# LARC: Low-Rank Adaptive Residual Connections for Learning in Frozen Models

arXiv: https://arxiv.org/abs/2609.40063 · HTML: https://mlsanity.com/paper/2609.40063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Using Fast Weights to Attend to the Recent Past](https://mlsanity.com/paper/1610.06258/) (2016)
- [Provable Meta-Learning with Low-Rank Adaptations](https://mlsanity.com/paper/2410.22264/) (2024)
- [MMLA: Memory-Mediated Learning Architecture for Predictive Dual-State Adaptation](https://mlsanity.com/paper/2606.28876/) (2026)
- [Meta-Learning at Scale for Large Language Models via Low-Rank Amortized Bayesian Meta-Learning](https://mlsanity.com/paper/2508.14285/) (2025)

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

- [MMLA-RSI: Recursive Self-Improvement through RTT and RTMA](https://mlsanity.com/paper/2610.20294/) (2026)

## Abstract (arXiv)

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map h+BAh adds a low-rank correction to a hidden representation. A slow state ρ learns starting factors across tasks; a private fast state Phi copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.