Non-deterministic behavior of bundle with odd-dimensional hypervectors

[BooBSD]

Hello,

Why does bundle return a different vector each time, even for hypervectors with odd dimensionality?

julia> a = BipolarHV(D=255)
255-element BipolarHV
1 / -1 : 123 / 132


julia> b = BipolarHV(D=255)
255-element BipolarHV
1 / -1 : 128 / 127


julia> a + b
255-element BipolarHV
1 / -1 : 124 / 131


julia> a + b
255-element BipolarHV
1 / -1 : 134 / 121


julia> a + b
255-element BipolarHV
1 / -1 : 111 / 144


julia> a + b
255-element BipolarHV
1 / -1 : 122 / 133

Thank you.

[cvigilv]

This is the intended behavior. When bundling an odd number of hypervectors, there is a scenario where for a given position in the hypervector you can have a +1 and a -1, resulting in a tie. In this cases, we randomly assign one of the values accepted by the hypervector type ({-1,+1} for BipolarHV, {false,true} for BinaryHV).

TernaryHV allows for ties, where you can have 0 as a state in the hypervector.

Unsure if this help, let us know as we are actively developing the package and intend to wrap up v1.0 within the next few months.

[BooBSD]

This is the intended behavior.

A tiebreaker can also be implemented using the isodd(i) condition. When the votes are tied, we assign 1 to odd indices and 0 to even indices. This ensures that the outcome is deterministic (always the same for the same input data) and balanced (not skewed toward zeros or ones).

[cvigilv]

This is a great idea! Maybe we could add a flag for deterministic tie-breaking, we used to have it but thought it wasn't really necessary.

If you are up for the challenge, we are more than happy to accept PR, otherwise we will add them to the list of improvements we are currently implementing.

[MichielStock]

I think it is better to use a seed based on the hash of the inputs to break ties. Having a rule fixed per index will likely induce bias, no?

[cvigilv]

We could use the sum of the hypervector been bundles as the seed also. I’ll look up what makes the most sense performance wise and propose a PR.

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