Visual on-policy distillation (OPD) improves the training of compact visual autoregressive models by learning from trajectories generated by the current student. However, these online rollouts are still produced token by token with autoregressive decoding, which adds substantial cost to every on-policy training step. Speculative Jacobi Decoding (SJD) provides an alternative because it can process multiple tokens in parallel without an auxiliary draft model, but the original method is designed for single-sequence inference. We introduce HB-SJD, a batched SJD rollout backend for visual OPD. HB-SJD allows each image to advance independently according to its own decoding progress, while images at different sequence positions are still verified in batched model forwards. As images finish, HB-SJD switches between Full and Compact execution to reduce the cost of later rollout rounds. HB-SJD only replaces the student rollout backend and leaves the teacher, distillation objective, and optimization procedure unchanged. Experiments with LlamaGen show that HB-SJD substantially reduces rollout and end-to-end training time while preserving the generation quality of the distilled student.
Key-value (KV) cache growth is a major bottleneck in autoregressive decoding, as memory and bandwidth scale linearly with context length. Existing KV eviction methods often rely on static heuristics or proxy scores, which poorly track future token utility and cause brittle eviction as relevance shifts. To address this, we introduce KVpop, which learns a fixed-budget KV eviction policy by directly supervising the keep-or-drop decision. The scorer is trained against a novel future-attention target, computed efficiently without materializing dense attention maps. We further introduce a delayed memory-based scorer that, uniquely among learned eviction methods, defers scoring for a fixed number of steps to exploit near-future context. On AIME and HMMT mathematical reasoning, KVpop retains 98% of full-attention performance on Qwen3-4B at 75% KV cache compression and 97% at 88% compression, consistently outperforming established eviction baselines. Qwen3-8B shows even stronger results, reaching near-full teacher performance. These results show that supervising eviction with future-attention signals cuts memory costs while maintaining quality.