Decorrelating neurons using persistence

• URL: http://arxiv.org/abs/2308.04870v1
• Date: Wed, 9 Aug 2023 11:09:14 GMT
• Title: Decorrelating neurons using persistence
• Authors: Rub\'en Ballester, Carles Casacuberta, Sergio Escalera
• Abstract summary: We present two regularisation terms computed from the weights of a minimum spanning tree of a clique. We demonstrate that naive minimisation of all correlations between neurons obtains lower accuracies than our regularisation terms. We include a proof of differentiability of our regularisers, thus developing the first effective topological persistence-based regularisation terms.
• Score: 29.25969187808722
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel way to improve the generalisation capacity of deep learning models by reducing high correlations between neurons. For this, we present two regularisation terms computed from the weights of a minimum spanning tree of the clique whose vertices are the neurons of a given network (or a sample of those), where weights on edges are correlation dissimilarities. We provide an extensive set of experiments to validate the effectiveness of our terms, showing that they outperform popular ones. Also, we demonstrate that naive minimisation of all correlations between neurons obtains lower accuracies than our regularisation terms, suggesting that redundancies play a significant role in artificial neural networks, as evidenced by some studies in neuroscience for real networks. We include a proof of differentiability of our regularisers, thus developing the first effective topological persistence-based regularisation terms that consider the whole set of neurons and that can be applied to a feedforward architecture in any deep learning task such as classification, data generation, or regression.

Related papers

• Seeking Next Layer Neurons' Attention for Error-Backpropagation-Like Training in a Multi-Agent Network Framework [6.446189857311325]
  We propose a local objective for neurons that align them to exhibit similarities to error-backpropagation. We examine a neural network comprising decentralized, self-interested neurons seeking to maximize their local objective. We demonstrate the learning capacity of these multi-agent neural networks through experiments on three datasets.
  arXiv  Detail & Related papers  (2023-10-15T21:07:09Z)
• 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)
• Learning a Neuron by a Shallow ReLU Network: Dynamics and Implicit Bias for Correlated Inputs [5.7166378791349315]
  We prove that, for the fundamental regression task of learning a single neuron, training a one-hidden layer ReLU network converges to zero loss. We also show and characterise a surprising distinction in this setting between interpolator networks of minimal rank and those of minimal Euclidean norm.
  arXiv  Detail & Related papers  (2023-06-10T16:36:22Z)
• Spiking neural network for nonlinear regression [68.8204255655161]
  Spiking neural networks carry the potential for a massive reduction in memory and energy consumption. They introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. A framework for regression using spiking neural networks is proposed.
  arXiv  Detail & Related papers  (2022-10-06T13:04:45Z)
• Neuronal Correlation: a Central Concept in Neural Network [22.764342635264452]
  We show that neuronal correlation can be efficiently estimated via weight matrix. We show that neuronal correlation significantly impacts on the accuracy of entropy estimation in high-dimensional hidden spaces.
  arXiv  Detail & Related papers  (2022-01-22T15:01:50Z)
• Dynamic Neural Diversification: Path to Computationally Sustainable Neural Networks [68.8204255655161]
  Small neural networks with a constrained number of trainable parameters, can be suitable resource-efficient candidates for many simple tasks. We explore the diversity of the neurons within the hidden layer during the learning process. We analyze how the diversity of the neurons affects predictions of the model.
  arXiv  Detail & Related papers  (2021-09-20T15:12:16Z)
• 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)
• Online neural connectivity estimation with ensemble stimulation [5.156484100374058]
  We propose a method based on noisy group testing that drastically increases the efficiency of this process in sparse networks. We show that it is possible to recover binarized network connectivity with a number of tests that grows only logarithmically with population size. We also demonstrate the feasibility of inferring connectivity for networks of up to tens of thousands of neurons online.
  arXiv  Detail & Related papers  (2020-07-27T23:47:03Z)
• Hyperbolic Neural Networks++ [66.16106727715061]
  We generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar'e ball model. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.
  arXiv  Detail & Related papers  (2020-06-15T08:23:20Z)
• A new inference approach for training shallow and deep generalized linear models of noisy interacting neurons [4.899818550820575]
  We develop a two-step inference strategy that allows us to train robust generalized linear models of interacting neurons. We show that, compared to classical methods, the models trained in this way exhibit improved performance. The method can be extended to deep convolutional neural networks, leading to models with high predictive accuracy for both the neuron firing rates and their correlations.
  arXiv  Detail & Related papers  (2020-06-11T15:09:53Z)
• Understanding Generalization in Deep Learning via Tensor Methods [53.808840694241]
  We advance the understanding of the relations between the network's architecture and its generalizability from the compression perspective. We propose a series of intuitive, data-dependent and easily-measurable properties that tightly characterize the compressibility and generalizability of neural networks.
  arXiv  Detail & Related papers  (2020-01-14T22:26:57Z)

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.