arXiv:2603.06651v1 Announce Type: cross Abstract: Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian gradient descent algorithms address these issues but fail to represent complex hypersurfaces via a single classic manifold. We propose geodesic gradient descent (GGD), a generic and learning-rate-free Riemannian gradient descent algorithm. At each iteration, GGD uses an n-dimensional sphere to approximate a local neighborhood on the objective function-induced hypersurface, adapting to arbitrarily complex geometries. A tangent vector derived from the Euclidean gradient is projected onto the sphere to form a geodesic, ensuring the update trajectory stays on the hypersurface. Parameter updates are performed using the endpoint of the geodesic. The maximum step size of the gradient in GGD is equal to a quarter of the arc length on the n-dimensional sphere, thus eliminating the need for a learning rate. Experimental results show that compared with the classic Adam algorithm, GGD achieves test MSE reductions ranging from 35.79% to 48.76% for fully connected networks on the Burgers' dataset, and cross-entropy loss reductions ranging from 3.14% to 11.59% for convolutional neural networks on the MNIST dataset.

arXiv:2602.18702v1 Announce Type: cross Abstract: Long video understanding is challenging due to rich and complicated multimodal clues in long temporal range.Current methods adopt reasoning to improve the model's ability to analyze complex video clues in long videos via text-form reasoning.However,the existing literature suffers from the fact that the text-only reasoning under fixed video context may exacerbate hallucinations since detailed crucial clues are often ignored under limited video context length due to the temporal redundancy of long videos.To address this gap,we propose Video-TwG,a curriculum reinforced framework that employs a novel Think-with-Grounding paradigm,enabling video LLMs to actively decide when to perform on-demand grounding during interleaved text-video reasoning, selectively zooming into question-relevant clips only when necessary.Video-TwG can be trained end-to-end in a straightforward manner, without relying on complex auxiliary modules or heavily annotated reasoning tracesIn detail,we design a Two-stage Reinforced Curriculum Strategy, where the model first learns think-with-grounding behavior on a small short-video GQA dataset with grounding labels,and then scales to diverse general QA data with videos of diverse domains to encourage generalization. Further, to handle complex think-with-grounding reasoning for various kinds of data,we propose TwG-GRPO algorithm which features the fine-grained grounding reward, self-confirmed pseudo reward and accuracy-gated mechanism.Finally,we propose to construct a new TwG-51K dataset that facilitates training. Experiments on Video-MME, LongVideoBench, and MLVU show that Video-TwG consistently outperforms strong LVU baselines.Further ablation validates the necessity of our Two-stage Reinforced Curriculum Strategy and shows our TwG-GRPO better leverages diverse unlabeled data to improve grounding quality and reduce redundant groundings without sacrificing QA performance.