For my presentation for a reading group. I have not in any way contributed this study, which is done by the researchers named on the first slide. https://papers.nips.cc/paper/6418-interaction-networks-for-learning-about-objects-relations-and-physics

1. 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 Club
Presenter: Ken Kuroki (@enuroi)
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2. 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)
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3. Model at a Glance
3
O1
O2
O1,t O2,t r
fR
et+1
O2,t
fO
et+1
O2,t+1

4. Model in Detail 1
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Rr =
0 0
1 1
0 0
Rs =
1 0
0 0
0 1

5. Model in Detail 2
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NR : number of relations
NO : number of objects
bk : <oi, oj, rk>
(rearranges the objects and relations into interaction terms)
Relation
e: multiple for one object
c: aggregated by a

6. 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

7. Implementation 2
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m(G) = Ds
Ds
DR
NR
ORr
ORs
Ra
= B
[b1, b2, ..., bk]
[e1, e2, ..., ek] = E
fR

8. Implementation 3
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G, X, E
E = ERr
– T
[O; X; E] = C
–
Ds
Ds
DR
NR
O
X
E
–
fR
a
P = Ot+1
DA
fA
(Free energy)

9. 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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10. Optimization
• Used Adam
Learning rate 0.001, and downscaled by *0.8 for 40
epochs
• L2 regularization
(penalty factor by grid search)
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11. 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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12. Experiments
1. N-body
2. Bouncing balls
3. String
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13. 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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14. Results
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15. 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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16. 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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