Speculative decoding speed-of-light: Optimal lower bounds via branching random walks

conference paper Speculative decoding speed-of-light: Optimal lower bounds via branching random walks published yes Sergei Pankratov author f773bf05-72ef-11ef-b75a-a383d22f454b Dan-Adrian Alistarh author 4A899BFC-F248-11E8-B48F-1D18A9856A870000-0003-3650-940X DaAl department GradSch department EACL: Conference of the European Chapter of the Association for Computational Linguistics Speculative generation has emerged as a promising technique to accelerate inference in large language models (LLMs) by leveraging parallelism to verify multiple draft tokens simultaneously. However, the fundamental limits on the achievable speedup remain poorly understood. In this work, we establish the first “tight” lower bounds on the runtime of any deterministic speculative generation algorithm. This is achieved by drawing a parallel between the token generation process and branching random walks, which allows us to analyze the optimal draft tree selection problem. We prove, under basic assumptions, that the expected number of tokens successfully predicted per speculative iteration is bounded as \mathbb{E}[X] ≤ (𝜇 + 𝜇(2))log(B )/𝜇2 + O(1), where B is the verifier’s batch size, 𝜇 is the expected entropy of the verifier’s output distribution, and 𝜇(2) is this entropy’s second moment. This result provides new insights into the limits of parallel token generation, and could guide the design of future speculative decoding systems. Empirical evaluations on Llama models validate our theoretical predictions, confirming the tightness of our bounds in practical settings. Association for Computational Linguistics2026Rabat, Morocco eng Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics 2512.1171810.18653/v1/2026.eacl-long.301 6404–6418 Pankratov S, Alistarh D-A. 2026. Speculative decoding speed-of-light: Optimal lower bounds via branching random walks. Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics. EACL: Conference of the European Chapter of the Association for Computational Linguistics, 6404–6418. Pankratov, Sergei, and Dan-Adrian Alistarh. “Speculative Decoding Speed-of-Light: Optimal Lower Bounds via Branching Random Walks.” In Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics, 6404–6418. Association for Computational Linguistics, 2026. <a href="https://doi.org/10.18653/v1/2026.eacl-long.301">https://doi.org/10.18653/v1/2026.eacl-long.301</a>. Pankratov, S., & Alistarh, D.-A. (2026). Speculative decoding speed-of-light: Optimal lower bounds via branching random walks. In Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (pp. 6404–6418). Rabat, Morocco: Association for Computational Linguistics. <a href="https://doi.org/10.18653/v1/2026.eacl-long.301">https://doi.org/10.18653/v1/2026.eacl-long.301</a> Pankratov S, Alistarh D-A. Speculative decoding speed-of-light: Optimal lower bounds via branching random walks. In: Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics. Association for Computational Linguistics; 2026:6404–6418. doi:<a href="https://doi.org/10.18653/v1/2026.eacl-long.301">10.18653/v1/2026.eacl-long.301</a> S. Pankratov and D.-A. Alistarh, “Speculative decoding speed-of-light: Optimal lower bounds via branching random walks,” in Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics, Rabat, Morocco, 2026, pp. 6404–6418. Pankratov, Sergei, and Dan-Adrian Alistarh. “Speculative Decoding Speed-of-Light: Optimal Lower Bounds via Branching Random Walks.” Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics, Association for Computational Linguistics, 2026, pp. 6404–6418, doi:<a href="https://doi.org/10.18653/v1/2026.eacl-long.301">10.18653/v1/2026.eacl-long.301</a>. S. Pankratov, D.-A. Alistarh, in:, Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics, Association for Computational Linguistics, 2026, pp. 6404–6418. 223022026-07-13T10:48:03Z2026-07-14T06:18:11Z