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temporal derivative timing of learning logic update with meta-stable and thalamus VA sync logic.
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<p id="HeilbronnerRodriguez-RomagueraQuirkEtAl16">Heilbronner, S.R., Rodriguez-Romaguera, J., Quirk, G.J., Groenewegen, H.J., & Haber, S.N. (2016). Circuit-based corticostriatal homologies between rat and primate. <i>Biological Psychiatry, 80</i>, 509–521. <a href="http://www.sciencedirect.com/science/article/pii/S0006322316323885">http://www.sciencedirect.com/science/article/pii/S0006322316323885</a><a href="http://doi.org/10.1016/j.biopsych.2016.05.012"> http://doi.org/10.1016/j.biopsych.2016.05.012</a></p>
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<p id="HelfrichKnight19">Helfrich, R.F., & Knight, R.T. (2019). <i>Cognitive neurophysiology: Event-related potentials. </i>In Handbook of Clinical Neurology (pp. 543–558). Elsevier. <a href="https://www.sciencedirect.com/science/chapter/handbook/pii/B9780444640321000369">https://www.sciencedirect.com/science/chapter/handbook/pii/B9780444640321000369</a><a href="http://doi.org/10.1016/B978-0-444-64032-1.00036-9"> http://doi.org/10.1016/B978-0-444-64032-1.00036-9</a></p>
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<p id="KurodaSchweighoferKawato01">Kuroda, S., Schweighofer, N., & Kawato, M. (2001). Exploration of signal transduction pathways in cerebellar long-term depression by kinetic simulation. <i>Journal of Neuroscience, 21</i>, 5693–5702. <a href="https://www.jneurosci.org/content/21/15/5693">https://www.jneurosci.org/content/21/15/5693</a><a href="http://doi.org/10.1523/JNEUROSCI.21-15-05693.2001"> http://doi.org/10.1523/JNEUROSCI.21-15-05693.2001</a></p>
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<p id="LaCameraFontaniniMazzucato19">La Camera, G., Fontanini, A., & Mazzucato, L. (2019). Cortical computations via metastable activity. <i>Current Opinion in Neurobiology, 58</i>, 37–45. <a href="http://www.sciencedirect.com/science/article/pii/S0959438818302198">http://www.sciencedirect.com/science/article/pii/S0959438818302198</a><a href="http://doi.org/10.1016/j.conb.2019.06.007"> http://doi.org/10.1016/j.conb.2019.06.007</a></p>
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<p id="RecanatesiPereira-ObilinovicMurakamiEtAl22">Recanatesi, S., Pereira-Obilinovic, U., Murakami, M., Mainen, Z., & Mazzucato, L. (2022). Metastable attractors explain the variable timing of stable behavioral action sequences. <i>Neuron, 110</i>, 139-153.e9. <a href="https://www.cell.com/neuron/abstract/S0896-6273(21)00779-0">https://www.cell.com/neuron/abstract/S0896-6273(21)00779-0</a><a href="http://doi.org/10.1016/j.neuron.2021.10.011"> http://doi.org/10.1016/j.neuron.2021.10.011</a></p>
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<p id="RedishElgaTouretzky96">Redish, A.D., Elga, A.N., & Touretzky, D.S. (1996). A coupled attractor model of the rodent head direction system. <i>Network: computation in neural systems, 7</i>, 671. <a href="https://iopscience.iop.org/article/10.1088/0954-898X/7/4/004/meta">https://iopscience.iop.org/article/10.1088/0954-898X/7/4/004/meta</a></p>
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<p id="SatoParentLevesqueEtAl00">Sato, F., Parent, M., Levesque, M., & Parent, A. (2000). Axonal branching pattern of neurons of the subthalamic nucleus in primates. <i>Journal of Comparative Neurology, 424</i>, 142–152. <a href="http://onlinelibrary.wiley.com/doi/abs/10.1002/1096-9861%2820000814%29424%3A1%3C142%3A%3AAID-CNE10%3E3.0.CO%3B2-8">http://onlinelibrary.wiley.com/doi/abs/10.1002/1096-9861%2820000814%29424%3A1%3C142%3A%3AAID-CNE10%3E3.0.CO%3B2-8</a><a href="http://doi.org/https://doi.org/10.1002/1096-9861(20000814)424:1<142::AID-CNE10>3.0.CO;2-8"> http://doi.org/https://doi.org/10.1002/1096-9861(20000814)424:1<142::AID-CNE10>3.0.CO;2-8</a></p>
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<p id="SaundersMacoskoWysokerEtAl18">Saunders, A., Macosko, E.Z., Wysoker, A., Goldman, M., Krienen, F.M., Rivera, H., Bien, E., Baum, M., Bortolin, L., Wang, S., Goeva, A., Nemesh, J., Kamitaki, N., Brumbaugh, S., Kulp, D., & McCarroll, S.A. (2018). Molecular Diversity and Specializations among the Cells of the Adult Mouse Brain. <i>Cell, 174</i>, 1015-1030.e16. <a href="https://www.cell.com/cell/abstract/S0092-8674(18)30955-3">https://www.cell.com/cell/abstract/S0092-8674(18)30955-3</a><a href="http://doi.org/10.1016/j.cell.2018.07.028"> http://doi.org/10.1016/j.cell.2018.07.028</a></p>
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content/temporal-derivative.md

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You can see that across different combinations of prediction and outcome driver states, the `diff` value exhibits two distinct peaks: one at the start when the onset of prediction-phase activity drives `fast` and `slow` to change at their different rates, and another just after onset of the outcome (plus) phase. Therefore, if we trigger learning to occur some number of cycles (milliseconds) after the onset of the first second peak, it should generally happen around the end of the plus phase.
