EddieCunningham

Iterate on an idea with the user, challenging their viewpoint in constructive ways until both parties are content with the outcome. Use when the user wants to develop an idea, refine a half-formed concept, pressure-test their thinking, or mentions "brainstorm".

Computes the Levi-Civita connection, Christoffel symbols, Riemann curvature tensor, Ricci tensor, and scalar curvature from a Riemannian metric using the local_coordinates JAX library. Use when the user works with curvature quantities, parallel transport, Koszul formula, Bianchi identities, or needs to verify that a metric is flat or that curvature tensor symmetries hold.

Solves the geodesic equation and computes exponential and logarithmic maps on Riemannian manifolds using the local_coordinates JAX library. Use when the user works with geodesics, parallel transport along a curve, Taylor expansions of the exponential map in Riemann normal coordinates, injectivity radius, or ODE integration of the geodesic system.

Builds RiemannianMetric objects in the local_coordinates JAX library from metric component functions, including raising and lowering indices, changing basis, and constructing the inverse metric. Use when the user defines a metric tensor, needs to convert between coordinate and orthonormal bases, or wants to verify symmetry and positive definiteness.

Interview the user relentlessly about a plan or design until reaching shared understanding, resolving each branch of the decision tree. Use when user wants to stress-test a plan, get grilled on their design, or mentions "grill me".

Use this skill when constructing, training, evaluating, saving, loading, or documenting the JAX plus Equinox conformal coordinate frame field for disentanglement, a noise-conditional model that learns a local conformal frame J(x) = lambda(x) U(x) from data through score matching, integrability, and independence losses.

Use this skill when constructing, applying, training, saving, loading, or documenting a standalone learnable orthogonal matrix in JAX plus Equinox, parameterized by the matrix exponential of a skew-symmetric matrix, the Cayley transform, or a QR factorization.

Use this skill when constructing, applying, training, saving, loading, or documenting a network-predicted orthogonal transformation on vectors in JAX plus Equinox, where a small residual MLP predicts the parameters of an orthogonal matrix from an input, using the matrix exponential, the Cayley transform, or a QR factorization.

A JAX-based library for linear stochastic differential equations, state-space models, and Gaussian inference. Use when working with time series interpolation, diffusion models, Kalman filtering, or probabilistic modeling with linear-Gaussian systems.

Work with probability path distributions for diffusion models, including bridge path marginals, memoryless sampling, and efficient batch computation. Use when you need to sample from or evaluate the distribution p(x_t | y_1) at intermediate times.

Perform inference in chain-structured Gaussian Conditional Random Fields using efficient message passing. Use for discrete-time probabilistic modeling, computing marginals, sampling joint distributions, or Kalman-style filtering and smoothing.

Convert between diffusion model representations including clean data predictions (y1), scores, probability flows, and drifts. Use when building or training diffusion-based generative models.

Work with Gaussian distributions in three parameterizations for numerical stability and efficiency. Use when you need to sample, combine distributions, or convert between mean/covariance and precision/natural forms.

Use specialized matrix types with symbolic tags for efficient linear algebra. Use when working with diagonal, block, or tagged matrices to avoid unnecessary dense computations.

Condition Linear SDEs on observations to interpolate sparse data, perform Bayesian inference on time series, or create bridges between boundary conditions. Use when working with time series interpolation, state estimation, or posterior sampling.