  Structural probes learn a linear transformation to find how dependency trees
are embedded in the hidden states of language models. This simple design may
not allow for full exploitation of the structure of the encoded information.
Hence, to investigate the structure of the encoded information to its full
extent, we incorporate non-linear structural probes. We reformulate the design
of non-linear structural probes introduced by White et al. making its design
simpler yet effective. We also design a visualization framework that lets us
qualitatively assess how strongly two words in a sentence are connected in the
predicted dependency tree. We use this technique to understand which non-linear
probe variant is good at encoding syntactical information. Additionally, we
also use it to qualitatively investigate the structure of dependency trees that
BERT encodes in each of its layers. We find that the radial basis function
(RBF) is an effective non-linear probe for the BERT model than the linear
probe.
