Speculative sampling (SpS) has been successful in accelerating the decoding throughput of auto-regressive large language models by leveraging smaller draft models. SpS strictly enforces the generated distribution to match that of the verifier LLM. This is unnecessarily restrictive as slight variations of the verifier's distribution, such as sampling with top-$k$ or temperature, would also be acceptable. Typical acceptance sampling (TAS) alleviates this issue by accepting more tokens using entropy-based heuristics. However, this approach distorts the verifier distribution, potentially degrading output quality when the verifier encodes critical information. In this work, we formalize the speculative sampling algorithm through the lens of constrained optimization. Based on this formulation, we propose Cactus (constrained acceptance speculative sampling), a method that guarantees controlled divergence from the verifier distribution and increasing acceptance rates. Empirical results across a wide range of benchmarks confirm the effectiveness of our approach.

Standard decoding strategies for text generation, including top-k, nucleus sampling, and contrastive search, select tokens based on likelihood, restricting selection to high-probability regions. Human language production operates differently: tokens are chosen for communicative appropriateness rather than statistical frequency. This mismatch creates a truncation blind spot: contextually appropriate but statistically rare tokens remain accessible to humans yet unreachable by likelihood-based decoding. We hypothesize this contributes to the detectability of machine-generated text. Analyzing over 1.8 million texts across eight language models, five decoding strategies, and 53 hyperparameter configurations, we find that 8-18% of human-selected tokens fall outside typical truncation boundaries. Simple classifiers trained on predictability and lexical diversity achieve remarkable detection rates. Crucially, neither model scale nor architecture correlates strongly with detectability; truncation parameters account for most variance. Configurations achieving low detectability often produce incoherent text, indicating that evading detection and producing natural text are distinct objectives. These findings suggest detectability is enhanced by likelihood-based token selection, not merely a matter of model capability.

Apart from linguistic transformations, synthesizing among statements usually requires specific synthesis rulesofstatements.

However, statements different from the original statement could also be logically consistent with respecttoagivencontext.

However, there's a lack of insight into how these models perform in terms

In this work, we study the performance of byte-level and subword-level autoregressive models when trained using a fixed compute budget.

Experimental results on six widely-used benchmarks demonstrate that compared to baselines,DEEPEN achieves consistent improvements across all benchmarks.