The spec says:

The particular scheme for anisotropic texture filtering is implementation dependent. Implementations should consider the magFilter, minFilter and mipmapMode of the sampler to control the specifics of the anisotropic filtering scheme used.

Consider this sampler state (assuming that samplerAnisotropy feature is enabled):

VkSamplerCreateInfo sampler;
sampler.magFilter = VK_FILTER_NEAREST;
sampler.minFilter = VK_FILTER_NEAREST;
sampler.mipmapMode = VK_SAMPLER_MIPMAP_MODE_NEAREST;
sampler.maxAnisotropy    = 1.0;
sampler.anisotropyEnable = VK_TRUE;

To what extent the implementations are free to interpret this state? Sampling a single-level texture on NVIDIA and AMD produces regular nearest look while the same state on Intel produces an image as if linear interpolation is used.