# Resonant Sparse Geometry Networks

arXiv: https://arxiv.org/abs/2601.18064 · HTML: https://mlsanity.com/paper/2601.18064/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 85 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 30 of 34)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)

## Built on by (most cited first, 3 of 3)

- [Selective Synchronization Attention](https://mlsanity.com/paper/2602.14445/) (2026)
- [RAG-GNN: Integrating Retrieved Knowledge with Graph Neural Networks for Precision Medicine](https://mlsanity.com/paper/2602.00586/) (2026)
- [Hebbian-Oscillatory Co-Learning](https://mlsanity.com/paper/2603.08731/) (2026)

## Abstract (arXiv)

We introduce Resonant Sparse Geometry Networks (RSGN), a brain-inspired architecture with self-organizing sparse hierarchical input-dependent connectivity. Unlike Transformer architectures that employ dense attention mechanisms with O(n^2) computational complexity, RSGN embeds computational nodes in learned hyperbolic space where connection strength decays with geodesic distance, achieving dynamic sparsity that adapts to each input. The architecture operates on two distinct timescales: fast differentiable activation propagation optimized through gradient descent, and slow Hebbian-inspired structural learning for connectivity adaptation through local correlation rules. We provide rigorous mathematical analysis demonstrating that RSGN achieves O(n*k) computational complexity, where k << n represents the average active neighborhood size. Experimental evaluation on hierarchical classification and long-range dependency tasks demonstrates that RSGN achieves 96.5% accuracy on long-range dependency tasks while using approximately 15x fewer parameters than standard Transformers. On challenging hierarchical classification with 20 classes, RSGN achieves 23.8% accuracy (compared to 5% random baseline) with only 41,672 parameters, nearly 10x fewer than the Transformer baselines which require 403,348 parameters to achieve 30.1% accuracy. Our ablation studies confirm the contribution of each architectural component, with Hebbian learning providing consistent improvements. These results suggest that brain-inspired principles of sparse, geometrically-organized computation offer a promising direction toward more efficient and biologically plausible neural architectures.