Interaction Networks for Learning about Objects,Relations and Physics

Peter Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, koray kavukcuoglu (Google DeepMind)

NIPS 2016 Reading ClubPresenter: Ken Kuroki (@enuroi)

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Background & Purpose

• Some attempts to learn physical dynamics so far. (rigid bodies, fluid dynamics, 3D trajectory etc.)

• This study aims to construct a general-purpose learnable physics engine. (that can learn novel physical systems)

2

Model at a Glance

3

O1

O2

O1,t O2,t r

fR

et+1

O2,t

fO

et+1

O2,t+1

Model in Detail 1

4

Rr =0 0 1 1 0 0

Rs =1 0 0 0 0 1

Model in Detail 2

5

NR : number of relationsNO : number of objectsbk : <oi, oj, rk> (rearranges the objects and relations into interaction terms)

Relatione: multiple for one object c: aggregated by a

Implementation 1

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O = Ds

NO

R = NR

NO

NR

NO

Rr Rs

receiver sender

DR

NR

Ra

attributes

, ,

object1's status vector

Implementation 2

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m(G) = Ds

Ds

DR

NR

ORr

ORs

Ra

= B[b1, b2, ..., bk]

[e1, e2, ..., ek] = E

fR

Implementation 3

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G, X, EE = ERr– T

[O; X; E] = C–

Ds

Ds

DR

NR

O

X

E–

fR

a

P = Ot+1

DA

fA

(Free energy)

Architecture• MLP (bias, ReLU)

By hyperparamerter search...

• FR : four 150-length hidden layers, output length 50

• FO : one 100-length hidden layer, output length 2 (x and y velocity)

• FA : one 25-length hidden layer

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Optimization

• Used AdamLearning rate 0.001, and downscaled by *0.8 for 40 epochs

• L2 regularization (penalty factor by grid search)

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Training

Simulated 2000 scenes over 1000 time steps

• Training : 1 million sample, for 2000 epochs (mini-batches of 100 to balance distributions)

• Validation : 200k sample

• Test data : 200k sample

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Experiments

1. N-body

2. Bouncing balls

3. String

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Comparison

Alternative Models:

1. Constant velocity (output=input)

2. MLP (two 300-length hidden layers) input: flattened vector of all the input data

3. Interaction Network without E (interaction)

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Results

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Discussion

1. Performed better than alternatives

2. Baseline MLP couldn't effectively learn interaction

3. To understand "intuitive physics engine" in human

4. Potential to expand the model

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Presenter's Comments

1. Can be applied to a larger system? (time & memory-wise)

2. Probably it can be parallelized

3. Really advantageous to alternatives?

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