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Widely popular transformer-based NLP models such as BERT and Turing-NLG have enormous capacity trending to billions of parameters. Current execution methods demand brute-force resources such as HBM devices and high speed interconnectivity for data parallelism. In this paper, we introduce a new relay-style execution technique called L2L (layer-to-layer) where at any given moment, the device memory is primarily populated only with the executing layer(s)'s footprint. The model resides in the DRAM memory attached to either a CPU or an FPGA as an entity we call eager param-server (EPS). To overcome the bandwidth issues of shuttling parameters to and from EPS, the model is executed a layer at a time across many micro-batches instead of the conventional method of minibatches over whole model. L2L is implemented using 16GB V100 devices for BERT-Large running it with a device batch size of up to 256. Our results show 45% reduction in memory and 40% increase in the throughput compared to the state-of-the-art baseline. L2L is also able to fit models up to 50 Billion parameters on a machine with a single 16GB V100 and 512GB CPU memory and without requiring any model partitioning. L2L scales to arbitrary depth allowing researchers to develop on affordable devices which is a big step toward democratizing AI. By running the optimizer in the host EPS, we show a new form of mixed precision for faster throughput and convergence. In addition, the EPS enables dynamic neural architecture approaches by varying layers across iterations. Finally, we also propose and demonstrate a constant memory variation of L2L and we propose future enhancements. This work has been performed on GPUs first, but also targeted towards all high TFLOPS/Watt accelerators.