Related papers: The $\alpha$-induction of Graded Local Conformal N…
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D_{2n}-E_{6,8} Dynkin diagrams such…
Given two neural network classifiers with the same input and output domains, our goal is to compare the two networks in relation to each other over an entire input region (e.g., within a vicinity of an input sample). To this end, we…
Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…
Gradients have been used to quantify feature importance in machine learning models. Unfortunately, in nonlinear deep networks, not only individual neurons but also the whole network can saturate, and as a result an important input feature…
The implicit bias induced by the training of neural networks has become a topic of rigorous study. In the limit of gradient flow and gradient descent with appropriate step size, it has been shown that when one trains a deep linear network…
The backpropagation algorithm, despite its widespread use in neural network learning, may not accurately emulate the human cortex's learning process. Alternative strategies, such as the Forward-Forward Algorithm (FFA), offer a closer match…
Feedback Alignment (FA) methods are biologically inspired local learning rules for training neural networks with reduced communication between layers. While FA has potential applications in distributed and privacy-aware ML, limitations in…
We introduce the Genetic-Gated Networks (G2Ns), simple neural networks that combine a gate vector composed of binary genetic genes in the hidden layer(s) of networks. Our method can take both advantages of gradient-free optimization and…
Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in…
We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of…
We consider a type III subfactor $N\subset M$ of finite index with a finite system of braided $N$-$N$ morphisms which includes the irreducible constituents of the dual canonical endomorphism. We apply $\alpha$-induction and, developing…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window…
We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical…
Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically…
Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between…
Attention networks have proven to be an effective approach for embedding categorical inference within a deep neural network. However, for many tasks we may want to model richer structural dependencies without abandoning end-to-end training.…
Despite its great success, backpropagation has certain limitations that necessitate the investigation of new learning methods. In this study, we present a biologically plausible local learning rule that improves upon Hebb's well-known…
Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…
In this note, we explain how to prove several basic results about finite index extensions of irreducible local M\"obius covariant nets in the setting of Connes fusion.