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Found 18 papers, 6 papers with code
Linear Classification of Neural Manifolds with Correlated Variability
Understanding how the statistical and geometric properties of neural activations relate to network performance is a key problem in theoretical neuroscience and deep learning.
The Implicit Bias of Gradient Descent on Generalized Gated Linear Networks
Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance.
Neural Population Geometry Reveals the Role of Stochasticity in Robust Perception
Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems.
Divisive Feature Normalization Improves Image Recognition Performance in AlexNet
In conclusion, divisive normalization enhances image recognition performance, most strongly when combined with canonical normalization, and in doing so it reduces manifold capacity and sparsity in early layers while increasing them in final layers, and increases low- or mid-wavelength power in the first-layer receptive fields.
Understanding the Logit Distributions of Adversarially-Trained Deep Neural Networks
Motivated by a recent study on learning robustness without input perturbations by distilling an AT model, we explore what is learned during adversarial training by analyzing the distribution of logits in AT models.
Credit Assignment Through Broadcasting a Global Error Vector
We prove that these weight updates are matched in sign to the gradient, enabling accurate credit assignment.
Statistical Mechanics of Neural Processing of Object Manifolds
In this thesis, we generalize Gardner's analysis and establish a theory of linear classification of manifolds synthesizing statistical and geometric properties of high dimensional signals.
On the geometry of generalization and memorization in deep neural networks
Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance.
Syntactic Perturbations Reveal Representational Correlates of Hierarchical Phrase Structure in Pretrained Language Models
While vector-based language representations from pretrained language models have set a new standard for many NLP tasks, there is not yet a complete accounting of their inner workings.
Neural population geometry: An approach for understanding biological and artificial neural networks
One approach to addressing this challenge is to utilize mathematical and computational tools to analyze the geometry of these high-dimensional representations, i. e., neural population geometry.
Representational correlates of hierarchical phrase structure in deep language models
Importing from computational and cognitive neuroscience the notion of representational invariance, we perform a series of probes designed to test the sensitivity of Transformer representations to several kinds of structure in sentences.
On 1/n neural representation and robustness
In this work, we investigate the latter by juxtaposing experimental results regarding the covariance spectrum of neural representations in the mouse V1 (Stringer et al) with artificial neural networks.
Emergence of Separable Manifolds in Deep Language Representations
In addition, we find that the emergence of linear separability in these manifolds is driven by a combined reduction of manifolds' radius, dimensionality and inter-manifold correlations.
Untangling in Invariant Speech Recognition
Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network.
Probing emergent geometry in speech models via replica theory
The success of deep neural networks in visual tasks have motivated recent theoretical and empirical work to understand how these networks operate.
Classification and Geometry of General Perceptual Manifolds
The effects of label sparsity on the classification capacity of manifolds are elucidated, revealing a scaling relation between label sparsity and manifold radius.
Learning Data Manifolds with a Cutting Plane Method
We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom.
Linear Readout of Object Manifolds
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.
