Related papers: Interpreting Deep Learning by Establishing a Rigor…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…
Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. Deep learning performs a sophisticated coarse graining. Since coarse graining is a key ingredient of the…
Deep learning is a broad set of techniques that uses multiple layers of representation to automatically learn relevant features directly from structured data. Recently, such techniques have yielded record-breaking results on a diverse set…
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…
Self-similarity, where observables at different length scales exhibit similar behavior, is ubiquitous in natural systems. Such systems are typically characterized by power-law correlations and universality, and are studied using the…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
Theoretical understanding of how deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse-graining. It reminds us…
We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow…
The Renormalisation Group (RG) provides a framework in which it is possible to assess whether a deep-learning network is sensitive to small changes in the input data and hence prone to error, or susceptible to adversarial attack. Distinct…
Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…
Physicists have had a keen interest in the areas of Artificial Intelligence (AI) and Machine Learning (ML) for some time now, with a special inclination towards unravelling the mechanism at the core of the process of learning. In…
We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by…
We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns…
We explore how minimal neural networks can invert the renormalization group (RG) coarse-graining procedure in the two-dimensional Ising model, effectively ``dreaming up'' microscopic configurations from coarse-grained states. This task -…
Separating relevant and irrelevant information is key to any modeling process or scientific inquiry. Theoretical physics offers a powerful tool for achieving this in the form of the renormalization group (RG). Here we demonstrate a…
Reentrant computation-recursive self-coupling in which a network continuously reinjects and reinterprets its own internal state-plays a central role in biological cognition but remains poorly characterized in neural network architectures.…
Deep graph neural networks (GNNs) have achieved excellent results on various tasks on increasingly large graph datasets with millions of nodes and edges. However, memory complexity has become a major obstacle when training deep GNNs for…