We have measured the dielectric response of amorphous insulators in th
e audio frequency range at temperatures between 500 mu K and 400 mK. W
e compare the measured superlinear behavior with a model incorporating
higher order terms at low frequencies. Temperature independent dielec
tric response at low fields and low temperatures has also been observe
d which may indicate a low energy cutoff in the two-level system distr
ibution of order 1 mK in some materials. We also find anomalously high
sensitivity of the dielectric response to rf noise.