Branch, or Layer? Zeroth-Order Optimization for Continual Learning of Vision-Language Models

Continual learning in vision-language models (VLMs) faces critical challenges in balancing parameter efficiency, memory consumption, and optimization stability. While First-Order (FO) optimization (e.g., SGD) dominate current approaches, their deterministic gradients often trap models in suboptimal local minima and incur substantial memory overhead. This paper pioneers a systematic exploration of Zeroth-Order (ZO) optimization for vision-language continual learning (VLCL). We first identify the incompatibility of naive full-ZO adoption in VLCL due to modality-specific instability. To resolve this, we selectively applying ZO to either vision or language modalities while retaining FO in the complementary branch. Furthermore, we develop a layer-wise optimization paradigm that interleaves ZO and FO across network layers, capitalizing on the heterogeneous learning dynamics of shallow versus deep representations. A key theoretical insight reveals that ZO perturbations in vision branches exhibit higher variance than language counterparts, prompting a gradient sign normalization mechanism with modality-specific perturbation constraints. Extensive experiments on four benchmarks demonstrate that our method achieves state-of-the-art performance, reducing memory consumption by 89.1% compared to baselines. Code will be available upon publication.