Kundan Kumar
@pheonix1729
Ph.D. Student, Indian Institute of Science. Neuromorphic Engineering & Analog IC/FPGA Design | IEEE HKN ( #IamHKN) | BITS Pilani Alumni
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Many recent posts on free energy. Here is a summary from my class “Statistical mechanics of learning and computation” on the many relations between free energy, KL divergence, large deviation theory, entropy, Boltzmann distribution, cumulants, Legendre duality, saddle points,…
In continuous generative diffusion, the conditional entropy rate is the constant term that separates the score matching and the denoising score matching loss This can be directly interpreted as the information transfer (bit rate) from the state x_t and the final generation x_0.
Jensen's inequality gives the difference between the average value of a convex function φ, and its value at the center, where both “average” and “center” are defined in terms of some distribution p_X. When the function φ is flat, or the distribution is narrow, they agree.
1/18 Today I will try to describe a mathematical trick that can logically explain what happens in Quantum Mechanics and Special Relativity.
On Tuesday, in my class, we have learnt that all a neural net does is stretching / contracting the space fabric. For example this 3-layer net (1 hidden layer of 100 positive neurons) gets its 5D logits (2D projections) linearly separable by the classifier hyperplanes (lines).
Happy birthday to Sir Andrew J. Wiles! He received the Abel Prize in 2016 for "his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory." #Abelprize #Abelprize2016 #science #mathematics
The mathematician John Conway didn’t fit into a box. 🧵
Freeman Dyson on how he struggled to learn quantum mechanics from Paul Dirac
Oldies but goldies: Mark Kac, Can you hear the shape of a drum? 1966. Non-isometric shapes can have the same Laplacian eigenvalues (spectrum). Displaying here some Laplacian eigenvectors. en.wikipedia.org/wiki/Hearing_t…
Book #OTD "Functions of Matrices: Theory and Computation" by Nicholas J. Higham epubs.siam.org/doi/10.1137/1.…
The l^p functional is convex and hence a norm for p>=1. It is sparsity-inducing for p<=1. The l^1 norm is the heart of the lasso, aka basis pursuit. en.wikipedia.org/wiki/Basis_pur… en.wikipedia.org/wiki/Lasso_(st…
Exact Fisher-Rao geodesics and guaranteed approximations of Fisher-Rao distances for multivariate normal distributions. doi.org/10.1016/bs.hos…
The dynamics of a system of rods (multiple pendulums) is an ODE evolution on a 2nd-order algebraic variety. Defines highly complex patterns as soon as n>2. en.wikipedia.org/wiki/Double_pe…
A throwback to some algorithmic botany #rstats #creativecoding #plottertwitter
Oldies but goldies: Nina Amenta, Marshall Bern, Manolis Kamvysselis, A New Voronoi-Based Surface Reconstruction Algorithm, 1998. Introduces the power-crust algorithm, one of the first reconstruction methods with theoretical guarantees. web.cs.ucdavis.edu/~amenta/pubs/c…
Every technical person knows about ordinary least-squares (OLS) but most don’t know *total* least-squares (TLS). These measure fitting error differently: OLS minimizes sum of sq. vertical distances whereas TLS minimizes the sum of orthogonal distances from data to fit line 1/2
The Kabsch-Nadas formula solves in closed form the orthogonal least square problem (aka orthogonal Procrustes). At the heart of the iterative closest point method for registration. en.wikipedia.org/wiki/Orthogona… en.wikipedia.org/wiki/Kabsch_al…
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