Related papers: Neural Network Symmetrisation in Concrete Settings

We propose that simple neural networks (NNs) trained on crossing symmetry can reconstruct conformal correlators restricted to a line to remarkable accuracy. The input is minimal: an external scaling dimension, a spectral gap, and the value…

We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an…

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…

Normalization, $D(X + 1) \to D(X) + 1$, is almost a distributive law; but because one of the distributive law axioms only holds up-to-idempotent, it yields a non-associative composition of normalized kernels. We introduce the Markov magmoid…

Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly…

Theorems from universal algebra such as that of Murski\u{i} from the 1970s have a striking similarity to universal approximation results for neural nets along the lines of Cybenko's from the 1980s. We consider here a discrete analogue of…

In recent years, there has been considerable innovation in the world of predictive methodologies. This is evident by the relative domination of machine learning approaches in various classification competitions. While these algorithms have…

Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…

We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…

This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations…

Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…

We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive…

Ensuring the realism of computer-generated synthetic images is crucial to deep neural network (DNN) training. Due to different semantic distributions between synthetic and real-world captured datasets, there exists semantic mismatch between…

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually…

We introduce the neural network approach to global fits of parton distribution functions. First we review previous work on unbiased parametrizations of deep-inelastic structure functions with faithful estimation of their uncertainties, and…

Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the…

We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…

It is frequently hypothesized that cortical networks operate close to a critical point. Advantages of criticality include rich dynamics well-suited for computation and critical slowing down, which may offer a mechanism for dynamic memory.…

These notes are based on lectures I gave at TASI 2024 on Physics for Machine Learning. The focus is on neural network theory, organized according to network expressivity, statistics, and dynamics. I present classic results such as the…

Convolutional Neural Networks (CNNs) have recently achieved remarkably strong performance on the practically important task of sentence classification (kim 2014, kalchbrenner 2014, johnson 2014). However, these models require practitioners…