## What is Sharpness-Aware Minimization (SAM)?

Introduction Consider the general machine learning set-up. We have a class of models parameterized by (e.g. for linear regression, would be the coefficients of the model). Each of these models takes in some input and outputs a result . We want to select the parameter which minimizes some population loss: where is the loss incurred […]

What is Sharpness-Aware Minimization (SAM)?

## What is a block-angular matrix?

A matrix is said to be in block-angular form if it is of the form where the ‘s are arbitrary rectangular matrices (they need not be square). These matrices appear in optimization in the context of the Dantzig-Wolfe decomposition in linear programming (LP). The problem with the Dantzig-Wolfe decomposition solves is of the form The […]

What is a block-angular matrix?

## What is the Birkhoff polytope?

A square matrix is said to be doubly stochastic if its entries are all non-negative and each row and column sums to one, i.e. The Birkhoff polytope, denoted by , is the set of all doubly stochastic matrices. One interesting fact about the Birkhoff polytope is that it is a convex polytope, with the vertices […]

What is the Birkhoff polytope?

## What is Minkowski’s Representation Theorem?

Minkowski’s representation theorem is a fundamental result on how polyhedra can be represented. Preliminary definitions In , a polyhedron is a set which can be described as , where and . is an extreme point of a polyhedron if there do not exist such that . is a ray of a polyhedron if is non-zero […]

What is Minkowski’s Representation Theorem?

## CAPITALISM IN THE 21st CENTURY THROUGH THE PRISM OF VALUE.CAPITALISM IN THE 21st CENTURY. More of a diamond than a prism.

Review of the recently published book authored by Guglielmo Carchedi & Michael Roberts. the-prism-or-diamond-final-1Download

CAPITALISM IN THE 21st CENTURY THROUGH THE PRISM OF VALUE.CAPITALISM IN THE 21st CENTURY. More of a diamond than a prism.

## Polycrisis and depression in the 21st century

‘Polycrisis’ is the buzz word among leftists right now.  The word expresses the coming together and interlocking of various crises: economic (inflation and slump); environmental (climate and pandemic); and geopolitical (war and international divisions). Indeed, I raised a similar idea early last year.  So it is no surprise that the latest Human Development Report from the […]

Polycrisis and depression in the 21st century

## Fernando Moragón: “El enemigo nº 1 de Europa es EE.UU”

Hola. Os dejamos un análisis de Fernando Moragón, experto en Geopolítica, especialmente asiática, en el que nos explica con hechos cómo Estados Unidos está destruyendo cualquier posibilidad de recuperación económica en Europa. Interesante y, a la vez, terrible. Pinchad en este mismo enlace, o en la imagen, para acceder al contenido. Que los medios de […]

Fernando Moragón: “El enemigo nº 1 de Europa es EE.UU”

## THE DAYS OF THE US TECH LEVIATHANS ARE DRAWING TO A CLOSE.

the-tech-leviathans-stumble-1Download It is worth noting that Huawei, for the first time in 2022, broke into the ranks of the 10 ten corporations, both foreign and local, obtaining patents within the USA in 2022. https://www.huaweicentral.com/ibm-loses-first-time-in-10-years-huawei-enters-top-10-in-us-patent-race/

THE DAYS OF THE US TECH LEVIATHANS ARE DRAWING TO A CLOSE.

## ASSA 2023 part one: the mainstream – fiction and reality

As usual, there were hundreds of sessions and papers at this year’s ASSA 2023, the annual conference of the American Economics Association (AEA).  In this post, I shall concentrate my report on the mainstream economics sessions and on what I considered to be key topics and the most illuminating. Let’s start with the US economy.  […]

ASSA 2023 part one: the mainstream – fiction and reality

## THE SELF-ASSEMBLING BRAIN, HOW NEURAL NETWORKS GROW SMARTER

Written by Peter Robin Hiesinger WHO IS THE SMARTEST OF US ALL Review by Gunnel Minett How the brain works and how the neurones link up and develop is something that has intrigued science throughout history. What makes a neural network intelligent? Is it genes behind this process (connectivity) or is it the environment (learning)? […]

THE SELF-ASSEMBLING BRAIN, HOW NEURAL NETWORKS GROW SMARTER