  Concentration inequalities are widely used for analyzing machine learning
algorithms. However, current concentration inequalities cannot be applied to
some of the most popular deep neural networks, notably in natural language
processing. This is mostly due to the non-causal nature of such involved data,
in the sense that each data point depends on other neighbor data points. In
this paper, a framework for modeling non-causal random fields is provided and a
Hoeffding-type concentration inequality is obtained for this framework. The
proof of this result relies on a local approximation of the non-causal random
field by a function of a finite number of i.i.d. random variables.
