Structured Computation and Representation in Deep Reinforcement - - PowerPoint PPT Presentation

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Structured Computation and Representation in Deep Reinforcement - - PowerPoint PPT Presentation

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Structured Computation and Representation in Deep Reinforcement Learning Jessica B. Hamrick AAMAS/ICML/IJCAI Workshop on Prediction and Generative Modeling in RL Stockholm, Sweden July 15, 2018 Understanding the World in Terms of Objects and

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Structured Computation and Representation in Deep Reinforcement Learning

Jessica B. Hamrick

AAMAS/ICML/IJCAI Workshop on Prediction and Generative Modeling in RL Stockholm, Sweden July 15, 2018

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Jessica Hamrick (@jhamrick)

Understanding the World in Terms of Objects and Relations

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Jessica Hamrick (@jhamrick)

Understanding the World in Terms of Objects and Relations

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Jessica Hamrick (@jhamrick)

Understanding the World in Terms of Objects and Relations

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Jessica Hamrick (@jhamrick)

Understanding the World in Terms of Objects and Relations

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Jessica Hamrick (@jhamrick)

Structure

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Jessica Hamrick (@jhamrick)

Structure

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The arrangement of and relations between the parts


  • r elements of something complex.

(Oxford English Dictionary)

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Jessica Hamrick (@jhamrick)

Structure

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In humans: Evolution → Structure The arrangement of and relations between the parts


  • r elements of something complex.

(Oxford English Dictionary)

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Jessica Hamrick (@jhamrick)

Structure

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In humans: Evolution → Structure In ML: Structure → Inductive bias / prior / regularizer The arrangement of and relations between the parts


  • r elements of something complex.

(Oxford English Dictionary)

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Jessica Hamrick (@jhamrick)

Two Types of Structure

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Jessica Hamrick (@jhamrick)

Two Types of Structure

  • 1. Structured Computation: the way that

individual computations or functions are composed into more complex structures.

4

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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of

the data that computations are performed

  • ver, e.g. sets, graphs, programs, etc.

Two Types of Structure

  • 1. Structured Computation: the way that

individual computations or functions are composed into more complex structures.

4

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Jessica Hamrick (@jhamrick)

A Caveat

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Jessica Hamrick (@jhamrick)

A Caveat

Structured computation and structured representation go hand in hand!

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Jessica Hamrick (@jhamrick)

A Caveat

Structured computation and structured representation go hand in hand! Often, a structured representation entails
 a particular structure in the computation, and vice versa.

5

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Jessica Hamrick (@jhamrick)

A Caveat

Structured computation and structured representation go hand in hand! Often, a structured representation entails
 a particular structure in the computation, and vice versa. But it can still be useful to think separately about:
 (1) how computations are arranged and composed, and
 (2) the specific form of the representations.

5

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Jessica Hamrick (@jhamrick)

A Caveat

Structured computation and structured representation go hand in hand! Often, a structured representation entails
 a particular structure in the computation, and vice versa. But it can still be useful to think separately about:
 (1) how computations are arranged and composed, and
 (2) the specific form of the representations.

5

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Jessica Hamrick (@jhamrick)

A Caveat

Structured computation and structured representation go hand in hand! Often, a structured representation entails
 a particular structure in the computation, and vice versa. But it can still be useful to think separately about:
 (1) how computations are arranged and composed, and
 (2) the specific form of the representations.

5

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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Two Types of Structure

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

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Jessica Hamrick (@jhamrick)

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Claim: flexibility, adaptivity and generalization are about
 having the right structure (which may or may not mean having a model!)

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

Fully-Connected Layer Unstructured computation Unstructured representation

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

Fully-Connected Layer Unstructured computation Unstructured representation

Sharing in space

Convolutional Layer Structured computation Unstructured representation

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

Fully-Connected Layer Unstructured computation Unstructured representation

Sharing in space

Convolutional Layer Structured computation Unstructured representation

Sharing in time

Recurrent Layer Structured computation Unstructured representation

8

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

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GoogLeNet with Inception modules, Szegedy et al. (2015)

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Jessica Hamrick (@jhamrick)

Structure in Model-Free Deep RL

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Action-Value Network

  • r

Policy Network State Action

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Jessica Hamrick (@jhamrick)

Structure in Model-Free Deep RL

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Action-Value Network

  • r

Policy Network State Action

Mostly unstructured computation

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Jessica Hamrick (@jhamrick)

Structure in Model-Free Deep RL

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Action-Value Network

  • r

Policy Network State Action

Mostly unstructured computation Unstructured representation

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Jessica Hamrick (@jhamrick)

Structure in Model-Based Deep RL

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State Action

Search / Planning / Optimization Model

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Jessica Hamrick (@jhamrick)

Structure in Model-Based Deep RL

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State Action

Search / Planning / Optimization Model

Structured computation!

