A Light Bilevel Refinement Aligns Self-Supervised Representations for Stronger Task-Specific Learning

Fine-tuning large-scale pre-trained models is a recent prevalent paradigm for adapting general representations to specialized tasks. However, when a new version of a pre-trained model becomes available, expertise acquired through fine-tuning cannot be directly reused because it is tied to the parameterization of the original model, requiring another costly fine-tuning. To address this inefficiency, recent work uses task vectors, defined as the parameter difference between a fine-tuned model and its base model, to transfer expertise across models. While existing methods bridge disparate models by matching activations or gradients, a significant performance gap remains relative to direct fine-tuning, suggesting that these partial correspondences are insufficient. In this work, instead of viewing a task vector merely as a parameter offset, we revisit the formation of task vectors and show that they can be derived as accumulated bilinear interactions between input-side activations and output-side gradients. Motivated by this observation, we formulate task-vector transfer as a dual-space alignment problem and propose BiCo, a training-free framework for transferring task vectors through Bilinear Coordinate alignment. BiCo estimates orthogonal Procrustes mappings in both spaces using a single forward-backward pass on a small calibration set, without any parameter update. Across extensive computer vision and natural language processing benchmarks, BiCo consistently outperforms existing transfer methods across models that differ in width, depth, and pre-training configuration.

Self-supervised learning (SSL) has achieved remarkable representation learning performance, but many existing methods rely on large batch sizes, memory banks, momentum encoders, or global synchronization mechanisms that substantially increase computational cost and training complexity. In this work, we propose Semantic Mutual Information (SMI), a lightweight self-supervised objective derived from a mutual-information-inspired dependency formulation under Gaussian assumptions. Unlike conventional correlation matching objectives that operate on high-dimensional feature correlation matrices, SMI performs optimization on a sample-level dependency matrix through a nonlinear transformation of pairwise correlations. This formulation induces distinct optimization dynamics that emphasize strongly dependent semantic pairs while maintaining representation diversity. Experimental results on ImageNet using a ResNet-50 backbone demonstrate that SMI achieves competitive linear evaluation performance relative to state-of-the-art SSL approaches while substantially reducing computational complexity. Across multiple low-resource benchmarks, SMI consistently improves transfer performance over Barlow Twins, particularly on fine-grained datasets. Furthermore, analyses of optimization dynamics and representation geometry suggest improved alignment--redundancy balance, greater feature diversity, and more spatially localized semantic representations. These results indicate that nonlinear dependency optimization provides an effective and computationally efficient alternative to conventional correlation-based self-supervised learning objectives.

Self-supervision is a powerful technique for learning visual representations from unlabeled data. Existing techniques primarily adopt a two-stage approach for self-supervised learning (SSL): a pretraining stage on unlabeled data followed by a finetuning stage on labeled data. While this pipeline has demonstrated extreme effectiveness, the interaction between self-supervised and supervised learning objectives remains insufficiently understood. In this work, we systematically investigate whether jointly optimizing the self-supervised and supervised objectives during training provides a better alternative. We compare two training paradigms: (1) the aforementioned pretraining followed by finetuning (PFT) and (2) joint training (JT), where self-supervised and supervised losses are optimized simultaneously in the same network. Across eight representative SSL methods and diverse computer vision tasks on natural, medical, crisis response, and remote sensing data, we evaluate performance under varying percentages of labeled data. Our results reveal that the relative effectiveness of PFT and JT depends strongly on the task at hand, the availability of labeled data, and the complexity of the domain. We find that JT consistently improves data and training efficiency while being robust in low-label settings, while PFT is more reliable in more specialized domains. We further analyze representation quality, robustness, and cross-domain generalization, providing new insights into how self-supervised and supervised objectives interact during optimization. We establish a comprehensive empirical benchmark for hybrid SSL-based semi-supervised learning and offer practical guidance for selecting appropriate training strategies across diverse vision applications.