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Page 413 Yang et al. Intell Robot 2024;4(4):406-21 I http://dx.doi.org/10.20517/ir.2024.24

Figure 2. Structure of TSA detection model. TSA: Time synchronization attack.

Where each sub-component of the data encapsulated in the capsule is subjected to positional encoding. This
ensures that the prediction includes the correlation between the input data’s amplitude and positional phase.
In other words, the prediction captures the correlation between the amplitude and phase of the actual input
data. Using the measured value as an example, the corresponding peak value in the complex wave is simplified,
and the positional encoding data is expressed. The predictive measurement after encoding is given by:

(17)
ˆ | = × + |
ˆ | = × + |

ˆ | = ˆ | , ˆ | (18)
Where ˆ | is the contribution of the child capsule to the father capsule . Assuming that a child capsule

provides input, based on dynamic routing, the contribution from the latent parent capsule is derived as follows:

Õ

= ˆ | , ∈ {1, . . . , } (19)

∥ ∥
= ( ) = ℎ( ) = · (20)
2
1 + ∥ ∥ ∥ ∥
Where ( ) is a non-linear activation function. The iterative update of the selection coefficient uses the
function, expressed as:

= | (21)

The parent capsule is the result of a non-linear compression and normalization of the weighted sum of
predictedvectors, andtheexistenceprobabilityoftheparentcapsuleisexpressedas ∥ ∥ . Theparentcapsule’s
2
prediction is regularized using dynamic routing with iterative weighted averaging and non-linear compression.
The iterative value of | is updated as:

| = | + ˆ | · (22)