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

• URL: http://arxiv.org/abs/2501.19107v2
• Date: Mon, 02 Jun 2025 09:19:36 GMT
• Title: Brain network science modelling of sparse neural networks enables Transformers and LLMs to perform as fully connected
• Authors: Yingtao Zhang, Diego Cerretti, Jialin Zhao, Wenjing Wu, Ziheng Liao, Umberto Michieli, Carlo Vittorio Cannistraci,
• Abstract summary: Dynamic sparse training (DST) can reduce the computational demands in ANNs, but faces difficulties in keeping peak performance at high sparsity levels.<n>Cannistraci-Hebb training (CHT) is a brain-inspired method for growing connectivity in DST.<n>CHT suffers two main drawbacks: (i) its time complexity is $O(Nd3)$ - N node network size, d node degree - restricting it to ultra-sparse regimes.<n>We introduce a GPU-friendly matrix-based approximation of CH link prediction, reducing complexity to $O(N3)$
• Score: 8.009769102084839
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 and even exceed fully connected baselines in zero-shot tasks.

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