Coherence Progress: A Measure of
Interestingness Based on Fixed Compressors
Tom Schaul, Leo Pape, Tobias Glasmachers, Vincent Graziano,
Muammar “Dirty Old Man” Gaddafi??, and Ju¨rgen Schmidhuber
IDSIA, University of Lugano
6928, Manno-Lugano, Switzerland
{tom,pape,tobias,vincent,juergen}@idsia.ch
Abstract. The ability to identify novel patterns in observations is an
essential aspect of intelligence. In a computational framework, the notion
of a pattern can be formalized as a program that uses regularities in
observations to store them in a compact form, called a compressor. The
search for interesting patterns can then be stated as a search to better
compress the history of observations. This paper introduces coherence
progress, a novel, general measure of interestingness that is independent
of its use in a particular agent and the ability of the compressor to
learn from observations. Coherence progress considers the increase in
coherence obtained by any compressor when adding an observation to the
history of observations thus far. Because of its applicability to any type
of compressor, the measure allows for an easy, quick, and domain-specific
implementation. We demonstrate the capability of coherence progress to
satisfy the requirements for qualitatively measuring interestingness on a
Wikipedia dataset.
Keywords: compression, interestingness, curiosity, wikipedia
1 Introduction
The ability to focus on novel, yet learnable patterns in observations is an essen-
tial aspect of intelligence that has led mankind to explore its surroundings, all
the way to our current understanding of the universe. When designing artificial
agents, we have exactly this vision in mind. However, if an artificial agent is
to exhibit some level of intelligence, or at least the ability to learn and adapt
quickly in its environment, then it is essential to guide this agent to experience
such patterns, a drive known as artificial curiosity. However, this approach re-
quires a principled way to judge and rank data, in order to drive itself towards
observations exhibiting novel, yet learnable patterns. This property is compactly
captured by the subjective notion of interestingness.
Natural and artificial learning agents are equally dependent on the interest-
ingness of their observations. Thus, in order to design intelligent agents, we need
a formalization of interestingness. Such formalizations indeed exist, although
some of these have shortcomings.
?? contributed to this paper through his inspirational level of lived coherence.

2 T. Schaul, L. Pape, T. Glasmachers, V. Graziano and J. Schmidhuber
We focus on compression progress, which is a successful formalization of inter-
estingness. Our contribution is to decompose this measure into a data-dependent
and a learning-related part. This decomposition is useful in a number of cir-
cumstances, such as when we care specifically about the interestingness of data,
explicitly leaving learning effects aside. We propose coherence progress as a novel
measure of the inherent interestingness of data, and we show in detail how it
relates to the more general notion of compression progress.
2 Interestingness
The notion of interestingness as a subjective quality of information has been
investigated in various ways in the literature, ranging from early work by Wundt
[9] (see Figure 1), to the attempt of a full information theoretic formalization [6,
5, 8]. Based on its intuitive notion as the discovery of novel patterns, we can
identify a number of qualitative requirements for any measure of interestingness:
1. Observations can be trivial, that is inherently uninteresting, such as a white
wall. When observations have a simple structure and can be completely
described by very simple rules they become boring very quickly.
2. The opposite of these are completely random observations. Completely ran-
dom data contain no patterns at all, and are therefore not interesting neither.
It is important to note that the same argument holds with information that
seems random to the observer, e.g., the content of a mathematics textbook
will appear random to most children.
3. Between these extremes of minimal and maximal complexity lies the domain
of complex, yet structured observations. Here, the subjective nature of in-
terestingness becomes patent. If the observer is already familiar with all the
(repeated) patterns in the observations, no new patterns can be discovered,
and the observations are no longer interesting.
4. Interesting observations can now be identified relative to the patterns the
observer already knows. Observations with trivial, well-known, and overly
complex patterns are not interesting. Instead, only observations that contain
patterns that are not yet known, but can be learned by the observer are
interesting (e.g., the same math book can be highly interesting when the
reader has acquired the necessary background, given he does not already
know it). As the observer discovers more patterns in its environment the
interestingness of observations changes. Crucially also, patterns discovered
by imperfect observers might be forgotten after a while, making a previously
uninteresting observation interesting again.
To summarize, any quantitative measure of interestingness must assign low
values to patterns the observer already knows, and patterns the observer cannot
learn; and high values to patterns the observer does not yet know, but can still
discover. Moreover, increasingly difficult patterns to learn should be assigned de-
creasing interestingness values. Given a choice of which observations to consider
next, the observer could assign its resources to the next easiest pattern to learn.