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.

Hyperbolic Learning with Multimodal Large Language Models

Hyperbolic embeddings have demonstrated their effectiveness in capturing measures of uncertainty and hierarchical relationships across various deep-learning tasks, including image segmentation and active learning. However, their application in modern vision-language models (VLMs) has been limited. A notable exception is MERU, which leverages the hierarchical properties of hyperbolic space in the CLIP ViT-large model, consisting of hundreds of millions parameters. In our work, we address the challenges of scaling multi-modal hyperbolic models by orders of magnitude in terms of parameters (billions) and training complexity using the BLIP-2 architecture. Although hyperbolic embeddings offer potential insights into uncertainty not present in Euclidean embeddings, our analysis reveals that scaling these models is particularly difficult. We propose a novel training strategy for a hyperbolic version of BLIP-2, which allows to achieve comparable performance to its Euclidean counterpart, while maintaining stability throughout the training process and showing a meaningful indication of uncertainty with each embedding.

Hyperbolic Active Learning for Semantic Segmentation under Domain Shift

For the task of semantic segmentation (SS) under domain shift, active learning (AL) acquisition strategies based on image regions and pseudo labels are state-of-the-art (SoA). The presence of diverse pseudo-labels within a region identifies pixels between different classes, which is a labeling efficient active learning data acquisition strategy. However, by design, pseudo-label variations are limited to only select the contours of classes, limiting the final AL performance. We approach AL for SS in the Poincar\'e hyperbolic ball model for the first time and leverage the variations of the radii of pixel embeddings within regions as a novel data acquisition strategy. This stems from a novel geometric property of a hyperbolic space trained without enforced hierarchies, which we experimentally prove. Namely, classes are mapped into compact hyperbolic areas with a comparable intra-class radii variance, as the model places classes of increasing explainable difficulty at denser hyperbolic areas, i.e. closer to the Poincar\'e ball edge. The variation of pixel embedding radii identifies well the class contours, but they also select a few intra-class peculiar details, which boosts the final performance. Our proposed HALO (Hyperbolic Active Learning Optimization) surpasses the supervised learning performance for the first time in AL for SS under domain shift, by only using a small portion of labels (i.e., 1%). The extensive experimental analysis is based on two established benchmarks, i.e. GTAV $\rightarrow$ Cityscapes and SYNTHIA $\rightarrow$ Cityscapes, where we set a new SoA. The code will be released.

HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations

Self-paced learning has been beneficial for tasks where some initial knowledge is available, such as weakly supervised learning and domain adaptation, to select and order the training sample sequence, from easy to complex. However its applicability remains unexplored in unsupervised learning, whereby the knowledge of the task matures during training. We propose a novel HYperbolic Self-Paced model (HYSP) for learning skeleton-based action representations. HYSP adopts self-supervision: it uses data augmentations to generate two views of the same sample, and it learns by matching one (named online) to the other (the target). We propose to use hyperbolic uncertainty to determine the algorithmic learning pace, under the assumption that less uncertain samples should be more strongly driving the training, with a larger weight and pace. Hyperbolic uncertainty is a by-product of the adopted hyperbolic neural networks, it matures during training and it comes with no extra cost, compared to the established Euclidean SSL framework counterparts. When tested on three established skeleton-based action recognition datasets, HYSP outperforms the state-of-the-art on PKU-MMD I, as well as on 2 out of 3 downstream tasks on NTU-60 and NTU-120. Additionally, HYSP only uses positive pairs and bypasses therefore the complex and computationally-demanding mining procedures required for the negatives in contrastive techniques. Code is available at https://github.com/paolomandica/HYSP.