Deep Learning (DL) training platforms are built by interconnecting multiple DL accelerators (e.g., GPU/TPU) via fast, customized interconnects with 100s of gigabytes (GBs) of bandwidth. However, as we identify in this work, driving this bandwidth is quite challenging. This is because there is a pernicious balance between using the accelerator's compute and memory for both DL computations and communication. This work makes two key contributions. First, via real system measurements and detailed modeling, we provide an understanding of compute and memory bandwidth demands for DL compute and comms. Second, we propose a novel DL collective communication accelerator called Accelerator Collectives Engine (ACE) that sits alongside the compute and networking engines at the accelerator endpoint. ACE frees up the endpoint's compute and memory resources for DL compute, which in turn reduces the required memory BW by 3.5X on average to drive the same network BW compared to state-of-the-art baselines. For modern DL workloads and different network sizes, ACE, on average, increases the effective network bandwidth utilization by 1.44X (up to 2.67X), resulting in an average of 1.41X (up to 1.51X), 1.12X (up to 1.17X), and 1.13X (up to 1.19X) speedup in iteration time for ResNet-50, GNMT and DLRM when compared to the best baseline configuration, respectively.