The Effect of Data Dimensionality on Neural Network Prunability
- URL: http://arxiv.org/abs/2212.00291v1
- Date: Thu, 1 Dec 2022 05:33:25 GMT
- Title: The Effect of Data Dimensionality on Neural Network Prunability
- Authors: Zachary Ankner, Alex Renda, Gintare Karolina Dziugaite, Jonathan
Frankle, Tian Jin
- Abstract summary: We study the properties of input data that may contribute to the prunability of a neural network.
For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold.
- Score: 28.845848452511955
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Practitioners prune neural networks for efficiency gains and generalization
improvements, but few scrutinize the factors determining the prunability of a
neural network the maximum fraction of weights that pruning can remove without
compromising the model's test accuracy. In this work, we study the properties
of input data that may contribute to the prunability of a neural network. For
high dimensional input data such as images, text, and audio, the manifold
hypothesis suggests that these high dimensional inputs approximately lie on or
near a significantly lower dimensional manifold. Prior work demonstrates that
the underlying low dimensional structure of the input data may affect the
sample efficiency of learning. In this paper, we investigate whether the low
dimensional structure of the input data affects the prunability of a neural
network.
Related papers
- Residual Random Neural Networks [0.0]
Single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature.
We show that one can obtain good classification results even if the number of hidden neurons has the same order of magnitude as the dimensionality of the data samples.
arXiv Detail & Related papers (2024-10-25T22:00:11Z) - Verified Neural Compressed Sensing [58.98637799432153]
We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task.
We show that for modest problem dimensions (up to 50), we can train neural networks that provably recover a sparse vector from linear and binarized linear measurements.
We show that the complexity of the network can be adapted to the problem difficulty and solve problems where traditional compressed sensing methods are not known to provably work.
arXiv Detail & Related papers (2024-05-07T12:20:12Z) - Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence.
We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers.
This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
arXiv Detail & Related papers (2023-07-20T13:34:11Z) - A Theoretical Analysis on Feature Learning in Neural Networks: Emergence
from Inputs and Advantage over Fixed Features [18.321479102352875]
An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction.
We consider learning problems motivated by practical data, where the labels are determined by a set of class relevant patterns and the inputs are generated from these.
We prove that neural networks trained by gradient descent can succeed on these problems.
arXiv Detail & Related papers (2022-06-03T17:49:38Z) - Robust Deep Neural Network Estimation for Multi-dimensional Functional
Data [0.22843885788439797]
We propose a robust estimator for the location function from multi-dimensional functional data.
The proposed estimators are based on the deep neural networks with ReLU activation function.
The proposed method is also applied to analyze 2D and 3D images of patients with Alzheimer's disease.
arXiv Detail & Related papers (2022-05-19T14:53:33Z) - Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs.
By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
arXiv Detail & Related papers (2022-02-01T17:11:13Z) - Dive into Layers: Neural Network Capacity Bounding using Algebraic
Geometry [55.57953219617467]
We show that the learnability of a neural network is directly related to its size.
We use Betti numbers to measure the topological geometric complexity of input data and the neural network.
We perform the experiments on a real-world dataset MNIST and the results verify our analysis and conclusion.
arXiv Detail & Related papers (2021-09-03T11:45:51Z) - And/or trade-off in artificial neurons: impact on adversarial robustness [91.3755431537592]
Presence of sufficient number of OR-like neurons in a network can lead to classification brittleness and increased vulnerability to adversarial attacks.
We define AND-like neurons and propose measures to increase their proportion in the network.
Experimental results on the MNIST dataset suggest that our approach holds promise as a direction for further exploration.
arXiv Detail & Related papers (2021-02-15T08:19:05Z) - Towards Robust Neural Networks via Close-loop Control [12.71446168207573]
Deep neural networks are vulnerable to various perturbations due to their black-box nature.
Recent study has shown that a deep neural network can misclassify the data even if the input data is perturbed by an imperceptible amount.
arXiv Detail & Related papers (2021-02-03T03:50:35Z) - Information contraction in noisy binary neural networks and its
implications [11.742803725197506]
We consider noisy binary neural networks, where each neuron has a non-zero probability of producing an incorrect output.
Our key finding is a lower bound for the required number of neurons in noisy neural networks, which is first of its kind.
This paper offers new understanding of noisy information processing systems through the lens of information theory.
arXiv Detail & Related papers (2021-01-28T00:01:45Z) - Beyond Dropout: Feature Map Distortion to Regularize Deep Neural
Networks [107.77595511218429]
In this paper, we investigate the empirical Rademacher complexity related to intermediate layers of deep neural networks.
We propose a feature distortion method (Disout) for addressing the aforementioned problem.
The superiority of the proposed feature map distortion for producing deep neural network with higher testing performance is analyzed and demonstrated.
arXiv Detail & Related papers (2020-02-23T13:59:13Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.