Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heating up decision boundaries: isocapacitory saturation, adversarial
  scenarios and generalization bounds   In the present work we study classifiers' decision boundaries via Brownian
motion processes in ambient data space and associated probabilistic techniques.
Intuitively, our ideas correspond to placing a heat source at the decision
boundary and observing how effectively the sample points warm up. We are
largely motivated by the search for a soft measure that sheds further light on
the decision boundary's geometry. En route, we bridge aspects of potential
theory and geometric analysis (Mazya, 2011, Grigoryan-Saloff-Coste, 2002) with
active fields of ML research such as adversarial examples and generalization
bounds. First, we focus on the geometric behavior of decision boundaries in the
light of adversarial attack/defense mechanisms. Experimentally, we observe a
certain capacitory trend over different adversarial defense strategies:
decision boundaries locally become flatter as measured by isoperimetric
inequalities (Ford et al, 2019); however, our more sensitive heat-diffusion
metrics extend this analysis and further reveal that some non-trivial geometry
invisible to plain distance-based methods is still preserved. Intuitively, we
provide evidence that the decision boundaries nevertheless retain many
persistent "wiggly and fuzzy" regions on a finer scale. Second, we show how
Brownian hitting probabilities translate to soft generalization bounds which
are in turn connected to compression and noise stability (Arora et al, 2018),
and these bounds are significantly stronger if the decision boundary has
controlled geometric features.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin