Deep learning for recommendation data is one of the most pervasive and challenging AI workload in recent times. State-of-the-art recommendation models are one of the largest models matching the likes of GPT-3 and Switch Transformer. Challenges in deep learning recommendation models (DLRM) stem from learning dense embeddings for each of the categorical tokens. These embedding tables in industrial scale models can be as large as hundreds of terabytes. Such large models lead to a plethora of engineering challenges, not to mention prohibitive communication overheads, and slower training and inference times. Of these, slower inference time directly impacts user experience. Model compression for DLRM is gaining traction and the community has recently shown impressive compression results. In this paper, we present Random Offset Block Embedding Array (ROBE) as a low memory alternative to embedding tables which provide orders of magnitude reduction in memory usage while maintaining accuracy and boosting execution speed. ROBE is a simple fundamental approach in improving both cache performance and the variance of randomized hashing, which could be of independent interest in itself. We demonstrate that we can successfully train DLRM models with same accuracy while using $1000 \times$ less memory. A $1000\times$ compressed model directly results in faster inference without any engineering effort. In particular, we show that we can train DLRM model using ROBE array of size 100MB on a single GPU to achieve AUC of 0.8025 or higher as required by official MLPerf CriteoTB benchmark DLRM model of 100GB while achieving about $3.1\times$ (209\%) improvement in inference throughput.