Multiple Importance Sampling for Guided Speculative Inference

Large language models (LLMs) have achieved state-of-the-art performance across a wide range of tasks, motivating two important aspects of deployment: inference efficiency and output provenance, which can be tackled by speculative sampling and watermarking, respectively. However, recent works have shown that combining these two goals is highly nontrivial and can be potentially impossible. In this work, we develop a novel multi-draft speculative sampling algorithm based on Poisson processes that improves the frontier of this fundamental trade-off. The proposed algorithm has strong sampling efficiency on its own and, more interestingly, is naturally watermarkable: we can embed an unbiased watermark without degrading speculative acceptance. Moreover, our algorithm is based on an exact list-coupling-without-communication scheme, which yields a drafter invariance property that benefits both sampling and watermarking. It is the first multi-draft, drafter-invariant speculative sampling scheme that maintains both watermark strength and sampling efficiency, and we experimentally verify its strong performance in both aspects.

Generating diverse responses is crucial for test-time scaling of large language models (LLMs), yet standard stochastic sampling mostly yields surface-level lexical variation, limiting semantic exploration. In this paper, we propose Exploratory Sampling (ESamp), a decoding approach that explicitly encourages semantic diversity during generation. ESamp is motivated by the well-known observation that neural networks tend to make lower-error predictions on inputs similar to those encountered before, and incur higher prediction error on novel ones. Building on this property, we train a lightweight Distiller at test time to predict deep-layer hidden representations of the LLM from its shallow-layer representations to model the LLM's depth-wise representation transitions. During decoding, the Distiller continuously adapts to the mappings induced by the current generation context. ESamp uses the prediction error as a novelty signal to reweight candidate token extensions conditioned on the current prefix, thereby biasing decoding toward less-explored semantic patterns. ESamp is implemented with an asynchronous training--inference pipeline, with less than 5% worst case overhead (1.2% in the optimized release). Empirical results show that ESamp significantly boosts the Pass@k efficiency of reasoning models, showing superior or comparable performance to strong stochastic and heuristic baselines. Notably, ESamp achieves robust generalization across mathematics, science, and code generation benchmarks and breaks the trade-off between diversity and coherence in creative writing. Our code has released at: https://github.com/LinesHogan/tLLM.

We study how to improve LLM reasoning at inference time without updating model weights or using external reward models. Recent reward-free power-sampling methods define the sequence-level power target $π_α(y\mid x)\propto p_0(y\mid x)^α$, where $α>1$, which increases the relative probability of completions that are already likely under the base model. Existing methods use Metropolis--Hastings or Sequential Monte Carlo (SMC) to approximately sample from this target. However, two challenges arise at different levels. At the target level, full-sequence sharpening can concentrate probability on a few exact reasoning--answer trajectories, suppressing alternative paths that support the same answer. At the sampler level, finite-particle SMC can suffer from path collapse when resampling repeatedly duplicates a few high-weight prefixes. To address these challenges, we propose Decoupled Marginal Sharpening (DMS), which separately controls how strongly the model favors particular reasoning paths and how strongly it favors final answers after aggregating support across those paths. At the target level, DMS first samples from a sharpened reasoning distribution, then marginalizes the model's answer probabilities over the resulting weighted reasoning population and sharpens the induced answer marginal. Separate exponents allow mild reasoning sharpening to encourage exploration of diverse paths, followed by stronger answer-marginal sharpening to concentrate probability on answers with greater aggregate support across those paths. At the sampler level, we develop Fully Adapted Annealed SMC, which combines an annealed sequence of power targets with locally fully adapted proposals and predictive ancestor resampling. Experiments on MATH500, GPQA-Diamond, HumanEval, and AIME24/25 across three base models show that DMS achieves the highest mean pass@1 among the compared methods in all tasks.