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In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a…

Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…

Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…

The categorization properties of an attractor network of three-state neurons which infers three-state concepts from examples are studied. The evolution equations governing the parallel dynamics at zero temperature for the overlap between…

We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…

Despite the tremendous successes of deep neural networks (DNNs) in various applications, many fundamental aspects of deep learning remain incompletely understood, including DNN trainability. In a trainability study, one aims to discern what…

There has been an increasing interest in learning dynamics simulators for model-based control. Compared with off-the-shelf physics engines, a learnable simulator can quickly adapt to unseen objects, scenes, and tasks. However, existing…

We draw upon a previously largely untapped literature on human collective intelligence as a source of inspiration for improving deep learning. Implicit in many algorithms that attempt to solve Deep Reinforcement Learning (DRL) tasks is the…

In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of…

A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work…

Image inpainting techniques have shown promising improvement with the assistance of generative adversarial networks (GANs) recently. However, most of them often suffered from completed results with unreasonable structure or blurriness. To…

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their…

It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$,…

The problem of distance metric learning is mostly considered from the perspective of learning an embedding space, where the distances between pairs of examples are in correspondence with a similarity metric. With the rise and success of…

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…

Automatic Modulation Recognition (AMR) plays a crucial role in wireless communication systems. Deep learning AMR strategies have achieved tremendous success in recent years. Modulated signals exhibit long temporal dependencies, and…

We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex…