Contrastive learning (CL) pretrains feature embeddings to scatter instances in the feature space so that the training data can be well discriminated. Most existing CL techniques usually encourage learning such feature embeddings in the highdimensional space to maximize the instance discrimination. However, this practice may lead to undesired results where the scattering instances are sparsely distributed in the high-dimensional feature space, making it difficult to capture the underlying similarity between pairwise instances. To this end, we propose a novel framework called contrastive learning with low-dimensional reconstruction (CLLR), which adopts a regularized projection layer to reduce the dimensionality of the feature embedding. In CLLR, we build the sparse / low-rank regularizer to adaptively reconstruct a low-dimensional projection space while preserving the basic objective for instance discrimination, and thus successfully learning contrastive embeddings that alleviate the above issue. Theoretically, we prove a tighter error bound for CLLR; empirically, the superiority of CLLR is demonstrated across multiple domains. Both theoretical and experimental results emphasize the significance of learning low-dimensional contrastive embeddings.

Evolutionary Reinforcement Learning (ERL), training the Reinforcement Learning (RL) policies with Evolutionary Algorithms (EAs), have demonstrated enhanced exploration capabilities and greater robustness than using traditional policy gradient. However, ERL suffers from the high computational costs and low search efficiency, as EAs require evaluating numerous candidate policies with expensive simulations, many of which are ineffective and do not contribute meaningfully to the training. One intuitive way to reduce the ineffective evaluations is to adopt the surrogates. Unfortunately, existing ERL policies are often modeled as deep neural networks (DNNs) and thus naturally represented as high-dimensional vectors containing millions of weights, which makes the building of effective surrogates for ERL policies extremely challenging. This paper proposes a novel surrogate-assisted ERL that integrates Autoencoders (AE) and Hyperbolic Neural Networks (HNN). Specifically, AE compresses high-dimensional policies into low-dimensional representations while extracting key features as the inputs for the surrogate. HNN, functioning as a classification-based surrogate model, can learn complex nonlinear relationships from sampled data and enable more accurate pre-selection of the sampled policies without real evaluations. The experiments on 10 Atari and 4 Mujoco games have verified that the proposed method outperforms previous approaches significantly. The search trajectories guided by AE and HNN are also visually demonstrated to be more effective, in terms of both exploration and convergence. This paper not only presents the first learnable policy embedding and surrogate-modeling modules for high-dimensional ERL policies, but also empirically reveals when and why they can be successful.

Knowing the learning dynamics of policy is significant to unveiling the mysteries of Reinforcement Learning (RL). It is especially crucial yet challenging to Deep RL, from which the remedies to notorious issues like sample inefficiency and learning instability could be obtained. In this paper, we study how the policy networks of typical DRL agents evolve during the learning process by empirically investigating several kinds of temporal change for each policy parameter. In popular MuJoCo and DeepMind Control Suite (DMC) environments, we find common phenomena for TD3 and RAD agents: (1) the activity of policy network parameters is highly asymmetric and policy networks advance monotonically along a very limited number of major parameter directions; (2) severe detours occur in parameter update and harmonic-like changes are observed for all minor parameter directions. By performing a novel temporal SVD along the policy learning path, the major and minor parameter directions are identified as the columns of the right unitary matrix associated with dominant and insignificant singular values respectively.

Traffic flow forecasting is a critical spatio-temporal data mining task with wide-ranging applications in intelligent route planning and dynamic traffic management. Recent advancements in deep learning, particularly through Graph Neural Networks (GNNs), have significantly enhanced the accuracy of these forecasts by capturing complex spatio-temporal dynamics. However, the scalability of GNNs remains a challenge due to their exponential growth in model complexity with increasing nodes in the graph. Existing methods to address this issue, including sparsification, decomposition, and kernel-based approaches, either do not fully resolve the complexity issue or risk compromising predictive accuracy. This paper introduces GraphSparseNet (GSNet), a novel framework designed to improve both the scalability and accuracy of GNN-based traffic forecasting models. GraphSparseNet is comprised of two core modules: the Feature Extractor and the Relational Compressor. These modules operate with linear time and space complexity, thereby reducing the overall computational complexity of the model to a linear scale. Our extensive experiments on multiple real-world datasets demonstrate that GraphSparseNet not only significantly reduces training time by 3.51x compared to state-of-the-art linear models but also maintains high predictive performance.

Contrastive learning (CL) pretrains feature embeddings to scatter instances in the feature space so that the training data can be well discriminated. Most existing CL techniques usually encourage learning such feature embeddings in the highdimensional space to maximize the instance discrimination. However, this practice may lead to undesired results where the scattering instances are sparsely distributed in the high-dimensional feature space, making it difficult to capture the underlying similarity between pairwise instances. To this end, we propose a novel framework called contrastive learning with low-dimensional reconstruction (CLLR), which adopts a regularized projection layer to reduce the dimensionality of the feature embedding. In CLLR, we build the sparse / low-rank regularizer to adaptively reconstruct a low-dimensional projection space while preserving the basic objective for instance discrimination, and thus successfully learning contrastive embeddings that alleviate the above issue. Theoretically, we prove a tighter error bound for CLLR; empirically, the superiority of CLLR is demonstrated across multiple domains.

