We introduce a novel index, the Distribution of Cosine Similarity (DOCS), for quantitatively assessing the similarity between weight matrices in Large Language Models (LLMs), aiming to facilitate the analysis of their complex architectures. Leveraging DOCS, our analysis uncovers intriguing patterns in the latest open-source LLMs: adjacent layers frequently exhibit high weight similarity and tend to form clusters, suggesting depth-wise functional specialization. Additionally, we prove that DOCS is theoretically effective in quantifying similarity for orthogonal matrices, a crucial aspect given the prevalence of orthogonal initializations in LLMs. This research contributes to a deeper understanding of LLM architecture and behavior, offering tools with potential implications for developing more efficient and interpretable models.

Semi-supervised learning algorithms that use pseudo-labeling have become increasingly popular for improving model performance by utilizing both labeled and unlabeled data. In this paper, we offer a fresh perspective on the selection of pseudo-labels, inspired by theoretical insights. We suggest that pseudo-labels with a high degree of local variance are more prone to inaccuracies. Based on this premise, we introduce the Local Variance Match (LVM) method, which aims to optimize the selection of pseudo-labels in semi-supervised learning (SSL) tasks. Our methodology is validated through a series of experiments on widely-used image classification datasets, such as CIFAR-10, CIFAR-100, and SVHN, spanning various labeled data quantity scenarios. The empirical findings show that the LVM method substantially outpaces current SSL techniques, achieving state-of-the-art results in many of these scenarios. For instance, we observed an error rate of 5.41% on CIFAR-10 with a single label for each class, 35.87% on CIFAR-100 when using four labels per class, and 1.94% on SVHN with four labels for each class. Notably, the standout error rate of 5.41% is less than 1% shy of the performance in a fully-supervised learning environment. In experiments on ImageNet with 100k labeled data, the LVM also reached state-of-the-art outcomes. Additionally, the efficacy of the LVM method is further validated by its stellar performance in speech recognition experiments.

In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with (normalized) gradients, focusing on their role in margin maximization. Inspired by this analysis, we propose a novel algorithm called Progressive Rescaling Gradient Descent (PRGD) and show that PRGD can maximize the margin at an exponential rate. This stands in stark contrast to all existing algorithms, which maximize the margin at a slow polynomial rate. Specifically, we identify mild conditions on data distribution under which existing algorithms such as gradient descent (GD) and normalized gradient descent (NGD) provably fail in maximizing the margin efficiently. To validate our theoretical findings, we present both synthetic and real-world experiments. Notably, PRGD also shows promise in enhancing the generalization performance when applied to linearly non-separable datasets and deep neural networks.

In this paper, we propose a novel Siamese Adversarial Network (SAN) architecture for automatic speech recognition, which aims at solving the difficulty of fuzzy audio recognition. Specifically, SAN constructs two sub-networks to differentiate the audio feature input and then introduces a loss to unify the output distribution of these sub-networks. Adversarial learning enables the network to capture more essential acoustic features and helps the models achieve better performance when encountering fuzzy audio input. We conduct numerical experiments with the SAN model on several datasets for the automatic speech recognition task. All experimental results show that the siamese adversarial nets significantly reduce the character error rate (CER). Specifically, we achieve a competitive 4.37 CER result on the AISHELL-1 dataset without any language models. To reveal the generality of the siamese adversarial net, we also conduct experiments on the phoneme recognition task, which also shows the superiority of the siamese adversarial network.