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Jessica Hamrick (@jhamrick)

Structure in Model-Based Deep RL

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State Action

Search / Planning / Optimization Model

Structured computation!

  • AlphaGo (Silver et al., 2016)
  • Imagination-Based Decision Making and Planning (Hamrick et al., 2017; Pascanu et al., 2017)
  • Imagination-Augmented Agents (Weber et al., 2017)
  • Gradient Based Planning (Henaff et al., 2017)
  • Value Prediction Networks (Oh et al., 2017)
  • Universal Planning Networks (Srinivas et al., 2018)
  • … and more!
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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Outline

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

12

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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Outline

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

12

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Jessica Hamrick (@jhamrick)

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Jessica Hamrick (@jhamrick)

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Jessica Hamrick (@jhamrick)

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Jessica Hamrick (@jhamrick)

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Jessica Hamrick (@jhamrick)

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Jessica Hamrick (@jhamrick)

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“Reactive Controller”

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Jessica Hamrick (@jhamrick) Controller (MLP):
 Proposes a control that is sent to the world to minimize performance loss

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“Reactive Controller”

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Jessica Hamrick (@jhamrick) Controller (MLP):
 Proposes a control that is sent to the world to minimize performance loss World: The true environment that the agent is acting in

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“Reactive Controller”

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Jessica Hamrick (@jhamrick)

Reactive controller: simple task

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Jessica Hamrick (@jhamrick)

Reactive controller: simple task

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Jessica Hamrick (@jhamrick)

Reactive controller: hard task

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Jessica Hamrick (@jhamrick)

Reactive controller: hard task

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

“Iterative” Controller

Memory (LSTM):
 Encodes the full history of controls and opinions Expert (IN, MLP, etc.): Model of the world that evaluates proposed controls

21

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Jessica Hamrick (@jhamrick)

Iterative controller

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Jessica Hamrick (@jhamrick)

Iterative controller

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Jessica Hamrick (@jhamrick)

Iterative controller

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This is using a learned expert, which is trained simultaneously with the agent

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Jessica Hamrick (@jhamrick)

Metacontroller

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller

Manager (MLP): Meta-level policy that determines whether to send the proposed control to the world, or to an expert, in

  • rder to minimize

performance loss + resource loss Experts (IN, MLP, etc.): Different models of the world, each with different resource costs

23

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Jessica Hamrick (@jhamrick)

Metacontroller: simple task

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Jessica Hamrick (@jhamrick)

Metacontroller: simple task

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Jessica Hamrick (@jhamrick)

Metacontroller: hard task

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Jessica Hamrick (@jhamrick)

Metacontroller: hard task

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Jessica Hamrick (@jhamrick)

Imagination-Based Planner

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(Pascanu, Li, et al., 2017)

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Jessica Hamrick (@jhamrick)

Imagination-Based Planner

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(Pascanu, Li, et al., 2017)

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Jessica Hamrick (@jhamrick)

Takeaways

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Jessica Hamrick (@jhamrick)

Takeaways

  • 1. It can be useful to think about the choice of computation

(which then allows e.g. choosing between multiple models).

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Jessica Hamrick (@jhamrick)

Takeaways

  • 1. It can be useful to think about the choice of computation

(which then allows e.g. choosing between multiple models).

  • 2. Enables a natural tradeoff between model-free and model-

based computation by choosing the amount of computation being performed.

27

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Jessica Hamrick (@jhamrick)

Takeaways

  • 1. It can be useful to think about the choice of computation

(which then allows e.g. choosing between multiple models).

  • 2. Enables a natural tradeoff between model-free and model-

based computation by choosing the amount of computation being performed.

  • 3. Building in these choices is a type of structured

computation that goes beyond the distinction of simply having a model or not having a model.

27

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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Outline

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

28

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Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Outline

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

28

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Jessica Hamrick (@jhamrick)

Structure in Deep Networks

Fully-Connected Layer Unstructured computation Unstructured representation

Sharing in space

Convolutional Layer Structured computation Unstructured representation

Sharing in time

Recurrent Layer Structured computation Unstructured representation

29

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Jessica Hamrick (@jhamrick)

Graph Networks

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Jessica Hamrick (@jhamrick)

Graph Networks

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Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

  • 1. Takes graphs as input, return graphs as output
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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

  • 1. Takes graphs as input, return graphs as output
  • 2. Invariant to the permutation of the nodes and edges
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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

  • 1. Takes graphs as input, return graphs as output
  • 2. Invariant to the permutation of the nodes and edges
  • 3. Invariant to the number of nodes and edges
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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017)

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Jessica Hamrick (@jhamrick)

Graph Networks

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Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017) Globals

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Nodes

V

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Edges

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slide-89
SLIDE 89

Jessica Hamrick (@jhamrick)

