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Deep Neural Networks have gained significant attraction due to their wide applicability in different domains. DNN sizes and training samples are constantly growing, making training of such workloads more challenging. Distributed training is a solution to reduce the training time. High-performance distributed training platforms should leverage multi-dimensional hierarchical networks, which interconnect accelerators through different levels of the network, to dramatically reduce expensive NICs required for the scale-out network. However, it comes at the expense of communication overhead between distributed accelerators to exchange gradients or input/output activation. In order to allow for further scaling of the workloads, communication overhead needs to be minimized. In this paper, we motivate the fact that in training platforms, adding more intermediate network dimensions is beneficial for efficiently mitigating the excessive use of expensive NIC resources. Further, we address different challenges of the DNN training on hierarchical networks. We discuss when designing the interconnect, how to distribute network bandwidth resources across different dimensions in order to (i) maximize BW utilization of all dimensions, and (ii) minimizing the overall training time for the target workload. We then implement a framework that, for a given workload, determines the best network configuration that maximizes performance, or performance-per-cost.