, also known as causal relation), the synaptic weight is increased; instead, when the postsynaptic neuron fires before the arrival of the presynaptic pulse (negative differ- ence, also known as anticausal difference), the synaptic weight is depressed." From Gerstner and Kistler (2002) plotted on data from Bi and Poo (2001).

How do inhibitory neurons, which have successfully inhibited an activation spike of a neuron, strengthen their connections with such neurons, as the neurons they stop don't spike?

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The learning rule you describe (i.e. the change of synaptic weights from source neuron to target neuron depending on the temporal difference between source and target activity) is often referred to as 'classical' or 'standard' STDP (spike-timing dependent plasticity) and is focused on connections between excitatory cells. However, this simple form of plasticity is not enough to explain all experimental observations and has also computational problems with respect to stability i.e. there is in fact no 'standard' STDP, because the weight change is not only dependent on the temporal difference, but also on the voltage, location of the synapse, firing rate, the cell-type and probably other factors, see e.g. this article from 2010 dealing with questions surrounding STDP by Lisman and Spruston.

In short, the form of the learning rule depends on several factors and synaptic plasticity works differently for inhibitory cells. As the question as to how plasticity works involving inhibitory cells is not an easy topic, I will refer to this review paper which deals with different induction protocols and potential functional implications (e.g. stability, homeostasis): Review paper on inhibitory synaptic plasticity by Vogels et al.

Very recently, there also has been a research topic in Frontiers of Cellular Neuroscience on this topic: The editorial article briefly summarizes the different contributions

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Short answer
The question is kind of broad, and I decided to give four notable examples from credible sources of long-term potentiation of inhibitory responses (iLTP) below. Upregulation of postsynaptic GABAA and GABAB currents are the predominant effectors responsible for iLTP. The mechanism through which these effects are initiated are, however, variable between the various systems described. As far as I can see, non of the examples are Hebbian (i.e., non of the examples below are dependent on spike-timing).

Background
Repetitive firing of interneurons has been shown to enhance the spike-mediated inhibitory postsynaptic currents in CA1 pyramidal neurons in the hippocampus. this enhancement was mediated by GABAB receptors. The hippocampus is a brain structure where most of the research in long-term potentiation has been done in the past decades. It is a hot spot of learning and synaptic plasticiy where long-term potentiation is also induced by repetitive (tetanic) stimulation. The enhanced inhibitory responses were mediated by astrocytes that in turn affected the inhibitory responses in the pyramidal neurons. Astrocytes may therefore be a necessary intermediary in activity-dependent modulation of inhibitory synapses in the hippocampus. The mechanism through which the glial cells did this was not described in the paper. It was not mediated via Cl- or K+ (Kang et al., 1998).

In hippocampal neurons it has been shown that prolonged depolarization of cultured cells leads to increased expression of inhibitory GABAA receptors that ultimately decrease the artificially-induced high spike rate activity to normal levels (Rannals & Kapur, 2011). This increase in GABAA activity was accompanied by a larger activity of GABA syntheszing enzyme GAD, likely showing increased GABA release.

In the thalamus, postsynaptic thalamocortical (TC) cells show inhibitory long-term potentiation (iLTP). This iLTP was explicitly shown to be non-Hebbian, because it did not depend on the timing between presynaptic and postsynaptic activity. Instead, it was shown to be induced by postsynaptic burst activity alone. iLTP required postsynaptic dendritic Ca2+ influx that triggered the synthesis of nitric oxide that retrogradely activated presynaptic guanylyl cyclase, in turn resulting in the presynaptic expression of iLTP (Sieber et al., 2013).

A last example of iLTP was described in the visual cortex. When blocking excitatory postsynaptoc potentials, tetanic stimulation of layer IV neurons resulted in iLTP of layer V neurons postsynaptically mediated by increased GABAA receptor currents. Interestingly, the tetanic stimuli used were much like the stimuli used to evoked excitatory LTP (eLTP) in hippocampus as described above, and conditions favoring iLTP were much the same as the conditions needed to establish eLTP in the hippocampus (Komatsu, 1994).

References
- Kang et al., Nature Neurosci (1998); 1(8):683-92
- Komatsu, J Neurosci (1994); 14(11): 6489-99
- Rannals & Kapur, J Neurosci (2011); 31(48): 17701–12
- Sieber et al., J Neurosci (2013); 33(40): 15675-85

Further Reading
- How do neurons decide how to alter their output signals?

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