Neural Collapse in Multi-Task Learning

Neural collapse (NC) plays a key role in understanding deep neural networks. However, existing empirical and theoretical studies of NC primarily focus on the single-task scenarios. This paper studies neural collapse in multi-task learning. We consider two standard feature-based multi-task learning scenarios: Single-Source Multi-Task Classification (SSMTC) and Multi-Source Multi-Task Classification (MSMTC). Interestingly, we find that the task-specific linear classifier and features converge to the Simplex Equiangular Tight Frame (ETF) in the setting of MSMTC. In the setting of SSMTC, task-specific linear classifier converges to the task-specific ETF and these task-specific ETFs are mutually orthogonal. Moreover, the shared features across tasks converge to the scaled sum of the weight vectors associated with the task-specific labels in each task's classifier. We also provide the theoretical guarantee for our empirical findings. Through detailed analysis, we uncover the mechanism of MTL where each task learns task-specific latent features that together form the shared features. Moreover, we reveal an inductive bias in MTL that task correlation reconfigures the geometry of taskspecific classifiers and promotes alignment among the features learned by each task.