Related papers: Polyhedrons and Perceptrons Are Functionally Equiv…
Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…
This paper builds upon our previous work on the Reconciled Polynomial Network (RPN). The original RPN model was designed under the assumption of input data independence, presuming the independence among both individual instances within data…
In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the…
Recent studies have made great progress in functional brain network classification by modeling the brain as a network of Regions of Interest (ROIs) and leveraging their connections to understand brain functionality and diagnose mental…
In machine learning, the use of an artificial neural network is the mainstream approach. Such a network consists of layers of neurons. These neurons are of the same type characterized by the two features: (1) an inner product of an input…
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…
Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…
The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant…
We propose a new network architecture, the Fractal Pyramid Networks (PFNs) for pixel-wise prediction tasks as an alternative to the widely used encoder-decoder structure. In the encoder-decoder structure, the input is processed by an…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…
In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure…
In this paper, we will introduce a novel deep model named Reconciled Polynomial Network (RPN) for deep function learning. RPN has a very general architecture and can be used to build models with various complexities, capacities, and levels…
We argue that many properties of fully-connected feedforward neural networks (FCNNs), also called multi-layer perceptrons (MLPs), are explainable from the analysis of a single pair of operations, namely a random projection into a…
Perceptrons are the basic computational unit of artificial neural networks, as they model the activation mechanism of an output neuron due to incoming signals from its neighbours. As linear classifiers, they play an important role in the…
Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for…
The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard…
A machine learning (ML) feature network is a graph that connects ML features in learning tasks based on their similarity. This network representation allows us to view feature vectors as functions on the network. By leveraging function…
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…
We describe how hierarchical concepts can be represented in three types of layered neural networks. The aim is to support recognition of the concepts when partial information about the concepts is presented, and also when some of the…