Numerical Error Analysis of Large Language Models

Large language models based on transformer architectures have become integral to state-of-the-art natural language processing applications. However, their training remains computationally expensive and exhibits instabilities, some of which are expected to be caused by finite-precision computations. We provide a theoretical analysis of the impact of round-off errors within the forward pass of a transformer architecture which yields fundamental bounds for these effects. In addition, we conduct a series of numerical experiments which demonstrate the practical relevance of our bounds. Our results yield concrete guidelines for choosing hyperparameters that mitigate round-off errors, leading to more robust and stable inference.

PLPP: Prompt Learning with Perplexity Is Self-Distillation for Vision-Language Models

Pre-trained Vision-Language (VL) models such as CLIP have demonstrated their excellent performance across numerous downstream tasks. A recent method, Context Optimization (CoOp), further improves the performance of VL models on downstream tasks by introducing prompt learning. CoOp optimizes a set of learnable vectors, aka prompt, and freezes the whole CLIP model. However, relying solely on CLIP loss to fine-tune prompts can lead to models that are prone to overfitting on downstream task. To address this issue, we propose a plug-in prompt-regularization method called PLPP (Prompt Learning with PerPlexity), which use perplexity loss to regularize prompt learning. PLPP designs a two-step operation to compute the perplexity for prompts: (a) calculating cosine similarity between the weight of the embedding layer and prompts to get labels, (b) introducing a language model (LM) head that requires no training behind text encoder to output word probability distribution. Meanwhile, we unveil that the essence of PLPP is inherently a form of self-distillation. To further prevent overfitting as well as to reduce the additional computation introduced by PLPP, we turn the hard label to soft label and choose top-$k$ values for calculating the perplexity loss. For accelerating model convergence, we introduce mutual self-distillation learning, that is perplexity and inverted perplexity loss. The experiments conducted on four classification tasks indicate that PLPP exhibits superior performance compared to existing methods.

Training Overhead Ratio: A Practical Reliability Metric for Large Language Model Training Systems

Large Language Models (LLMs) are revolutionizing the AI industry with their superior capabilities. Training these models requires large-scale GPU clusters and significant computing time, leading to frequent failures that significantly increase training costs. Despite its significance, this field lacks a metric for evaluating reliability. In this work, we introduce a novel reliability metric called \emph{Training Overhead Ratio} (TOR) to evaluate the reliability of fault-tolerant LLM training systems. TOR is defined as the ratio of optimal training time to the observed training time of a system, serving as a practical tool for users to estimate the actual time required to train an LLM on a given system. Furthermore, our investigation identifies the key factor for enhancing reliability and present TOR equations for various types of failures encountered in practice.