Graph Networks

31

Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017) Globals

u

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Nodes

V

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vi

<latexit sha1_base64="UuhsKP3lpHlY+K0A8uvGImQtNkI=">AB83icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFNKJPpB06mYSZm0IJ/Q03LhRx68+482+ctlo64GBwzn3cs+cMJXCoOt+O6Wt7Z3dvfJ+5eDw6PikenrWMUmGW+zRCa6F1LDpVC8jQIl76Wa0ziUvBtO7hd+d8q1EYl6wlnKg5iOlIgEo2gl348pjsMon84HYlCtuQ13CbJvILUoEBrUP3yhwnLYq6QSWpM3NTDHKqUTDJ5xU/MzylbEJHvG+pojE3Qb7MPCdXVhmSKNH2KSRL9fdGTmNjZnFoJxcZzbq3EP/z+hlGd0EuVJohV2x1KMokwYQsCiBDoTlDObOEMi1sVsLGVFOGtqaKLcFb/Im6Vw3PLfhPd7UmvWijJcwCXUwYNbaMIDtKANDFJ4hld4czLnxXl3PlajJafYOYc/cD5/AHRgkdw=</latexit><latexit sha1_base64="UuhsKP3lpHlY+K0A8uvGImQtNkI=">AB83icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFNKJPpB06mYSZm0IJ/Q03LhRx68+482+ctlo64GBwzn3cs+cMJXCoOt+O6Wt7Z3dvfJ+5eDw6PikenrWMUmGW+zRCa6F1LDpVC8jQIl76Wa0ziUvBtO7hd+d8q1EYl6wlnKg5iOlIgEo2gl348pjsMon84HYlCtuQ13CbJvILUoEBrUP3yhwnLYq6QSWpM3NTDHKqUTDJ5xU/MzylbEJHvG+pojE3Qb7MPCdXVhmSKNH2KSRL9fdGTmNjZnFoJxcZzbq3EP/z+hlGd0EuVJohV2x1KMokwYQsCiBDoTlDObOEMi1sVsLGVFOGtqaKLcFb/Im6Vw3PLfhPd7UmvWijJcwCXUwYNbaMIDtKANDFJ4hld4czLnxXl3PlajJafYOYc/cD5/AHRgkdw=</latexit><latexit sha1_base64="UuhsKP3lpHlY+K0A8uvGImQtNkI=">AB83icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFNKJPpB06mYSZm0IJ/Q03LhRx68+482+ctlo64GBwzn3cs+cMJXCoOt+O6Wt7Z3dvfJ+5eDw6PikenrWMUmGW+zRCa6F1LDpVC8jQIl76Wa0ziUvBtO7hd+d8q1EYl6wlnKg5iOlIgEo2gl348pjsMon84HYlCtuQ13CbJvILUoEBrUP3yhwnLYq6QSWpM3NTDHKqUTDJ5xU/MzylbEJHvG+pojE3Qb7MPCdXVhmSKNH2KSRL9fdGTmNjZnFoJxcZzbq3EP/z+hlGd0EuVJohV2x1KMokwYQsCiBDoTlDObOEMi1sVsLGVFOGtqaKLcFb/Im6Vw3PLfhPd7UmvWijJcwCXUwYNbaMIDtKANDFJ4hld4czLnxXl3PlajJafYOYc/cD5/AHRgkdw=</latexit><latexit sha1_base64="UuhsKP3lpHlY+K0A8uvGImQtNkI=">AB83icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFNKJPpB06mYSZm0IJ/Q03LhRx68+482+ctlo64GBwzn3cs+cMJXCoOt+O6Wt7Z3dvfJ+5eDw6PikenrWMUmGW+zRCa6F1LDpVC8jQIl76Wa0ziUvBtO7hd+d8q1EYl6wlnKg5iOlIgEo2gl348pjsMon84HYlCtuQ13CbJvILUoEBrUP3yhwnLYq6QSWpM3NTDHKqUTDJ5xU/MzylbEJHvG+pojE3Qb7MPCdXVhmSKNH2KSRL9fdGTmNjZnFoJxcZzbq3EP/z+hlGd0EuVJohV2x1KMokwYQsCiBDoTlDObOEMi1sVsLGVFOGtqaKLcFb/Im6Vw3PLfhPd7UmvWijJcwCXUwYNbaMIDtKANDFJ4hld4czLnxXl3PlajJafYOYc/cD5/AHRgkdw=</latexit>

u

<latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit>

e0

k

<latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit>

Edge update

e0

i!j = φe(vi, vj, ei!j, u)

<latexit sha1_base64="VbNmaAiBTb5ju/G+yhwMDQ4YLfU=">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</latexit><latexit sha1_base64="VbNmaAiBTb5ju/G+yhwMDQ4YLfU=">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</latexit><latexit sha1_base64="VbNmaAiBTb5ju/G+yhwMDQ4YLfU=">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</latexit><latexit sha1_base64="VbNmaAiBTb5ju/G+yhwMDQ4YLfU=">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</latexit>

e0

j!i

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slide-90
SLIDE 90

Jessica Hamrick (@jhamrick)

