Related papers: Latent Space Topology Evolution in Multilayer Perc…

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…

In this paper, we described and developed a framework for Multilayer Perceptron (MLP) to work on low level image processing, where MLP will be used to perform image super-resolution. Meanwhile, MLP are trained with different types of images…

Meta-learning consists in learning learning algorithms. We use a Long Short Term Memory (LSTM) based network to learn to compute on-line updates of the parameters of another neural network. These parameters are stored in the cell state of…

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal…

Multilayer networks or MLNs (also called multiplexes or network of networks) are being used extensively for modeling and analysis of data sets with multiple entity and feature types and associated relationships. Although the concept of…

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically…

Multi-Layer Perceptrons (MLPs) make powerful functional representations for sampling and reconstruction problems involving low-dimensional signals like images,shapes and light fields. Recent works have significantly improved their ability…

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body…

Latent space models for network data characterize each node through a vector of latent features whose pairwise similarities define the edge probabilities among the pairs of nodes. Although this formulation has led to successful…

Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…

Multi-layer perceptrons (MLPs) are a standard tool for learning and function approximation, but they inherently yield outputs that are globally smooth. As a result, they struggle to represent functions that are continuous yet deliberately…

A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…

While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…

Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with…

Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

Whether Large Language Models (LLMs) develop coherent internal world models remains a core debate. While conventional Next-Token Prediction (NTP) focuses on one-step-ahead supervision, Multi-Token Prediction (MTP) has shown promise in…