Paolo Mandica
Publications
Semantic Adapter Routing with Fine-Tuning Task Embeddings
Parameter-efficient fine-tuning (PEFT) has led to model ecosystems in which a single backbone is paired with many task-specialized adapters. Given such a library, routing aims to select the most appropriate adapter for a user query. While existing adapter routers typically require access to adapter weights or supervised training, we develop training-free semantic adapter routing methods using task embeddings. In ARIADNE, we reframe adapter selection as a classification problem, where PEFT adapters are represented by task embeddings and an unlabeled query is routed to the nearest adapter in the encoder's latent space. Evaluated on 23 tasks, ARIADNE recovers 97.4% of Oracle task performance and scales to 44 adapters at 89.7% selection accuracy, without touching a single adapter parameter. However, training data needed for ARIADNE may not be available when adapters come from public hubs or third-party providers. To overcome this limitation, we introduce GRACE, which recovers an adapter's fine-tuning data from its output logits alone via a modified contrastive decoding diffing (CDD) procedure. Synthetic data generated from CDD-UM is then used to construct task embeddings. Across three backbones (Llama-3.2-1B, Qwen2.5-3B, Qwen2.5-32B), GRACE recovers 72--100\% of Oracle task accuracy and matches or exceeds ARROW on 48 of 69 task/backbone combinations, while requiring neither training data nor model weights. Overall, we demonstrate that fine-tuning task embeddings provide an accurate and efficient path to semantic adapter routing.
GPart: End-to-End Isometric Fine-Tuning via Global Parameter Partitioning
Low-rank adaptation (LoRA) has become the dominant paradigm for parameter-efficient fine-tuning (PEFT) of large language models (LLMs). However, its bilinear structure introduces a critical limitation: the mapping from trainable parameters to weight updates is not distance-preserving, distorting the optimization landscape. Methods that project a low-dimensional vector into LoRA's parameter space, such as Uni-LoRA, improve parameter efficiency, but the subsequent bilinear LoRA map breaks end-to-end isometry, leaving the core distance-preservation problem unresolved. We propose GPart (Global Partition fine-tuning), a highly parameter-efficient fine-tuning method which removes the low-rank bottleneck entirely. Our method uses a single isometric partition matrix to map a $d$-dimensional trainable vector directly into the full weight space of the model. The result is an extremely minimal fine-tuning pipeline: one random projection, end-to-end isometric, with a single clean hyperparameter ($d$) and storage cost of $d+1$ values (the trainable vector plus a random seed). GPart builds on the theoretical premise that effective fine-tuning can emerge from random low-dimensional subspaces of the full weight space, without imposing low-rank matrix structure. We empirically demonstrate the superior or comparable performance of GPart to existing PEFT methods on natural language understanding, computer vision tasks, and mathematical reasoning. Overall, GPart achieves state-of-the-art efficiency and performance by removing structural constraints, offering a straightforward and elegant path to PEFT.