Graph Networks

31

Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017) Globals

u

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Nodes

V

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Edges

E

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vi

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u

<latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit>

e0

k

<latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit>

Edge update

e0

i!j = φe(vi, vj, ei!j, u)

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e0

j!i

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u

<latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit>

e0

k

<latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit>

v0

i

<latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit>

Node update

v0

i = φv(vi,

X

j

e0

j!i, u)

<latexit sha1_base64="V2b5Xhg8CWMzWvpKav0COk0EaOE=">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</latexit><latexit sha1_base64="V2b5Xhg8CWMzWvpKav0COk0EaOE=">ACSHicdVBNS8NAFNzUr1q/qh69LBZBQUqi1XgRCl48KlgVmho25d2624SdjeVEvLzvHj05m/w4kERb25rFRUdWBhm5vHeTpBwprRtP1iFicmp6ZnibGlufmFxqby8cq7iVFJo0JjH8jIgCjiLoKGZ5nCZSCAi4HARXB8N/Ys+SMXi6EwPEmgJ0olYyCjRvLvieI7gZh1s9duUlkgk49JIu8/ub361t7KlU+D38KULuZz1Psk5XEynjG8zy8fj2VybNt/xyxa7u7Lt7uzY2xK3tOe6IHNhuDTtVe4QKGuPEL97ZimAiJNOVGq6diJbmVEakY5CUvVZAQek060DQ0IgJUKxsVkeMNo7RxGEvzIo1H6veJjAilBiIwyeGJ6rc3FP/ymqkOD1oZi5JUQ0Q/FoUpxzrGw1Zxm0mgmg8MIVQycyumXSIJ1ab7kinh86f4f3K+U3XsqnNaq9SPx3U0RpaR5vIQS6qo2N0ghqIolv0iJ7Ri3VnPVmv1tHtGCNZ1bRDxQK7yitPI=</latexit><latexit sha1_base64="V2b5Xhg8CWMzWvpKav0COk0EaOE=">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</latexit><latexit sha1_base64="V2b5Xhg8CWMzWvpKav0COk0EaOE=">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</latexit>

e0

j!i

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slide-91
SLIDE 91

Jessica Hamrick (@jhamrick)

Graph Networks

31

Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018) Gori et al. (2005), Scarselli et al. (2005), Scarselli et al. (2009), Li et al. (2015), Gilmer et al. (2017) Globals

u

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Nodes

V

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Edges

E

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vi

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u

<latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit>

e0

k

<latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit><latexit sha1_base64="a1hco1MShws4KpmpFnenOcfEqyc=">AB9HicdVDLSgMxFM34rPVdekmWMSuhkxtsd0V3LisYB/QDiWT3mlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrTciHtba+sbm1ndvJ7+7tHxwWjo7bKkokgxaLRCS7HlUgeAgtzbWAbiyBp6Aje5zvzOFKTiUXinZzG4AR2F3OeMaiO5/YDqsenML8YTAaFIrGdCilXy5jY1XqdVOqG1KqXpEywY5MFimiF5qDw3h9GLAkg1ExQpXoOibWbUqk5EzDP9xMFMWUTOoKeoSENQLnpIvQcnxtliP1ImhdqvFC/b6Q0UGoWeGYyC6l+e5n4l9dLtF9zUx7GiYaQLQ/5icA6wlkDeMglMC1mhlAmucmK2ZhKyrTpKW9K+Pop/p+0y7ZjurqtFBulVR05dIrOUAk56Ao10A1qohZi6B49oCf0bE2tR+vFel2OrlmrnRP0A9bJyRskI=</latexit>

Edge update

e0

i!j = φe(vi, vj, ei!j, u)

