Vocabulary casting

Consider this SPA model:

In [1]:
%matplotlib inline

import matplotlib.pyplot as plt

import nengo
import nengo_spa as spa
In [2]:
d = 16
vocab1 = spa.Vocabulary(16)
vocab2 = spa.Vocabulary(16)

with spa.Network() as model:
    state1 = spa.State(vocab=vocab1)
    state2 = spa.State(vocab=vocab2)

In this model state1 and state2 are assigned to different and independent vocabularies. This means we cannot simply connect state1 and state2 in SPA actions because Nengo cannot know how to transform (“cast”) from one vocabulary to the other vocabulary. We are required to tell Nengo how we want to do this cast. Currently there two methods implemented.

Reinterpretation

The reinterpret method can only be used with vocabularies of the same dimension. It will not change the semantic pointer passed from one state to the other, but changes it interpretation.

In [3]:
d1 = 16
d2 = 16
vocab1 = spa.Vocabulary(d1)
vocab1.populate('A')
vocab2 = spa.Vocabulary(d2)
vocab2.populate('A')

with spa.Network() as model:
    state1 = spa.State(vocab=vocab1)
    state2 = spa.State(vocab=vocab2)
    spa.sym.A >> state1
    spa.reinterpret(state1) >> state2

    p = nengo.Probe(state2.output, synapse=0.03)
In [4]:
with nengo.Simulator(model) as sim:
    sim.run(0.5)
In [5]:
plt.plot(sim.trange(), spa.similarity(sim.data[p], vocab1), label='vocab1')
plt.plot(sim.trange(), spa.similarity(sim.data[p], vocab2), label='vocab2')
plt.xlabel("Time [s]")
plt.ylabel("Similarity")
plt.legend(loc='best')
Out[5]:
<matplotlib.legend.Legend at 0x7f8f6c8914a8>
../_images/examples_vocabulary_casting_7_1.png

Translation

Translation matches the vocabularies by the keys and uses the outer product of the corresponding semantic pointers as a transformation matrix to transform vectors from one vocabulary to another vocabulary. This works also with vocabularies of differing dimensionality.

In [6]:
d1 = 16
d2 = 32
vocab1 = spa.Vocabulary(d1)
vocab1.populate('A')
vocab2 = spa.Vocabulary(d2)
vocab2.populate('A')

with spa.Network() as model:
    state1 = spa.State(vocab=vocab1)
    state2 = spa.State(vocab=vocab2)
    spa.sym.A >> state1
    spa.translate(state1, vocab2) >> state2

    p = nengo.Probe(state2.output, synapse=0.03)
In [7]:
with nengo.Simulator(model) as sim:
    sim.run(0.5)
In [8]:
plt.plot(sim.trange(), spa.similarity(sim.data[p], vocab2), label='vocab2')
plt.xlabel("Time [s]")
plt.ylabel("Similarity")
plt.legend(loc='best')
Out[8]:
<matplotlib.legend.Legend at 0x7f8f6d354668>
../_images/examples_vocabulary_casting_11_1.png

Further options

Both translate and reinterpret try to infer the target vocabularies, but this might not be possible in all cases. Thus, both functions take an additional argument which can either be a SPA module or a vocabulary. If it is a SPA module (e.g., translate(state1, state2)), that module’s vocabulary will be used as target vocabulary. If it is a vocabulary, the given vocabulary will be used as target vocabulary (e.g., translate(state1, vocab2)). Note that in the latter case a dictionary specifying the names and vocabularies has to be passed as the vocabs argument to the Actions instance like so: Actions('translate(state1, vocab2) -> state2').

Note that you can give the second argument to translate and reinterpret also as a keyword argument (e.g., translate(state1, vocab=state2).