Sparsity is All You Need: Rethinking Biological Pathway-Informed Approaches in Deep Learning

Sparsity is All You Need: Rethinking Biological Pathway-Informed Approaches in Deep Learning Isabella Caranzano 1, Corrado Pancotti 1, Cesare Rollo 1, Flavio Sartori 1, Pietro Liò 2, Piero Fariselli 1, Tiziana Sanavia 1 1 Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Torino, Italy 2 Department of Computer Science and Technology, University of Cambridge, Cambridge, UK Abstract Biologically-informed neural networks typically leverage pathway annotations to enhance performance in biomedical applications. We hypothesized that the benefits of pathway integration does not arise from its biological relevance, but rather from the sparsity it introduces. We conducted a comprehensive analysis of all relevant pathway-based neural network models for predictive tasks, critically evaluating each study's contributions. From this review, we curated a subset of methods for which the source code was publicly available. The comparison of the biologically informed state-of-the-art deep learning models and their randomized counterparts showed that models based on randomized information performed equally well as biologically informed ones across different metrics and datasets. Notably, in 3 out of the 15 analyzed models, the randomized versions even outperformed their biologically informed counterparts. Moreover, pathway-informed models did not show any clear advantage in interpretability, as randomized models were still able to identify relevant disease biomarkers despite lacking explicit pathway information. Our findings suggest that pathway annotations may be too noisy or inadequately explored by current methods. Therefore, we propose a methodology that can be applied to different domains and can serve as a robust benchmark for systematically comparing novel pathway-informed models against their randomized counterparts. This approach enables researchers to rigorously determine whether observed performance improvements can be attributed to biological insights. Background & Summary When dealing with deep learning models, many functions that are efficiently computable through a machine learning approach exhibit what is called "compositional sparsity", meaning that they can be decomposed into a few simpler functions, each depending on only a arXiv:2505.04300v1 Deep networks, such as Convolutional Neural Networks (CNNs) and Transformers, align with the compositional structure of many target functions, leading to better generalization since they approximate such functions efficiently without falling victim to the "curse of dimensionality", i.e. the exponential growth of computational complexity with input dimension [37, 12, 31, 13, 32]. This compositional sparsity can be further enhanced by introducing prior constraints on features, such as grouping features into concepts or modelling interactions among them.