The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner.

The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner.

As a powerful tool for characterizing cellular subpopulations and cellular heterogeneity, single cell RNA sequencing (scRNA-seq) technology offers advantages of high throughput and multidimensional analysis. However, the process of data acquisition is often constrained by high cost and limited sample availability. To overcome these limitations, we propose a hybrid model based on Diffusion model and White-Box transformer that aims to generate synthetic and biologically plausible scRNA-seq data. Diffusion model progressively introduce noise into the data and then recover the original data through a denoising process, a forward and reverse process that is particularly suitable for generating complex data distributions. White-Box transformer is a deep learning architecture that emphasizes mathematical interpretability. By minimizing the encoding rate of the data and maximizing the sparsity of the representation, it not only reduces the computational burden, but also provides clear insight into underlying structure. Our White-Box Diffusion Transformer combines the generative capabilities of Diffusion model with the mathematical interpretability of White-Box transformer. Through experiments using six different single-cell RNA-Seq datasets, we visualize both generated and real data using t-SNE dimensionality reduction technique, as well as quantify similarity between generated and real data using various metrics to demonstrate comparable performance of White-Box Diffusion Transformer and Diffusion Transformer in generating scRNA-seq data alongside significant improvements in training efficiency and resource utilization. Our code is available at https://github.com/lingximamo/White-Box-Diffusion-Transformer

Self-supervised learning (SSL) methods learn from unlabeled data and achieve high generalization performance on downstream tasks. However, they may also suffer from overfitting to their training data and lose the ability to adapt to new tasks. To investigate this phenomenon, we conduct experiments on various SSL methods and datasets and make two observations: (1) Overfitting occurs abruptly in later layers and epochs, while generalizing features are learned in early layers for all epochs; (2) Coding rate reduction can be used as an indicator to measure the degree of overfitting in SSL models. Based on these observations, we propose Undoing Memorization Mechanism (UMM), a plug-and-play method that mitigates overfitting of the pre-trained feature extractor by aligning the feature distributions of the early and the last layers to maximize the coding rate reduction of the last layer output. The learning process of UMM is a bi-level optimization process. We provide a causal analysis of UMM to explain how UMM can help the pre-trained feature extractor overcome overfitting and recover generalization. We also demonstrate that UMM significantly improves the generalization performance of SSL methods on various downstream tasks.

The key to effective point cloud compression is to obtain a robust context model consistent with complex 3D data structures. Recently, the advancement of large language models (LLMs) has highlighted their capabilities not only as powerful generators for in-context learning and generation but also as effective compressors. These dual attributes of LLMs make them particularly well-suited to meet the demands of data compression. Therefore, this paper explores the potential of using LLM for compression tasks, focusing on lossless point cloud geometry compression (PCGC) experiments. However, applying LLM directly to PCGC tasks presents some significant challenges, i.e., LLM does not understand the structure of the point cloud well, and it is a difficult task to fill the gap between text and point cloud through text description, especially for large complicated and small shapeless point clouds. To address these problems, we introduce a novel architecture, namely the Large Language Model-based Point Cloud Geometry Compression (LLM-PCGC) method, using LLM to compress point cloud geometry information without any text description or aligning operation. By utilizing different adaptation techniques for cross-modality representation alignment and semantic consistency, including clustering, K-tree, token mapping invariance, and Low Rank Adaptation (LoRA), the proposed method can translate LLM to a compressor/generator for point cloud. To the best of our knowledge, this is the first structure to employ LLM as a compressor for point cloud data. Experiments demonstrate that the LLM-PCGC outperforms the other existing methods significantly, by achieving -40.213% bit rate reduction compared to the reference software of MPEG Geometry-based Point Cloud Compression (G-PCC) standard, and by achieving -2.267% bit rate reduction compared to the state-of-the-art learning-based method.

Deep learning has achieved remarkable success in graph-related tasks, yet this accomplishment heavily relies on large-scale high-quality annotated datasets. However, acquiring such datasets can be cost-prohibitive, leading to the practical use of labels obtained from economically efficient sources such as web searches and user tags. Unfortunately, these labels often come with noise, compromising the generalization performance of deep networks. To tackle this challenge and enhance the robustness of deep learning models against label noise in graph-based tasks, we propose a method called ERASE (Error-Resilient representation learning on graphs for lAbel noiSe tolerancE). The core idea of ERASE is to learn representations with error tolerance by maximizing coding rate reduction. Particularly, we introduce a decoupled label propagation method for learning representations. Before training, noisy labels are pre-corrected through structural denoising. During training, ERASE combines prototype pseudo-labels with propagated denoised labels and updates representations with error resilience, which significantly improves the generalization performance in node classification. The proposed method allows us to more effectively withstand errors caused by mislabeled nodes, thereby strengthening the robustness of deep networks in handling noisy graph data. Extensive experimental results show that our method can outperform multiple baselines with clear margins in broad noise levels and enjoy great scalability. Codes are released at https://github.com/eraseai/erase.

The central question of ensemble learning has been: what factors make an ensemble system good or bad? It has We propose a fundamental theory on ensemble been widely believed that accurate and diverse models lead learning that answers the central question: what to better performance for ensemble systems. Guided by factors make an ensemble system good or bad? this intuition, many heuristical metrics have been proposed Previous studies used a variant of Fano's inequality to measure accuracy and diversity (Kohavi et al., 1996; of information theory and derived a lower Skalak et al., 1996; Cunningham & Carney, 2000; Shipp bound of the classification error rate on the basis & Kuncheva, 2002). However, these metrics lack theoretical of the accuracy and diversity of models. We grounding, and indeed, Kuncheva & Whitaker (2003) revisit the original Fano's inequality and argue empirically showed that there are no connections between that the studies did not take into account the information the metrics and system performance through a broad range lost when multiple model predictions of experiments. Turning to theoretical viewpoints, Geman are combined into a final prediction. To address et al. (1992) decomposed the squared error loss used in regression this issue, we generalize the previous theory to tasks into the bias and covariance of models. Bias incorporate the information loss, which we name here corresponds to accuracy and covariance diversity.

We propose a federated methodology to learn low-dimensional representations from a dataset that is distributed among several clients. In particular, we move away from the commonly-used cross-entropy loss in federated learning, and seek to learn shared low-dimensional representations of the data in a decentralized manner via the principle of maximal coding rate reduction (MCR2). Our proposed method, which we refer to as FLOW, utilizes MCR2 as the objective of choice, hence resulting in representations that are both between-class discriminative and within-class compressible. We theoretically show that our distributed algorithm achieves a first-order stationary point. Moreover, we demonstrate, via numerical experiments, the utility of the learned low-dimensional representations.

Ten years into the revival of deep networks and artificial intelligence, we propose a theoretical framework that sheds light on understanding deep networks within a bigger picture of Intelligence in general. We introduce two fundamental principles, Parsimony and Self-consistency, that address two fundamental questions regarding Intelligence: what to learn and how to learn, respectively. We believe the two principles are the cornerstones for the emergence of Intelligence, artificial or natural. While these two principles have rich classical roots, we argue that they can be stated anew in entirely measurable and computable ways. More specifically, the two principles lead to an effective and efficient computational framework, compressive closed-loop transcription, that unifies and explains the evolution of modern deep networks and many artificial intelligence practices. While we mainly use modeling of visual data as an example, we believe the two principles will unify understanding of broad families of autonomous intelligent systems and provide a framework for understanding the brain.