Despite its popularity in practice, theoretical guarantees for high-dimensional problems are only available under strong structural assumptions (e.g., sparsity).

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple alternating (implicit) gradient-based algorithms can match the convergence rate of single-level gradient descent (GD) when addressing bilevel problems with a strongly convex lower-level objective. However, it remains unclear whether this result can be generalized to bilevel problems beyond this basic setting.

To address these shortcomings, we introduce a pioneering technique that replaces the spatial model with a topological one within the RANSAC process.

Text-to-Query systems have surprisingly not been investigated so far.

We illustrate the architecture in Figure 1 in the main paper. We use a kernel size of 5. This is essentially an equivariant version of LayerNorm. In the geometric layers, the input state is split into scalar and vector components. The vector components are linearly transformed to reduce the number of channels to 16.

We integrate this model in a planning loop, where conditioning and classifier guidance let us softly break the symmetry for specific tasks as needed.

In this paper, we study the same problem in the Massart noise model that we now define.