Notes

On Compiler Adding compilation flags to gcc not always makes it faster, it just enables a specific set of optimization methods. It’s also good to turn on platform specific flags to turn on some specific optimization methods to that architecture. Remember that compilers are conservative, meaning they do not apply that optimization if they think it does not always apply. What are they good at Compilers are good at: mapping program to machine ▪ register allocation ▪ instruction scheduling ▪ dead code elimination ▪ eliminating minor inefficiencies ...

Introduction to Convolutional NN Design Goals We want to be invariant to some transformations but also at the same time to be specific to some thing. Convolutional Neural Networks (CNNs) are a class of deep neural networks that are particularly effective for image processing tasks. They are designed to automatically and adaptively learn spatial hierarchies of features from images. Compared to standard Fully connected Neural Networks, they reuse weights, making their number of parameter much fewer. ...

Diffusion is a physical process that models random motion, first analyzed by Brown when studying pollen grains in water. In this section, we will first analyze a simplified 1-dimensional version, and then delve into diffusion models for images, the ones closest to (Ho et al. 2020). The Diffusion Process This note follows original Einstein’s presentation, here we have a simplified version. Let’s suppose we have a particle at $t = 0$ at some position $i$. We have a probability of jumping to the left of $p$ to right of $q$, the rest is staying at the same position. ...

Egocentric vision is a sub-field of computer vision that studies vision understanding from a centered point of view, that typical of animals. One historical thing is MIT 1997 they had to bring around very heavy cameras. Now we have glasses. Other examples of egocentric vision are cars with cameras that see their surrounding, or robots equipped with cameras mimicking human vision. The difference of egocentric vision compared to standard vision techniques is the high variability and instability of the video, and the concept of movement and interactions inside the image. Standard computer vision is disembodied and controlled field of view. ...

The algorithm has been the same, some ideas are in Fourier Series, but architectures change, which means there are new ways to make this algorithm even faster. Example of transforms We have learned in Algebra lineare numerica, Cambio di Base that linear transforms are usually a change of basis. They are matrix vector multiplications (additions and multiplications by constants). The optimizations are based on what sorts of transforms we have (e.g. Sparse Matrix Vector Multiplication, or dense versions). The same idea applies also for Fourier transforms. ...

Many problems in scientific computing include: Solving linear equations Eigenvalue computations Singular value decomposition LU/Cholesky/QR decompositions etc… And the userbase is quite large for this types of computation (number of scientists in the world is growing exponentially ) Quick History of Performance Computing Early seventies it was EISPACK and LINPACK. Then In similar years Matlab was invented, which simplified a lot compared to previous systems. LAPACK redesigned the algorithms in previous libraries to have better block-based locality. BLAS are kernel functions for each computer, while LAPACK are the higher level functions build on top of BLAS (1, 2,3). Then another innovation was ATLAS, which automatically generates the code for BLAS for each architecture. This is called autotuning because it does a search of possible enumerations and chooses the fastest one. Now autotuning has been done a lot for NN systems. ...

Generative Adversarial Network has been introduced in 2014 by Ian Goodfellow (at that time they where still gray and white). Now the images have been improved with Diffusion Models, that can be considered the new paradigm. This idea has been considered by Yann LeCun as one of the most important ideas. Nowadays (2025), they are still used for super-resolution and other applications, but it has still some limitations (mainly stability), and now has good competition against other models. The resolution purported by GAN is much higher than VAE (see Autoencoders#Variational Autoencoders). This is a easy plugin to improve the results of other models (VAE, flow, Diffusion). Also ChatGPT has some sort of adversarial learning for example, not explained in the same manner as here. ...

Introduction: a neuron I am lazy, so I’m skipping the introduction for this set of notes. Look at Andrew Ng’s Coursera course for this part (here are the notes). Historical paper is (Rosenblatt 1958). One can view a perceptron to be a Log Linear Models with the temperature of the softmax that goes to 0 (so that it is an argmax). Trained with a stochastic gradient descent with a batch of 1 (this is called the perceptron update rule, see The Perceptron Model). ...

Normalizing flows have both latent space and can produce tractable explicit probability distributions (closer to Autoregressive Modelling, they have tractable distributions, but not a latent space). This means we are able to get the likelihoods of a certain sample. This approach to modelling a flexible distribution is called a normalizing flow because the transformation of a probability distribution through a sequence of mappings is somewhat analogous to the flow of a fluid. From (Bishop & Bishop 2024) ...

An historical perspective The origins of motion capture One of the earliest starts of motion capturing is the famous horse in 1878 in motion “video”. This was the start of all the modern cameras. One of the earliest human body motion capture was in military for moving efficiency purposes in 1883. This website has many historical resources on the topic. The problem is still a problem in modern times. If we want to create models to mimic humans, it surely could be nice to understand how humans move and think. This is the general line of though of this line of research. ...