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e0

j!i

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u0

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v0

i

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sha1_base64="6WjtAQy1eEki3DeLmUkI9Sk/Os=">AB53icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFtkMnkph06mYSZiVBCf8CNC0Xc+kvu/BunaRbaemDgcM65zL0nSAXxnW/ncrG5tb2TnW3trd/cHhUPz7p6SRTDLsEYkaBFSj4BK7huBg1QhjQOB/WB6u/D7T6g0T+SDmaXox3QsecQZNVbqPNYbstQNaJV5IGlLD5r1GYsCxGaZigWg89NzV+TpXhTOC8Nso0pRN6RiHlkoao/bzYs85ubBKSKJE2ScNKdTfEzmNtZ7FgU3G1Ez0qrcQ/OGmYlu/JzLNDMo2fKjKBPEJGRxNAm5QmbEzBLKFLe7EjahijJjq6nZErzVk9dJ7LluS3v/qrRbpZ1VOEMzqEJHlxDG+6gA1gEMIzvMKbw50X5935WEYrTjlzCn/gfP4A6WMYA=</latexit><latexit sha1_base64="6WjtAQy1eEki3DeLmUkI9Sk/Os=">AB53icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFtkMnkph06mYSZiVBCf8CNC0Xc+kvu/BunaRbaemDgcM65zL0nSAXxnW/ncrG5tb2TnW3trd/cHhUPz7p6SRTDLsEYkaBFSj4BK7huBg1QhjQOB/WB6u/D7T6g0T+SDmaXox3QsecQZNVbqPNYbstQNaJV5IGlLD5r1GYsCxGaZigWg89NzV+TpXhTOC8Nso0pRN6RiHlkoao/bzYs85ubBKSKJE2ScNKdTfEzmNtZ7FgU3G1Ez0qrcQ/OGmYlu/JzLNDMo2fKjKBPEJGRxNAm5QmbEzBLKFLe7EjahijJjq6nZErzVk9dJ7LluS3v/qrRbpZ1VOEMzqEJHlxDG+6gA1gEMIzvMKbw50X5935WEYrTjlzCn/gfP4A6WMYA=</latexit><latexit sha1_base64="6WjtAQy1eEki3DeLmUkI9Sk/Os=">AB53icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFtkMnkph06mYSZiVBCf8CNC0Xc+kvu/BunaRbaemDgcM65zL0nSAXxnW/ncrG5tb2TnW3trd/cHhUPz7p6SRTDLsEYkaBFSj4BK7huBg1QhjQOB/WB6u/D7T6g0T+SDmaXox3QsecQZNVbqPNYbstQNaJV5IGlLD5r1GYsCxGaZigWg89NzV+TpXhTOC8Nso0pRN6RiHlkoao/bzYs85ubBKSKJE2ScNKdTfEzmNtZ7FgU3G1Ez0qrcQ/OGmYlu/JzLNDMo2fKjKBPEJGRxNAm5QmbEzBLKFLe7EjahijJjq6nZErzVk9dJ7LluS3v/qrRbpZ1VOEMzqEJHlxDG+6gA1gEMIzvMKbw50X5935WEYrTjlzCn/gfP4A6WMYA=</latexit><latexit sha1_base64="6WjtAQy1eEki3DeLmUkI9Sk/Os=">AB53icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFtkMnkph06mYSZiVBCf8CNC0Xc+kvu/BunaRbaemDgcM65zL0nSAXxnW/ncrG5tb2TnW3trd/cHhUPz7p6SRTDLsEYkaBFSj4BK7huBg1QhjQOB/WB6u/D7T6g0T+SDmaXox3QsecQZNVbqPNYbstQNaJV5IGlLD5r1GYsCxGaZigWg89NzV+TpXhTOC8Nso0pRN6RiHlkoao/bzYs85ubBKSKJE2ScNKdTfEzmNtZ7FgU3G1Ez0qrcQ/OGmYlu/JzLNDMo2fKjKBPEJGRxNAm5QmbEzBLKFLe7EjahijJjq6nZErzVk9dJ7LluS3v/qrRbpZ1VOEMzqEJHlxDG+6gA1gEMIzvMKbw50X5935WEYrTjlzCn/gfP4A6WMYA=</latexit><latexit sha1_base64="6WjtAQy1eEki3DeLmUkI9Sk/Os=">AB53icbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9gFtkMnkph06mYSZiVBCf8CNC0Xc+kvu/BunaRbaemDgcM65zL0nSAXxnW/ncrG5tb2TnW3trd/cHhUPz7p6SRTDLsEYkaBFSj4BK7huBg1QhjQOB/WB6u/D7T6g0T+SDmaXox3QsecQZNVbqPNYbstQNaJV5IGlLD5r1GYsCxGaZigWg89NzV+TpXhTOC8Nso0pRN6RiHlkoao/bzYs85ubBKSKJE2ScNKdTfEzmNtZ7FgU3G1Ez0qrcQ/OGmYlu/JzLNDMo2fKjKBPEJGRxNAm5QmbEzBLKFLe7EjahijJjq6nZErzVk9dJ7LluS3v/qrRbpZ1VOEMzqEJHlxDG+6gA1gEMIzvMKbw50X5935WEYrTjlzCn/gfP4A6WMYA=</latexit>

Globals update

u0 = φu( X

i

v0

i,

X

i,j

e0

i!j, u)

