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

arXiv: https://arxiv.org/abs/2501.19107 · HTML: https://mlsanity.com/paper/2501.19107/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 63 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Multi30K: Multilingual English-German Image Descriptions](https://mlsanity.com/paper/1605.00459/) (2016)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [More ConvNets in the 2020s: Scaling up Kernels Beyond 51x51 using Sparsity](https://mlsanity.com/paper/2207.03620/) (2022)
- [Deep Rewiring: Training very sparse deep networks](https://mlsanity.com/paper/1711.05136/) (2017)
- [Do We Actually Need Dense Over-Parameterization? In-Time Over-Parameterization in Sparse Training](https://mlsanity.com/paper/2102.02887/) (2021)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Sparse Training via Boosting Pruning Plasticity with Neuroregeneration](https://mlsanity.com/paper/2106.10404/) (2021)
- [Top-KAST: Top-K Always Sparse Training](https://mlsanity.com/paper/2106.03517/) (2021)
- [MEST: Accurate and Fast Memory-Economic Sparse Training Framework on the Edge](https://mlsanity.com/paper/2110.14032/) (2021)
- [AC/DC: Alternating Compressed/DeCompressed Training of Deep Neural Networks](https://mlsanity.com/paper/2106.12379/) (2021)
- [Powerpropagation: A sparsity inducing weight reparameterisation](https://mlsanity.com/paper/2110.00296/) (2021)
- [Dynamic Sparse Training with Structured Sparsity](https://mlsanity.com/paper/2305.02299/) (2023)
- [SPDF: Sparse Pre-training and Dense Fine-tuning for Large Language Models](https://mlsanity.com/paper/2303.10464/) (2023)
- [Deep Expander Networks: Efficient Deep Networks from Graph Theory](https://mlsanity.com/paper/1711.08757/) (2017)
- [Dynamic Sparsity Is Channel-Level Sparsity Learner](https://mlsanity.com/paper/2305.19454/) (2023)

## Built on by (most cited first, 4 of 4)

- [NeuroTrails: Training with Dynamic Sparse Heads as the Key to Effective Ensembling](https://mlsanity.com/paper/2505.17909/) (2025)
- [Heterogeneous Connectivity in Sparse Networks: Fan-in Profiles, Gradient Hierarchy, and Topological Equilibria](https://mlsanity.com/paper/2604.10560/) (2026)
- [Scaling Interpretable Transformers with Parity Bottleneck Layers](https://mlsanity.com/paper/2607.20652/) (2026)
- [BARTER: Compact Dynamic Sparse Training with Standard Dense Kernels](https://mlsanity.com/paper/2610.16147/) (2026)

## Abstract (arXiv)

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(Nd3) - 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(N3). 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.