A further key notion in the theory of regularity structures is that of a model for a regularity structure, which is a concrete way of associating to any τ τ ∈ ∈ T and x 0 ∈ ∈ R d a "Taylor polynomial" based at x 0 and represented by τ τ , subject to some consistency requirements. More precisely, a model for T = ( A , T , G ) on R d , with d ≥ ≥ 1 consists of two maps