Thelimitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges.

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-call meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.

For example, a citation network has multiple types of nodes (e.g., authors, papers, conferences) and edges defined by their relations (e.g., author-paper, paper-conference), and it is called a heterogeneous graph. A naïve approach is to ignore the node/edge types and treat them as in a homogeneous graph (a standard graph with one type of nodes and edges).

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-call meta-paths.

Interpreting the representation and generalization powers has been a long-standing issue in the field of machine learning (ML) and artificial intelligence. This work contributes to uncovering the emergence of universal scaling laws in quantum-probabilistic ML. We take the generative tensor network (GTN) in the form of a matrix product state as an example and show that with an untrained GTN (such as a random TN state), the negative logarithmic likelihood (NLL) $L$ generally increases linearly with the number of features $M$, i.e., $L \simeq k M + const$. This is a consequence of the so-called ``catastrophe of orthogonality,'' which states that quantum many-body states tend to become exponentially orthogonal to each other as $M$ increases. We reveal that while gaining information through training, the linear scaling law is suppressed by a negative quadratic correction, leading to $L \simeq \beta M - \alpha M^2 + const$. The scaling coefficients exhibit logarithmic relationships with the number of training samples and the number of quantum channels $\chi$. The emergence of the quadratic correction term in NLL for the testing (training) set can be regarded as evidence of the generalization (representation) power of GTN. Over-parameterization can be identified by the deviation in the values of $\alpha$ between training and testing sets while increasing $\chi$. We further investigate how orthogonality in the quantum feature map relates to the satisfaction of quantum probabilistic interpretation, as well as to the representation and generalization powers of GTN. The unveiling of universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum probabilistic framework.

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-call meta-paths.

This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for regression tasks was benchmarked against a collection of linear models through a combination of simulated and real-world data training studies. First, a selection of five arbitrarily designed multi-step surrogate functions were developed to reflect various features commonly found within experimental processes. A graph transformer network outperformed all tested linear models in scenarios that featured hidden interactions between process steps and sequence dependent features, while retaining equivalent performance in sequence agnostic scenarios. Then, a similar comparison was applied to real-world literature data on algorithm guided colloidal atomic layer deposition. Using the complete reaction sequence as training data, the graph neural network outperformed all linear models in predicting the three spectral properties for most training set sizes. Further implementation of graph neural networks and geometric representation of scientific processes for the prediction of experiment outcomes could lead to algorithm driven navigation of higher dimension parameter spaces and efficient exploration of more dynamic systems.

Generative models have seen significant advancements in recent years, yet often remain challenging and costly to train and use. We introduce Generative Topological Networks (GTNs) -- a new class of generative models that addresses these shortcomings. GTNs are trained deterministically using a simple supervised learning approach grounded in topology theory. GTNs are fast to train, and require only a single forward pass in a standard feedforward neural network to generate samples. We demonstrate the strengths of GTNs in several datasets, including MNIST, celebA and the Hands and Palm Images dataset. Finally, the theory behind GTNs offers insights into how to train generative models for improved performance.

Abstract--Graph Neural Networks (GNNs) have been generalized to process the heterogeneous graphs by various approaches. Unfortunately, these approaches usually model the heterogeneity via various complicated modules. This paper aims to propose a simple yet effective framework to assign adequate ability to the homogeneous GNNs to handle the heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Network (RE-GNN), which employs only one parameter per relation to embed the importance of distinct types of relations and node-type-specific self-loop connections. To optimize these relation embeddings and the model parameters simultaneously, a gradient scaling factor is proposed to constrain the embeddings to converge to suitable values. Besides, we interpret the proposed RE-GNN from two perspectives, and theoretically demonstrate that our RE-GCN possesses more expressive power than GTN (which is a typical heterogeneous GNN, and it can generate meta-paths adaptively). Extensive experiments demonstrate that our RE-GNN can effectively and efficiently handle the heterogeneous graphs and can be applied to various homogeneous GNNs.

I recently started an AI-focused educational newsletter, that already has over 100,000 subscribers. TheSequence is a no-BS (meaning no hype, no news etc) ML-oriented newsletter that takes 5 minutes to read. The goal is to keep you up to date with machine learning projects, research papers and concepts. A common analogy in artificial intelligence(AI) circles is that training data is the new oil for machine learning models. Just like the precious commodity, training data is scarce and hard to get at scale.