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This notebook …
The reasoning behind the design choices is explained in XXX.
Define a function to calculate the weighted sum of an arbitrary number of VSA vectors.
# function to make an atomic VSA vector
vsa_mk_atom <- function(
vsa_dim, # integer - dimensionality of VSA vector
seed = NULL # integer - seed for random number generator
) # value # one randomly selected VSA vector of dimension vsa_dim
{
### Set up the arguments ###
# The OCD error checking is probably more useful as documentation
if(missing(vsa_dim))
stop("vsa_dim must be specified")
if(!(is.vector(vsa_dim, mode = "integer") && length(vsa_dim) == 1))
stop("vsa_dim must be an integer")
if(vsa_dim < 1)
stop("vsa_dim must be (a lot) greater than zero")
# check that the specified seed is an integer
if(!is.null(seed) &&!(is.vector(seed, mode = "integer") && length(seed) == 1))
stop("seed must be an integer")
# if seed is set the the vector is fixed
# otherwise it is randomised
set.seed(seed)
# Construct a random bipolar vector
sample(c(-1L, 1L), size = vsa_dim, replace = TRUE)
}Do some very small scale testing.
vsa_mk_atom(10L) [1] 1 -1 -1 1 1 -1 -1 -1 -1 1vsa_mk_atom(10L) [1] 1 -1 -1 -1 -1 -1 -1 -1 1 1vsa_mk_atom(10L, seed = 1L) [1] -1 1 -1 -1 1 -1 -1 -1 1 1vsa_mk_atom(10L, seed = 1L) [1] -1 1 -1 -1 1 -1 -1 -1 1 1Define a function to calculate the cosine similarity of two VSA vectors.
# function to calculate the cosine similarity of two VSA vectors
# Allow for the possibility that the vectors might not be bipolar
vsa_sim <- function(
v1, v2 # numeric - VSA vectors of identical dimension (not necessarily bipolar)
) # value # numeric - cosine similarity of the VSA vectors
{
### Set up the arguments ###
# The OCD error checking is probably more useful as documentation
if(missing(v1) || missing(v2))
stop("two VSA vector arguments must be specified")
if(!is.vector(v1, mode = "numeric"))
stop("v1 must be an numeric vector")
if(!is.vector(v2, mode = "numeric"))
stop("v2 must be an numeric vector")
vsa_dim <- length(v1)
if(length(v2) != vsa_dim)
stop("v1 and v2 must be the same length")
sum(v1*v2) / sqrt(sum(v1*v1) * sum(v2*v2))
}Do some very small scale testing.
# create vectors to add
v1 <- vsa_mk_atom(10L)
v2 <- vsa_mk_atom(10L)
v1 [1] -1 1 1 1 -1 1 1 -1 1 -1v2 [1] 1 1 1 -1 -1 1 -1 1 -1 1vsa_sim(v1, v1)[1] 1vsa_sim(v1, -v1)[1] -1vsa_sim(v1, v2)[1] -0.2vsa_sim(v1, v2/3)[1] -0.2Define a function to calculate the weighted sum of an arbitrary number of VSA vectors.
# function to add (weighted sum) an arbitrary number of VSA vectors
# Weighted add is implemented as weighted sampling from the source vectors
vsa_add <- function(
..., # >= 2 VSA vectors of identical dimension as arguments to add
sample_spec, # integer vector - sorce (argument VSA vector) for each element of result
sample_wt # numeric vector - argument vector sampling weights
) # value # one VSA vector, the weighted sum (sampled) of the argument vectors
{
### Set up the arguments ###
# The OCD error checking is probably more useful as documentation
args_list <- list(...)
args_n <- length(args_list)
if(args_n < 2)
stop("number of source VSA vector arguments must be >= 2")
if(!all(sapply(args_list, is.vector, mode = "integer")))
stop("all source VSA vectors must be integer vectors")
vsa_dim <- length(args_list[[1]])
if(!all(sapply(args_list, length) == vsa_dim))
stop("all source VSA vectors must be the same length")
if(!missing(sample_spec) && !missing(sample_wt))
stop("at most one of wt and sample_spec can be given")
if(!missing(sample_spec))
# sample_spec supplied
{
if(!is.vector(sample_spec, mode = "integer"))
stop("sample_spec must be an integer vector")
if(length(sample_spec) != vsa_dim)
stop("sample_spec must be same length as source VSA vectors")
if(!all(sample_spec %in% 1:args_n))
stop("each element of sample_spec must be the index of a source VSA vector")
}
else
# sample spec not supplied - make a new random one
{
# create a sampling weight vector if not supplied
if(missing(sample_wt))
sample_wt <- rep(1, length.out = args_n) # equal weighting for all source VSA vectors
if(length(sample_wt) != args_n)
stop("number of weights must equal number of source VSA vectors")
if(min(sample_wt) < 0)
stop("all weights must be >= 0")
if(max(sample_wt) <= 0)
stop("at least one weight must be > 0")
# For each element of the result work out which source VSA vector to sample
sample_spec <- sample.int(n = args_n, size = vsa_dim,
replace = TRUE, prob = sample_wt)
}
### Set up the selection matrix ###
# Each row corresponds to an element of the output vector
# Each row specifies the (row,col) cell to select from the VSA source vectors
sel <- as.matrix(data.frame(row = 1L:vsa_dim, col = sample_spec),
ncol = 2, byrow = FALSE)
### Construct the result vector
as.data.frame(args_list)[sel]
}Do some very small scale testing.
# create vectors to add
# make unique valuse so they can be uniquely tracked
x1 <- 10L:19L
x2 <- 20L:29L
x3 <- 30L:39L
# specify the sampling
vsa_add(x1,x2,x3, sample_spec = c(1L,2L,3L,1L,2L,3L,1L,2L,3L,1L)) [1] 10 21 32 13 24 35 16 27 38 19vsa_add(x1,x2,x3, sample_spec = c(1L,2L,3L,1L,2L,3L,1L,2L,3L,1L)) [1] 10 21 32 13 24 35 16 27 38 19sample_spec is specified.vsa_add(x1,x2,x3, sample_wt = c(0, 0, 1)) [1] 30 31 32 33 34 35 36 37 38 39vsa_add(x1,x2,x3) [1] 20 31 32 33 34 25 36 27 18 29vsa_add(x1,x2,x3) [1] 10 31 12 13 14 15 26 27 28 29vsa_add(x1,x2,x3) [1] 10 21 12 13 14 15 16 37 28 19
sessionInfo()R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 21.04
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
locale:
[1] LC_CTYPE=en_AU.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_AU.UTF-8 LC_COLLATE=en_AU.UTF-8
[5] LC_MONETARY=en_AU.UTF-8 LC_MESSAGES=en_AU.UTF-8
[7] LC_PAPER=en_AU.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices datasets utils methods base
other attached packages:
[1] here_1.0.1 fs_1.5.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.7 whisker_0.4 knitr_1.33 magrittr_2.0.1
[5] workflowr_1.6.2 R6_2.5.0 rlang_0.4.11 fansi_0.5.0
[9] stringr_1.4.0 tools_4.1.0 xfun_0.24 utf8_1.2.1
[13] git2r_0.28.0 htmltools_0.5.1.1 ellipsis_0.3.2 rprojroot_2.0.2
[17] yaml_2.2.1 digest_0.6.27 tibble_3.1.2 lifecycle_1.0.0
[21] bookdown_0.22 crayon_1.4.1 later_1.2.0 vctrs_0.3.8
[25] promises_1.2.0.1 glue_1.4.2 evaluate_0.14 rmarkdown_2.9
[29] stringi_1.7.2 compiler_4.1.0 pillar_1.6.1 httpuv_1.6.1
[33] renv_0.13.2 pkgconfig_2.0.3