Distribution-Aware Companding Quantization of Large Language Models

Large Language Models (LLMs) possess latent multi-token prediction (MTP) abilities despite being trained only for next-token generation. We introduce ESP (Embedding-Space Probing), a simple and training-free MTP method that probes an LLM using on-the-fly mask tokens drawn from its embedding space, enabling parallel future-token prediction without modifying weights or relying on draft models. ESP constructs a speculative token tree by sampling Top-K candidates from mask-token logits and applies a lightweight pruning rule to retain high-probability continuations. During generation, predictions are verified in parallel, yielding lossless decoding while significantly reducing model calls and increasing token throughput. ESP consistently outperforms existing training-free baselines, improving acceptance length by 7-11% over LADE on LLaMA3 and 7-8% on Qwen3, and increasing throughput by up to 15-19% over the strongest baseline. Finally, we provide theoretical insight and empirical evidence showing that decoder layers naturally align mask-token representations with next-token states, enabling accurate multi-step prediction without retraining or auxiliary models.

Next-token prediction (NTP) is the standard pretraining objective for large language models, yet it provides an explicit training signal only for the immediate next token, which can lead models to exploit local patterns instead of capturing longer-range structure and ideas. Multi-token prediction (MTP) addresses this by training models to predict several future tokens. However, existing MTP methods often introduce a large number of new parameters with limited improvements in downstream performance. Latent MTP approaches address this efficiency issue by encoding future tokens into a vector representation. However, these approaches usually rely on external helper models for future token encoding. We propose LightMTP, a lightweight, i.e., parameter-efficient, latent MTP approach that bootstraps the future token representations from the model's own hidden states. Our two LightMTP variants extend supervision to more future tokens without requiring the additional computational overhead of conventional MTP nor the external supervision latent MTP normally relies on. LightMTP adds at most 1% extra parameters, retains better performance on general language modeling benchmarks, and achieves similar gains in planning, coding, and reasoning.

Multi-token prediction (MTP) improves the throughput of autoregressive generation by enabling the language model to draft multiple next tokens per forward pass, while a verification step over draft tokens ensures that token distribution of the backbone is preserved. Every open MTP-family release (MiMo-7B, DeepSeek-V3, Qwen3) trains its heads jointly with the backbone over the full pretraining run of tens of trillions of tokens, thus setting the drafter quality at pretraining time. We ask whether a lightweight post-training pass on target-generated chain-of-thought is enough to reach the same expected throughput speedup on a frozen reasoning model, and study how a serving-time system built on such a checkpoint can be optimized. We present three findings. 1) On a frozen Qwen3-8B with $K{=}3$ chained MTP heads, we show that a post-training recipe with plain cross-entropy on $\approx\!2.5$B tokens reaches or exceeds the expected speedup of jointly trained MiMo-7B on math, coding and knowledge benchmarks. Our post-training recipe utilizes $10^3$-$10^4\times$ less MTP-training tokens as compared with joint pre-training of MiMO-7B MTP baseline. 2) We propose a chain-aware relaxation of draft token verification rule that allows a bounded drift from backbone language model token distribution. We show that this relaxation lifts expected speedups by $+12$ to $+16\%$ per benchmark while preserving task accuracy. 3) We propose an adaptive controller that dynamically chooses the number of MTP heads to be engaged at inference time and demonstrate recovery of upto $11$--$14\%$ loss in speedup using fixed maximum MTP draft length.