arXiv subjects

Zhiquan Tan

Publications and source records attributed to Zhiquan Tan.

25 records · Page 2Linked to original sources

arXiv2024

Contrastive Learning Is Spectral Clustering On Similarity Graph

Contrastive learning is a powerful self-supervised learning method, but we have a limited theoretical understanding of how it works and why it works. In this paper, we prove that contrastive learning with the standard InfoNCE loss is equivalent to spectral clustering on the similarity graph. Using this equivalence as the building block, we extend our analysis to the CLIP model and rigorously characterize how similar multi-modal objects are embedded together. Motivated by our theoretical insights, we introduce the Kernel-InfoNCE loss, incorporating mixtures of kernel functions that outperform the standard Gaussian kernel on several vision datasets. The code is available at https://github.com/yifanzhang-pro/Kernel-InfoNCE.

cs.LG↗

arXiv2024

Understanding Grokking Through A Robustness Viewpoint

Recently, an interesting phenomenon called grokking has gained much attention, where generalization occurs long after the models have initially overfitted the training data. We try to understand this seemingly strange phenomenon through the robustness of the neural network. From a robustness perspective, we show that the popular $l_2$ weight norm (metric) of the neural network is actually a sufficient condition for grokking. Based on the previous observations, we propose perturbation-based methods to speed up the generalization process. In addition, we examine the standard training process on the modulo addition dataset and find that it hardly learns other basic group operations before grokking, for example, the commutative law. Interestingly, the speed-up of generalization when using our proposed method can be explained by learning the commutative law, a necessary condition when the model groks on the test dataset. We also empirically find that $l_2$ norm correlates with grokking on the test data not in a timely way, we propose new metrics based on robustness and information theory and find that our new metrics correlate well with the grokking phenomenon and may be used to predict grokking.

cs.LG↗

arXiv2024

The Information of Large Language Model Geometry

This paper investigates the information encoded in the embeddings of large language models (LLMs). We conduct simulations to analyze the representation entropy and discover a power law relationship with model sizes. Building upon this observation, we propose a theory based on (conditional) entropy to elucidate the scaling law phenomenon. Furthermore, we delve into the auto-regressive structure of LLMs and examine the relationship between the last token and previous context tokens using information theory and regression techniques. Specifically, we establish a theoretical connection between the information gain of new tokens and ridge regression. Additionally, we explore the effectiveness of Lasso regression in selecting meaningful tokens, which sometimes outperforms the closely related attention weights. Finally, we conduct controlled experiments, and find that information is distributed across tokens, rather than being concentrated in specific "meaningful" tokens alone.

cs.LG↗

arXiv2023

Trade-off Between Efficiency and Consistency for Removal-based Explanations

In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques. Code is available at https://github.com/trusty-ai/efficient-consistent-explanations.

cs.LG↗

arXiv2023

Distributed Matrix Multiplication with a Smaller Recovery Threshold through Modulo-based Approaches

This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication problems to reduce the recovery threshold. This technique exploits the special structure of interpolation points and can be applied to many existing coded matrix designs. Recently studied discrete Fourier transform based code achieves a smaller recovery threshold than the optimal MatDot code with the expense that it cannot resist stragglers. We also propose a distributed matrix multiplication scheme based on the idea of locally repairable code to reduce the recovery threshold of MatDot code and provide resilience to stragglers. We also apply our constructions to a type of matrix computing problems, where generalized linear models act as a special case.

cs.IT↗

arXiv2023

Privacy-Preserving Polynomial Computing Over Distributed Data

In this letter, we delve into a scenario where a user aims to compute polynomial functions using their own data as well as data obtained from distributed sources. To accomplish this, the user enlists the assistance of $N$ distributed workers, thereby defining a problem we refer to as privacy-preserving polynomial computing over distributed data. To address this challenge, we propose an approach founded upon Lagrange encoding. Our method not only possesses the ability to withstand the presence of stragglers and byzantine workers but also ensures the preservation of security. Specifically, even if a coalition of $X$ workers collude, they are unable to acquire any knowledge pertaining to the data originating from the distributed sources or the user.

cs.CR↗

arXiv2023

SEAL: Simultaneous Label Hierarchy Exploration And Learning

Label hierarchy is an important source of external knowledge that can enhance classification performance. However, most existing methods rely on predefined label hierarchies that may not match the data distribution. To address this issue, we propose Simultaneous label hierarchy Exploration And Learning (SEAL), a new framework that explores the label hierarchy by augmenting the observed labels with latent labels that follow a prior hierarchical structure. Our approach uses a 1-Wasserstein metric over the tree metric space as an objective function, which enables us to simultaneously learn a data-driven label hierarchy and perform (semi-)supervised learning. We evaluate our method on several datasets and show that it achieves superior results in both supervised and semi-supervised scenarios and reveals insightful label structures. Our implementation is available at https://github.com/tzq1999/SEAL.

cs.LG↗