arXiv:2605.24969v1 Announce Type: cross Abstract: Long-tailed recognition suffers from a persistent head--tail trade-off: improving tail performance often degrades head accuracy and can increase training instability. Despite strong empirical results from re-weighting, decoupled training, and multi-expert methods, key design choices about representation sharing between head and tail classes and supervision weighting across class groups remain largely heuristic. In this work, we propose OSDTW, a principled task-decomposition framework that partitions the original single-label recognition problem into a head task and a tail task, implemented with a shared encoder and task-specific decoders. To handle the mutual exclusivity and statistical dependence between the two label groups, we introduce a factorized model and show that the resulting Kullback--Leibler divergence-based generalization error can be written as the sum of task-wise terms up to an additive constant, yielding a well-defined task-wise objective. We further develop a three-stage training pipeline: independent task training to estimate task-wise optima and the Fisher information matrix, weighted joint training to learn a shared encoder, and branch assembly to construct the final decoupled model. Under a block-diagonal Fisher approximation, we derive a computable second-order expansion of the expected generalization error, decomposing it into encoder variance, encoder bias, and decoder variance. This bias--variance decomposition provides a computable proxy to select the shared depth and task weights, enabling efficient hyper-parameter search. Experiments on standard long-tailed benchmarks demonstrate the effectiveness of the proposed approach over strong baselines.

arXiv:2601.10779v2 Announce Type: replace-cross Abstract: In multi-source transfer learning, a key challenge lies in how to appropriately differentiate and utilize heterogeneous source tasks. However, existing multi-source methods typically focus on optimizing either the source weights or the amount of transferred samples, largely neglecting their joint consideration. In this work, we propose a theoretical framework, Unified Optimization of Weights and Quantities (UOWQ), that jointly determines the optimal source weights and transfer quantities for each source task. Specifically, the framework formulates multi-source transfer learning as a parameter estimation problem based on an asymptotic analysis of a Kullback--Leibler divergence--based generalization error measure, leading to two main theoretical findings: 1) using all available source samples is always optimal when the weights are properly adjusted; 2) the optimal source weights are characterized by a principled optimization problem whose structure explicitly incorporates the Fisher information, parameter discrepancy, parameter dimensionality, and transfer quantities. Building on the theoretical results, we further propose a practical algorithm for multi-source transfer learning, and extend it to multi-task learning settings where each task simultaneously serves as both a source and a target. Extensive experiments on real-world benchmarks, including DomainNet and Office-Home, demonstrate that UOWQ consistently outperforms strong baselines. The results validate both the theoretical predictions and the practical effectiveness of our framework.