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Parallel Tensor Train through Hierarchical Decomposition

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Fig. 1: Splitting of dimensions in TT and PTT decompositions for a d- d-dimensional tensor
Figure 2 exhibits that the above expression can also be represented graphi- graphi-cally by a linear chain where sum over circle nodes (indices α k ) are assumed to compute an entry of the tensor
Fig. 4: Diagramatic representation of unfolding matrices at all non-leaf nodes for a 6-dimensional tensor by Algorithm 1.
Table 1: Summary of all considered approaches.
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