arXiv:2603.03099v2 Announce Type: replace-cross Abstract: Despite Adam demonstrating faster empirical convergence than SGD in many applications, much of the existing theory yields guarantees essentially comparable to those of SGD, leaving the empirical performance gap insufficiently explained. In this paper, we uncover a key second-moment normalization in Adam and develop a stopping-time/martingale analysis that provably distinguishes Adam from SGD under the classical bounded variance model (a second moment assumption). In particular, we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a $\delta^{-1/2}$ dependence on the confidence parameter $\delta$, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a $\delta^{-1}$ dependence.

arXiv:2603.03099v1 Announce Type: cross Abstract: Despite Adam demonstrating faster empirical convergence than SGD in many applications, much of the existing theory yields guarantees essentially comparable to those of SGD, leaving the empirical performance gap insufficiently explained. In this paper, we uncover a key second-moment normalization in Adam and develop a stopping-time/martingale analysis that provably distinguishes Adam from SGD under the classical bounded variance model (a second moment assumption). In particular, we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a $\delta^{-1/2}$ dependence on the confidence parameter $\delta$, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a $\delta^{-1}$ dependence.

arXiv:2506.17337v3 Announce Type: replace-cross Abstract: Vision Language Models (VLMs) have shown promise in automating image diagnosis and interpretation in clinical settings. However, developing specialist medical VLMs requires substantial computational resources and carefully curated datasets, and it remains unclear under which conditions generalist and specialist medical VLMs each perform best. This study highlights the complementary strengths of specialist medical and generalist VLMs. Specialists remain valuable in modality-aligned use cases, but we find that efficiently fine-tuned generalist VLMs can achieve comparable or even superior performance in most tasks, particularly when transferring to unseen or rare OOD medical modalities. These results suggest that generalist VLMs, rather than being constrained by their lack of specialist medical pretraining, may offer a scalable and cost-effective pathway for advancing clinical AI development.