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e0

j!i

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u

<latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit><latexit sha1_base64="Wl/NKcf+4FQq41kPZqpr8GSpKP8=">AB8XicbVDLSsNAFL2pr1pfVZduBovQVUlE0GXBjcsK9oFtKJPpTt0MgkzE6GE/oUbF4q49W/c+TdO2iy09cDA4Zx7mXNPkAiujet+O6WNza3tnfJuZW/4PCoenzS0XGqGLZLGLVC6hGwSW2DTcCe4lCGgUCu8H0Nve7T6g0j+WDmSXoR3QsecgZNVZ6HETUTIwS+fDas1tuAuQdeIVpAYFWsPq12AUszRCaZigWvc9NzF+RpXhTOC8Mkg1JpRN6Rj7lkoaofazReI5ubDKiISxsk8aslB/b2Q0noWBXYyT6hXvVz8z+unJrzxMy6T1KBky4/CVBATk/x8MuIKmREzSyhT3GYlbEIVZcaWVLEleKsnr5POZcNzG979Va1ZL+owxmcQx08uIYm3EL2sBAwjO8wpujnRfn3flYjpacYucU/sD5/AHw2JD/</latexit>

e0

k

<latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit><latexit sha1_base64="TmBm7ikN3ChoJpDcsfwhm1T5rLk=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvYVZkRQZcFNy4r2Ae0Q8mkd9rQTGZMoUy9DvcuFDErR/jzr8x03ahrQcCh3Pu5Z6cIBFcG9f9dgobm1vbO8Xd0t7+weFR+fikpeNUMWyWMSqE1CNgktsGm4EdhKFNAoEtoPxXe63J6g0j+WjmSboR3QoecgZNVbyexE1oyDMcHbZH/fLFbfmzkHWibckFVi0S9/9QYxSyOUhgmqdzE+NnVBnOBM5KvVRjQtmYDrFrqaQRaj+bh56RC6sMSBgr+6Qhc/X3RkYjradRYCfzkHrVy8X/vG5qwls/4zJDUq2OBSmgpiY5A2QAVfIjJhaQpniNithI6oM7anki3BW/3yOmld1Ty35j1cV+rVZR1FOINzqIHN1CHe2hAExg8wTO8wpszcV6cd+djMVpwljun8AfO5w/CAJH+</latexit>

v0

i

<latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit><latexit sha1_base64="eLXdOBZMDToGpT2JKCAlGanL8=">AB9HicdVDLSgMxFL3js9ZX1aWbYBG7GjK1xXZXcOygn1AO5RMmlDMw+TKEM/Q43LhRx68e482/MtBVU9EDgcM693JPjxYIrjfGHtba+sbm1ndvJ7+7tHxwWjo7bKkokZS0aiUh2PaKY4CFra4F68aSkcATrONrjO/M2VS8Si807OYuQEZhdznlGgjuf2A6LHnp9P5xYAPCkVsOxVcrpYRtqv1Oq7UDalVL3EZI8fGCxRheag8N4fRjQJWKipIEr1HBxrNyVScyrYPN9PFIsJnZAR6xkakoApN12EnqNzowyRH0nzQo0W6veNlARKzQLPTGYh1W8vE/yeon2a27KwzjRLKTLQ34ikI5Q1gAacsmoFjNDCJXcZEV0TCSh2vSUNyV8/RT9T9pl2zFd3VaKjdKqjhycwhmUwIEraMANKEFO7hAZ7g2Zpaj9aL9bocXbNWOyfwA9bJztsklE=</latexit>

Node update

v0

i = φv(vi,

X

j

e0

j!i, u)

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e0

j!i

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slide-92
SLIDE 92

Jessica Hamrick (@jhamrick)

The Gluing Task

Goal: glue blocks together to make the tower stable, using the minimum amount of glue.

32

Joint work with Kelsey Allen (MIT)

slide-93
SLIDE 93

Jessica Hamrick (@jhamrick)

The Gluing Task

Goal: glue blocks together to make the tower stable, using the minimum amount of glue.

32

Joint work with Kelsey Allen (MIT)

slide-94
SLIDE 94

Jessica Hamrick (@jhamrick)

The Gluing Task

Goal: glue blocks together to make the tower stable, using the minimum amount of glue.

32

Joint work with Kelsey Allen (MIT)

slide-95
SLIDE 95

Jessica Hamrick (@jhamrick)

The Gluing Task

Goal: glue blocks together to make the tower stable, using the minimum amount of glue.

32

Joint work with Kelsey Allen (MIT)

slide-96
SLIDE 96

Jessica Hamrick (@jhamrick)

33

slide-97
SLIDE 97

Jessica Hamrick (@jhamrick)

33

slide-98
SLIDE 98

Jessica Hamrick (@jhamrick)

Learning a Policy Over the Edges of a Graph

34

slide-99
SLIDE 99

Jessica Hamrick (@jhamrick)

Learning a Policy Over the Edges of a Graph

34

slide-100
SLIDE 100

Jessica Hamrick (@jhamrick)

Learning a Policy Over the Edges of a Graph

34

GM

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GN1

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GN2

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GNM

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...

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G1

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G0

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GM

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G0

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GNcore

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×M

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slide-101
SLIDE 101

Jessica Hamrick (@jhamrick)

Learning a Policy Over the Edges of a Graph

34

GM

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GN1

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GN2

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GNM

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...

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G1

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G0

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GM

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G0

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GNcore

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×M

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slide-102
SLIDE 102

Jessica Hamrick (@jhamrick)

Learning a Policy Over the Edges of a Graph

34

See also:

  • NerveNet (Wang et al., 2017)
  • Graph Network Models for Continuous

Control (Sanchez-Gonzalez et al., 2018)

  • Relational Deep RL (Zambaldi et al., 2018)

GM

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GN1

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GN2

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GNM

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...

