Related papers: Statistical Translation, Heat Kernels and Expected…

The goal of transfer learning is to improve the performance of target learning task by leveraging information (or transferring knowledge) from other related tasks. In this paper, we examine the problem of transfer distance metric learning…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Machine translation is a popular test bed for research in neural sequence-to-sequence models but despite much recent research, there is still a lack of understanding of these models. Practitioners report performance degradation with large…

Gridded data formats, where the observed multivariate data are aggregated into grid cells, ensure confidentiality and reduce storage requirements, with the trade-off that access to the underlying point data is lost. Heat maps are a highly…

In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be…

Machine learning is advancing towards a data-science approach, implying a necessity to a line of investigation to divulge the knowledge learnt by deep neuronal networks. Limiting the comparison among networks merely to a predefined…

Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…

We construct a long-time asymptotic profile to the initial value problem of the n-dimensional heat equation. Specifically, we present a modified heat kernel as a long-time asymptotic profile which changes the mass, the center of mass and…

Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…

Recent advancements in diffusion models have significantly impacted the trajectory of generative machine learning research, with many adopting the strategy of fine-tuning pre-trained models using domain-specific text-to-image datasets.…

Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

When performing predictions that use Machine Learning (ML), we are mainly interested in performance and interpretability. This generates a natural trade-off, where complex models generally have higher skills but are harder to explain and…

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in…

We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) by distilling knowledge from a teacher GNN model trained on a complete graph to a student GNN model…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…

Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful…