In this section, we discuss about the training of ACDC model with eight different motor sequence. After trained this network, we extract the temporal signature and analysis various temporal properties such as time shifting, time re-scaling, time compositionality, and trained with completely new motor sequence. To perform this analysis, we adopt following experimental setup.
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CMPE 691 Neural Engineering and Instrumentation
Experimental setup and data set
As mentioned before, we adopt Thunderstruck data set from “The ACDC model of flexible sequences and rhythms in recurrent neural circuits”. We carry out the software training and testing using python framework in AMD® Ryzen(R) 7 5700G CPU. Later, we perform data curation and figure analysis in Matlab® academic edition R2022a.
As aforementioned, we choose eight different motor input sequences as this [200 300 400 500 600 700 800] ms array. Since, we train ACDC model with eight different motor sequence, we employ eight A neurons in thalamus unit, eight G and N neurons in basal ganglia unit, and 200 excitatory neurons in RNN clusters. We carry out the learnig sequence for 1000 ms and 1500 epochs for learning evolution. As mentioned before, we employ Hebbian learninig for RNN-G connectivity and delta learning for G-A conectivity.
Input asserted to the ACDC network
Figure 1: Input to the ACDC network
As mentioned before, we adopt eight different motor sequences such that [200 300 400 500 600 700 800 900] ms as illustrated in Fig. 1. These inputs are fed to RNN clusters to generate the action sequence.
RNN cluster dynamics with time
Figure 2: RNN excitatory neurons changing with time
After providing the sequential motor input, the RNN clusters begin to learn these action sequence with the help of Hebbian learning and therefore, with the number of training epoch the accuracy increase. It is to be noted that, we divided total 200 excitatory neurons into 10 clusters each of having 20 excitatory neurons. As illustrated in Fig. 2, with each of the input motor sequence, 20 random excitatory neuron from the RNN cluster potentiate to hold this pattern, which later project to the G gate neurons.
RNN confusion matrix with time
Figure 3: Connectivity of RNN indices
Then, we analyze the effect on RNN dynamics with number of epochs. As illustrated in Fig. 3, we formulate a confusion matrix with number of trials. It visualizes how the input action sequences change RNN weight matrix and how they become saturated with time. Later, we extract this weight matrix for our temporal analysis.
RNN to G neuron dynamics
Figure 4: RNN to G neurons connectivity
Now, after the excitatory clusters trained by the input sequence, it projects the information to corresponding G gate neurons in the basal ganglia unit. As illustrated in Fig. 4, after training each RNN clusters project to the corresponding G index. As mentioned before, these weights are not hardware rather trained through the Hebbian learning.
G neurons activation with time
Figure 5: G nodes activity with time
After the training with the RNN projection, the G neurons of basal ganglia mimic the input action sequence successfully. It is illustrated from the Fig. 5 that, after a RNN cluster project to a corresponding G neurons, they experience maximum activation threshold. For each motor action sequence, one corresponding G neuron triggers the next level of A neurons.
G-A neurons connectivity with time
Figure 6: Connection between G and A nodes with time
After successfully learned the input sequence by the G neuron, it projects the information to the corresponding A neuron in thalamus. AS illustrated in the Fig. 6, each of the G neuron is responsible for activating the corresponding A neuron. It is to be noted that, both G and A neurons are non-linear gated neuron with Tanh activation function. As mentioned earlier, we employ delta rule to establish the correspondence between these G-A pairs.
A neuron activation with time
Figure 7: A neurons activity with time
After the training, it is illustrated from the Fig. 7 that, all the input motor sequences are successfully captured by the A units. After completing 1500 epoch of training, we find the miss-match error 0.002 compared with our input as illustrated in Fig. 1, which proves the efficacy of the trained model.
A-RNN activation with time
Figure 8: Connection between RNN and A neurons with time
As mentioned before, the A neurons in thalamus act as an hub, which control all the three different module such as next excitatory cluster in RNN module, N neurons for inhibition on basal ganglia unit, shared inhibitory cluster present in the RNN unit. In Fig. 8, we demonstrate the connectivity for A-RNN next excitatory cluster. It is to be noted that since the next cluster which will be activated by the A neurons are fixed, the weight remain same through out the training.