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G1

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G0

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GM

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G0

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GNcore

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×M

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π(E)

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slide-103
SLIDE 103

Jessica Hamrick (@jhamrick)

Agent Variations

Human: human baseline MLP: multilayer perceptron agent GN-FC: fully connected graph network agent


(nodes=blocks, edges=all-to-all)

GN: sparse graph network agent


(nodes=blocks, edges=contacts)

35

(Trained & tested on towers of size 2-10 blocks)

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SLIDE 104

Jessica Hamrick (@jhamrick)

Results

36

Optimal

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SLIDE 105

Jessica Hamrick (@jhamrick)

Results

37

Optimal Optimal No Glue

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SLIDE 106

Jessica Hamrick (@jhamrick)

Generalization Results

38

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SLIDE 107

Jessica Hamrick (@jhamrick)

Generalization Results

38

(Train on 2-6, 8, & 9 blocks, test on 7 & 10)

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SLIDE 108

Jessica Hamrick (@jhamrick)

Generalization Results

38

(Train on 2-6, 8, & 9 blocks, test on 7 & 10)

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SLIDE 109

Jessica Hamrick (@jhamrick)

Generalization Results

38

(Train on 2-6, 8, & 9 blocks, test on 7 & 10)

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SLIDE 110

Jessica Hamrick (@jhamrick)

Generalization Results

38

(Train on 2-6, 8, & 9 blocks, test on 7 & 10)

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SLIDE 111

Jessica Hamrick (@jhamrick)

Force Propagation

39

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SLIDE 112

Jessica Hamrick (@jhamrick)

Force Propagation

Edge update

40

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SLIDE 113

Jessica Hamrick (@jhamrick)

Force Propagation

Edge update Node update

41

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SLIDE 114

Jessica Hamrick (@jhamrick)

Force Propagation

Edge update Node update

42

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SLIDE 115

Jessica Hamrick (@jhamrick)

Force Propagation

Edge update Node update

43

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SLIDE 116

Jessica Hamrick (@jhamrick)

Force Propagation

Edge update Node update

44

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SLIDE 117

Jessica Hamrick (@jhamrick)

Takeaways

45

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SLIDE 118

Jessica Hamrick (@jhamrick)

Takeaways

  • 1. Model-free RL with an appropriate representation of

the data can be highly effective, even when it comes to transfer!

45

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SLIDE 119

Jessica Hamrick (@jhamrick)

Takeaways

  • 1. Model-free RL with an appropriate representation of

the data can be highly effective, even when it comes to transfer!

  • 2. Combining the right structured computation with the

right structured representation can lead to the emergence of behavior that looks model-based.

45

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SLIDE 120

Jessica Hamrick (@jhamrick)

  • 2. Structured Representation: the format of the data

that computations are performed over.

Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018, CogSci) Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018, arXiv)

Outline

  • 1. Structured Computation: the way that individual

computations or functions are composed into more complex structures.

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017, ICLR)

46

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SLIDE 121

Jessica Hamrick (@jhamrick)

Other Structured Approaches

47

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SLIDE 122

Jessica Hamrick (@jhamrick)

Other Structured Approaches

Structured computation that integrates hierarchical and model-based RL
 (e.g. Value Prediction Networks, Oh et al. 2017)

47

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SLIDE 123

Jessica Hamrick (@jhamrick)

Other Structured Approaches

Structured computation that integrates hierarchical and model-based RL
 (e.g. Value Prediction Networks, Oh et al. 2017) Structured computation that separates inference from planning
 (e.g. QMDP-Net, Karkus et al. 2017)

47

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SLIDE 124

Jessica Hamrick (@jhamrick)

Other Structured Approaches

Structured computation that integrates hierarchical and model-based RL
 (e.g. Value Prediction Networks, Oh et al. 2017) Structured computation that separates inference from planning
 (e.g. QMDP-Net, Karkus et al. 2017) Structured computation which converts unstructured representations to structured representations
 (e.g. Relational Neural Expectation Maximization, van Steenkiste et al., 2018)

47

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SLIDE 125

Jessica Hamrick (@jhamrick)

Other Structured Approaches

Structured computation that integrates hierarchical and model-based RL
 (e.g. Value Prediction Networks, Oh et al. 2017) Structured computation that separates inference from planning
 (e.g. QMDP-Net, Karkus et al. 2017) Structured computation which converts unstructured representations to structured representations
 (e.g. Relational Neural Expectation Maximization, van Steenkiste et al., 2018) Structured representations which are inferred and adapted online
 (e.g. Neural Relational Inference, Kipf et al. 2018)

47

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SLIDE 126

Jessica Hamrick (@jhamrick)

