Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

Modern deep learning applications require increasingly more compute to train state-of-the-art models. To address this demand, large corporations and institutions use dedicated High-Performance Computing clusters, whose construction and maintenance are both environmentally costly and well beyond the budget of most organizations. As a result, some research directions become the exclusive domain of a few large industrial and even fewer academic actors. To alleviate this disparity, smaller groups may pool their computational resources and run collaborative experiments that benefit all participants. This paradigm, known as grid-or volunteer computing, has seen successful applications in numerous scientific areas. However, using this approach for machine learning is difficult due to high latency, asymmetric bandwidth, and several challenges unique to volunteer computing. In this work, we carefully analyze these constraints and propose a novel algorithmic framework designed specifically for collaborative training. We demonstrate the effectiveness of our approach for SwAV and ALBERT pretraining in realistic conditions and achieve performance comparable to traditional setups at a fraction of the cost. Finally, we provide a detailed report of successful collaborative language model pretraining with 40 participants.

Self-supervised learning on graphs aims to learn graph representations in an unsupervised manner. While graph contrastive learning (GCL - relying on graph augmentation for creating perturbation views of anchor graphs and maximizing/minimizing similarity for positive/negative pairs) is a popular self-supervised method, it faces challenges in finding label-invariant augmented graphs and determining the exact extent of similarity between sample pairs to be achieved. In this work, we propose an alternative self-supervised solution that (i) goes beyond the label invariance assumption without distinguishing between positive/negative samples, (ii) can calibrate the encoder for preserving not only the structural information inside the graph, but the matching information between different graphs, (iii) learns isometric embeddings that preserve the distance between graphs, a by-product of our objective. Motivated by optimal transport theory, this scheme relies on an observation that the optimal transport plans between node representations at the output space, which measure the matching probability between two distributions, should be consistent with the plans between the corresponding graphs at the input space. The experimental findings include: (i) The plan alignment strategy significantly outperforms the counterpart using the transport distance; (ii) The proposed model shows superior performance using only node attributes as calibration signals, without relying on edge information; (iii) Our model maintains robust results even under high perturbation rates; (iv) Extensive experiments on various benchmarks validate the effectiveness of the proposed method.

In the supplementary material, we describe the domain specific languages used in our experiments (Section 1), demonstrate how the proposed CKY-E2 method works by a concrete example (Section 2.1), show formal properties of CKY-E2 (Section 2.2), present dataset setups and analyze model behaviors (Section 3), and list environmental details for experiments (Section??). In this section, we will present and discuss the domain-specific languages (DSLs) we use for two domains: visual reasoning and language-guided navigation. We will further introduce the neurosymbolic module we have designed for executing programs in these two domains. Overall, each DSL contains a set of types and a set of deterministic modules that have been manually designed for realizing necessary operations in these domains. However, in contrast to realizing them as we do in standard programming languages (with for-loops and if-conditions), we will be using tensor operations (e.g., tensor additions and multiplications) to realize them so that the output of each program is differentiable with respect to all of its inputs. We refer readers to the original papers for a detailed introduction to the DSL and neuro-symbolic program execution. Here we only highlight the key aspects of our language and its neuro-symbolic realization, and discuss the difference between our implementation and the ones in original papers. Our visual reasoning DSL is a subset of CLEVR, containing 6 types and 8 primitive operations. Table 1 illustrates all 6 types and how they are internally represented in neuro-symbolic execution. Table 2 further shows all operations in the DSL. There are two main differences between the DSL used by G2L2 and the original CLEVRDSL.