Let an HTM model do anomaly detection on a scalar timeseries `x(t)`

, which doesn’t have very low frequencies, and which we can assume samples a physical phenomenon, like temperature. Let’s also interpolate `x`

and make `y(t)= x(t/2)`

. `y`

therefore has *no extra information* on the underlying phenomenon (no extra anomalies), but exhibits the same anomalous behaviour as `x`

, albeit with many extra uninformative transitions.

Is it reasonable to expect that a sufficiently large HTM model should perform equivalently on predicting anomalies in `x`

and in `y`

? Is this a desirable property? And what would happen in practice?

I would call this property time scale invariance.