# Riemannian--Lorentz Fusion of Vision Transformers and State-Space Models

arXiv: https://arxiv.org/abs/2609.19384 · HTML: https://mlsanity.com/paper/2609.19384/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [PlainMamba: Improving Non-Hierarchical Mamba in Visual Recognition](https://mlsanity.com/paper/2403.17695/) (2024)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [SpectFormer: Frequency and Attention is what you need in a Vision Transformer](https://mlsanity.com/paper/2304.06446/) (2023)
- [Revisiting Weight Averaging for Model Merging](https://mlsanity.com/paper/2412.12153/) (2024)
- [Scattering Vision Transformer: Spectral Mixing Matters](https://mlsanity.com/paper/2311.01310/) (2023)
- [MergeME: Model Merging Techniques for Homogeneous and Heterogeneous MoEs](https://mlsanity.com/paper/2502.00997/) (2025)
- [Transport and Merge: Cross-Architecture Merging for Large Language Models](https://mlsanity.com/paper/2602.05495/) (2026)
- [HAMSA: Scanning-Free Vision State Space Models via SpectralPulseNet](https://mlsanity.com/paper/2604.14724/) (2026)

## Abstract (arXiv)

Scaling deep learning faces critical bottlenecks: data exhaustion, exponential training costs, and resource concentration. Model merging combines pre-trained checkpoints without gradient descent, offering orders-of-magnitude savings versus retraining. Combining independently trained vision models is difficult when their architectures and parameter shapes differ. Existing weight-space merging methods generally assume aligned, shape-compatible checkpoints, whereas a Vision Transformer (ViT) and a state-space model (SSM) implement token mixing with different operators. We study a hybrid Heterogeneous merging setting that retains both architectures while aligning parameter groups by semantic role. Our proposed Riemannian--Lorentz Parameter Fusion (RLPF) method projects aligned groups to common coordinates, lifts selected coordinates to the Lorentz hyperboloid model of hyperbolic space, computes a regularized geodesic barycenter, and decodes the result into the two branches. A learned gate then combines branch logits for each input. Component groups use fixed curvature values, with normalization parameters treated as Euclidean. In the results available in this manuscript, the fine-tuned system obtains 82.37% on CIFAR-10, 75.04% on Oxford-IIIT Pet, and 78.58% top-1 accuracy on ImageNet-1K; the corresponding best-parent accuracies are 76.54%, 71.42%, and 76.42%. On ImageNet-1K, the reported pre-fine-tuning initialization reaches 77.80%. These results support further study of geometry-aware heterogeneous fusion, but not a training-free single-checkpoint merge: RLPF is a two-branch hybrid whose gate and reported final models are trained.