2026-09-25

On-policy distillation (OPD) corrects a student on the responses it writes, but its signal is the teacher's next-token distribution: it tells the student what the teacher says but misses how it thinks. Latent supervision promises the missing part by aligning the student's latent states to the teacher's. Recent methods such as OPRD bring this signal into on-policy distillation. However, we observe two failures of this recipe when distilling Qwen3-4B and Qwen3-8B into Qwen3-1.7B-Base. Early gain, late collapse: latent supervision alone lifts MATH-500 accuracy from 25 to 46 in 10 steps, but subsequent training degrades performance down to 11 with no recovery. Better alignment, worse behavior: although the alignment metric steadily improves throughout this collapse, the most aligned model turns out to be the worst performing. Further analysis suggests a mismatch in how the latent signal is applied: layers paired by depth play different roles in the two models, so continued alignment may pull the student toward teacher states it cannot understand. To address this, we propose LastOPD, which applies the latent signal only at the last-layer state, the common interface both LM heads read, and only during a 10-step crossfade into token-level OPD. This keeps the useful part of the latent signal and hands the student to token-level supervision before the collapse sets in. Extensive experiments show that LastOPD improves MATH-500 over token-only OPD by 5.55 and 4.02 points with the 4B and 8B teachers, leads on most held-out datasets, and reaches the final score of token-only OPD in about half the steps. Code is available at https://github.com/Muyiiiii/LastOPD.

Static pruning imposes one sparse structure on every prompt, even though reasoning, retrieval, generation, coding, and translation can depend on different parts of a language model. We introduce Task-Aware Spectral Pruning (TASP), a post-training framework that calibrates module-level spectral descriptors against measured task-specific ablation effects, closes grouped-query-attention and SwiGLU dependencies during sparse-mask construction, and routes each user turn to one compiled mask that remains fixed throughout prefill and decoding. A module-disjoint pilot first determines whether the spectral signal is informative before full calibration. Under the stated retrospective operating rule, the pilot passes on the evaluated Llama-3-8B and Llama-3-70B checkpoints but rejects Qwen2.5-1.5B, demonstrating that applicability is model-dependent rather than universal. At a 43% active-FLOP reduction, the Llama-3-70B benchmark harness retains 97.7 +/- 0.2% of the dense BF16 score. In the deployment-matched INT8-weight/BF16-compute runtime on a single A100 80GB, the compiled sparse path retains 97.3 +/- 0.2% relative to dense BF16 and reduces decode latency from 45.2 +/- 0.4 to 31.3 +/- 0.4 ms/token, yielding a 1.44x speedup. Factorized ablations, disjoint-module tests, compiled structured baselines, routing-corruption studies, and an explicit 136-GPU-hour calibration audit further delimit the source and operating regime of these gains

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, \textsc{FlashLoop} delivers lossless accuracy while achieving up to 1.64$\times$ end-to-end speedup and up to 6$\times$ KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.