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The {\it straight-through estimator} (STE) is commonly used to optimizequantized neural networks, yet its contexts of effective performance are stillunclear despite empirical successes.To make a step forward in thiscomprehension, we apply STE to a well-understood problem: {\it sparse supportrecovery}. We introduce the {\it Support Exploration Algorithm} (SEA), a novelalgorithm promoting sparsity, and we analyze its performance in supportrecovery (a.k.a. model selection) problems. SEA explores more supports than thestate-of-the-art, leading to superior performance in experiments, especiallywhen the columns of $A$ are strongly coherent.The theoretical analysisconsiders recovery guarantees when the linear measurements matrix $A$ satisfiesthe {\it Restricted Isometry Property} (RIP).The sufficient conditions ofrecovery are comparable but more stringent than those of the state-of-the-artin sparse support recovery. Their significance lies mainly in theirapplicability to an instance of the STE.

Straight-Through meets Sparse Recovery: the Support Exploration Algorithm