Giuseppe Bruno, Shi Chen, Zhengjiang Lin, Yury Polyanskiy, Philippe Rigollet
We study the long-context limit of softmax self-attention with a fixed query and a random context of $n$ i.i.d. keys on the sphere with the intrinsic dimension of the key distribution held fixed, viewing the inverse temperature $β_n$ as the scaling parameter that decides whether attention degenerates into uniform averaging or collapses onto the single closest key. We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $β_n^\ast \asymp n^{2/(d-1)}$ for uniform keys on $\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across all regimes of $β_n$: a subcritical regime in which the output reduces to a local average around $q$ with explicit deterministic bias and Gaussian fluctuations; a critical regime in which a finite collection of nearest keys retains macroscopic mass without single-key collapse; and a supercritical regime in which all mass concentrates on the closest key. Of notable interest is the subcritical case with identity value matrix where the attention map approximately implements a backward heat equation.
Xinyu Chen, Song Wu, Dingbao Shao, Jiahang Li, Jiang Lin, Yuhang Liu, Duo Li, Jiaxin Hu 等 15 位作者
Instruction-guided video editing requires executing a requested change while preserving the source video's appearance and temporal structure. We present SemantiScene-Edit, a video editor that couples a multimodal encoder with a pretrained video diffusion transformer. The encoder jointly processes source frames and the editing instruction, and learnable queries convey their semantic context to the generator through a trainable connector and cross-attention. A complementary visual pathway concatenates source-video latents with noisy target latents before patch embedding, supplying dense spatial and temporal information for content preservation. We train the model with flow matching and a three-stage image--video curriculum comprising semantic alignment, joint adaptation, and high-resolution refinement. To support training, we construct over 1.2 million instruction-conditioned video-editing records covering object addition, removal, replacement, and attribute modification. We also construct a 100-case benchmark for evaluating instruction execution, source preservation, temporal consistency, and visual quality. Comparative experiments show that SemantiScene-Edit effectively follows editing instructions while retaining source content. At inference, the model requires only a source video and a natural-language instruction.