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Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…

Deep convolutional neural networks (CNNs) trained on objects and scenes have shown intriguing ability to predict some response properties of visual cortical neurons. However, the factors and computations that give rise to such ability, and…

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…

Credit assignment--how changes in individual neurons and synapses affect a network's output--is central to learning in brains and machines. Noise correlation, which estimates gradients by correlating perturbations of activity with changes…

Invariant object recognition is one of the most fundamental cognitive tasks performed by the brain. In the neural state space, different objects with stimulus variabilities are represented as different manifolds. In this geometrical…

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better…

Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

Neurons in the brain represent information in their collective activity. The fidelity of this neural population code depends on whether and how variability in the response of one neuron is shared with other neurons. Two decades of studies…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable…

Deep neural networks achieve remarkable performance in multiple fields. However, after proper training they suffer from an inherent vulnerability against adversarial examples (AEs). In this work we shed light on inner representations of the…

A deep neural network (DNN) with piecewise linear activations can partition the input space into numerous small linear regions, where different linear functions are fitted. It is believed that the number of these regions represents the…

A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…

Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…

Deep learning has excelled in image recognition tasks through neural networks inspired by the human brain. However, the necessity for large models to improve prediction accuracy introduces significant computational demands and extended…

While on some natural distributions, neural-networks are trained efficiently using gradient-based algorithms, it is known that learning them is computationally hard in the worst-case. To separate hard from easy to learn distributions, we…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…