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We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-to-end training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.

This allows for the use of gradient-based end-to-end training to integrate deep-learning and the classical inverse problem methods.

I still don't see that this derivation gives any additional insight into the problem, however. Partial derivatives: Thanks, I believe some clarifying remarks will make it easier to follow. Deep learning: The main appeal of this paper is that it presents a general mechanism that can be integrated into any gradient-based learning framework. However, the other reviewers have raised legitimate concerns that there are no experiments which demonstrate the approach in an end-to-end setting, and I agree. While you have shown that the stabilised variant works, it has only been demonstrated on relatively shallow problems.

The reviewers agree that there exist some interesting technical details in the paper, but they raise concerns regarding the novelty of the technique and the absence of end-to-end feature learning in some of the experiments. That said, the introduction of the lambda term to regularize the Hessian even though straightforward is likely to lead to more stable meta-learning and non-trivial performance gains. Accordingly I recommend accept as a poster. For the record, I asked for an additional unofficial feedback from another expert in the field and they provided me with the following comments: " I would give it a weak accept. The main contribution seems to be a gradient update wrt to hyperparameters.

We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-to- end training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.

We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-to- end training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.