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@ -75,60 +75,43 @@ Assume the input is a step function, $I(t)=I_0$ for $t<0$ and $I(t)=I_1$ for $t\
Insert the solution of the DEQ for the inhibitory unit into the DEQ for the excitatory unit. You have now simplified the system to only one DEQ - super!
## ADV 5. Fit the **DivInE**-model to physiological data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\task{ADV-\#5}{Fit the \emph{DivInE}-model to physiological data}
How well can our circuit quantitatively fit physiological data? Let's find out! We provide you with population data from macaque area MT, and your task will be to fit the model to the data.
\goal{Learn how to setup objective functions, implement some simple fitting procedures, learn about gradient descent and other methods...}
### a.
We provide you with a file in which we stored eight neural response functions to a stimulus change (acceleration and deceleration of a moving grating). The stimulus change happened at time $t=0$, see the time axis stored in the same file.
How well can our circuit quantitatively fit physiological data? Let's find out! We provide you with population data from macaque area MT (thanks to Detlef Wegener!), and your task will be to fit the model to the data.
### b.
Fit the model output to the physiological response, as best as possible. In the following, we will give you some tips and tricks how this could be done:
\vspace*{-0.3cm}\begin{enumerate}[a)]
\item We provide you with a file in which we stored eight neural response functions to a stimulus change (acceleration and deceleration of a moving grating). The stimulus change happened at time $t=0$, see the time axis stored in the same file.
\item Fit the model output to the physiological response, as best as possible. In the following, we will give you some tips and tricks how this could be done:
\begin{itemize}
\item From the analysis performed above, you know that for an input step (which is comparable to the experimental situation here), you only need one DEQ.
\item Now it is a good idea to get rid of as many free parameters as possible: From the physiological traces you can see that before and after the stimulus change, the activity settles into a stationary state, say $A_e^0$ and $A_e^1$. You can extract these values directly from the experimental data.
\item You can now rewrite the DEQ by using the new parameters $A_e^0$ and $A_e^1$, and the maximum activation $A_e^{max}$, to get rid of the parameters $m_e, m_i, I$ and $B$. This leaves you with only three parameters to fit.
\item For performing the fit, you have to define an objective function which evaluates how close your fit to the original data is. For example, the mean quadratic distance between model and physiological traces.
\item Inform yourself about different methods for optimizing an objective function with respect to a set of free parameters. For example, grid search or (stochastic) gradient descent. Understand also the caveats of these methods!
\item Take care of delays in the physiological response, the stimulus signal needs some time to travel to area MT!
\end{itemize}
\end{enumerate}
* From the analysis performed above, you know that for an input step (which is comparable to the experimental situation here), you only need one DEQ.
* Now it is a good idea to get rid of as many free parameters as possible: From the physiological traces you can see that before and after the stimulus change, the activity settles into a stationary state, say $A_e^0$ and $A_e^1$. You can extract these values directly from the experimental data.
* You can now rewrite the DEQ by using the new parameters $A_e^0$ and $A_e^1$, and the maximum activation $A_e^{max}$, to get rid of the parameters $m_e, m_i, I$ and $B$. This leaves you with only three parameters to fit.
* For performing the fit, you have to define an objective function which evaluates how close your fit to the original data is. For example, the mean quadratic distance between model and physiological traces.
* Inform yourself about different methods for optimizing an objective function with respect to a set of free parameters. For example, grid search or (stochastic) gradient descent. Understand also the caveats of these methods!
* Take care of delays in the physiological response, the stimulus signal needs some time to travel to area MT!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\task{ADV-\#6}{The \emph{DivInE}-model and attention}
\goal{That's for good students, the tasks are less specific and leave lots of room for exploring own ideas...}
## ADV 6. The **DivInE**-model and attention
Attention serves to enhance neural responses to selected stimuli relative to representations of unattended stimuli. Hereby divisive inhibition seems to play a central role as a control mechanism -- several studies in our lab are currently investigating corresponding effects. If you are interested in learning more about these studies, and extend your project in that direction, we offer you two possibilites (talk to your tutor for receiving detailed guidance and instructions). Ref. [2] tells you more about attention can be introduced in your model.
\vspace*{-0.3cm}\begin{enumerate}[a)]
\item \textbf{Divisive normalization enhances transients [4]:} How does attention enhance transient responses? You can investigate this numerically in your model, and compare it to the MT data we provide for you. We recommend you to have a look at three typical features of a neural response to a current step: the change in sustained response, the relative peak response, and the initial increase of the transient. What do you observe? How would you investigate corresponding effects systematically?
\item \textbf{Divisive normalization increases working range of selective attention [5]:} When two stimuli are in the receptive field of a cortical neuron, and one of those stimuli is attended, the cell responds as if only the attended stimulus was present. Most probably, the brain achieves this effect by generating a small rate advantage in the presynaptic population driven by the attended stimulus, which is amplified by recurrent processes for effectively routing only the attended signal to postsynaptic circuits. However, this mechanism is challenged if the attended stimulus provides a much weaker input drive than the non-attended stimulus. How could selective processing still work? One potential answer is that divisive normalization increases the 'working range' over which a rate advantage for the attended stimulus is created. You can easily investigate this effect by simulating two coupled DivInE-circuits.
