  We advance an information-theoretic model of human language processing in the
brain, in which incoming linguistic input is processed at two levels, in terms
of a heuristic interpretation and in terms of error correction. We propose that
these two kinds of information processing have distinct electroencephalographic
signatures, corresponding to the well-documented N400 and P600 components of
language-related event-related potentials (ERPs). Formally, we show that the
information content (surprisal) of a word in context can be decomposed into two
quantities: (A) heuristic surprise, which signals processing difficulty of word
given its inferred context, and corresponds with the N400 signal; and (B)
discrepancy signal, which reflects divergence between the true context and the
inferred context, and corresponds to the P600 signal. Both of these quantities
can be estimated using modern NLP techniques. We validate our theory by
successfully simulating ERP patterns elicited by a variety of linguistic
manipulations in previously-reported experimental data from Ryskin et al.
(2021). Our theory is in principle compatible with traditional cognitive
theories assuming a `good-enough' heuristic interpretation stage, but with
precise information-theoretic formulation.
