Average pairwise Hamming distance of a subset in a hypercube
Yijia Fang, Hao Huang
AI 速览：作者证明密度为1/8的{0,1}^n子集的平均成对汉明距离至少为(n-3)/2，且等号仅由(n-3)维子立方体达到。
In this note, we prove that for a subset $\mathcal{F}$ of $\{0,1\}^n$ of density $\frac{1}{8}$, its average pairwise Hamming distance is at least $\frac{n-3}{2}$, with equality attained only by $(n-3)$-dimensional subcubes. This answers a question of Lei Yu, and solves an important open case of a more general question posed by Ahlswede and Katona in 1977.
JEDI: Joint-Embedding Demonstration Compression for In-Context Imitation Learning
Jiazhao Liang, Zhewen He, Shuaihang Yuan, Hao Huang, Yi Fang
AI 速览：JEDI 将演示压缩为在冻结视频-JEPA 空间中预测查询回合下一阶段关键帧的潜在槽，以支持多示例上下文模仿学习。
In-context imitation learning (ICIL) adapts robot policies through test-time demonstrations, but long multimodal trajectories constrain how many examples fit in context. We ask what a compressed demonstration should preserve. We propose JEDI, which compresses demonstrations into latent slots trained to predict the query episode's next-stage keyframe in a frozen video-JEPA space. Task and process counterfactuals help the slots preserve execution details, while the predictor selects demonstrations from a bank. Post-training with keypoint tokens enables human-hand conditioning on robots. Experiments on LIBERO and real robots show that JEDI supports many-shot context; LIBERO objective controls show improved success and demonstration following over action-only compression. These findings support query-future prediction as a training objective for preserving execution-relevant information in compressed demonstrations.