Speculative decoding is a powerful technique that accelerates Large Language Model (LLM) inference by leveraging a lightweight speculative draft model. However, existing designs suffers in performance due to misalignment between training and inference. Recent methods have tried to solve this issue by adopting a multi-step training strategy, but the complex inputs of different training steps make it harder for the draft model to converge. To address this, we propose CORAL, a novel framework that improves both accuracy and efficiency in speculative drafting. CORAL introduces Cross-Step Representation Alignment, a method that enhances consistency across multiple training steps, significantly improving speculative drafting performance. Additionally, we identify the LM head as a major bottleneck in the inference speed of the draft model. We introduce a weight-grouping mechanism that selectively activates a subset of LM head parameters during inference, substantially reducing the latency of the draft model. We evaluate CORAL on three LLM families and three benchmark datasets, achieving speedup ratios of 2.50x-4.07x, outperforming state-of-the-art methods such as EAGLE-2 and HASS. Our results demonstrate that CORAL effectively mitigates training-inference misalignment and delivers significant speedup for modern LLMs with large vocabularies.

Despite the effectiveness in improving the robustness of neural networks, adversarial training has suffered from the natural accuracy degradation problem, i.e., accuracy on natural samples has reduced significantly. In this study, we reveal that natural accuracy degradation is highly related to the disruption of the natural sample topology in the representation space by quantitative and qualitative experiments. Based on this observation, we propose Topology-pReserving Adversarial traINing (TRAIN) to alleviate the problem by preserving the topology structure of natural samples from a standard model trained only on natural samples during adversarial training. As an additional regularization, our method can easily be combined with various popular adversarial training algorithms in a plug-and-play manner, taking advantage of both sides. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny ImageNet show that our proposed method achieves consistent and significant improvements over various strong baselines in most cases. Specifically, without additional data, our proposed method achieves up to 8.78% improvement in natural accuracy and 4.50% improvement in robust accuracy.