Nonlinear data visualization using t-distributed stochastic neighbor embedding (t-SNE) enables the representation of complex single-cell transcriptomic landscapes in two or three dimensions to depict biological populations accurately. However, t-SNE often fails to account for uncertainties in the original dataset, leading to misleading visualizations where cell subsets with noise appear indistinguishable. To address these challenges, we introduce uncertainty-aware t-SNE (Ut-SNE), a noise-defending visualization tool tailored for uncertain single-cell RNA-seq data. By creating a probabilistic representation for each sample, Our Ut-SNE accurately incorporates noise about transcriptomic variability into the visual interpretation of single-cell RNA sequencing data, revealing significant uncertainties in transcriptomic variability. Through various examples, we showcase the practical value of Ut-SNE and underscore the significance of incorporating uncertainty awareness into data visualization practices. This versatile uncertainty-aware visualization tool can be easily adapted to other scientific domains beyond single-cell RNA sequencing, making them valuable resources for high-dimensional data analysis.

Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant t-SNE. Distances between points in high dimensions are used to define a probability distribution on pairs of points, measuring how similar the points are. The aim is to map these points to low dimensions in an optimal way so that similar points are closer together. This is carried out by minimizing the relative entropy between two probability distributions. We consider the gradient flow of the relative entropy and analyze its long-time behavior. This is a self-contained mathematical problem about the behavior of a system of nonlinear ordinary differential equations. We find optimal bounds for the diameter of the evolving sets as time tends to infinity. In particular, the diameter may blow up for the t-SNE version, but remains bounded for SNE.

Diffusion models generate high-quality samples by corrupting data with Gaussian noise and iteratively reconstructing it with deep learning, slowly transforming noisy images into refined outputs. Understanding this data evolution is important for interpretability but is complex due to its high-dimensional evolutionary nature. While traditional dimensionality reduction methods like t-distributed stochastic neighborhood embedding (t-SNE) aid in understanding high-dimensional spaces, they neglect evolutionary structure preservation. Hence, we propose Tree of Diffusion Life (TDL), a method to understand data evolution in the generative process of diffusion models. TDL samples a diffusion model's generative space via instances with varying prompts and employs image encoders to extract semantic meaning from these samples, projecting them to an intermediate space. It employs a novel evolutionary embedding algorithm that explicitly encodes the iterations while preserving the high-dimensional relations, facilitating the visualization of data evolution. This embedding leverages three metrics: a standard t-SNE loss to group semantically similar elements, a displacement loss to group elements from the same iteration step, and an instance alignment loss to align elements of the same instance across iterations. We present rectilinear and radial layouts to represent iterations, enabling comprehensive exploration. We assess various feature extractors and highlight TDL's potential with prominent diffusion models like GLIDE and Stable Diffusion with different prompt sets. TDL simplifies understanding data evolution within diffusion models, offering valuable insights into their functioning.

Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two categories: feature selection and feature transformation. Feature selection retains significant features, while feature transformation projects data into a lower-dimensional space, with linear and nonlinear methods. While nonlinear methods excel in preserving local structures and capturing nonlinear relationships, they may struggle with interpreting global structures and can be computationally intensive. Recent algorithms, such as the t-SNE, UMAP, TriMap, and PaCMAP prioritize preserving local structures, often at the expense of accurately representing global structures, leading to clusters being spread out more in lower-dimensional spaces. Moreover, these methods heavily rely on hyperparameters, making their results sensitive to parameter settings. To address these limitations, this study introduces a clustering-based approach, namely CBMAP (Clustering-Based Manifold Approximation and Projection), for dimensionality reduction. CBMAP aims to preserve both global and local structures, ensuring that clusters in lower-dimensional spaces closely resemble those in high-dimensional spaces. Experimental evaluations on benchmark datasets demonstrate CBMAP's efficacy, offering speed, scalability, and minimal reliance on hyperparameters. Importantly, CBMAP enables low-dimensional projection of test data, addressing a critical need in machine learning applications. CBMAP is made freely available at https://github.com/doganlab/cbmap and can be installed from the Python Package Directory (PyPI) software repository with the command pip install cbmap.

This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be achieved using a kernel trick only in the high dimensional space or in both spaces, leading to an end-to-end kernelized version. The proposed kernelized version of the t-SNE algorithm can offer new views on the relationships between data points, which can improve performance and accuracy in particular applications, such as classification problems involving kernel methods. The differences between t-SNE and its kernelized version are illustrated for several datasets, showing a neater clustering of points belonging to different classes.