Learning Dynamics with Synchronous, Asynchronous and General Semantics

Abstract

Abstract.Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far, the systems that LFIT handles are restricted to synchronous deterministic dynamics, i.e., all variables update their values at the same time and, for each state of the system, there is only one possible next state. However, other dynamics exist in the field of logical modeling, in particular the asynchronous semantics which is widely used to model biological systems. In this paper, we focus on a method that learns the dynamics of the system independently of its semantics. For this purpose, we propose a modeling of multi-valued systems as logic programs in which a rule represents what can occurs rather than what will occurs. This modeling allows us to represent nondeterminism and to propose an extension of LFIT in the form of a semantics free algorithm to learn from discrete multi-valued transitions, regardless of their update schemes. We show through theoretical results that synchronous, asynchronous and general semantics are all captured by this method. Practical evaluation is performed on randomly generated systems and benchmarks from biological literature to study the scalability of this new algorithm regarding the three aforementioned semantics.Keywords: Dynamical semantics, learning from interpretation transition, dynamical systems, Inductive Logic Programming IntroductionLearning the dynamics of systems with many interactive components becomes more and more important due to many applications, e.g., multi-agent systems, robotics and bioinformatics. Knowledge of a system dynamics can be used by agents and robots for planning and scheduling. In bioinformatics, learning the dynamics of biological systems can correspond to the identification of the influence of genes and can help to understand their interactions. While building a model, the choice of a relevant semantics associated to the studied system represents a major issue with regard to the kind of dynamical properties to analyze. The differences and common features of different semantics w.r.t. properties of interest (attractors, oscillators, etc.) constitutes an area of research per itself, especially in the field of Boolean networks. In [8], the author exhibits the translation from Boolean networks into logic programs and discusses the point attractors in both synchronous and asynchronous semantics. In [6], A. Garg et al. address the differences and complementarity of synchronous and asynchronous semantics to model biological networks and identify attractors. The benefits of the synchronous model are to be computationally tractable, while classical state space exploration algorithms fail on asynchronous ones. For some applications, like the biological ones, asynchronous semantics is said to capture more realistic behaviors: at a given time, a single gene can change its expression level. This results in a potential combinatorial explosion of the number of reachable states. To illustr...

Learning any memory-less discrete semantics for dynamical systems represented by logic programs

“…In previous sections we presented a modified version of GULA: the General Usage LFIT Algorithm from [46], which takes as arguments a different set of variables for conditions and conclusions of rules. This modification allows to use this modified algorithm to learn constraints and thus CDMVLP.…”

“…This paper is a substantial extension of [46] where a first version of GULA was introduced. In [46], there was no distinction between feature and target variables, i.e., variables at time step t and t + 1.…”

“…The semantics of a system's dynamics can indeed differ with regard to the synchronism of its variables, the determinism of its evolution and the influence of its history. The LFIT framework [20,48,46] proposed several modeling and learning algorithms to tackle those different semantics.…”

“…We show from theoretical results that this algorithm can learn un-der a wide range of update semantics including synchronous (deterministic or not), asynchronous and generalized semantics. [46] proposed a first version of GULA that we substantially extend in this manuscript. In [46], there was no distinction between feature and target variables, i.e., variables at time step t and t + 1.…”

“…Empirical evaluation provided in [46] was limited to scalability in complete observability cases. With the goal to process real data, we introduce a heuristic method allowing to use GULA to learn from partial observations and predict from unobserved data.…”