Other Structured Approaches

Structured computation that integrates hierarchical and model-based RL
 (e.g. Value Prediction Networks, Oh et al. 2017) Structured computation that separates inference from planning
 (e.g. QMDP-Net, Karkus et al. 2017) Structured computation which converts unstructured representations to structured representations
 (e.g. Relational Neural Expectation Maximization, van Steenkiste et al., 2018) Structured representations which are inferred and adapted online
 (e.g. Neural Relational Inference, Kipf et al. 2018) Structured representations which encode stronger notions of hierarchy
 (e.g. Hierarchical Relation Networks, Mrowca et al., 2018)

47

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SLIDE 127

Jessica Hamrick (@jhamrick)

48

Flexibility, adaptivity and generalization are about
 having the right structure.

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SLIDE 128

Jessica Hamrick (@jhamrick)

48

Flexibility, adaptivity and generalization are about
 having the right structure.

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SLIDE 129

Jessica Hamrick (@jhamrick)

48

Flexibility, adaptivity and generalization are about
 having the right structure.

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SLIDE 130

Jessica Hamrick (@jhamrick)

Thanks!

Peter Battaglia Kelsey Allen Victor Bapst Tina Zhu Kevin McKee Josh Tenenbaum Andy Ballard Razvan Pascanu Oriol Vinyals Nicolas Heess Alvaro Sanchez-Gonalez Yujia Li Matt Botvinick Theo Weber David Reichert Tobias Pfaff DeepMind

49

Hamrick, Ballard, Pascanu, Vinyals, Heess, & Battaglia (2017) Hamrick*, Allen*, Bapst, Zhu, McKee, Tenenbaum, & Battaglia (2018) *equal contribution Battaglia, Hamrick, Bapst, Sanchez-Gonzalez, Zambaldi, et al. (2018)

vi

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Jessica Hamrick (@jhamrick)

Extra Slides

50

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SLIDE 132

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

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SLIDE 133

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 134

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 135

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 136

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 137

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 138

Jessica Hamrick (@jhamrick)

Reactive Controller Results

51 Number of simulations Performance Loss

Performance Loss

0.5

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SLIDE 139

Jessica Hamrick (@jhamrick)

Number of simulations Performance Loss

Iterative Controller Results

Performance Loss Number of simulations

0.5 52

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SLIDE 140

Jessica Hamrick (@jhamrick)

Number of simulations Performance Loss

Iterative Controller Results

Performance Loss Number of simulations

0.5 53

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SLIDE 141

Jessica Hamrick (@jhamrick)

Number of simulations Performance Loss

Iterative Controller Results

Performance Loss Number of simulations

0.5 53

This is using a learned expert, which is trained simultaneously with the agent

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SLIDE 142

Jessica Hamrick (@jhamrick)

Iterative Controller Results

Number of simulations Performance Loss 54

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SLIDE 143

Jessica Hamrick (@jhamrick)

Iterative Controller Results

Number of simulations Performance Loss Number of simulations Performance Loss 54

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SLIDE 144

Jessica Hamrick (@jhamrick)

Iterative Controller Results

Number of simulations Performance Loss Number of simulations Performance Loss Number of simulations Performance Loss 54

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SLIDE 145

Jessica Hamrick (@jhamrick)

Metacontroller Results

Effect of difficulty (IN expert)

55

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SLIDE 146

Jessica Hamrick (@jhamrick)

Metacontroller Results

Effect of difficulty (IN expert)

55

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SLIDE 147

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Performance Loss Number of simulations

56

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SLIDE 148

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Resource Loss Performance Loss Number of simulations

56

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SLIDE 149

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Sum of performance and resource loss Zero resource cost

Number of simulations

57

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SLIDE 150

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Number of simulations

58

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SLIDE 151

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Different resource costs

Number of simulations

58

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SLIDE 152

Jessica Hamrick (@jhamrick)

Metacontroller Results

Total cost (five planets)

Different resource costs

Number of simulations

59

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SLIDE 153

Jessica Hamrick (@jhamrick)

Metacontroller Results

Multiple experts (MLP + IN)

60

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SLIDE 154

Jessica Hamrick (@jhamrick)

Metacontroller Results

Multiple experts (MLP + IN)

Total number of simulations Increasing cost of MLP Increasing cost of Int. Net.

61

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Jessica Hamrick (@jhamrick)

Metacontroller Results

Multiple experts (MLP + IN)

Total number of simulations Fraction of sims using MLP expert Increasing cost of MLP Increasing cost of MLP Increasing cost of Int. Net. Increasing cost of Int. Net.

62

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Jessica Hamrick (@jhamrick)

Training the Controller and Memory

63

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SLIDE 157

Jessica Hamrick (@jhamrick)

Training the Manager

64

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SLIDE 158

Jessica Hamrick (@jhamrick)

Training the Experts

65

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SLIDE 159

Jessica Hamrick (@jhamrick)

Training the Critic

66