Month: September 2020

Uncategorized

Visualizing sample simplex trajectories in Deep Learning

Softmax is a distribution over choices, it maps a vector into the probability simplex that is defined as \Delta_{n-1}=\{p\in\mathbb{R}^n\; \vert\; 1^\top p = 1 \; \; {\rm and} \;\; p \geq 0 \}, where the sum of all elements of the vector must equal 1. Softmax is used a lot in classification and I thought it would be interesting to visualize (when possible, on lower dimensions) the trajectories of individual samples in that simplex as predicted by the network while the network is being trained.

In the animations below you’ll see the trajectories of the sample individual sample (from the test set) over the simplex of 3 classes (dog, cat, horse) from CIFAR-10 and using a simple shallow CNN both with Adam and SGD. Each frame is generated after 10 optimization steps and the video is from 4 epochs with CIFAR-10 dataset with only the 3 aforementioned classes.

Trajectory of a CNN using Adam with LR of 0.001

Trajectory of a CNN using SGD with LR of 0.001 and momentum

by Christian S. Perone
Article, Philosophy

A new professional ethics: Karl Popper and Xenophanes’ epistemology

It is not a secret that I admire the work of Karl Popper, both as a philosopher but also as a very precise historian that tried to dismiss many misunderstandings of the past.

I was reading the book The World of Parmenides, which is a collection of Popper’s essays on the Presocratic Enlightenment, and found a very interesting insight on how the epistemology of Xenophanes led naturally to a professional ethics. This link isn’t widespread nowadays, but it certainly deserves more divulgation as it is a natural consequence of the conjectural knowledge we possess.

(more…)

by Christian S. Perone