From graphs to neural networks: complexity and simplicity in the - - PowerPoint PPT Presentation

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From graphs to neural networks: complexity and simplicity in the - - PowerPoint PPT Presentation

Sep 27, 2023 146 likes •394 views

From graphs to neural networks: complexity and simplicity in the framework of mathema9cs Martha-Ivon Crdenas Ar8ficial intelligence research group: So? Compu8ng SOCO. UPC Systems Pharmacology and Bioinforma8cs group. Ins8tut de Neurocincies.

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From graphs to neural networks: complexity and simplicity in the framework of mathema9cs

Martha-Ivon Cárdenas

mcardenas@cs.upc.edu

Ar8ficial intelligence research group: So? Compu8ng SOCO. UPC Systems Pharmacology and Bioinforma8cs group. Ins8tut de Neurociències. UAB

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Learning from Graphs: pa<ern recogni9on To bridge AI with pa<ern modelling in secondary/high school To introduce the concept of computa9onal sciences STEAM methodology can help us with this task Not only sta9s9cs data but also rela9onal data

Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Graphs in a nutshell

Simplicity Powerful analysis Visualiza9on of interacions Not only about geometry

Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Graphs in a nutshell

Simplicity Powerful analysis Visualiza9on of interacions Not only about geometry

Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Networks: airplains in Europe

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Networks: Facebook

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

y = mx + b Linear perceptron Neuron

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

y = mx + b Linear perceptron - activation function Neuron

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

y = mx + b Connected linear perceptrons Neurons

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Connected linear perceptrons Neural network

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Graph Degree matrix Adjacency matrix Laplacian matrix

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Giving math sense to neural networks Learning

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Classification Clustering Rules

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Decoding the meaning of the data

Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Minimize the error: backpropaga8on

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Decoding the meaning of the data

Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Minimize the error: backpropaga8on

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

2D visualiza9on

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cytoscape.org

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Zometool

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Funny classifica9on

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Martha-Ivon Cárdenas: From graphs to neural networks: complexity and simplicity in the framework of mathema8cs (AI4ME 2020)

Thank you

mcardenas@cs.upc.edu