Weightless Fine-Tuning: Personalizing LLMs via Logit-Space Transport
Authors: Bohan Zhang, Anqi Ni, Yixin Wang, Paramveer S. Dhillon
Abstract
Supervised fine-tuning (SFT) is a standard approach for adapting LLMs to a target distribution, but in settings such as personalization, where each author requires separate weight access, optimization, storage, and retraining, its costs become prohibitive. We propose Weightless Fine-Tuning (WFT), a training-free decoding-time method that approximates the distributional effect of SFT without weight updates. WFT computes supervised residuals on an author's training sequence and transports them to the current prompt through a cross-prefix transport operator estimated from dropout-induced cross-covariance. The operator captures how a perturbation at one context propagates to predictions at another, replacing gradient-based parameter updates with logit-space corrections. On three LaMP personalization benchmarks, WFT achieves the best average performance across datasets, matches or exceeds SFT on individual tasks, and outperforms other lightweight baselines on average. In a budget-controlled comparison, WFT approaches SFT performance using less than 7% of the effective computation. Logit-level analysis shows a cosine similarity of 0.875 between the logit shifts induced by WFT and SFT over 95% of the next-token probability mass, suggesting that WFT captures the distributional effect of supervised adaptation without modifying model weights.
Standard supervised fine-tuning (SFT) assigns the same explicit loss weight to every expert demonstration, regardless of the model's changing competence over training queries. Reinforcement learning (RL) based methods adapt update strength using model-generated rollouts, but often require substantially more sampling and can be unstable on hard tasks. We propose \textbf{Online Self-Weighted Fine-Tuning (OSW-FT)}, a simple method that augments SFT with online, trajectory-level weighting. For each query, OSW-FT estimates the model's current success rate using a small number of inference-only rollouts and rescales the standard SFT loss accordingly. The optimization direction remains anchored to the expert trajectory, while the update magnitude adapts online. For binary-verifiable reasoning, we connect this weighting to SFT and RL at the gradient level, inspired by variance-reduction principles. The resulting estimator is unbiased for the exact OSW-FT surrogate update for any finite rollout count, and we analyze convergence with respect to the corresponding surrogate objective. Evaluated across Qwen3 series ranging from 0.6B to 4B on multiple challenging benchmarks (e.g., AIME), OSW-FT consistently improves over SFT on small-to-medium scale models. OSW-FT offers a favorable compute-performance trade-off as a practical approach for fine-tuning small-to-medium LLMs on binary-verifiable reasoning tasks with only \textbf{2 online rollouts}.
Large language models (LLMs) remain expensive to fine-tune because full-parameter updates require substantial memory, compute, and per-task storage. We study whether saliency signals originally developed for pruning can be reused to choose where a model should adapt. We propose Super, a sparse parameter-efficient fine-tuning (PEFT) method that fixes a small trainable support using a Wanda-style activation-weighted magnitude score [Sun et al., 2023] computed from a calibration pass. We then introduce Supra, a hybrid adapter that combines this sparse update with LoRA while preserving a matched trainable-parameter budget through a simple budget-splitting rule. In single-seed Math17K arithmetic experiments on Llama-3.2-1B and Meta-Llama-3-8B, the best Super/Supra variants achieve the highest average accuracy among the tested schedule-selected adapter configurations. We also include a PaFi-style magnitude-only support as a closest training-free sparse baseline and find that low-score supports under both magnitude and Wanda-style orderings can be effective. These results suggest that simple pruning-inspired orderings can provide useful fixed sparse supports for PEFT, especially when combined with low-rank adapters.
In this paper, we study the problem of personalized survey response prediction using fine-tuned large language models (LLMs). This task poses unique challenges: limited per-user training data, scalability of model storage, and the need to exploit shared structure across survey questions. To address these issues, we propose Aplaud (Adaptive Personalized Low-rank and User-specific Nested Decomposition), a lightweight and scalable framework for LLM personalization. Aplaud extends the LoRA paradigm by separating adaptation into a frozen, shared low-rank basis and a compact user-specific correction, augmented with a rank-one residual for finer personalization. To further reduce per-user parameter cost and mitigate overfitting, the correction matrix can be factorized into an even lower-rank form. Empirical results demonstrate that Aplaud achieves efficient, scalable personalization across users while outperforming state-of-the-art LoRA-based personalized LLM approaches in both generalization and inference efficiency.