A formal graph system (FGS for short) is a logic program consisting of definite clauses whose arguments are graph patterns instead of first-order terms. The definite clauses are referred to as graph rewriting rules. An FGS is shown to be a useful unifying framework for learning graph languages. In this paper, we show the polynomial-time PAC learnability of a subclass of FGS languages defined by parameterized hereditary FGSs with bounded degree, from the viewpoint of computational learning theory. That is, we consider VH-FGSLk,Δ(m, s, t, r, w, d) as the class of FGS languages consisting of graphs of treewidth at most k and of maximum degree at most Δ which is defined by variable-hereditary FGSs consisting of m graph rewriting rules having TGP patterns as arguments. The parameters s, t, and r denote the maximum numbers of variables, atoms in the body, and arguments of each predicate symbol of each graph rewriting rule in an FGS, respectively. The parameters w and d denote the maximum number of vertices of each hyperedge and the maximum degree of each vertex of TGP patterns in each graph rewriting rule in an FGS, respectively. VH-FGSLk,Δ(m, s, t, r, w, d) has infinitely many languages even if all the parameters are bounded by constants. Then we prove that the class VH-FGSLk,Δ(m, s, t, r, w, d) is polynomial-time PAC learnable if all m, s, t, r, w, d, Δ are constants except for k.

This letter describes the concepts that the learnability of multilayer neural networks exists in a constrained hypersurface in learning space which is formed by input and output subspace of multilayer neural networks, and that a priori information, providing constraints on the learning space, is required for generalization.

This paper attempts to account for intelligibility of practices-based learning (so-called 'learning control') for skill refinement from the viewpoint of Newtonian mechanics. It is shown from an axiomatic approach that an extended notion of passivity for the residual error dynamics of robots plays a crucial role in their ability of learning. More precisely, it is shown that the exponentially weighted passivity with respect to residual velocity vector and torque vector leads the robot system to the convergence of trajectory tracking errors to zero with repeating practices. For a class of tasks when the endpoint is constrained geometrically on a surface, the problem of convergence of residual tracking errors and residual contact-force errors is also discussed on the basis of passivity analysis.