Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences. One effective way to accelerate inference is Speculative Decoding, which employs a small model to sample a sequence of draft tokens and a large model to validate. Given its empirical effectiveness, the theoretical understanding of Speculative Decoding is falling behind. This paper tackles this gap by conceptualizing the decoding problem via markov chain abstraction and studying the key properties, output quality and inference acceleration, from a theoretical perspective. Our analysis covers the theoretical limits of speculative decoding, batch algorithms, and output quality-inference acceleration tradeoffs. Our results reveal the fundamental connections between different components of LLMs via total variation distances and show how they jointly affect the efficiency of decoding algorithms.

The recent emergence of Large Language Models based on the Transformer architecture has enabled dramatic advancements in the field of Natural Language Processing. However, these models have long inference latency, which limits their deployment and makes them prohibitively expensive for various real-time applications. The inference latency is further exacerbated by autoregressive generative tasks, as models need to run iteratively to generate tokens sequentially without leveraging token-level parallelization. To address this, we propose Big Little Decoder (BiLD), a framework that can improve inference efficiency and latency for a wide range of text generation applications. The BiLD framework contains two models with different sizes that collaboratively generate text.

The growing demand for on-device large language model (LLM) inference highlights the need for efficient mobile edge computing (MEC) solutions, especially in resource-constrained settings. Speculative decoding offers a promising solution by partitioning token generation between a lightweight draft model on mobile devices and a powerful target model on edge servers, but suffers from communication overhead and asynchronous delays. This paper is the first to propose a unified framework that jointly optimizes user association and resource allocation (UARA) to support efficient parallel speculative decoding. We solve the UARA problem using a multi-agent deep reinforcement learning algorithm. To evaluate our approach under realistic conditions, we conduct experiments using the Sionna simulator. Results show that our method achieves up to 28.0% and an average of 23.7% reduction in end-to-end latency without compromising inference accuracy, enabling scalable and low-latency LLM services in MEC systems.

We present Cacheback Decoding, a training-free and model-agnostic speculative decoding method that exploits the locality in language to accelerate Large Language Model (LLM) inference. Cacheback leverages only Least Recently Used (LRU) cache tables of token n-grams to generate draft sequences. Cacheback achieves state-of-the-art performance among comparable methods despite its minimalist design, and its simplicity allows easy integration into existing systems. Cacheback also shows potential for fast adaptation to new domains.

Speculative decoding accelerates LLM inference by utilizing otherwise idle computational resources during memory-to-chip data transfer. Current speculative decoding methods typically assume a considerable amount of available computing power, then generate a complex and massive draft tree using a small autoregressive language model to improve overall prediction accuracy. However, methods like batching have been widely applied in mainstream model inference systems as a superior alternative to speculative decoding, as they compress the available idle computing power. Therefore, performing speculative decoding with low verification resources and low scheduling costs has become an important research problem. We believe that more capable models that allow for parallel generation on draft sequences are what we truly need. Recognizing the fundamental nature of draft models to only generate sequences of limited length, we propose SpecFormer, a novel architecture that integrates unidirectional and bidirectional attention mechanisms. SpecFormer combines the au-toregressive model's ability to extract information from the entire input sequence with the parallel generation benefits of non-autoregressive models. This design eliminates the reliance on large prefix trees and achieves consistent acceleration, even in large-batch scenarios. Through lossless speculative decoding experiments across models of various scales, we demonstrate that SpecFormer sets a new standard for scaling LLM inference with lower training demands and reduced computational costs.

