So the spiking model derived in the gain paper is basically now completely capabable of implementing the rate models, but there is now a new dimension. There are all of the time constants that can be altered without changing the relationship between rate models and spiking models -- there is always some counter balance to the time constant, decreasing the tau could be compensated by increasing w.
So that opens up a lot of possibilities about how the time constants relate to all types of neuronal phenomenon and what that could mean in terms of what a rate model even would mean in spiking neurons. Adaptation is a nice illustration of something that would on the surface seems as a variability that would break the rate model, but actually it can stay consistent within the rate model terms. I(t) is a temporal variable, and our model was just the most simple equilibrium direct model -- there are a bunch of ways to maintain the linearity. The spiking-current relationship can stay linear while varying through time. The translation of current to spike is essentially as if you are running a filter through a temporal signal, this is actually just a linear transformation. Its kinda like the complex plane -- the Rate model is like the real valued numbers, but that is just a single line among an infinitely large set of other lines and that is the spiking model.
short-term plasticity: i have this idea about how to implement normalization with STP, i've gone pretty far on it already. its coming.
long-term plasticity: at this scale we have to ask what exactly are we trying to learn? This is a level above the general population-code, and onto the specifics about what exactly are the things the population code are representing or learning? The P-cells are just one of a small set of sensory neurons that all form synapses with some population of interneurons that likely greatly overlaps. The entire sensory environment seems to be projected as a vector in a high dimensional space onto these interneurons (like in the leech), which represent all the information is a population code. A particular sensory dimension does not point down a particular neurons axis, but the linear combination of multiple neurons. In an almost (or perhaps in a warped subspace or something?) orthogonal direction are vectors that represent the other dimensions of the sensory world. The various weights of the projection tuned to send the population in one direction in a high dimensional space. LTP sets up all of these weights and communication between neurons wires the circuit up to form these population representations. What do simple rules like STDP mean in these spiking models? How do the neurons differentiate themselves to form a full basis of the information?
neuromodulators: at an intermediate scale neuromodulators may play a role in maintaining the long-term and slower kinetics of the nervous system (all while maintaining the rate model). It is really interesting how many CPGs are modulated by neuromodulators, perhaps there is a high-dimensional neuro-modulator space that can activate many different types of CPGs. The CPGs likely use the neuromodulators as a positive feedback loop to maintain the patterns over larger, but also adjustable time-scales. If dopamine activates swimming, then there is likely a dopamine signal that could get regulated to adjust the length of the swim. I think the CPGs are wired up in feed-back circuits and perhaps have intrinsically rhythmic properties to generate the temporal patterns of the rhythms (i guess transmitter kinetics is definitely another time-scale). But these longer 10s to 100s of seconds time scales seem to be controlled by positive feedback-loops with neuro-modulators. These could have their own slower kinetics that drive seconds-level changes in behavioral transitions, and can obviously be modulated. The neuromodulators are just altering the population code and the transformation of the sensory world into behavioral output. If the sensory cells activated the interneuron population code to point in the direction that means "you just got shocked! start swimming!", then the synapses from the interneurons to the CPG/motor neurons would activate the swim CPG. With no feedback the sensory shock could set up a positive dopamine feedback loop that could take seconds to decay -- the sensory population code can settle back to its current sensory environment (since it is no longer being shocked, it will no longer be in the shock basin), and the pattern generator can just continue. The sensory environment can shut down the pattern generator if it wants, or leave it on if it needs by maintaining the neuromodulation -- and by direct shutdown of the motor neurons if it needs to end the pattern faster.
So the interganglionic connections would likely be sensory pop-code to sensory pop-code, and CPG/motor to CPG/motor, mainly. Perhaps sensory-pop to CPG, but less CPG to sensory-pop. It would seem like if there were feedback connections from CPG to sensory-pop then that would just be for like a reference signal, perhaps a predictive signal that could even modulate the sensory-pop, but likely would not drive it. It would be a nice signal to have to adjust the sensory feedback and close the loop.
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