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 .

翻译：本文提出虚拟参数锐化（VPS），一种推理时技术，通过动态的、以激活为条件的低秩扰动来增强冻结的Transformer线性层。与LoRA等学习静态低秩适配器的参数高效微调方法不同，VPS基于批次激活统计量和可选的梯度信号即时构建其扰动因子，从而实现无需持久参数更新的测试时适应。该扰动形式为 ΔW = γ * W^T V U^T W，其中选择矩阵 U 和 V 通过稀疏激活引导选择或西尔维斯特耦合回归构建。我们对扰动的谱特性进行了理论分析，并描述了一种基于激活能量和词元级熵调节扰动幅度的自适应策略系统。该系统针对具有真值监督的任务，结合了多目标验证与迭代优化机制。我们提出了完整的算法框架，分析了其数学基础，并探讨了以激活为条件的计算可能增强大语言模型推理能力的机制。实现代码与实验代码可在 https://github.com/Saba-Kublashvili/vps-virtual-parameter-synthesis 获取。