# Manifold-Constrained Hyper-Connections for Parameter-Efficient Finetuning

arXiv: https://arxiv.org/abs/2607.18130 · HTML: https://mlsanity.com/paper/2607.18130/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 20 Jul 2026.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [Foundational Models Defining a New Era in Vision: A Survey and Outlook](https://mlsanity.com/paper/2307.13721/) (2023)
- [Overtrained Language Models Are Harder to Fine-Tune](https://mlsanity.com/paper/2503.19206/) (2025)
- [LoFiT: Localized Fine-tuning on LLM Representations](https://mlsanity.com/paper/2406.01563/) (2024)
- [mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations](https://mlsanity.com/paper/2601.05732/) (2026)
- [KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices](https://mlsanity.com/paper/2601.21579/) (2026)
- [JPmHC Dynamical Isometry via Orthogonal Hyper-Connections](https://mlsanity.com/paper/2602.18308/) (2026)
- [Ablate and Rescue: A Causal Analysis of Residual Stream Hyper-Connections](https://mlsanity.com/paper/2603.14833/) (2026)
- [go-mHC: Direct Parameterization of Manifold-Constrained Hyper-Connections via Generalized Orthostochastic Matrices](https://mlsanity.com/paper/2604.02309/) (2026)
- [Analyzing Stream Collapse in Hyper-Connections: From Diagnosis to Mitigation](https://mlsanity.com/paper/2606.03483/) (2026)
- [TBP-mHC: full expressivity for manifold-constrained hyper connections through transportation polytopes](https://mlsanity.com/paper/2605.21724/) (2026)
- [Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2606.07574/) (2026)
- [Forecasting Smog Clouds With Deep Learning](https://mlsanity.com/paper/2410.02759/) (2024)

## Built on by (most cited first, 1 of 1)

- [T-Router: Learning Thalamic Routing for Reasoning with Parameter-Efficient Reinforcement Learning](https://mlsanity.com/paper/2609.39109/) (2026)

## Abstract (arXiv)

Finetuning methods for foundation models usually change weights, prompts, or hidden states, while leaving the residual topology fixed. We ask whether residual topology itself can become a finetuning object. To study this, we adapt manifold-constrained hyper-connections (mHC), recently introduced for pre-training, to frozen-backbone finetuning. mHC turns a Transformer into an input-dependent multi-stream residual architecture, routing representations through multiple streams at every sub-layer. Across mHC variants, we find that dynamic residual routing can finetune Transformers, but that its role differs from pre-training: by preserving stream mixing and learning only how sub-layers access streams, loss is improved and trainable parameters are reduced. Overall, our results identify residual routing as a promising architectural axis for efficient finetuning of foundation models.