Related papers: The edge of chaos: quantum field theory and deep n…
We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos. Dropout shifts the perfect-alignment fixed point, making the depth scale for information propagation finite even at critical…
Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT,…
We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these…
We develop a diagrammatic approach to effective field theories (EFTs) corresponding to deep neural networks at initialization, which dramatically simplifies computations of finite-width corrections to neuron statistics. The structures of…
Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories…
We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads, defining $n$-point correlators by averaging over random network parameters in the NN-QFT framework. For a single attention…
We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a (d+1)-dimensional space. All interactions are localized on the defect. We derive a unitary non-canonical quantum…
A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After…
In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher "spin" operators. We construct an effective field theory (EFT)…
Motivated by the idea that criticality and universality of phase transitions might play a crucial role in achieving and sustaining learning and intelligent behaviour in biological and artificial networks, we analyse a theoretical and a…
We analyze the expressivity of a universal deep neural network that can be organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads. While the maximal expressive power increases with the depth of the…
Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly…
Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires…
Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been…
In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework…
For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory…
We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
In recent years, the mean field theory has been applied to the study of neural networks and has achieved a great deal of success. The theory has been applied to various neural network structures, including CNNs, RNNs, Residual networks, and…
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the…