On How Iterative Magnitude Pruning Discovers Local Receptive Fields in Fully Connected Neural Networks

• URL: http://arxiv.org/abs/2412.06545v1
• Date: Mon, 09 Dec 2024 14:56:23 GMT
• Title: On How Iterative Magnitude Pruning Discovers Local Receptive Fields in Fully Connected Neural Networks
• Authors: William T. Redman, Zhangyang Wang, Alessandro Ingrosso, Sebastian Goldt,
• Abstract summary: iterative magnitude pruning (IMP) has become a popular method for extracting sparseworks that can be trained to high performance. Recent work has shown that applying IMP to fully connected neural networks (FCNs) leads to the emergence of local receptive fields (RFs) We propose that IMP iteratively maximizes the non-Gaussian statistics present in the representations of FCNs, creating a feedback loop that enhances localization.
• Score: 92.66231524298554
• License:
• Abstract: Since its use in the Lottery Ticket Hypothesis, iterative magnitude pruning (IMP) has become a popular method for extracting sparse subnetworks that can be trained to high performance. Despite this, the underlying nature of IMP's general success remains unclear. One possibility is that IMP is especially capable of extracting and maintaining strong inductive biases. In support of this, recent work has shown that applying IMP to fully connected neural networks (FCNs) leads to the emergence of local receptive fields (RFs), an architectural feature present in mammalian visual cortex and convolutional neural networks. The question of how IMP is able to do this remains unanswered. Inspired by results showing that training FCNs on synthetic images with highly non-Gaussian statistics (e.g., sharp edges) is sufficient to drive the formation of local RFs, we hypothesize that IMP iteratively maximizes the non-Gaussian statistics present in the representations of FCNs, creating a feedback loop that enhances localization. We develop a new method for measuring the effect of individual weights on the statistics of the FCN representations ("cavity method"), which allows us to find evidence in support of this hypothesis. Our work, which is the first to study the effect IMP has on the representations of neural networks, sheds parsimonious light one way in which IMP can drive the formation of strong inductive biases.

Related papers

• Expressivity of Neural Networks with Random Weights and Learned Biases [44.02417750529102]
  Recent work has pushed the bounds of universal approximation by showing that arbitrary functions can similarly be learned by tuning smaller subsets of parameters. We provide theoretical and numerical evidence demonstrating that feedforward neural networks with fixed random weights can be trained to perform multiple tasks by learning biases only. Our results are relevant to neuroscience, where they demonstrate the potential for behaviourally relevant changes in dynamics without modifying synaptic weights.
  arXiv  Detail & Related papers  (2024-07-01T04:25:49Z)
• Beyond IID weights: sparse and low-rank deep Neural Networks are also Gaussian Processes [3.686808512438363]
  We extend the proof of Matthews et al. to a larger class of initial weight distributions. We show that fully-connected and convolutional networks with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training.
  arXiv  Detail & Related papers  (2023-10-25T12:38:36Z)
• Why Neural Networks Work [0.32228025627337864]
  We argue that many properties of fully-connected feedforward neural networks (FCNNs) are explainable from the analysis of a single pair of operations. We show how expand-and-sparsify can explain the observed phenomena that have been discussed in the literature.
  arXiv  Detail & Related papers  (2022-11-26T18:15:17Z)
• The Spectral Bias of Polynomial Neural Networks [63.27903166253743]
  Polynomial neural networks (PNNs) have been shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate a $textitspectral bias$ towards low-frequency functions, which yields faster learning of low-frequency components during training. Inspired by such studies, we conduct a spectral analysis of the Tangent Kernel (NTK) of PNNs. We find that the $Pi$-Net family, i.e., a recently proposed parametrization of PNNs, speeds up the
  arXiv  Detail & Related papers  (2022-02-27T23:12:43Z)
• Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks [79.74580058178594]
  We analyze the performance of training a pruned neural network by analyzing the geometric structure of the objective function. We show that the convex region near a desirable model with guaranteed generalization enlarges as the neural network model is pruned.
  arXiv  Detail & Related papers  (2021-10-12T01:11:07Z)
• Path classification by stochastic linear recurrent neural networks [2.5499055723658097]
  We show that RNNs retain a partial signature of the paths they are fed as the unique information exploited for training and classification tasks. We argue that these RNNs are easy to train and robust and back these observations with numerical experiments on both synthetic and real data.
  arXiv  Detail & Related papers  (2021-08-06T12:59:12Z)
• FF-NSL: Feed-Forward Neural-Symbolic Learner [70.978007919101]
  This paper introduces a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FF-NSL) FF-NSL integrates state-of-the-art ILP systems based on the Answer Set semantics, with neural networks, in order to learn interpretable hypotheses from labelled unstructured data.
  arXiv  Detail & Related papers  (2021-06-24T15:38:34Z)
• A tensor network representation of path integrals: Implementation and analysis [0.0]
  We introduce a novel tensor network-based decomposition of path integral simulations involving Feynman-Vernon influence functional. The finite temporarily non-local interactions introduced by the influence functional can be captured very efficiently using matrix product state representation. The flexibility of the AP-TNPI framework makes it a promising new addition to the family of path integral methods for non-equilibrium quantum dynamics.
  arXiv  Detail & Related papers  (2021-06-23T16:41:54Z)
• Towards Evaluating and Training Verifiably Robust Neural Networks [81.39994285743555]
  We study the relationship between IBP and CROWN, and prove that CROWN is always tighter than IBP when choosing appropriate bounding lines. We propose a relaxed version of CROWN, linear bound propagation (LBP), that can be used to verify large networks to obtain lower verified errors.
  arXiv  Detail & Related papers  (2021-04-01T13:03:48Z)
• How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks [80.55378250013496]
  We study how neural networks trained by gradient descent extrapolate what they learn outside the support of the training distribution. Graph Neural Networks (GNNs) have shown some success in more complex tasks.
  arXiv  Detail & Related papers  (2020-09-24T17:48:59Z)

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.