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1. In this work, we presented four different AEs
for the task of autoencoding images of line seg-
ments. Though the results are all different, we
find it challenging to measure them according to
well-specified criteria and then somehow com-
pose these measurements into a single numerical
grade. For example: AE1 yields thin lines with
moderate uncertainty regarding the edges. AE2
yields thick lines and struggles with short lines
or lines near the image borders. AE3 results in
relatively thin lines with high confidence at the
edges but, again, has difficulty with lines that are
short or near the image frame. Lastly, AE4 yields
lines with significant uncertainty in areas far from
the original line position. How does one translate
such critique into an order relation?
Loss function values cannot readily serve as this
ordering measure since some models use addi-
tional terms and some deviations that appear small
to the human eye turn out to produce large loss
values. For example, a reconstructed image of a
vertical line identical to the input but shifted by
one pixel to the right would result in a great loss
value, while a human observer may initially see
the two images as identical.
Moreover, with or without such measures of qual-
ity, it is difficult to measure how much of an AE
result is due to domain knowledge (which simpli-
fies the learning task), over-fitting to the training
data, or superior general learning techniques.
2. In the field of ML, autoencoding is referred to as
being unsupervised since inputs are not labeled.
We observe that the process involves many as-
pects of external control, including the choice of
the ML architecture, the loss function, and the in-
put representation for the real-world concept that
is to be autoencoded. Furthermore, learning a
concept may require knowledge of and assump-
tions about other concepts, as in the reliance on
understanding endpoints in some of our experi-
ments. Recall that such a-priori knowledge or as-
sumptions may also result in a bias in the ML pro-
cess itself.
We believe that methodologies for design of such
ML and AE solutions should include search-
ing for and documenting the reliance—explicit
or implicit—on external knowledge and assump-
tions. The goal is not necessarily to avoid such re-
liance altogether but to construct relevant ontolo-
gies that may dictate alternative orders for learn-
ing and autoencoding in a given domain.
3. In building a model based on observation and
sensing, each representation, like an image or an
audio or touch signal, extracts only a limited num-
ber of features of the real-world object. Modeling
all properties and interactions of a given object
type may require multiple representations or the
use of pre-existing domain knowledge. For ex-
ample, a unique property of a line segment, com-
pared to an arc or a line with multiple angles, is
its “straightness”. In a classical rectangular grid
of pixels arranged densely in fixed locations, each
pixel is surrounded by exactly eight other pix-
els. The straightness of the line is not directly
represented; it has to be inferred from emergent
step patterns. An alternative image representation
could be floating sparse pixels whose location and
distance from each other are specified as numbers
with decimal precision that exceeds the resolution
of any standard pixel-based image. This approach
may represent straightness better, but the property
of the continuity of the line may have to be in-
ferred using other methods.
In summary, automated ontology acquisition will
likely require and contribute advances in algorithms
and techniques in ML, perception and knowledge
management.
5 FUTURE WORK
Our ongoing exploration and plans include dealing
with combinations of the following and more:
• Develop methodologies for measuring and com-
paring the quality of AE reconstructed outputs,
like (i) measuring the success of a human or pro-
gram in matching reconstructed outputs to the re-
spective inputs and (ii) measuring how close prop-
erties of the reconstructed output are to properties
of the corresponding real-world entity rather than
only to the (input) image of that entity.
• Investigate different adjustments to the loss func-
tion.
• Use higher resolution images with thicker and
smoother lines.
• Investigate additional domain-specific properties.
• Study interpretability of the resulting code.
ACKNOWLEDGEMENTS
We thank the anonymous reviewers for their com-
ments and suggestions. We thank Irun R. Cohen for
valuable discussions and insights. This work was par-
tially supported by research grants to David Harel
Toward Automated Modeling of Abstract Concepts and Natural Phenomena: Autoencoding Straight Lines
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