Numerical validation is at the core of machine learning research as it allows us to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automatize, publish and reproduce optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard ML tasks: $\ell_2$-regularized logistic regression, Lasso and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details.

A natural way to model the evolution of an object (growth of a leaf for instance) is to estimate a plausible deforming path between two observations. This interpolation process can generate deceiving results when the set of considered deformations is not relevant to the observed data. To overcome this issue, the framework of deformation modules allows to incorporate in the model structured deformation patterns coming from prior knowledge on the data. The goal of this article is twofold. First defining new deformation modules incorporating structures coming from the elastic properties of the objects. Second, presenting the IMODAL library allowing to perform registration through structured deformations. This library is modular: adapted priors can be easily defined by the user, several priors can be combined into a global one and various types of data can be considered such as curves, meshes or images. It can be downloaded at https://github.com/imodal.

The KeOps library provides a fast and memory-efficient GPU support for tensors whose entries are given by a mathematical formula, such as kernel and distance matrices. KeOps alleviates the main bottleneck of tensor-centric libraries for kernel and geometric applications: memory consumption. It also supports automatic differentiation and outperforms standard GPU baselines, including PyTorch CUDA tensors or the Halide and TVM libraries. KeOps combines optimized C++/CUDA schemes with binders for high-level languages: Python (Numpy and PyTorch), Matlab and GNU R. As a result, high-level “quadratic” codes can now scale up to large data sets with millions of samples processed in seconds. KeOps brings graphics-like performances for kernel methods and is freely available on standard repositories (PyPi, CRAN). To showcase its versatility, we provide tutorials in a wide range of settings online at www.kernel-operations.io.

Geometric methods rely on tensors that can be encoded using a symbolic formula and data arrays, such as kernel and distance matrices. We present an extension for standard machine learning frameworks that provides comprehensive support for this abstraction on CPUs and GPUs: our toolbox combines a versatile, transparent user interface with fast runtimes and low memory usage. Unlike general purpose acceleration frameworks such as XLA, our library turns generic Python code into binaries whose performances are competitive with state-of-the-art geometric libraries - such as FAISS for nearest neighbor search - with the added benefit of flexibility. We perform an extensive evaluation on a broad class of problems: Gaussian modelling, K-nearest neighbors search, geometric deep learning, non-Euclidean embeddings and optimal transport theory. In practice, for geometric problems that involve 1k to 1M samples in dimension 1 to 100, our library speeds up baseline GPU implementations by up to two orders of magnitude.

This paper introduces a general setting for the construction of data fidelity metrics between oriented or non-oriented geometric shapes like curves, curve sets or surfaces. These metrics are based on the representation of shapes as distributions of their local tangent or normal vectors and the definition of reproducing kernels on these spaces. The construction, that combines in one common setting and extends the previous frameworks of currents and varifolds, provides a very large class of kernel metrics which can be easily computed without requiring any kind of parametrization of shapes and which are smooth enough to give robustness to certain imperfections that could result e.g. from bad segmentation. We then give a sense, with synthetic examples, of the versatility and potentialities of such metrics when used in various problems like shape comparison, clustering and diffeomorphic registration.