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We present a logic based interpretable model for learning on graphs and an algorithm to distill this model from a Graph Neural Network (GNN). Recent results have shown connections between the expressivity of GNNs and the two-variable fragment of first-order logic with counting quantifiers (C2). We introduce a decision-tree based model which leverages an extension of C2 to distill interpretable logical classifiers from GNNs. We test our approach on multiple GNN architectures. The distilled models are interpretable, succinct, and attain similar accuracy to the underlying GNN. Furthermore, when the ground truth is expressible in C2, our approach outperforms the GNN., Comment: To Appear in the Proceedings of KR 2024

The field of deep generative modeling has grown rapidly and consistently over the years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models do not sufficiently address several fundamental issues that hinder their widespread adoption across domains. In this work, we aim to identify key unresolved challenges in modern generative AI paradigms that should be tackled to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with valuable insights for exploring fruitful research directions, thereby fostering the development of more robust and accessible generative AI solutions.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks., Comment: accepted for publication at ICML 2023

Mixture of experts (MoE), introduced over 20 years ago, is the simplest gated modular neural network architecture. There is renewed interest in MoE because the conditional computation allows only parts of the network to be used during each inference, as was recently demonstrated in large scale natural language processing models. MoE is also of potential interest for continual learning, as experts may be reused for new tasks, and new experts introduced. The gate in the MoE architecture learns task decompositions and individual experts learn simpler functions appropriate to the gate's decomposition. In this paper: (1) we show that the original MoE architecture and its training method do not guarantee intuitive task decompositions and good expert utilization, indeed they can fail spectacularly even for simple data such as MNIST and FashionMNIST; (2) we introduce a novel gating architecture, similar to attention, that improves performance and results in a lower entropy task decomposition; and (3) we introduce a novel data-driven regularization that improves expert specialization. We empirically validate our methods on MNIST, FashionMNIST and CIFAR-100 datasets., Comment: 14 pages including appendix

Self-supervised learning methods have witnessed a recent surge of interest after proving successful in multiple application fields. In this work, we leverage these techniques, and we propose 3D versions for five different self-supervised methods, in the form of proxy tasks. Our methods facilitate neural network feature learning from unlabeled 3D images, aiming to reduce the required cost for expert annotation. The developed algorithms are 3D Contrastive Predictive Coding, 3D Rotation prediction, 3D Jigsaw puzzles, Relative 3D patch location, and 3D Exemplar networks. Our experiments show that pretraining models with our 3D tasks yields more powerful semantic representations, and enables solving downstream tasks more accurately and efficiently, compared to training the models from scratch and to pretraining them on 2D slices. We demonstrate the effectiveness of our methods on three downstream tasks from the medical imaging domain: i) Brain Tumor Segmentation from 3D MRI, ii) Pancreas Tumor Segmentation from 3D CT, and iii) Diabetic Retinopathy Detection from 2D Fundus images. In each task, we assess the gains in data-efficiency, performance, and speed of convergence. Interestingly, we also find gains when transferring the learned representations, by our methods, from a large unlabeled 3D corpus to a small downstream-specific dataset. We achieve results competitive to state-of-the-art solutions at a fraction of the computational expense. We publish our implementations for the developed algorithms (both 3D and 2D versions) as an open-source library, in an effort to allow other researchers to apply and extend our methods on their datasets., Comment: Proceedings of NeurIPS 2020 (Please cite the proceedings version). For source code, see https://github.com/HealthML/self-supervised-3d-tasks

We propose a novel transfer learning approach for orphan screening called corresponding projections. In orphan screening the learning task is to predict the binding affinities of compounds to an orphan protein, i.e., one for which no training data is available. The identification of compounds with high affinity is a central concern in medicine since it can be used for drug discovery and design. Given a set of prediction models for proteins with labelled training data and a similarity between the proteins, corresponding projections constructs a model for the orphan protein from them such that the similarity between models resembles the one between proteins. Under the assumption that the similarity resemblance holds, we derive an efficient algorithm for kernel methods. We empirically show that the approach outperforms the state-of-the-art in orphan screening., Comment: Machine Learning for Health (ML4H) Workshop at NeurIPS 2018 arXiv:cs/0101200

We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other parallelisation techniques, it can be applied to a broad class of learning algorithms without further mathematical derivations and without writing dedicated code, while at the same time maintaining theoretical performance guarantees. Moreover, our parallelisation scheme is able to reduce the runtime of many learning algorithms to polylogarithmic time on quasi-polynomially many processing units. This is a significant step towards a general answer to an open question on the efficient parallelisation of machine learning algorithms in the sense of Nick's Class (NC). The cost of this parallelisation is in the form of a larger sample complexity. Our empirical study confirms the potential of our parallelisation scheme with fixed numbers of processors and instances in realistic application scenarios., Comment: Advances in Neural Information Processing Systems, 2017

We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building on this result, we devise highly scalable methods for learning in reproducing kernel Kre\u{\i}n spaces. The devised approaches provide a principled and theoretically well-founded means to tackle large scale learning problems with indefinite kernels. The main motivation for our work comes from problems with structured representations (e.g., graphs, strings, time-series), where it is relatively easy to devise a pairwise (dis)similarity function based on intuition and/or knowledge of domain experts. Such functions are typically not positive definite and it is often well beyond the expertise of practitioners to verify this condition. The effectiveness of the devised approaches is evaluated empirically using indefinite kernels defined on structured and vectorial data representations., Comment: The version accepted for presentation at ICML 2019