\end{enumerate}
### a.
**Divisive normalization enhances transients [4]:** How does attention enhance transient responses? You can investigate this numerically in your model, and compare it to the MT data we provide for you. We recommend you to have a look at three typical features of a neural response to a current step: the change in sustained response, the relative peak response, and the initial increase of the transient. What do you observe? How would you investigate corresponding effects systematically?
### b.
**Divisive normalization increases working range of selective attention [5]:** When two stimuli are in the receptive field of a cortical neuron, and one of those stimuli is attended, the cell responds as if only the attended stimulus was present. Most probably, the brain achieves this effect by generating a small rate advantage in the presynaptic population driven by the attended stimulus, which is amplified by recurrent processes for effectively routing only the attended signal to postsynaptic circuits. However, this mechanism is challenged if the attended stimulus provides a much weaker input drive than the non-attended stimulus. How could selective processing still work? One potential answer is that divisive normalization increases the 'working range' over which a rate advantage for the attended stimulus is created. You can easily investigate this effect by simulating two coupled DivInE-circuits.
% In this project, you will simulate this simple circuit and understand its dynamical properties analytically. You might then embed the circuit in a small network of similar units (a 'ring' model), and/or fit your model to physiological data recorded in monkey area MT.%\textbf{Extension to a Ring Model}
%\vspace*{-0.3cm}\begin{enumerate}[a)]
%\item The model provides a good fit for MT neurons that are driven with its preferred stimulus, i.e. with a grating moving into their preferred direction. Now we want to understand the dynamics of a population of MT neurons. Sketch a network circuit in which you replicate the DivInE-model and connect the units laterally, like in the ring model [1]. For the lateral connections, assume they implement a global divisive inhibition to the individual excitatory units.
%\item Implement the ring model and apply a 'tuned' input, i.e. an input which is maximal at the unit which has the same preferred direction as the current stimulus, and which falls off with distance between preferred direction and actual stimulus direction (you can assume a Gaussian dependence or take a von-Mises function). Simulate the network and characterize its behaviour to input steps with varying strength of the inhibitory feedback.
%\item If you wish, you can again compare the activation dynamics of your model to experimental data -- ask your tutor!
%\end{enumerate}
## Literature
[1] Carandini, M., \& Heeger, D. J. (2011). **Normalization as a canonical neural computation.** *Nat Rev Neurosci.* ; 13(1): 51–62. doi:10.1038/nrn3136.
% \textbf{Literature}
[2] Reynolds, J. H., \& Heeger, D. J. (2009). **The normalization model of attention.** *Neuron*, 61(2), 168–185. https://doi.org/10.1016/j.neuron.2009.01.002
% [1] Ben-Yishai, R., Bar-Or, R. L., and Sompolinsky, H. (1995). \textbf{Theory of orientation tuning in visual cortex.} Proceedings of the National Academy of Sciences of the United States of America, 92(9), 3844-3848.
[3] Traschütz A., Kreiter A. K., \& Wegener D. (2015). **Transient activity in monkey area MT represents speed changes and is correlated with human behavioral performance.** *J Neurophysiol.* 113: 890-903.
\literature{
[1] Carandini, M., \& Heeger, D. J. (2011). Normalization as a canonical neural computation. Nat Rev Neurosci. ; 13(1): 51–62. doi:10.1038/nrn3136.
[4] Ernst, U., Chen, X., Bohnenkamp, L., Galashan, F. O., \& Wegener, D. (2020). **A simple canonical circuitry for non-stationary normalization by inhibition to explain and predict change detection in monkey area MT.** In preparation.
[2] Reynolds, J. H., \& Heeger, D. J. (2009). The normalization model of attention. Neuron, 61(2), 168–185. https://doi.org/10.1016/j.neuron.2009.01.002
[5] Rausch, L.-P., Schünemann, M., Drebitz, E., Harnack, D., Kreiter, A. K., \& Ernst, U. (2020) **Strong attentional modulation of V1/V2 activity implements a robust, contrast-invariant control mechanism for selective information processing.** In preparation.
[3] Trasch\"utz A., Kreiter A. K., \& Wegener D. (2015). Transient activity in monkey area MT represents speed changes and is correlated with human behavioral performance. J Neurophysiol. 113: 890-903.
[4] Ernst, U., Chen, X., Bohnenkamp, L., Galashan, F. O., \& Wegener, D. (2020). A simple canonical circuitry for non-stationary normalization by inhibition to explain and predict change detection in monkey area MT. In preparation.
[5] Rausch, L.-P., Schünemann, M., Drebitz, E., Harnack, D., Kreiter, A. K., \& Ernst, U. (2020) Strong attentional modulation of V1/V2 activity implements a robust, contrast-invariant control mechanism for selective information processing. In preparation.
}