# Virtual Parameter Sharpening: Dynamic Low-Rank Perturbations for Inference-Time Reasoning Enhancement

arXiv: https://arxiv.org/abs/2602.19169 · HTML: https://mlsanity.com/paper/2602.19169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 8 of 8)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Rethinking the Role of Scale for In-Context Learning: An Interpretability-based Case Study at 66 Billion Scale](https://mlsanity.com/paper/2212.09095/) (2022)

## Abstract (arXiv)

I introduce Virtual Parameter Sharpening (VPS), an inference-time technique that augments frozen transformer linear layers with dynamic, activation-conditioned low-rank perturbations. Unlike parameter-efficient fine-tuning methods such as LoRA, which learn static low-rank adapters, VPS constructs its perturbation factors on the fly from batch activation statistics and optional gradient signals, enabling test-time adaptation without persistent parameter updates. The perturbation takes the form Delta W = gamma * W^T V U^T W, where selector matrices U and V are constructed via sparse activation-guided selection or Sylvester-coupled regression. We provide a theoretical analysis of the perturbation's spectral properties and describe an adaptive policy system that modulates perturbation magnitude based on activation energy and token-level entropy. This system incorporates multi-objective verification with iterative refinement for tasks with ground-truth supervision. We present the complete algorithmic framework, analyze its mathematical foundations, and discuss the mechanisms by which activation-conditioned computation may enhance reasoning capabilities in large language models. Implementation and experimental code are available at https://github.com/Saba-Kublashvili/vps-virtual-parameter-synthesis .