Cortical circuits are widely thought to operate in the so-called ``inhibition-stabilized network (ISN) regime’‘, whereby the excitatory (E) subcircuit is unstable in isolation but dynamically stabilized by feedback inhibition (I). So far, this regime has been studied both theoretically and experimentally in its one-dimensional, ``mean-field’‘ form, whereby the overall E population activity constitutes the main mode of instability, and stability is maintained by uniform, blanket inhibition. Here, we investigate the hypothesis that cortical circuits may in fact be operating in a richer, multi-dimensional ISN regime. Indeed, we developed a theory of inhibitory synaptic plasticity (ISP) which --- as we show analytically --- approximates a form of optimal meta-control of network dynamics. According to this theory, a biologically plausible form of Hebbian ISP learns detailed inhibitory feedback loops that successfully stabilize several distinct modes of instability in the excitatory subcircuit. Thus, in networks with rich patterns of excitatory recurrence, ISP automatically places the circuit in a form of multi-dimensional ISN regime. Can this regime be tested experimentally? A key diagnostic feature of the one-dimensional ISN regime is the paradoxical response of inhibitory neurons to external inputs: in ISNs, a positive tonic drive to the entire I population paradoxically \textit{suppresses} its activity at steady-state. Here, we show that the multi-dimensional ISN regime gives rise to a whole set of analogous paradoxical effects. Specifically, we show that there exist multiple, detailed stimulation patterns to the inhibitory neurons that lead to paradoxical effects. These patterns can be extracted analytically from the connectivity matrix, or empirically through a two-staged perturbation experiment. The multi-dimensional ISN regime predicts that optogenetically activating the I cells in these detailed patterns should cause each I cell to react in the opposite way to how it was driven. Recent advances in holographic optogenetics should soon enable experimental falsification of the multi-dimensional ISN regime.Cortical circuits are widely thought to operate in the so-called ``inhibition-stabilized network (ISN) regime’‘, whereby the excitatory (E) subcircuit is unstable in isolation but dynamically stabilized by feedback inhibition (I). So far, this regime has been studied both theoretically and experimentally in its one-dimensional, ``mean-field’‘ form, whereby the overall E population activity constitutes the main mode of instability, and stability is maintained by uniform, blanket inhibition. Here, we investigate the hypothesis that cortical circuits may in fact be operating in a richer, multi-dimensional ISN regime. Indeed, we developed a theory of inhibitory synaptic plasticity (ISP) which --- as we show analytically --- approximates a form of optimal meta-control of network dynamics. According to this theory, a biologically plausible form of Hebbian ISP learns detailed inhibitory feedback loops that successfully stabilize several distinct modes of instability in the excitatory subcircuit. Thus, in networks with rich patterns of excitatory recurrence, ISP automatically places the circuit in a form of multi-dimensional ISN regime. Can this regime be tested experimentally? A key diagnostic feature of the one-dimensional ISN regime is the paradoxical response of inhibitory neurons to external inputs: in ISNs, a positive tonic drive to the entire I population paradoxically suppresses its activity at steady-state. Here, we show that the multi-dimensional ISN regime gives rise to a whole set of analogous paradoxical effects. Specifically, we show that there exist multiple, detailed stimulation patterns to the inhibitory neurons that lead to paradoxical effects. These patterns can be extracted analytically from the connectivity matrix, or empirically through a two-staged perturbation experiment. The multi-dimensional ISN regime predicts that optogenetically activating the I cells in these detailed patterns should cause each I cell to react in the opposite way to how it was driven. Recent advances in holographic optogenetics should soon enable experimental falsification of the multi-dimensional ISN regime.