The paper introduces a convolutional neural network (CNN) that operates directly on graphs, allowing for end-to-end learning of prediction pipelines with inputs of arbitrary size and shape. The architecture generalizes standard molecular feature extraction methods based on circular fingerprints, offering several advantages over fixed fingerprints: 1. **Predictive Performance**: Neural graph fingerprints can provide better predictive performance on tasks such as solubility, drug efficacy, and organic photovoltaic efficiency. 2. **Parsimony**: Differentiable fingerprints can be optimized to encode only relevant features, reducing downstream computation and regularization requirements. 3. **Interpretability**: Features of neural graph fingerprints can be activated by similar but distinct molecular fragments, making the representation more meaningful. The authors replace the bottom layer of the traditional fingerprint computation with a differentiable neural network that processes a graph representing the molecule. The network applies convolutional operations to each atom and its neighborhood, followed by a global pooling step to combine features from all atoms. They demonstrate that neural graph fingerprints match or outperform standard circular fingerprints in predictive performance and are more interpretable. Experiments show that neural graph fingerprints preserve the distances between molecules and achieve similar or better predictive performance compared to circular fingerprints. Visualizations of the learned features reveal that neural graph fingerprints can be activated by variations of the same structure, making them more interpretable and allowing for shorter feature vectors. The paper also discusses limitations, such as computational cost, limited information propagation across the graph, and the inability to distinguish stereoisomers. Related work is reviewed, including neural Turing machines, neural nets for QSAR, and other methods for handling graphs in machine learning. The authors conclude that data-driven features have the potential to replace hand-crafted features in various applications, including virtual screening, drug design, and materials design.The paper introduces a convolutional neural network (CNN) that operates directly on graphs, allowing for end-to-end learning of prediction pipelines with inputs of arbitrary size and shape. The architecture generalizes standard molecular feature extraction methods based on circular fingerprints, offering several advantages over fixed fingerprints: 1. **Predictive Performance**: Neural graph fingerprints can provide better predictive performance on tasks such as solubility, drug efficacy, and organic photovoltaic efficiency. 2. **Parsimony**: Differentiable fingerprints can be optimized to encode only relevant features, reducing downstream computation and regularization requirements. 3. **Interpretability**: Features of neural graph fingerprints can be activated by similar but distinct molecular fragments, making the representation more meaningful. The authors replace the bottom layer of the traditional fingerprint computation with a differentiable neural network that processes a graph representing the molecule. The network applies convolutional operations to each atom and its neighborhood, followed by a global pooling step to combine features from all atoms. They demonstrate that neural graph fingerprints match or outperform standard circular fingerprints in predictive performance and are more interpretable. Experiments show that neural graph fingerprints preserve the distances between molecules and achieve similar or better predictive performance compared to circular fingerprints. Visualizations of the learned features reveal that neural graph fingerprints can be activated by variations of the same structure, making them more interpretable and allowing for shorter feature vectors. The paper also discusses limitations, such as computational cost, limited information propagation across the graph, and the inability to distinguish stereoisomers. Related work is reviewed, including neural Turing machines, neural nets for QSAR, and other methods for handling graphs in machine learning. The authors conclude that data-driven features have the potential to replace hand-crafted features in various applications, including virtual screening, drug design, and materials design.