Funded by EU-Project “Joint Action Science and Technology” (IST-FP6-003747)
Corresponding author: [email protected]
Generalisation of action sequences in
RNNPB networks with mirror properties
Raymond H. Cuijpers1,2, Floran Stuijt 2, Ida G. Sprinkhuizen-Kuyper 2
1 Eindhoven
University of Technology - Human Technology Interaction; P.O. Box 513, 5600 MB, Eindhoven; The Netherlands
University Nijmegen - Donders Institute for Brain, Cognition and Behaviour; P.O. Box 9104, 6500 HE Nijmegen ;The Netherlands
Question and Method
How many spatiotemporal patterns can be stored in an
RNNPB network? As an initial step we investigate how
robust the learnt patterns are against noise. Next, we look
how the network generalises to parametric variations of the
learnt examples.
Network architecture
Our RNNPB network consists of 1 input, 5 hidden, 1 output,
2 context and 2 PB nodes. Network connection weights are
updated using backpropagation through time (BPTT).
yt
output layer
hidden layer
input layer
fully connected BPTT
1-to-1 copy
context layer
PB layer
xt
Training Open loop. All weights are updated.
Reproduction Closed loop with no updating and the PB
vector is fixed to the learnt values
Recognition Open loop. Only the PB vector is updated
References
[1] J. Tani, M. Ito, and Y. Sugita. Self-organization of distributedly represented multiple
behavior schemata in a mirror system: reviews of robot experiments using rnnpb. Neural
Networks, 17(8-9):1273–1289, 2004.
[2] M. Ito and J. Tani. Generalization in learning multiple temporal patterns. In N. R. Pal, N.
Kasabov, R. K. Mudi, S. Pal, and S. K. Parui, editors, Neural Information Processing, LNCS
3316, pages 592–598. Springer Berlin / Heidelberg, 2004.
/ Human Technology Interaction
Results
Reproducing learnt examples
The RNNPB network
succesfully reproduces
3 simultaneously learnt
patterns.
However, the decay rate
and amplitude of the
aperiodic pattern still
deviate from the learning
pattern.
amplitude
It is still unclear how the human mirror neuron system (MNS)
could learn to recognise a large variety of action sequences.
Here we investigated a neural network with mirror
properties. The Recurrent Neural Network with Parametric
Bias (RNNPB) is capable of learning and reproducing
different spatio-temporal patterns such as joint angles of
action sequences [1].
1
0.8
0.6
0.4
0.2
0
Robust recognition
During recognition the
PB vector converges to the
learnt value: the distance is
zero.
When adding white noise
the correct pattern is recognised up to a noise level of
σ=0.2 (20% of amplitude).
sequence 1:
1
_
2
sin(0.3 t) + 12_
sequence 2:
1
_
2
sin(0.6 t) + 12_
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
learned sequence
sequence 3:0.9 - 0.8 exp(-t)
10
generated sequence
30
40
timestep
50
60
ε1
ε2
ε3
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
noise level σ
Generalising from learnt examples
The PB vector smoothly
0.7
varies with variations in
0.6
frequency of the pattern
0.5
to be recognised [2].
0.4
The same applies to variations
in amplitude, but the generalisation is degenerate for the
high frequency pattern
20
0.7
error of PB vector
Introduction
PB node 2
2 Radboud
p3
ω = 0.3
ω = 0.6
A = 0.8
ω = 0.2
A=0.7
A=1
p1
0.3
A=0.5
A=1
0.2
p2
0.1
0
0
ω = 0.7
A=0.65
A=0.5
0.1
Discussion and Conclusions
0.2
0.3
0.4
PB node 1
0.5
We have shown that the RNNPB architecture is capable of
robust recognition of learnt patterns and it can generalise
across them [2]. How to choose these learning examples
to optimize the network’s performance is still an open issue.
0.6
0.7