Related papers: Nonlinear classification of neural manifolds with …

Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to…

In order to assess the short-term memory performance of non-linear random neural networks, we introduce a measure to quantify the dependence of a neural representation upon the past context. We study this measure both numerically and…

Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete…

Interpretation and diagnosis of machine learning models have gained renewed interest in recent years with breakthroughs in new approaches. We present Manifold, a framework that utilizes visual analysis techniques to support interpretation,…

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…

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…

Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect…

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object…

Neural networks used for image classification tasks in critical applications must be tested with sufficient realistic data to assure their correctness. To effectively test an image classification neural network, one must obtain realistic…

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on…

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…

Deep neural networks (DNNs) have shown much empirical success in solving perceptual tasks across various cognitive modalities. While they are only loosely inspired by the biological brain, recent studies report considerable similarities…

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…

Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Systems neuroscience relies on two complementary views of neural data, characterized by single neuron tuning curves and analysis of population activity. These two perspectives combine elegantly in neural latent variable models that…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture…