The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

nnR

Neural networks made algebraic.

nnR represents a feed-forward neural network as an ordered list of weight matrices and bias vectors. It implements composition, stacking, sums, scalar multiplication, and constructive ReLU approximations without a training step. The calculus follows Rafi, Padgett, and Nakarmi (2024), building on Grohs, Hornung, Jentzen, and Zimmermann (2023) and Jentzen, Kuckuck, and von Wurstemberger (2023).

Highlights

• Algebraic operations: comp(), stk(), stk_many(), nn_sum(), nn_sum_many(), slm(), and srm().
• Constructive approximations: Sqr(), Prd(), Pwr(), and the general neural-network polynomial Pnm().
• Taylor families: Xpn(), Csn(), and Sne().
• Norm, maximum, multidimensional maximum-convolution, and trapezoidal-rule networks.
• Fast realization of one point or a column batch, plus reusable realized functions with realize_nn().
• Structural validation with is_nn() and validate_nn().

The approximation theorems cited above use ReLU activation. Sigmoid() and Tanh() are also available for exploration, but do not inherit those ReLU guarantees.

Quick start

library(nnR)

# c0 + c1*x + c2*x^2, with coefficients in ascending power order
polynomial <- Pnm(c(1, -2, 0.5), q = 3, eps = 0.2)

# A matrix is evaluated as a batch with one sample per column.
x <- matrix(seq(-1, 1, length.out = 9), nrow = 1)
observed <- inst(polynomial, ReLU, x)
expected <- 1 - 2 * x + 0.5 * x^2
cbind(observed = c(observed), expected = c(expected))

# Validate once and reuse the resulting function.
f <- realize_nn(polynomial, ReLU)
f(x)

Composition respects realization:

inner <- Aff(2, 1)
outer <- Aff(-3, 4)
z <- 0.5

inst(comp(outer, inner), ReLU, z)
inst(outer, ReLU, inst(inner, ReLU, z))

Maximum convolution accepts one sample per column in any dimension:

X <- matrix(c(0, 0, 1, 0, 0, 1, 1, 1), nrow = 2)
y <- colSums(X)
approximant <- MC(X, y, L = 1)
inst(approximant, ReLU, X)

See the package vignette and function reference for the full calculus and its mathematical definitions.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.