Althoughintuitive,sucha nativelabelassignment strategycannot revealtheunderlying semantic similarity between aquery anditspositivesandnegatives,andimpairs performance, since some negatives are semantically similar to the query or even share the same semantic class as the query.

We propose an adaptive version of the Condat-V u algorithm, which alternates between primal gradient steps anddual proximal steps.

We propose an adaptive version of the Condat-V u algorithm, which alternates between primal gradient steps anddual proximal steps.

According to Theorem 4. 1 in [1], the convergence rate of Adam is We prove Lemma 1 using the framework of online learning with bandit feedback. Let's consider a special case where It follows simply by plugging Lemma 3 into Theorem 2. In the main paper, we compared our method with Adam and Adam with importance sampling. In the main paper, we have shown the plots of loss value vs. wall clock time. Here, we include some plots of error rate vs. wall

Engineering design problems frequently require solving systems of partial differential equations with boundary conditions specified on object geometries in the form of a triangular mesh. These boundary geometries are provided by a designer and are problem dependent. The efficiency of the design process greatly benefits from fast turnaround times when repeatedly solving PDEs on various geometries. However, most current work that uses machine learning to speed up the solution process relies heavily on a fixed parameterization of the geometry, which cannot be changed after training. This severely limits the possibility of reusing a trained model across a variety of design problems. In this work, we propose a novel neural operator architecture which accepts boundary geometry, in the form of triangular meshes, as input and produces an approximate solution to a given PDE as output. Once trained, the model can be used to rapidly estimate the PDE solution over a new geometry, without the need for retraining or representation of the geometry with a pre-specified parameterization.

Results for 3DMatch are shown in Table 1: the performance gain achieved by Compass when deploying theproposed data augmentation validates itsimportance. Indeed, without theproposed augmentation FLARE performs better than Compass on this dataset. This dataset has been specifically proposed to verify the invariance to rotations of the learned 3D descriptors [1], and containsonlyatestsplit. In Figure 2, we consider two pairs of local surface patches and their corresponding feature maps: both patches forming a pair are extracted around the same keypoint on different fragments. The canonical pose computed for the first pair is repeatable, while the second pair represents a failure ofCompass.

This task is commonly addressed by handcrafted algorithms exploiting geometric cues deemed as distinctive and robust by the designer. Yet, one might conjecture that humans learn the notion oftheinherent orientation of3Dobjectsfromexperience andthatmachines may do so alike. In this work, we show the feasibility of learning a robust canonical orientation for surfaces represented as point clouds.