"Transformers are Universal In-context Learners": in this paper, we show that deep transformers with a fixed embedding dimension are universal approximators for an arbitrarily large number of tokens.

Oldies but goldies: A. Brandt, Multi-Level Adaptive Solutions to Boundary-Value Problems, 1977. Introduces the multigrid method, which is the fundamental tool to speed up the convergence of low frequencies for the resolution of PDEs.

Nonlinearity matters. Linear diffusion (heat) has non-compactly supported solutions. Non-linear diffusion (porous medium) drives dynamics with compactly supported solutions. The porous medium is the simplest case, studied in detail by Otto.

Oldies but goldies: M Eck, T DeRose, T Duchamp, H Hoppe, M Lounsbery, W Stuetzle, Multiresolution analysis of arbitrary meshes, 1995.

Optimization algorithms come with many flavors depending on the structure of the problem. Smooth vs non-smooth, convex vs non-convex, stochastic vs deterministic, etc.

Oldies but goldies: J. B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem, 1956. Computes the minimum spanning tree in n*log(n) operations.

The Laplacian pyramid is the ancestor of the wavelet transform. Defines a compact multiscale representation by iterative lowpass/highpass filterings.

Oldies but goldies: J Koenderink, The structure of images, 1984. Introduces (with A. Witkin) the notion of scale space, i.e., the multi-scale analysis of signals and images, which is at the heart of many vision architectures.

Oldies but goldies: D Hubel, T Wiesel, Receptive fields, binocular interaction and functional architecture in the cat's visual cortex, 1962. Describes the organisation of the visual cortex using oriented filters. Nobel prize in 1981.

Cats, bunnies, and elephants in graphics and applied maths.

Oldies but goldies: R.L. Harder and R.N. Desmarais, Interpolation using surface splines, 1972. Thin plate (biharmonic) splines is a popular interpolation method with a closed form thanks to the theory of reproducing Hilbert spaces. Defines a Sobolev space of smooth functions.

The solution of the Eikonal equation is solved by advancing a front in the normal direction, similar to a grass fire. The most famous Hamilton-Jacobi equation. Refraction occurs when the speed has a discontinuity (Snell-Descart)

Oldies but goldies: T Gonzalez, Clustering to minimize the maximum intercluster distance, 1985. Popularized the farthest point sampling greedy algorithm.

Reaction-diffusion with spatially varying weights.

Oldies but goldies: J Blinn, A Generalization of Algebraic Surface Drawing, 1982. "Metaballs" are levelsets of mixtures of radial basis functions, which generate blobby lava-lamp-like behaviors.

Birkhoff's contraction for Hilbert's metric is a key tool to quantify convergence of Markov-Chains (Perron-Frobenius).

Oldies but goldies: D Immel, M Cohen, D Greenberg, A radiosity method for non-diffuse environments, 1986. Describes conservation of light as an integral equation which is at the heart of global rendering techniques such as radiosity.

Wave equation on a surface.

Oldies but goldies: J. Bertrand, Theoreme relatif au mouvement d'un point attire vers un centre fixe, 1873. Only harmonic spring and gravity central forces produce periodic motions.

Multilayer perceptron with 1 hidden layer breaks the curse of dimensionality for Barron's functions.

Oldies but goldies: A. J. Lotka, Contribution to the Theory of Periodic Reaction, 1910. Lotka-Volterra is a non-linear ODE modeling chemical reaction or prey/predator behaviors which exhibits periodic solutions.