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Understanding the semantic meaning of tabular data requires Entity Linking (EL), in order to associate each cell value to a real-world entity in a Knowledge Base (KB). In this work, we focus on end-to-end solutions for EL on tabular data that do not rely on fact lookup in the target KB. Tabular data contains heterogeneous and sparse context, including column headers, cell values and table captions. We experiment with various models to generate a vector representation for each cell value to be linked. Our results show that it is critical to apply an attention mechanism as well as an attention mask, so that the model can only attend to the most relevant context and avoid information dilution. The most relevant context includes: same-row cells, same-column cells, headers and caption. Computational complexity, however, grows quadratically with the size of tabular data for such a complex model. We achieve constant memory usage by introducing a Tabular Entity Linking Lite model (TELL ) that generates vector representation for a cell based only on its value, the table headers and the table caption. TELL achieves 80.8% accuracy on Wikipedia tables, which is only 0.1% lower than the state-of-the-art model with quadratic memory usage.