Representations and generalization in artificial and brain neural networks
Humans and animals excel at generalizing from limited data, a capability yet to be fully
replicated in artificial intelligence. This perspective investigates generalization in biological …
replicated in artificial intelligence. This perspective investigates generalization in biological …
Modeling the influence of data structure on learning in neural networks: The hidden manifold model
Understanding the reasons for the success of deep neural networks trained using stochastic
gradient-based methods is a key open problem for the nascent theory of deep learning. The …
gradient-based methods is a key open problem for the nascent theory of deep learning. The …
Separability and geometry of object manifolds in deep neural networks
Stimuli are represented in the brain by the collective population responses of sensory
neurons, and an object presented under varying conditions gives rise to a collection of …
neurons, and an object presented under varying conditions gives rise to a collection of …
The gaussian equivalence of generative models for learning with shallow neural networks
Understanding the impact of data structure on the computational tractability of learning is a
key challenge for the theory of neural networks. Many theoretical works do not explicitly …
key challenge for the theory of neural networks. Many theoretical works do not explicitly …
Classification and geometry of general perceptual manifolds
Perceptual manifolds arise when a neural population responds to an ensemble of sensory
signals associated with different physical features (eg, orientation, pose, scale, location, and …
signals associated with different physical features (eg, orientation, pose, scale, location, and …
A unified theory of early visual representations from retina to cortex through anatomically constrained deep CNNs
The visual system is hierarchically organized to process visual information in successive
stages. Neural representations vary drastically across the first stages of visual processing: at …
stages. Neural representations vary drastically across the first stages of visual processing: at …
Linear classification of neural manifolds with correlated variability
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 …
performance is a key problem in theoretical neuroscience and deep learning. Here, we …
Beyond the storage capacity: data-driven satisfiability transition
Data structure has a dramatic impact on the properties of neural networks, yet its
significance in the established theoretical frameworks is poorly understood. Here we …
significance in the established theoretical frameworks is poorly understood. Here we …
Counting the learnable functions of geometrically structured data
Cover's function counting theorem is a milestone in the theory of artificial neural networks. It
provides an answer to the fundamental question of determining how many binary …
provides an answer to the fundamental question of determining how many binary …
Attributed graph force learning
In numerous network analysis tasks, feature representation plays an imperative role. Due to
the intrinsic nature of networks being discrete, enormous challenges are imposed on their …
the intrinsic nature of networks being discrete, enormous challenges are imposed on their …