In this paper, we investigate the limitations of the Vector Quantized Latent Diffusion Model (VQ-LDM) in restoration tasks. We identify a performance gap between the Vector Quantization (VQ) and Diffusion Model components, manifested as a significant discrepancy between the reconstruction quality of ground truth images processed via VQ autoregression and degraded images restored by VQ-LDM. Through experiments, we attribute this gap primarily to the lack of robustness in the mapped points of VQ within the original VQ-LDM framework. To address this issue, we propose a geometric based optimization approach. First, we introduce a simple yet effective method, termed interpolation-based latent initial state optimization, which mitigates the performance gap by replacing the original mapped points with interpolated values, supported by theoretical analysis. Here, the latent initial state refers specifically to the input of the diffusion model. Building upon this, we further propose a Chebyshev center-based latent initial state optimization, an elegant theoretical solution from a geometric perspective, that further enhances restoration performance. Our improvements consistently achieve superior results across nine benchmark datasets.

Striking an optimal balance between minimal drafting latency and high speculation accuracy to enhance the inference speed of Large Language Models remains a significant challenge in speculative decoding. In this paper, we introduce Falcon, an innovative semi-autoregressive speculative decoding framework fashioned to augment both the drafter's parallelism and output quality. Falcon incorporates the Coupled Sequential Glancing Distillation technique, which fortifies inter-token dependencies within the same block, leading to increased speculation accuracy. We offer a comprehensive theoretical analysis to illuminate the underlying mechanisms. Additionally, we introduce a Custom-Designed Decoding Tree, which permits the drafter to generate multiple tokens in a single forward pass and accommodates multiple forward passes as needed, thereby boosting the number of drafted tokens and significantly improving the overall acceptance rate. Comprehensive evaluations on benchmark datasets such as MT-Bench, HumanEval, and GSM8K demonstrate Falcon's superior acceleration capabilities. The framework achieves a lossless speedup ratio ranging from 2.91x to 3.51x when tested on the Vicuna and LLaMA2-Chat model series. These results outstrip existing speculative decoding methods for LLMs, including Eagle, Medusa, Lookahead, SPS, and PLD, while maintaining a compact drafter architecture equivalent to merely two Transformer layers.

Computational complexity and overthinking problems have become the bottlenecks for pre-training language models (PLMs) with millions or even trillions of parameters. A Flexible-Patience-Based Early Exiting method (F-PABEE) has been proposed to alleviate the problems mentioned above for single-label classification (SLC) and multi-label classification (MLC) tasks. F-PABEE makes predictions at the classifier and will exit early if predicted distributions of cross-layer are consecutively similar. It is more flexible than the previous state-of-the-art (SOTA) early exiting method PABEE because it can simultaneously adjust the similarity score thresholds and the patience parameters. Extensive experiments show that: (1) F-PABEE makes a better speedup-accuracy balance than existing early exiting strategies on both SLC and MLC tasks. (2) F-PABEE achieves faster inference and better performances on different PLMs such as BERT and ALBERT. (3) F-PABEE-JSKD performs best for F-PABEE with different similarity measures.