We present a novel two-view geometry estimation framework which is based on a differentiable robust loss function fitting. We propose to treat the robust fundamental matrix estimation as an implicit layer, which allows us to avoid backpropagation through time and significantly improves the numerical stability. To take full advantage of the information from the feature matching stage we incorporate learnable weights that depend on the matching confidences. In this way our solution brings together feature extraction, matching and two-view geometry estimation in a unified end-to-end trainable pipeline. We evaluate our approach on the camera pose estimation task in both outdoor and indoor scenarios. The experiments on several datasets show that the proposed method outperforms both classic and learning-based state-of-the-art methods by a large margin. The project webpage is available at: https://github.com/VladPyatov/ihls