Meaningful XAI Based on User-Centric Design Methodology

This report explores the concept of explainability in AI-based systems, distinguishing between "local" and "global" explanations. “Local” explanations refer to specific algorithmic outputs in their operational context, while “global” explanations encompass the system as a whole. The need to tailor explanations to users and tasks is emphasised, acknowledging that explanations are not universal solutions and can have unintended consequences. Two use cases illustrate the application of explainability techniques: an educational recommender system, and explainable AI for scientific discoveries. The report discusses the subjective nature of meaningfulness in explanations and proposes cognitive metrics for its evaluation. It concludes by providing recommendations, including the inclusion of “local” explainability guidelines in the EU AI proposal, the adoption of a user-centric design methodology, and the harmonisation of explainable AI requirements across different EU legislation and case law.Overall, this report delves into the framework and use cases surrounding explainability in AI-based systems, emphasising the need for “local” and “global” explanations, and ensuring they are tailored toward users of AI-based systems and their tasks

Fast in-place accumulated bilinear formulae

Bilinear operations are ubiquitous in computer science and in particular in computer algebra and symbolic computation. One of the most fundamental arithmetic operation is the multiplication, and when applied to, e.g., polynomials or matrices, its result is a bilinear function of its inputs. In terms of arithmetic operations, many sub-quadratic (resp. sub-cubic) algorithms were developed for these tasks. But these fast algorithms come at the expense of (potentially large) extra temporary space to perform the computation. On the contrary, classical, quadratic (resp. cubic) algorithms, when computed sequentially, quite often require very few (constant) extra registers. Further work then proposed simultaneously ``fast'' and ``in-place'' algorithms, for both matrix and polynomial operations We here propose algorithms to extend the latter line of work for accumulated algorithms arising from a bilinear formula. Indeed one of the main ingredient of the latter line of work is to use the (free) space of the output as intermediate storage. When the result has to be accumulated, i.e., if the output is also part of the input, this free space thus does not even exist. To be able to design accumulated in-place algorithm we thus relax the in-place model to allow algorithms to also modify their input, therefore to use them as intermediate storage for instance, provided that they are restored to their initial state after completion of the procedure. This is in fact a natural possibility in many programming environments. Furthermore, this restoration allows for recursive combinations of such procedures, as the (non concurrent) recursive calls will not mess-up the state of their callers. We propose here a generic technique transforming any bilinear algorithm into an in-place algorithm under this model. This then directly applies to polynomial and matrix multiplication algorithms, including fast ones

The World Price of Foreign Exchange Risk

We consider a world capital market in which the investor population is heterogenous. Investors of different countries differ in the prices of goods at which they consume the income from their investments. In such a setting, the international CAPM incorporates rewards for exchange rate risk, in addition to the traditional reward for market-covariance risk. The aim of the paper is to determine whether these additional risk premia empirically playa significant role in the pricing of securities. The test being conducted is a test of a conditional version of the CAPM. It builds on the recent empirical literature which points out that stock market returns may, to some extent, be predicted on the basis of a number of instrumental variables, such as interest rates and dividend yields. All previous tests of the international CAPM with exchange risk premia have been tests of the unconditional version and have been inconclusive.