Dense Hebbian neural networks: a replica symmetric picture of unsupervised learning

• URL: http://arxiv.org/abs/2211.14067v2
• Date: Sun, 2 Jul 2023 14:41:24 GMT
• Title: Dense Hebbian neural networks: a replica symmetric picture of unsupervised learning
• Authors: Elena Agliari, Linda Albanese, Francesco Alemanno, Andrea Alessandrelli, Adriano Barra, Fosca Giannotti, Daniele Lotito, Dino Pedreschi
• Abstract summary: We consider dense, associative neural-networks trained with no supervision. We investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations.
• Score: 4.133728123207142
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

Related papers

• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• Gradient Descent in Neural Networks as Sequential Learning in RKBS [63.011641517977644]
  We construct an exact power-series representation of the neural network in a finite neighborhood of the initial weights. We prove that, regardless of width, the training sequence produced by gradient descent can be exactly replicated by regularized sequential learning.
  arXiv  Detail & Related papers  (2023-02-01T03:18:07Z)
• Dense Hebbian neural networks: a replica symmetric picture of supervised learning [4.133728123207142]
  We consider dense, associative neural-networks trained by a teacher with supervision. We investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations.
  arXiv  Detail & Related papers  (2022-11-25T13:37:47Z)
• 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)
• The emergence of a concept in shallow neural networks [0.0]
  We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable archetypes'' We show that there exists a critical sample size beyond which the RBM can learn archetypes.
  arXiv  Detail & Related papers  (2021-09-01T15:56:38Z)
• Persistent Homology Captures the Generalization of Neural Networks Without A Validation Set [0.0]
  We suggest studying the training of neural networks with Algebraic Topology, specifically Persistent Homology. Using simplicial complex representations of neural networks, we study the PH diagram distance evolution on the neural network learning process. Results show that the PH diagram distance between consecutive neural network states correlates with the validation accuracy.
  arXiv  Detail & Related papers  (2021-05-31T09:17:31Z)
• Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning [50.24174211654775]
  We present a novel contrastive self-supervised learning framework for anomaly detection on attributed networks. Our framework fully exploits the local information from network data by sampling a novel type of contrastive instance pair. A graph neural network-based contrastive learning model is proposed to learn informative embedding from high-dimensional attributes and local structure.
  arXiv  Detail & Related papers  (2021-02-27T03:17:20Z)
• Estimation of the Mean Function of Functional Data via Deep Neural Networks [6.230751621285321]
  We propose a deep neural network method to perform nonparametric regression for functional data. The proposed method is applied to analyze positron emission tomography images of patients with Alzheimer disease.
  arXiv  Detail & Related papers  (2020-12-08T17:18:16Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Extending machine learning classification capabilities with histogram reweighting [0.0]
  We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. We treat the output from a convolutional neural network as an observable in a statistical system, enabling its extrapolation over continuous ranges in parameter space.
  arXiv  Detail & Related papers  (2020-04-29T17:20:16Z)
• Understanding the Effects of Data Parallelism and Sparsity on Neural Network Training [126.49572353148262]
  We study two factors in neural network training: data parallelism and sparsity. Despite their promising benefits, understanding of their effects on neural network training remains elusive.
  arXiv  Detail & Related papers  (2020-03-25T10:49:22Z)

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.