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You can see that across different combinations of prediction and outcome driver states, the `diff` value exhibits two distinct peaks: one at the start when the onset of prediction-phase activity drives `fast` and `slow` to change at their different rates, and another just after onset of the outcome (plus) phase. The first peak is generally much larger and more reliable in practice, reflecting changes in the overall sensory or internal (hidden) state of the network, while the second peak is proportional to the difference in the prediction versus outcome.
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Because the duration of the minus and plus phases is not in principle reliable, both peaks need to be detected. The first, generally larger one can be thought of as a "priming" pulse that provides initial activation to the learning process, while the second one triggers the final adaptation process that is sensitive to the difference between the `fast` and `slow` components.
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In primates for example, there is robust evidence for characteristic waves of neural activity following saccades, known as event-related potentials (ERPs) ([[@HelfrichKnight19]]), with the modal saccade fixation tightly centered at around 200 msec ([[@DevillezGuyaderCurranEtAl20]]). In rodents, there is evidence of brain-wide entrainment of neural activity at the theta cycle (also with a 200 msec period) ([[@SattlerWehr25]]), with strong evidence of overall cortex-wide neural activity characterized by periods of relative stability with rapid transitions between (i.e., _meta-stability_; [[@LaCameraFontaniniMazzucato19]]; [[@RecanatesiPereira-ObilinovicMurakamiEtAl22]]). These phasic transitions appear to be driven in part by motor events, consistent with the broad cortex-wide connectivity of the VA (ventral anterior) thalamus, receiving [[motor]] and [[prefrontal cortex]] inputs (see [[thalamus#frontal thalamus]]).
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The one case where there isn't a second peak is when the outcome matches the prediction, where no learning will occur in any case. It is possible to add a timeout for learning after the first peak: if no second peak occurs within some amount of time, then everything resets and the process starts over.
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<!--- It is also possible that driving learning to be a fixed number of cycles _prior_ to this transition would work even better. Yes, do this!! -->
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In our models, we have found that driving the timing of learning to occur a fixed number of cycles (milliseconds) after the onset of the first peak works well in practice. In a spiking network (e.g., the [[kinase algorithm]] for Axon), the time integrated values that drive learning are not nearly as smooth as those in [[#sim_diff]], because they have a significant contribution from postsynaptic spiking. However, much smoother values are available in the total excitatory and inhibitory conductances coming into each neuron, which sample from a large number of other neurons. The same peak-driven logic works well in this case, and is used in the [[kinase algorithm]].
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In a spiking network (e.g., the [[kinase algorithm]] for Axon), the time integrated values that drive learning are not nearly as smooth as those in [[#sim_diff]], because they have a significant contribution from postsynaptic spiking. However, much smoother values are available in the total excitatory and inhibitory conductances coming into each neuron, which sample from a large number of other neurons. The same peak-driven logic works well in this case, and is used in the [[kinase algorithm]].
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content/thalamus.md

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Interestingly, the layer 6 CT inputs to VAmc target the PV expressing neurons that project to the middle layers of cortex (core-style), while the layer 5 inputs arise from layer 5b upper PT neurons ([[@EconomoViswanathanTasicEtAl18]]) that target CB expressing neurons, which give rise to the layer 1 superficial and some deep layer projections (matrix-style). As discussed in [[@^EconomoViswanathanTasicEtAl18]], this subtype of 5b PT neurons is generally more active during motor preparation and planning, while the layer 5b lower PT neurons are more active during motor execution, and correspondingly send projections to the brainstem. These lower subtype are the neurons that project to the MD and AM thalamus, consistent with the idea that the VA (VAmc, VAgpi, and VAsnr) areas are functionally distinct.
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The broad connectivity of VAmc, similar to that of VAbg, seems ideally suited for _synchronizing_ processing across the frontal motor and PFC areas according to major motor-based events, such as saccades or large-scale body movements. There are generally abrupt transitions in cortical states at the onset of motor actions, and these broad, diffuse connections could effectively broadcast signals that facilitate these transitions, enabling the system to transition between preparatory activity and actual motor action ([[@ChurchlandShenoy24]]; [[@EconomoViswanathanTasicEtAl18]]).
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The broad connectivity of VAmc, similar to that of VAbg, seems ideally suited for _synchronizing_ processing across the frontal motor and PFC areas according to major motor-based events, such as saccades or large-scale body movements. There are generally abrupt transitions in cortical states at the onset of motor actions, and these broad, diffuse connections could effectively broadcast signals that facilitate these transitions, enabling the system to transition between preparatory activity and actual motor action ([[@ChurchlandShenoy24]]; [[@EconomoViswanathanTasicEtAl18]]). A growing literature on _meta-stable_ neural activity states with rapid transitions between relatively stable intervening states is consistent with this dynamic ([[@LaCameraFontaniniMazzucato19]]; [[@RecanatesiPereira-ObilinovicMurakamiEtAl22]]).
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The role of the AM in interconnecting the medial temporal lobe including the [[hippocampus]], subiculum, and the retrosplenial cortex (RSC) in the medial parietal lobe is critical for enabling episodic memories to be engaged in the service of goal planning, as is discussed a bit further in the section on [[#anterior thalamic areas]] (see also [[@XiaoZikopoulosBarbas09]]).
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