Brain network science modelling of sparse neural networks enables Transformers and LLMs to perform as fully connected

Dynamic sparse training (DST) can reduce the computational demands in ANNs, but faces difficulties in keeping peak performance at high sparsity levels. The Cannistraci-Hebb training (CHT) is a brain-inspired method for growing connectivity in DST. CHT leverages a gradient-free, topology-driven link regrowth, which has shown ultra-sparse (less than 1% connectivity) advantage across various tasks compared to fully connected networks. Yet, CHT suffers two main drawbacks: (i) its time complexity is $O(Nd^3)$ - N node network size, d node degree - restricting it to ultra-sparse regimes. (ii) it selects top link prediction scores, which is inappropriate for the early training epochs, when the network presents unreliable connections. Here, we design the first brain-inspired network model - termed bipartite receptive field (BRF) - to initialize the connectivity of sparse artificial neural networks. We further introduce a GPU-friendly matrix-based approximation of CH link prediction, reducing complexity to $O(N^3)$. We introduce the Cannistraci-Hebb training soft rule (CHTs), which adopts a flexible strategy for sampling connections in both link removal and regrowth, balancing the exploration and exploitation of network topology. Additionally, we integrate CHTs with a sigmoid gradual density decay (CHTss). Empirical results show that BRF offers performance advantages over previous network science models. Using 1% of connections, CHTs outperforms fully connected networks in MLP architectures on image classification tasks, compressing some networks to less than 30% of the nodes. Using 5% of the connections, CHTss outperforms fully connected networks in two Transformer-based machine translation tasks. Finally, at 30% connectivity, both CHTs and CHTss outperform other DST methods in language modeling task.