N neurons activation with time
Figure 9: Activation of N neurons with time
As mentioned above, another connection originated from A unit is A-N connectivity, which inhibits the corresponding G neuron in order to ensure only one sequence should be learned at a precised time and other G neurons remain inactive. This inhibition by N unit is very essential to remove pathological unstable dynamics, which hampers sequential action learning in basal-thalamus unit. Fig. 9, show the activation of the N unit. For instance, we know the first motor sequence comes at 200 ms, which potentiate G and A units and then A unit fully activates it sends inhibition to corresponding G unit, hence the action 1 inhibit G-1.
A to inhibitory neurons dynamics with time and epoch
Figure 10: Inhibitory neuron changes with time
This is the third connectivity generates from the A neurons of thalamus unit. This connectivity is hardware (i.e. fixed over time) however, need to control by the A unit in order to provide essential inhibition in RNN clusters in order to prevent unwanted dynamics and ensure a winner takes all architecture.
Learning a precisely timed motor sequence after training
Figure 11: Learning a fixed timed motor sequence
In Fig. 11, we show the learning of all the precise input motor sequence by the A neurons. Here, each A neuron of thalamus i progressively shifted towards the optimal action time, which is depicted by the color coded vertical dashed line and the corresponding time represents by the x-axis. Learning progresses from darker to brightest colors with number of epoch.
Learning curve with epoch
Figure 12: Error mitigation with number of trials
The learning dynamics of thee ACDC model with number of trial is illustrated in Fig. 12. We can see that error is decreasing with the number of epoch, which demonstrate the efficacy of our our model with respect to epoch.
Successfully reproduced previous learned sequence
Figure 13: Reproducing previous sequence with time
After successfully learning the input sequence, the model can retain the learning. So later, the model successfully reproduce the previous learned sequence with respect to time which is illustrated in Fig. 13.
Successfully reproduced previous learned sequence
Figure 14: Reproducing previous sequence with epoch
Once the model has learned the input sequence, it does not produce new sequence. It actually retains the learned the sequence which is bolstered by the Fig. 14. Here, we can see that A neurons activation is not changing with epoch.
Temporal shifting (early) by 100 ms
Figure 15:Temporal shifting early
The model can shifting the action early by 100 ms after successfully learned the input sequence which is illustrated in Fig. 15. We can see that precisely timed action sequence can be started earlier by injecting an additional positive input to the first G neurons but the temporal structure of the action sequence is not altered.
Temporal shifting (late) by 100 ms
Figure 16:Temporal shifting right
The model can shifting the action late by 100 ms after successfully learned the input sequence which is illustrated in Fig. 16. We can see that Precisely timed action sequences can be started later by injecting an additional negative input to the first G neurons but the temporal structure of the action sequence is not altered.
Temporal compressing with ratio 1:0.8
Figure 17:Temporal compressing
The model can compress the action by 0.8 after successfully learned the input sequence which is illustrated in Fig. 17. Action sequences can be compressed by adding a multiplicative input to all G neurons simultaneously. We can see that the sequence is not changing but it seems that it starts earlier due to compression.
Temporal dilating with ratio 1:1.2
Figure 18:Temporal dilating
The model can dilate the action by 1.2 after successfully learned the input sequence which is illustrated in Fig. 18. Action sequences can be dilated by adding a multiplicative input to all G neurons simultaneously. We can see that the sequence is not changing but it seems that it starts later due to dilation.
Temporal compositionality with five motor action
Figure 19:Temporal compositionality with five motors
The model can learn the action for five motor action after successfully learned the input sequence which is illustrated in Fig. 19. We can see five A neurons activity are activated on the tempo described by the multiplicative signal.
Multiplicative gain signal (Sustained Motor Action)
Figure 20: Gain signal by multiplicative
It is demonstrated in Fig. 20 that the ACDC model is able to output sustained motor activation as desired within a sequence. We can see the results of applying a multiplicative signal to the second N G neurons, inducing a sustained activation of the second action and sixth action which is colored red and yellow respectively.
Learning weight (Sustained Motor Action)
Figure 21: Gain signal by updating weight
It is depicted in Fig. 21 that ACDC model is able to output sustained motor activation as desired within a sequence. We can see the results of applying a multiplicative signal to the third and seventh N G neurons, inducing a sustained activation of the third and seventh action which is colored purple and black.
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