Sleep prevents catastrophic forgetting in spiking neural networks by forming joint synaptic weight representations — part 5/5

Cleaned-text code points [61189, 65199). Bibliography omitted here; source.md includes it.

A support vector machine with a radial basis function kernel was trained to classify synaptic weight configurations as being related to Task 1 or Task 2. Labeled training data were obtained by taking the excitatory synaptic weight matrices between the hidden and output layers from the last fifth of the Task 1 and Task 2 training phases (i.e. after performance had appeared to asymptote). These synaptic weight matrices were then flattened into column vectors, and the column vectors were concatenated to form a training data matrix of size number of features x number of samples. The number of features was equal to the total number of excitatory synapses between the hidden and output layer – 6272 dimensions. We then used this support vector machine to classify held out synaptic weight configurations from Task 1 and Task 2 training, as well as ones which resulted from Interleaved T1,T2 and Interleaved S,T1 training.

#### 2-D Synaptic Weight distributions (Figure 6)

First for each synapse we found how its synaptic strength changes between two slices in time, where the given synapse’s strength at time slice 1 is the point’s X-value and strength at time slice 2 is its Y-value. Then we binned this space and counted synapses in each bin to make two dimensional histograms where blue color corresponds to a single synapse found in a bin and brown corresponds to the max of 50 synapses. These two-dimensional histograms assist in visualizing the movement of all synapses between the two slices in time that are specified by the timelines at the top of each plot. Conceptually, it is important to note that if a synapse does not change in strength between time slice 1 and time slice 2, then point the synapse corresponds to in this space will lie on the diagonal of the plot since the X-value will match the Y-value. If a great change in the synapse’s strength has occurred between time slice 1 and time slice 2, then the synapse’s corresponding point will lie far from the diagonal since the X-value will be distant from the Y-value. The points on the X-(Y-) axis represent synapses that lost (gained) all synaptic strength between time slice 1 and time slice 2.

#### Distance from Solution Manifolds (Figure 7)

Each of the two solution manifolds (i.e. Task 1 and Task 2 specific manifolds) were defined by the point-sets in synaptic weight space which were capable of supporting robust performance on that particular task, namely the sets M T1 and M T2 . This included the synaptic weight states from the last fifth of training on a particular task (i.e. after performance on that task appeared to asymptote) and all of the synaptic weight states from the last fifth of both Interleaved T1,T2 and Interleaved S,T1/T2 training. The intersection of the two solution manifolds (i.e. the point-set M T1∩T2 ) was defined solely by the synaptic weight states from the last fifth of both Interleaved T1,T2 and Interleaved S,T1 training. As the network evolved along its trajectory in synaptic weight space, the distance from the current point in synaptic weight space, p t , to the two solution manifolds and their intersection were computed as follows:

Here, d n is the n-dimensional Euclidean-distance function, where n is the dimensionality of synaptic weight space (i.e. n = 6272 here), M τ is the point-set specific to the manifold or intersection in question (i.e. either M T1 , M T2 , or M T1⋉T2 ), and x is a particular element of the point-set M .

## Author Contributions

J.E.D. carried out experiments; J.E.D conducted computational analyses; R.G. designed experiments; R.G. and J.E.D. designed analysis approaches; R.G., J.E.D., P.S., and M.B. interpreted data; R.G., P.S., and M.B. conceived the project; R.G. and M.B. wrote the majority of the paper. All authors commented on and contributed to the paper.

## Conflicts of Interest

None.

## Acknowledgements

This study was supported by Lifelong Learning Machines program from DARPA/MTO (HR0011-18-2-0021) and ONR MURI (N000141612829)