相关论文: Geometric Foundations of Tuning without Forgetting…

In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be identified as a metric space according to the deformation,…

Recurrent Neural Network (RNN) is a fundamental structure in deep learning. Recently, some works study the training process of over-parameterized neural networks, and show that over-parameterized networks can learn functions in some notable…

Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider…

We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this…

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used…

While test-time fine-tuning is beneficial in few-shot learning, the need for multiple backpropagation steps can be prohibitively expensive in real-time or low-resource scenarios. To address this limitation, we propose an approach that…

Channel prediction permits to acquire channel state information (CSI) without signaling overhead. However, almost all existing channel prediction methods necessitate the deployment of a dedicated model to accommodate a specific…

Deep neural networks have achieved remarkable success in practice, yet a mechanistic understanding of how features evolve during training remains incomplete, especially in the large-depth limit. For ResNets under depth-$\mu$P scaling, prior…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Classification of topological phononics is challenging due to the lack of universal topological invariants and the randomness of structure patterns. Here, we show the unsupervised manifold learning for clustering topological phononics…

We introduce an unsupervised feature learning approach that embeds 3D shape information into a single-view image representation. The main idea is a self-supervised training objective that, given only a single 2D image, requires all unseen…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

We explore a new idea for learning based shape reconstruction from a point cloud, based on the recently popularized implicit neural shape representations. We cast the problem as a few-shot learning of implicit neural signed distance…

Object recognition is a key enabler across industry and defense. As technology changes, algorithms must keep pace with new requirements and data. New modalities and higher resolution sensors should allow for increased algorithm robustness.…

We present a geometric neural network-based tracking controller for systems evolving on matrix Lie groups under unknown dynamics, actuator faults, and bounded disturbances. Leveraging the left-invariance of the tangent bundle of matrix Lie…

Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix…

The performance of medical image classification has been enhanced by deep convolutional neural networks (CNNs), which are typically trained with cross-entropy (CE) loss. However, when the label presents an intrinsic ordinal property in…

Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to…

We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near…

This paper proposes a novel approach to improve the training efficiency and the generalization performance of Feed Forward Neural Networks (FFNNs) resorting to an optimal rescaling of input features (OFR) carried out by a Genetic Algorithm…