More "julian" idioms or keep it closer to HDC/VSA nomenclature?

[cvigilv]

I was looking at the current implementation of the vector types and its associated function and noticed that there are some operations that could be better modeled via overloading Base Julia functions. For example, instead of having something like empty_vector(T::AbstractHDV) we could have zeros(T::AbstractHDV). I compiled a list of things we could implement to make the package more "julian", but I'm unsure if this is better.

I'll leave the list here of the ones that come to my mind, which I can tackle once the refactor is done if it makes sense:

• Base.zeros(T::Type{AbstractHDV}, N::Int=10_000) for empty hypervector initialization
• Base.ones(T::Type{AbstractHDV}, N::Int=10_000) for filled hypervector initialization
• Base.inv(h::AbstractHDV) inverts the hypervector
• Base.isequal(h::AbstractHDV, u::AbstractHDV) for comparing equality
• Base.hash(h::AbstractHDV) for hashing hypervector (this is necessary for some things)
• Base.isapprox(u::T, v::T) where T<:AbstractHDV to check if hypervectors are similar (unlocks \approx operator)

If you have an idea for more, please add them to the list.

Why I think this is important? Mainly to make the use of the package more friendly or idiomatic. I think aiming to keep this as abstracted as possible would be nice since we could just write pipelines as simple algebra, for example let's replicate the "What's the dollar of Mexico?" exercise Pentti Kanerva proposed:

using HyperdimensionalComputing

# Some missing things
HyperdimensionalComputing.isapprox(u::T, v::T) where T<:BipolarHDV = similarity(u, v) > 1/sqrt(length(v)) # mean + 3*sd
HyperdimensionalComputing.hash(u::AbstractHDV) = hash(u.v, hash(typeof(v)))
HyperdimensionalComputing.isequal(u::T, v::T) where T<:AbstractHDV = hash(u) == hash(v)

# Holistic representation of countries
# 1. Concept hypervectors
COUNTRY = BipolarHDV()
CAPITAL = BipolarHDV()
MONEY = BipolarHDV()

# 2. Values hypervectors
USA = BipolarHDV()
MEX = BipolarHDV()

WDC = BipolarHDV()
MXC = BipolarHDV()

DOL = BipolarHDV()
PES = BipolarHDV()

# 3. Country representations
USTATES = (COUNTRY * USA) + (CAPITAL * WDC) + (MONEY * DOL)
MEXICO  = (COUNTRY * MEX) + (CAPITAL * MXC) + (MONEY * PES)

# Are USA and Mexico similar?
USTATES ≈ MEXICO # returns: false

# If we now pair USTATES with MEXICO, we get a bundle that pairs USA with Mexico, Washington DC
# with Mexico City, and dollar with peso, plus noise.
# This is, in principle, a mapping code from USA <-> Mexico, which can be used to extract 
# information using similarity
F_UM = USTATES * MEXICO

# What in Mexico corresponds to United States' dollar:
DOL * F_UM ≈ PES # returns: true

# Let's add Sweden
SWE = BipolarHDV()
STO = BipolarHDV()
KRO = BipolarHDV()

SWEDEN = (COUNTRY * SWE) + (CAPITAL * STO) + (MONEY * KRO)

# Can we reconstruct the mapping Sweden <-> Mexico from the mapping Sweden <-> USA <-> Mexico?
F_UM = USTATES * MEXICO
F_SU = SWEDEN * USTATES
F_SM = SWEDEN * MEXICO

F_SU * F_UM ≈ F_SM # returns: true

Easy to read, to implement and to maintain. LMKWYT

[MichielStock]

Some of these I like, I have implemented zero, hash, equal and approx. I think ones, inv, are not really appropriate.

I made some efforts having a general ≈ function but it is quite tricky!

[cvigilv]

Great! Let me know if you need any help with that

[cvigilv]

@MichielStock I think we could make use of the inv operation, since it's useful for some data structures, e.g. bundling-based sequence encoding.

There is also an inverse operation to bundling ⊖ : H × H → H which can be used to remove an item from a hypervector by bundling with the additive inverse. Because hypervectors are typically normalized to ensure that the resulting vector is in the same domain as the basis-hypervectors, bundling and inverse bundling become approximate operations.

Ref: Heddes, Mike, Igor Nunes, Tony Givargis, Alexandru Nicolau, and Alex Veidenbaum. “Hyperdimensional Computing: A Framework for Stochastic Computation and Symbolic AI.” Journal of Big Data 11, no. 1 (2024): 145. https://doi.org/10.1186/s40537-024-01010-8.