Sinkhorn doubly stochastic attention rank decay analysis

The self-attention mechanism is central to the success of Transformer architectures. However, standard row-stochastic attention has been shown to suffer from significant signal degradation across layers. In particular, it can induce rank collapse, resulting in increasingly uniform token representations, as well as entropy collapse, characterized by highly concentrated attention distributions. Recent work has highlighted the benefits of doubly stochastic attention as a form of entropy regularization, promoting a more balanced attention distribution and leading to improved empirical performance. In this paper, we study rank collapse across network depth and show that doubly stochastic attention matrices normalized with Sinkhorn algorithm preserve rank more effectively than standard Softmax row-stochastic ones. As previously shown for Softmax, skip connections are crucial to mitigate rank collapse. We empirically validate this phenomenon on both sentiment analysis and image classification tasks. Moreover, we derive a theoretical bound for the pure self-attention rank decay when using Sinkhorn normalization and find that rank decays to one doubly exponentially with depth, a phenomenon that has already been shown for Softmax.

How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured data, but their inherent functioning is different. The question is how do they compare in capturing the information contained in networked datasets? We address this objective by solving a link prediction task and we conduct three main experiments, on both synthetic and real networks: one focuses on how PGMs and GNNs handle input features, while the other two investigate their robustness to noisy features and increasing heterophily of the graph. PGMs do not necessarily require features on nodes, while GNNs cannot exploit the network edges alone, and the choice of input features matters. We find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, mimicking many real scenarios where node attributes might be scalar or noisy. Then, we find that PGMs are more robust than GNNs when the heterophily of the graph is increased. Finally, to assess performance beyond prediction tasks, we also compare the two frameworks in terms of their computational complexity and interpretability.