We present a lookahead quality gate (verifier) for speculative decoding for reasoning or chain-of-thought language models. The gate accepts the longest reliable prefix of each k-token lookahead (block-wise) draft. Unlike token-level likelihood search, which is myopic and often rewards verbosity, or tree-level sampling methods that trade accuracy for latency, our approach works at an intermediate granularity. It uses only the base model’s hidden states to compute a geometry-based quality score for each prefix, then accepts the longest prefix whose score exceeds a quantile-calibrated threshold estimated from unlabeled prompts. The method integrates seamlessly with speculative/blockwise decoding and adds minimal runtime overhead, requiring no auxiliary heads, reward models, or finetuning. On math and science benchmarks, it improves accuracy over sampling baselines while achieving 2.6-7.9× faster generation.

In this paper, we propose a new kernel-based co-occurrence measure that can be applied to sparse linguistic expressions (e.g., sentences) with a very short learning time, as an alternative to pointwise mutual information (PMI). As well as deriving PMI from mutual information, we derive this new measure from the Hilbert–Schmidt independence criterion (HSIC); thus, we call the new measure the pointwise HSIC (PHSIC). PHSIC can be interpreted as a smoothed variant of PMI that allows various similarity metrics (e.g., sentence embeddings) to be plugged in as kernels. Moreover, PHSIC can be estimated by simple and fast (linear in the size of the data) matrix calculations regardless of whether we use linear or nonlinear kernels. Empirically, in a dialogue response selection task, PHSIC is learned thousands of times faster than an RNN-based PMI while outperforming PMI in accuracy. In addition, we also demonstrate that PHSIC is beneficial as a criterion of a data selection task for machine translation owing to its ability to give high (low) scores to a consistent (inconsistent) pair with other pairs.