arXiv:2608. 19331v1 Announce Type: cross Abstract: We modify the NN/QFT duality [1] to incorporate the layerwise permutation symmetry of the network, resulting in a $(0\!
arXiv:2607. 07127v1 Announce Type: cross Abstract: Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials.
arXiv:2508. 11522v4 Announce Type: replace Abstract: Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks.
The paper introduces a supervised, scale‑shared neural architecture for two‑dimensional site percolation, implementing a neural renormalization group flow. The model recursively applies a learned coarse‑graining rule across scales, producing a latent field that predicts crossing probability and a fine‑graining decoder that reconstructs the largest‑cluster mask. Trained only on small lattices, it extrapolates to larger systems, accurately recovers the spanning cluster, and yields observables that follow expected finite‑size scaling near the critical point, highlighting the importance of critical fluctuations in the latent representation.
The paper presents a supervised, scale‑shared neural architecture that learns a coarse‑graining rule for two‑dimensional site percolation. By recursively applying this rule, the model generates a latent field from which the crossing probability is predicted and a fine‑graining decoder reconstructs the largest‑cluster mask. Trained only on small lattices, the network extrapolates to larger systems, accurately recovers the spanning cluster, and reproduces finite‑size scaling near the critical point, demonstrating that the latent representation captures critical fluctuations and scale‑dependent flows consistent with renormalization‑group theory.
The paper investigates the limits of implementing neural network field theory on a computer, focusing on function classes that are regular enough for computation. It presents a no‑go theorem showing that finite‑width network ensembles cannot consistently realize either a quantum or effective field theory due to violations of reflection positivity and lack of scale separation. The study distinguishes between finite‑width and infinite‑width interpretations, concluding that only smeared correlators of the infinite‑width limit are computable with controlled error, and identifies two possible ways to evade the theorem—by relaxing finite variance or exact rotation invariance.
arXiv:2606. 15986v1 Announce Type: cross Abstract: The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators.
arXiv:2603. 02984v2 Announce Type: replace-cross Abstract: Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters.
The paper models the dynamics of Stochastic Gradient Descent (SGD) as a percolation process, showing that architectural symmetries cause subnetworks to merge in discrete blocks rather than sequentially. These structural transitions produce variance spikes in a macroscopic order parameter, analogous to physical phase transitions. The authors also demonstrate that this trapping mechanism and its scaling cascade apply to Adam and AdamW under a heavy‑tailed noise model.
arXiv:2607. 28628v1 Announce Type: cross Abstract: Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems.
arXiv:2608. 08350v1 Announce Type: new Abstract: The initialisation of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive.
Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known.
arXiv:2606. 00045v1 Announce Type: new Abstract: Classical continuous-space neural networks fundamentally struggle to lock into exact mathematical symmetries, such as modular arithmetic and non-commutative algebra.