To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of {\em Maximal Coding Rate Reduction} ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

Leveraging the compositional nature of our world to expedite learning and facilitate generalization is a hallmark of human perception. In machine learning, on the other hand, achieving compositional generalization has proven to be an elusive goal, even for models with explicit compositional priors. To get a better handle on compositional generalization, we here approach it from the bottom up: Inspired by identifiable representation learning, we investigate compositionality as a property of the data-generating process rather than the data itself. This reformulation enables us to derive mild conditions on only the support of the training distribution and the model architecture, which are sufficient for compositional generalization. We further demonstrate how our theoretical framework applies to real-world scenarios and validate our findings empirically. Our results set the stage for a principled theoretical study of compositional generalization.

The \emph{Cheap Gradient Principle}~\citep{Griewank:2008:EDP:1455489} --- the computational cost of computing a $d$-dimensional vector of partial derivatives of a scalar function is nearly the same (often within a factor of $5$) as that of simply computing the scalar function itself --- is of central importance in optimization; it allows us to quickly obtain (high-dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures. The current state of affairs is markedly different with regards to computing sub-derivatives: widely used ML libraries, including TensorFlow and PyTorch, do \emph{not} correctly compute (generalized) sub-derivatives even on simple differentiable examples. This work considers the question: is there a \emph{Cheap Sub-gradient Principle}? Our main result shows that, under certain restrictions on our library of non-smooth functions (standard in non-linear programming), provably correct generalized sub-derivatives can be computed at a computational cost that is within a (dimension-free) factor of $6$ of the cost of computing the scalar function itself.

We speak of a \textit{computational law} when that law is intended to be enforced by software through an automated decision-making process. As digital technologies evolve to offer more solutions for public administrations, we see an ever-increasing number of computational laws. Traditionally, law is written in natural language. Computational laws, however, suffer various complications when written in natural language, such as underspecification and ambiguity which lead to a diversity of possible interpretations to be made by the coder. These could potentially result into an uneven application of the law. Thus, resorting to formal languages to write computational laws is tempting. However, writing laws in a formal language leads to further complications, for example, incomprehensibility for non-experts, lack of explicit motivation of the decisions made, or difficulties in retrieving the data leading to the outcome. In this paper, we investigate how certain legal principles fare in both scenarios: computational law written in natural language or written in formal language. We use a running example from the European Union's road transport regulation to showcase the tensions arising, and the benefits from each language.

The paper develops a mathematical framework for working with neural network representations in the context of finite differences and differential geometry. In this framework, data points going though layers have fixed coordinates but space is smoothly curved with each layer. The paper presents a very interesting framework for working with neural network representations, especially in the case of residual networks. Unfortunately, taking the limit as the number of layers goes to infinity does not make practical application very easy and somewhat limits the impact of this paper. The paper is not always completely clear.

Recent advances in the application of physics-informed learning into the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarly leveraging Navier-Stokes Equation or one of its various derivative to train a neural network. Here, we propose an alternative approach based on variational methods. The proposed approach uses the principle of minimum pressure gradient combined with the continuity constraint to train a neural network and predict the flow field in incompressible fluids. We describe the underlying principles of the proposed approach, then use a demonstrative example to illustrate its implementation and show that it reduces the computational time per training epoch when compared to the conventional approach.

Seventeenth-century Amsterdam is known for three things: Rembrandt, the Bubonic Plague and Tulip Mania. It was 1637, the height of the Dutch Golden Age. Tulip bulbs were scarce and demand for them soared. They were also a symbol of status. Acres of land were swapped for seeds that would yield no more than a few flowers.

Turing over his lifetime produced various groundbreaking seminal papers and works. In this write-up, I am going to delve into four such major works: "On Computable Numbers, with an Application to the Entscheidungsproblem" (1936); Bombe and Spider, Banburismus (1940–41); Computing Machinery and Intelligence (1950); Solvable and Unsolvable Problems (1954). David Hilbert and Wilhelm Ackermann discussed Entscheidungsproblem in their 1928 writing, The Principles of Mathematical Logic. They posed universal validity and satisfiability, which customarily was referred to as the decision problem (Hilbert et al., 1950). The decision problem can hence loosely be defined as coming up with an algorithm that takes an input and replies with a Yes or No depending on whether the statement is universally satisfiable.

AI is a general-purpose technology that has the potential to improve the welfare and well-being of people, to contribute to positive sustainable global economic activity, to increase innovation and productivity, and to help respond to key global challenges. It is deployed in many sectors ranging from production, finance and transport to healthcare and security. Alongside benefits, AI also raises challenges for our societies and economies, notably regarding economic shifts and inequalities, competition, transitions in the labour market, and implications for democracy and human rights. The OECD has undertaken empirical and policy activities on AI in support of the policy debate over the past two years, starting with a Technology Foresight Forum on AI in 2016 and an international conference on AI: Intelligent Machines, Smart Policies in 2017. The Organisation also conducted analytical and measurement work that provides an overview of the AI technical landscape, maps economic and social impacts of AI technologies and their applications, identifies major policy considerations, and describes AI initiatives from governments and other stakeholders at national and international levels.

Attribution for the core content is given to the textbook "Hands-On Unsupervised Learning Using Python: How to Build Applied Machine Learning Solutions from Unlabeled Data" which I would urge you to buy on Amazon