## 6 Hierarchical Learning with a Context
### Training with Genetic Algorithms and Hierarchical Learning  
The only required change in our Genetic Algorithm is to use the newly introduced hierarchical weighted average instead of the conventional flat one \(\frac{\overrightarrow{w^{\prime}}.\overrightarrow{x}}{\lfloor\overrightarrow{ w^{\prime}}\rVert_{1}}\). For the sake of brevity, we refer to the GA trainings on the flat and hierarchical completion rates as GA-F and GA-H, respectively.  
\begin{table}
\begin{tabular}{c c} \hline \hline
1. & Set microscope \\  & 1.1 & Connect the microscope into the socket \\  & 1.2 & Turn the microscope light on \\  & 1.3 & Set light intensity to two-thirds of maximum \\  & 1.4 & Set iris to fully open \\  & 1.5 & Lift the condenser lens to the top position \\  & 1.6 & Set lens 4X active \\ \hline
2. & Test microscope knobs \\  & 2.1 & Test coarse focus knob \\  & 2.2 & Test fine focus knob \\  & 2.3 & Test stage knob \\  & 2.4 & Test specimen holder knob \\ \hline
3. & Prepare actual microscoping \\  & 3.1 & Put test specimen on stage \\  & 3.2 & Enter microscope mode \\ \hline
4. & Perform actual microscoping \\  & 4.1 & Focus with lens 4X \\  & 4.2 & Focus with lens 10X \\  & 4.3 & Focus with lens 40X \\  & 4.4 & Focus with lens 100X \\ \hline \hline \end{tabular}
\end{table}
Table 2: The 16-step microscoping procedure divided into 4 sub-procedures.  
The results of \"hierarchical training\" (see Figures 14-16) seem to be an improvement over their \"flat\" counterparts (see Figures 7 and 8), as we observe convergence in more trainings and for a wider combinations of parameters.  
However, again, as in the flat weighted average case, the resulting weights are not realistic. For example, in the last example shown in Figure 16, training on expert 1's data sets results in the following weight vector (the weights corresponding to each sub-procedure are included in the first four pair of brackets, while the fifth one consists of the external weights).  
\[<\{1,1.11,1.35,2.85,4.16,1.92\},\]  
\[\{3.45,36.62,1,46.41\},\]  
\[\{1.1,1\},\]  
Figure 14: MSE to generations graphs for GA on hierarchical completion rate—re-substitution on expert 4 (population members: 100, crossover rate: 0.2, mutation rate: 0.3, generic fitness function: inverse, mutation method: doubling of a gene).  
Figure 15: MSE to generations graphs for GA on hierarchical completion rate—training on experts 2, 3, and 4 and testing on expert 1 (population members: 100, crossover rate: 0.5, mutation rate: 0.5, generic fitness function: negative exponential, mutation method: halving of a gene).  
115.96, 1, 11.34, 8.93],  
[3.23, 1, 2, 2.22] >  
The cosine similarity of the latter weight vector to the intuitive one is calculated to be only 35.09%. One also sees a big discrepancy between the weights regarding the sub-procedure of knob testing; testing the specimen holder knob has a weight of 46.41, while the weight for testing the stage knob is 1. Likewise, in the sub-procedure of focusing with the objective lenses, the weight for focusing with the 4X lens is 115.96, while the weights for focusing with any of the other objective lenses range from 1 to 11.34. Last but not least, the external weights have similar values which mistakenly treats all sub-procedures as being roughly equally important.  
As a consequence, we assume that, despite our hierarchical weighted average securing convergence more often than our flat one, it is still not a sufficient model of evaluation. In other words, an overdue deep approach to modelling (hierarchical instead of flat) might be more productive in terms of accuracy but, eventually, less meaningful; i.e., trying to fine tune the performance might deteriorate the level of explainability.