{"ID":2834102,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2602.19169","arxiv_id":"2602.19169","title":"Virtual Parameter Sharpening: Dynamic Low-Rank Perturbations for Inference-Time Reasoning Enhancement","abstract":"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 .","short_abstract":"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 facto...","url_abs":"https://arxiv.org/abs/2602.19169","url_pdf":"https://arxiv.org/pdf/2602.19169v1","authors":"[\"Saba Kublashvili\"]","published":"2025-12-02T16:54:22Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.MS\",\"math.PR\"]","methods":"[\"Transformer\",\"Language Model\",\"LoRA\"]","has_code":false,"code_links":[{"ID":606382,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2834102,"paper_url":"https://arxiv.org/abs/2602.19169","paper_title":"Virtual Parameter Sharpening: Dynamic Low-Rank Perturbations for Inference-Time Reasoning Enhancement","repo_url":"https://github.com/Saba-Kublashvili/vps-virtual-parameter-synthesis","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}