Getting started

Lenticulum learns relations instead of functions: one model of a joint space, queried in whichever direction you need. This page installs it, runs a first query, and points you to the tutorial that fits your background.

Install

Lenticulum is not registered yet. From a clone of the repository:

using Pkg
Pkg.develop(path = "/path/to/Lenticulum.jl")
Pkg.develop(path = "/path/to/Lenticulum.jl/lib/VariationalDiffusion.jl")   # and the others under lib/

A first query

A diffusion model of points on the unit circle, in closed form so that nothing needs training, asked for $y$ given $x = 0.6$. The relation has two answers, and implicit_roots returns both:

using VariationalDiffusion, LuxCore, Random
sched = VPSDE()
θ = range(0, 2π; length = 49)[1:48]
circle = NoisePredictor(GaussianMixtureEps(sched, vcat(cos.(θ)', sin.(θ)'); s = 0.05), sched)
ps, st = LuxCore.setup(Xoshiro(0), circle)
m = ImplicitDiffusion(circle, field_nodes(Xoshiro(1), 2; samples = 8))

answers, _ = implicit_roots(m, [0.6, 0.0], [Inf, 0.0], ps, st)   # x clamped (Inf), y free (0)
[round(a.z[2]; digits = 3) for a in answers]

2-element Vector{Float64}:
  0.772
 -0.78

Swap the precision vector to [0.0, Inf] and the same model answers "$x$ given $y$".

Where to go next

you come from	start with
machine learning	A relation without training, then Train a small diffusion model and Robot arm: one model, every direction
statistics or robotics (Kalman filters, GTSAM)	Localisation as a factor graph: odometry and GPS, smoothing versus filtering, and the noise level estimated from the marginal likelihood
physics	Symmetry is not a law and Discovering a force law
category theory	the theory vault, entry point Factors are Parameterized Statistical Games
looking for an API	the package pages, starting with LenticulumCore, and the Vocabulary

Every tutorial is also available as a Jupyter notebook, and every work cited is on the References page.