Modern web applications--from real-time content recommendation and dynamic pricing to CDN optimization--increasingly rely on time-series forecasting to deliver personalized experiences to billions of users. Large-scale Transformer-based models have achieved state-of-the-art performance in time-series forecasting but suffer from high computational costs, limiting their deployment in latency-sensitive web applications. To address this challenge, we propose a general inference acceleration framework that adapts speculative decoding to autoregressive time-series models. Our approach employs a smaller "draft" model to propose future time-series patches, which are then verified in parallel by a larger "target" model, reducing the number of sequential forward passes required. We address key technical challenges in adapting this technique from discrete language tokens to continuous time-series distributions, including the design of acceptance criteria for multivariate Gaussian patches and practical variants that balance efficiency with accuracy. Through experiments on time series forecasting benchmarks relevant to web applications, we demonstrate significant inference speedups while maintaining competitive accuracy. The framework requires no architectural modifications to existing foundation models, making it immediately applicable to accelerate deployed time-series forecasting systems. Our implementation can be found at https://github.com/PranavSubbaraman/STRIDE

We introduce AutoJudge, a method that accelerates large language model (LLM) inference with task-specific lossy speculative decoding. Instead of matching the original model output distribution token-by-token, we identify which of the generated tokens affect the downstream quality of the response, relaxing the distribution match guarantee so that the "unimportant" tokens can be generated faster. Our approach relies on a semi-greedy search algorithm to test which of the mismatches between target and draft models should be corrected to preserve quality and which ones may be skipped. We then train a lightweight classifier based on existing LLM embeddings to predict, at inference time, which mismatching tokens can be safely accepted without compromising the final answer quality. We evaluate the effectiveness of AutoJudge with multiple draft/target model pairs on mathematical reasoning and programming benchmarks, achieving significant speedups at the cost of a minor accuracy reduction. Notably, on GSM8k with the Llama 3.1 70B target model, our approach achieves up to $\approx2\times$ speedup over speculative decoding at the cost of $\le 1\%$ drop in accuracy. When applied to the LiveCodeBench benchmark, AutoJudge automatically detects programming-specific important tokens, accepting $\ge 25$ tokens per speculation cycle at $2\%$ drop in Pass@1. Our approach requires no human annotation and is easy to integrate with modern LLM inference frameworks.

Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences.

Speculative decoding accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens that are later verified by a stronger target model. While effective in centralized systems, its behavior in decentralized settings, where network latency often dominates compute, remains under-characterized. We present Decentralized Speculative Decoding (DSD), a plug-and-play framework for decentralized inference that turns communication delay into useful computation by verifying multiple candidate tokens in parallel across distributed nodes. We further introduce an adaptive speculative verification strategy that adjusts acceptance thresholds by token-level semantic importance, delivering an additional 15% to 20% end-to-end speedup without retraining. In theory, DSD reduces cross-node communication cost by approximately (N-1)t1(k-1)/k, where t1 is per-link latency and k is the average number of tokens accepted per round. In practice, DSD achieves up to 2.56x speedup on HumanEval and 2.59x on GSM8K, surpassing the Eagle3 baseline while preserving accuracy. These results show that adapting speculative decoding for decentralized execution provides a system-level optimization that converts network stalls into throughput, enabling faster distributed LLM inference with no model retraining or architectural changes.

Speculative decoding accelerates language model inference by separating generation into fast drafting and parallel verification. Its main limitation is drafter-verifier misalignment, which limits token acceptance and reduces overall effectiveness. While small drafting heads trained from scratch compensate with speed, they struggle when verification dominates latency or when inputs are out of distribution. In contrast, pretrained drafters, though slower, achieve higher acceptance rates thanks to stronger standalone generation capabilities, making them competitive when drafting latency is negligible relative to verification or communication overhead. In this work, we aim to improve the acceptance rates of pretrained drafters by introducing a lightweight dynamic alignment mechanism: a steering vector computed from the verifier's hidden states and injected into the pretrained drafter. Compared to existing offline alignment methods such as distillation, our approach boosts the number of accepted tokens by up to 35\% under standard sampling and 22\% under greedy sampling, all while incurring negligible computational overhead. Importantly, our approach can be retrofitted to existing architectures and pretrained models, enabling rapid adoption.