In this paper we show that feedforward neural networks corresponding to arbitrary directed acyclic graphs undergo transition to linearity as their "width" approaches infinity. The width of these general networks is characterized by the minimum indegree of their neurons, except for the input and first layers. Our results identify the mathematical structure underlying transition to linearity and generalize a number of recent works aimed at characterizing transition to linearity or constancy of the Neural Tangent Kernel for standard architectures.

Molecule property prediction has gained significant attention in recent years. The main bottleneck is the label insufficiency caused by expensive lab experiments. In order to alleviate this issue and to better leverage textual knowledge for tasks, this study investigates the feasibility of employing natural language instructions to accomplish molecule-related tasks in a zero-shot setting. We discover that existing molecule-text models perform poorly in this setting due to inadequate treatment of instructions and limited capacity for graphs. To overcome these issues, we propose GIMLET, which unifies language models for both graph and text data. By adopting generalized position embedding, our model is extended to encode both graph structures and instruction text without additional graph encoding modules.

More precisely, we use batches of size 2. Each batch contains one patch with the foreground oversampled. Furthermore, we split each silo's data into training and validation data with 80% and 20% split, respectively. All this pre-processing and patching is done using the nnU-Net library [IJK+21]. Loss function We use the same loss function as proposed by nnU-Net [IJK+21] for the KiTS19 dataset which is based on DICE [Dic45] and on the Cross Entropy loss.