Related papers: Descriptive Dimensionality and Its Characterizatio…
Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…
Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…
This paper proposes a novel pixel-level distribution regularization scheme (DRSL) for self-supervised domain adaptation of semantic segmentation. In a typical setting, the classification loss forces the semantic segmentation model to…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Diffusion Language Models (DLMs) offer attractive advantages over Auto-Regressive (AR) models, such as full-attention parallel decoding and flexible generation. However, standard DLM training uses a static, single-step masked prediction…
Deep learning (DL) models have achieved paradigm-changing performance in many fields with high dimensional data, such as images, audio, and text. However, the black-box nature of deep neural networks is a barrier not just to adoption in…
Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons…
We study the risk performance of distributed learning for the regularization empirical risk minimization with fast convergence rate, substantially improving the error analysis of the existing divide-and-conquer based distributed learning.…
Existing domain adaptation (DA) and generalization (DG) methods in object detection enforce feature alignment in the visual space but face challenges like object appearance variability and scene complexity, which make it difficult to…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
Current learning algorithms face many difficulties in learning simple patterns and using them to learn more complex ones. They also require more examples than humans do to learn the same pattern, assuming no prior knowledge. In this paper,…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
Evaluating large language models (LLMs) today rests on fixed benchmarks that apply the same set of items to any model, producing ceiling and floor effects that mask capability gaps. We argue that the most informative evaluation signal lies…
We propose Deep Companion Learning (DCL), a novel training method for Deep Neural Networks (DNNs) that enhances generalization by penalizing inconsistent model predictions compared to its historical performance. To achieve this, we train a…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…