Title: IQNAS: Interpretable Integer Quadratic programming Neural Architecture Search. Abstract: Realistic use of neural networks often requires adhering to multiple constraints on latency, energy and memory among others. A popular approach to find fitting networks is through constrained Neural Architecture Search (NAS). However, previous methods use complicated predictors for the accuracy of the network. Those predictors are hard to interpret and sensitive to many hyperparameters to be tuned, hence, the resulting accuracy of the generated models is often harmed.  In this work we resolve this by introducing Interpretable Integer Quadratic programming Neural Architecture Search (IQNAS), that is based on an accurate and simple quadratic formulation of both the accuracy predictor and the expected resource requirement, together with a scalable search method with theoretical guarantees. The simplicity of our proposed predictor together with the intuitive way it is constructed bring interpretability through many insights about the contribution of different design choices.  For example, we find that in the examined search space, adding depth and width is more effective at deeper stages of the network and at the beginning of each resolution stage. Our experiments show that IQNAS generates comparable to or better architectures than other state-of-the-art NAS methods within a reduced search cost for each additional generated network, while strictly satisfying the resource constraints.