Topology of Learning in Feedforward Neural Networks

Gabella Maxime

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Topology of Learning in Feedforward Neural Networks

机译：前馈神经网络学习的拓扑

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Understanding how neural networks learn remains one of the central challenges in machine learning research. From random at the start of training, the weights of a neural network evolve in such a way as to be able to perform a variety of tasks, such as classifying images. Here, we study the emergence of structure in the weights by applying methods from topological data analysis. We train simple feedforward neural networks on the MNIST data set and monitor the evolution of the weights. When initialized to zero, the weights follow trajectories that branch off recurrently, thus generating trees that describe the growth of the effective capacity of each layer. When initialized to tiny random values, the weights evolve smoothly along 2-D surfaces. We show that natural coordinates on these learning surfaces correspond to important factors of variation.

机译：了解神经网络如何学习如何仍然是机器学习研究中的中央挑战之一。从训练开始时从随机开始，神经网络的权重以能够执行各种任务的方式发展，例如分类图像。在这里，我们通过应用来自拓扑数据分析的方法来研究体重中的结构的出现。我们在Mnist数据集上培训简单的前馈神经网络并监控权重的演变。当初始化为零时，重量遵循分支频繁分支的轨迹，从而产生描述每层有效容量的生长的树木。当初始化为微小的随机值时，权重沿2-D曲面平滑地演变。我们表明，这些学习表面上的自然坐标对应于变异的重要因素。

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《Neural Networks and Learning Systems, IEEE Transactions on》 |2021年第8期|3588-3592|共5页
作者
Gabella Maxime;
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作者单位

MAGMA Learning CH-1015 Lausanne Switzerland;

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正文语种 eng
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关键词
Training; Neurons; Biological neural networks; Principal component analysis; Three-dimensional displays; Shape; Network topology; Bifurcation; feedforward neural networks; learning (artificial intelligence); machine learning; neural networks; topology;

机译：培训;神经元;生物神经网络;主成分分析;三维显示器;形状;网络拓扑;分叉的神经网络;学习（人工智能）;机器学习;神经网络;拓扑;拓扑;拓扑;拓扑;拓扑;拓扑;拓扑;

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3. Weighted Learning for Feedforward Neural Networks [J] . Rong-Fang Xu, Thao-Tsen Chen, Shie-Jue Lee 电子科技学刊：英文版 . 2014,第003期
4. Two Criteria for Learning in Feedforward Neural Networks [J] . 彭汉川, 甘强, 韦钰东南大学学报：英文版 . 1997,第002期
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8. GANN System to Optimize both Topology and Neural Weights of a Feedforward Neural Network [C] . Iulian-Constantin VIZITIU, Florin POPESCU International Conference on Communications . 2010

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9. Neural network control and an optoelectronic implementation of a multilayer feedforward neural network [D] . Yamamura, Alan Akihiro. 1992

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10. Effects of network topologies on stochastic resonance in feedforward neural network [O] . Jia Zhao, Yingmei Qin, Yanqiu Che, 2020

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12. Alternative learning algorithms for feedforward neural networks [R] . Vitela, J. E. 1996

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Topology of Learning in Feedforward Neural Networks

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