André Ribeiro

André Ribeiro, Aleksandar Ilic, Leonel Sousa

The development of large-scale neuromorphic hardware has made practical implementations of threshold gate-based circuits a near-term possibility. The complexity advantages regarding traditional computing classes, as evidenced in the literature, have prompted us to tackle Epistasis Detection, one of the most computationally complex combinatorial problems in bioinformatics. We propose specially designed circuits that calculate the relative frequencies of all dataset combinations in an efficient pipelined fashion, taking advantage of co-located memory and configurable parallelism, obtaining complexity gains. Overall, we obtain the runtime to be bounded by the number of combinations to calculate, without any additional complexity overhead, contrary to classical approaches, using log-linear space. To accomplish this, we propose a data encoding and combination generation strategy using Leaky Integrate and Fire (LIF) neurons, that feeds a constant depth threshold gate population count circuit. Accounting for typical hardware characteristics, such as limited fan-in and variable precisions, we obtain logarithmic depth and log-cubic linear connections, for the population count circuit by composing developed unbounded fan-in constant depth threshold gate circuits to perform population count and binary array sum.

André Ribeiro, Ana Luiza Tenório, Tiago da Silva et al.

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

André Ribeiro, Ana Luiza Tenório, Juan Belieni et al.

Sheaf diffusion has recently emerged as a promising design pattern for graph representation learning due to its inherent ability to handle heterophilic data and avoid oversmoothing. Meanwhile, cooperative message passing has also been proposed as a way to enhance the flexibility of information diffusion by allowing nodes to independently choose whether to propagate/gather information from/to neighbors. A natural question ensues: is sheaf diffusion capable of exhibiting this cooperative behavior? Here, we provide a negative answer to this question. In particular, we show that existing sheaf diffusion methods fail to achieve cooperative behavior due to the lack of message directionality. To circumvent this limitation, we introduce the notion of cellular sheaves over directed graphs and characterize their in- and out-degree Laplacians. We leverage our construction to propose Cooperative Sheaf Neural Networks (CSNNs). Theoretically, we characterize the receptive field of CSNN and show it allows nodes to selectively attend (listen) to arbitrarily far nodes while ignoring all others in their path, potentially mitigating oversquashing. Our experiments show that CSNN presents overall better performance compared to prior art on sheaf diffusion as well as cooperative graph neural networks.