Related papers: Induced and Complete Multinets

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…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…

MultiGrain is a network architecture producing compact vector representations that are suited both for image classification and particular object retrieval. It builds on a standard classification trunk. The top of the network produces an…

For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…

Insights are relative - influenced by a range of factors such as assumptions, scopes, or methods that together define a research perspective. In normative and empirical fields alike, this insight has led to the conclusion that no single…

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…

Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal…

Multimodal learning has seen remarkable progress, particularly with the emergence of large-scale pre-training across various modalities. However, most current approaches are built on the assumption of a deterministic, one-to-one alignment…

Capsule network (CapsNet) was introduced as an enhancement over convolutional neural networks, supplementing the latter's invariance properties with equivariance through pose estimation. CapsNet achieved a very decent performance with a…

Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

A complex system can be represented and analyzed as a network, where nodes represent the units of the network and edges represent connections between those units. For example, a brain network represents neurons as nodes and axons between…

We determine the relationship between the contact structure induced by a fibered knot, K, in the three-sphere and the contact structures induced by its various cables. Understanding this relationship allows us to classify fibered cable…

It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$,…

Bilinear pooling has been recently proposed as a feature encoding layer, which can be used after the convolutional layers of a deep network, to improve performance in multiple vision tasks. Different from conventional global average pooling…

A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…

The field of neuroscience is facing an unprecedented expanse in the volume and diversity of available data. Traditionally, network models have provided key insights into the structure and function of the brain. With the advent of big data…