Defining @cacheTag directive based on query input type

Is it possible to define @cacheTag format using properties from input type object that is passed to particular query?

I have following example:

input AuthorInput {
 firstName: String!
  lastName: String!
}

type Query {
  author(input: AuthorInput): Author
    @cacheControl(maxAge: 86400)
    @cacheTag(format: ${format})
}

In other case, where I would have arguments directly defined on query level:

type Query {
  author(firstName: String!, lastName: String!): Author
    @cacheControl(maxAge: 86400)
}

I would simply set ${format} as author-{$args.firstName}-{$args.firstName}. Since I have input object I tried setting author-{$args.input.firstName}-{$args.input.firstName} but I get following error when I was running subgraph schema checks against graph.

 CACHE_TAG_INVALID_FORMAT: [author-service] cacheTag format is invalid: invalid path element "input", which is not an object or interface type

Is it possible to set @cacheTag in such case?