  Insects, such as fruit flies and honey bees, can solve simple associative
learning tasks and learn abstract concepts such as "sameness" and "difference",
which is viewed as a higher-order cognitive function and typically thought to
depend on top-down neocortical processing. Empirical research with fruit flies
strongly supports that a randomized representational architecture is used in
olfactory processing in insect brains. Based on these results, we propose a
Randomly Weighted Feature Network (RWFN) that incorporates randomly drawn,
untrained weights in an encoder that uses an adapted linear model as a decoder.
The randomized projections between input neurons and higher-order processing
centers in the input brain is mimicked in RWFN by a single-hidden-layer neural
network that specially structures latent representations in the hidden layer
using random Fourier features that better represent complex relationships
between inputs using kernel approximation. Because of this special
representation, RWFNs can effectively learn the degree of relationship among
inputs by training only a linear decoder model. We compare the performance of
RWFNs to LTNs for Semantic Image Interpretation (SII) tasks that have been used
as a representative example of how LTNs utilize reasoning over first-order
logic to surpass the performance of solely data-driven methods. We demonstrate
that compared to LTNs, RWFNs can achieve better or similar performance for both
object classification and detection of the part-of relations between objects in
SII tasks while using much far fewer learnable parameters (1:62 ratio) and a
faster learning process (1:2 ratio of running speed). Furthermore, we show that
because the randomized weights do not depend on the data, several decoders can
share a single randomized encoder, giving RWFNs a unique economy of spatial
scale for simultaneous classification tasks.
