The531 raw RGB values are firstly divided by 256 (i.e.

We introduce a CISS framework that alleviates the forgetting problem and facilitates learning novel classes effectively. We have found that a logit can be decomposed into two terms. They quantify how likely an input belongs toaparticular class ornot, providing aclue forareasoning process ofa model. The KD technique, in this context, preserves the sum of two terms (i.e., a class logit), suggesting that each could be changed and thus the KD does not imitate thereasoning process.

All these factors yield challenges to the matching task.

Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of explainable AI (XAI) methods for the decision of the model. In this work, we analyze the potential issues with this approach and propose Principal Components-based Initialization (PCsInit), a strategy to incorporate PCA into the first layer of a neural network via initialization of the first layer in the network with the principal components, and its two variants PCsInit-Act and PCsInit-Sub. Explanations using these strategies are as direct and straightforward as for neural networks and are simpler than using PCA prior to training a neural network on the principal components. Moreover, as will be illustrated in the experiments, such training strategies can also allow further improvement of training via backpropagation.

Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling complex domains or incorporating empirical data. These methods leverage neural networks as basis functions to approximate PDE solutions. However, training such networks can be challenging, often resulting in limited accuracy. In this paper, we investigate the training dynamics of neural network-based PDE solvers with a focus on the impact of initialization techniques. We assess training difficulty by analyzing the eigenvalue distribution of the kernel and apply the concept of effective rank to quantify this difficulty, where a larger effective rank correlates with faster convergence of the training error. Building upon this, we discover through theoretical analysis and numerical experiments that two initialization techniques, partition of unity (PoU) and variance scaling (VS), enhance the effective rank, thereby accelerating the convergence of training error. Furthermore, comprehensive experiments using popular PDE-solving frameworks, such as PINN, Deep Ritz, and the operator learning framework DeepOnet, confirm that these initialization techniques consistently speed up convergence, in line with our theoretical findings.

This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is shown how the choice of integration technique implicitly regularizes the learned model, and how the solver's corresponding stability region affects training and prediction performance. From this analysis, a stability-informed parameter initialization technique is introduced. The effectiveness of the initialization method is displayed across several learning benchmarks and industrial applications.

Deep learning has grown tremendously over recent years, yielding state-of-the-art results in various fields. However, training such models requires huge amounts of data, increasing the computational time and cost. To address this, dataset distillation was proposed to compress a large training dataset into a smaller synthetic one that retains its performance -- this is usually done by (1) uniformly initializing a synthetic set and (2) iteratively updating/learning this set according to a predefined loss by uniformly sampling instances from the full data. In this paper, we improve both phases of dataset distillation: (1) we present a provable, sampling-based approach for initializing the distilled set by identifying important and removing redundant points in the data, and (2) we further merge the idea of data subset selection with dataset distillation, by training the distilled set on ``important'' sampled points during the training procedure instead of randomly sampling the next batch. To do so, we define the notion of importance based on the relative contribution of instances with respect to two different loss functions, i.e., one for the initialization phase (a kernel fitting function for kernel ridge regression and $K$-means based loss function for any other distillation method), and the relative cross-entropy loss (or any other predefined loss) function for the training phase. Finally, we provide experimental results showing how our method can latch on to existing dataset distillation techniques and improve their performance.