Related papers: Topological Regularization via Persistence-Sensiti…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
Mitigating shortcuts, where models exploit spurious correlations in training data, remains a significant challenge for improving generalization. Regularization methods have been proposed to address this issue by enhancing model…
Learned Optimizers (LOs), a type of Meta-learning, have gained traction due to their ability to be parameterized and trained for efficient optimization. Traditional gradient-based methods incorporate explicit regularization techniques such…
Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…
We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these…
The overdetermination of the mathematical problem underlying ptychography is reduced by a host of experimentally more desirable settings. Furthermore, reconstruction of the sample-induced phase shift is typically limited by uncertainty in…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
The focus of this paper is on topology optimization of continuum structures subject to thermally induced buckling. Popular strategies for solving such problems include Solid Isotropic Material with Penalization (SIMP) and Rational…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly. When $n$ nodes collaborate through $m$ pairwise regularizers, standard methods demand $\mathcal{O}(m)$ communications per iteration. This paper…