  We investigate deformations of Milnor algebras of smooth homogeneous
polynomials, and prove in particular that any smooth degree $d$ homogeneous
polynomial in $n+1$ variables that is not of Sebastiani-Thom type is determined
by the degree $k$ homogeneous component of its Jacobian ideal for any $d-1\leq
k\leq (n+1)(d-2)$. Our results generalize the previous result on the
reconstruction of a homogeneous polynomial from its Jacobian ideal.
