A semiotic reflection on the didactics of the Chain rule

Rodríguez, Omar Hernández; Fernández, Jorge M. López

doi:10.54870/1551-3440.1191

Cited by 15 publications

(9 citation statements)

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“…where η indicates the learning rate parameter. Following the chain rule in calculus [59], the partial differential derivatives in the above equations can be decomposed as follows:…”

Section: Learning Algorithmmentioning

confidence: 99%

Dendritic Neural Network: A Novel Extension of Dendritic Neuron Model

Tang,

Ji,

Todo

et al. 2024

IEEE Trans. Emerg. Top. Comput. Intell.

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The conventional dendritic neuron model (DNM) is a single-neuron model inspired by biological dendritic neurons that has been applied successfully in various fields. However, an increasing number of input features results in inefficient learning and gradient vanishing problems in the DNM. Thus, the DNM struggles to handle more complex tasks, including multiclass classification and multivariate time-series forecasting problems. In this study, we extended the conventional DNM to overcome these limitations. In the proposed dendritic neural network (DNN), the flexibility of both synapses and dendritic branches is considered and formulated, which can improve the model's nonlinear capabilities on high-dimensional problems. Then, multiple output layers are stacked to accommodate the various loss functions of complex tasks, and a dropout mechanism is implemented to realize a better balance between the underfitting and overfitting problems, which enhances the network's generalizability. The performance and computational efficiency of the proposed DNN compared to state-of-theart machine learning algorithms were verified on 10 multiclass classification and 2 high-dimensional binary classification datasets. The experimental results demonstrate that the proposed DNN is a promising and practical neural network architecture.

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“…where η indicates the learning rate parameter. Following the chain rule in calculus [59], the partial differential derivatives in the above equations can be decomposed as follows:…”

Section: Learning Algorithmmentioning

confidence: 99%

Dendritic Neural Network: A Novel Extension of Dendritic Neuron Model

Tang,

Ji,

Todo

et al. 2024

IEEE Trans. Emerg. Top. Comput. Intell.

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“…Moreover, the method underwent significant enhancements, resulting in the development of a backpropagation method. This advancement was achieved through the incorporation of a supervised learning strategy based on the chain rule (Rodriguez & Lopez Fernandez, 2010). Leveraging the intrinsic capacity of MLP to tackle nonlinearity issues (Amari, 1967;Ivakhnenko, 1967;Rodriguez & Lopez Fernandez, 2010), this study employed MLP to address the inherent nonlinear behaviors observed in input well logs, such as sonic velocity (Vp), PEF and neutron porosity (NPHI).…”

Section: Mineral Volume Inversion Using Multi-layer Perception (Mlp)mentioning

confidence: 99%

Rock Mineral Volume Inversion Using Statistical and Machine Learning Algorithms for Enhanced Geothermal Systems in Upper Rhine Graben, Eastern France

Joshua,

Marquis,

Maurer

et al. 2024

Journal of Geophysical Research: Machine Learning and Computati

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Accurately determining the mineralogical composition of rocks is essential for precise assessments of key petrophysical properties like effective porosity, water saturation, clay volume, and permeability. Mineral volume inversion is particularly critical in geological contexts characterized by heterogeneity, such as in the Upper Rhine Graben (URG), where both carbonate and siliciclastic formations are prevalent. The estimation of mineral volumes poses challenges that involve both linear and nonlinear relationships associated with geophysical data. To address this complexity, our methodology strategically integrates the robust insights from standard statistical approaches with three machine learning (ML) algorithms: multi‐layer perceptron, random forest regression, and gradient boosting regression. Furthermore, we propose a new hybrid ensemble model that incorporates a weighted average of multiple ML approaches to predict mineral composition within the Muschelkalk and Buntsandstein formations of the URG. ML techniques for mineral composition prediction in these formations exhibit robust predictive performance. The predicted mineral volumes align closely with quantitative estimates derived from X‐ray diffraction analysis. Additionally, they are in good qualitative agreement with mineral descriptions obtained from cores and cuttings of the Muschelkalk and Buntsandstein formations.

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“…Compute loss, L t , for outputs. Use the differentiation chain rule 1286 to backpropagate gradients of the loss to trainable parameters, θ t−1 .…”

Section: Optimizationmentioning

confidence: 99%

Review: Deep Learning in Electron Microscopy

Ede

2020

Preprint

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Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy.

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A semiotic reflection on the didactics of the Chain rule

Cited by 15 publications

References 0 publications

Dendritic Neural Network: A Novel Extension of Dendritic Neuron Model

Dendritic Neural Network: A Novel Extension of Dendritic Neuron Model

Rock Mineral Volume Inversion Using Statistical and Machine Learning Algorithms for Enhanced Geothermal Systems in Upper Rhine Graben, Eastern France

Review: Deep Learning in Electron Microscopy

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