Related papers: What can topology tell us about the neural code?
Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…
Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on…
Research on neural networks has gained significant momentum over the past few years. Because training is a resource-intensive process and training data cannot always be made available to everyone, there has been a trend to reuse pre-trained…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…
The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…
The human brain is a complex network that supports mental function. The nascent field of network neuroscience applies tools from mathematics to neuroimaging data in the hopes of shedding light on cognitive function. A critical question…
Can artificial intelligence unlock the secrets of the human brain? How do the inner mechanisms of deep learning models relate to our neural circuits? Is it possible to enhance AI by tapping into the power of brain recordings? These…
Neural networks (NNs) hold great promise for advancing inverse design via topology optimization (TO), yet misconceptions about their application persist. This article focuses on neural topology optimization (neural TO), which leverages NNs…
Building machines that learn and think like humans is essential not only for cognitive science, but also for computational neuroscience, whose ultimate goal is to understand how cognition is implemented in biological brains. A new cognitive…
Recent years have seen fast advances in neural recording circuits and systems as they offer a promising way to investigate real-time brain monitoring and the closed-loop modulation of psychological disorders and neurodegenerative diseases.…
Despite rapid advances in machine learning tools, the majority of neural decoding approaches still use traditional methods. Modern machine learning tools, which are versatile and easy to use, have the potential to significantly improve…
Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…
Deep neural networks are becoming more and more popular due to their revolutionary success in diverse areas, such as computer vision, natural language processing, and speech recognition. However, the decision-making processes of these…
Machine learning is a modern approach to problem-solving and task automation. In particular, machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive…
The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…
Deep neural networks have been increasingly used in software engineering and program analysis tasks. They usually take a program and make some predictions about it, e.g., bug prediction. We call these models neural program analyzers. The…
Neural Code Intelligence -- leveraging deep learning to understand, generate, and optimize code -- holds immense potential for transformative impacts on the whole society. Bridging the gap between Natural Language and Programming Language,…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…