### Kai Hormann: Novel Range Functions via Taylor Expansions and Recursive Lagrange Interpolation with Application to Real Root Isolation

Range functions are an important tool for interval computations, and they can be employed for the problem of root isolation. In this talk, I will first introduce two new classes of range functions for real functions. They are based on the remainder form by Cornelius and Lohner (1984) and provide different improvements for the remainder part of this form. On the one hand, I will show how centered Taylor expansions can be used to derive a generalization of the classical Taylor form with higher than quadratic convergence. On the other hand, I will discuss a recursive interpolation procedure, in particular based on quadratic Lagrange interpolation, leading to recursive Lagrange forms with cubic and quartic convergence. These forms can be used for isolating the real roots of square-free polynomials with the algorithm EVAL, a relatively recent algorithm that has been shown to be effective and practical. Finally, a comparison of the performance of these new range functions against the standard Taylor form will be given. Specifically, EVAL can exploit features of the recursive Lagrange forms which are not found in range functions based on Taylor expansion.
Experimentally, this yields at least a twofold speedup in EVAL.*Room B1.17*

### Gail Weiss: Thinking Like Transformers

Transformers - the purely attention based NN architecture - have emerged as a powerful tool in sequence processing. But how does a transformer think? When we discuss the computational power of RNNs, or consider a problem that they have solved, it is easy for us to think in terms of automata and their variants (such as counter machines and pushdown automata). But when it comes to transformers, no such intuitive model is available.
In this talk I will present a programming language, RASP (Restricted Access Sequence Processing), which we hope will serve the same purpose for transformers as finite state machines do for RNNs. In particular, we will identify the base computations of a transformer and abstract them into a small number of primitives, which are composed into a small programming language. We will go through some example programs in the language, and discuss how a given RASP program relates to the transformer architecture.*Room A1.02 - East Campus USI-SUPSI*

### Giorgio Corani: An overview of forecasts reconciliation

Often time series are organized into a hierarchy. For example, the total visitors of a country can be divided into regions and the visitors of each region can be further divided into sub-regions. This is a hierarchical time series. Hierarchical forecasts should be coherent; for instance, the sum of the forecasts of the different regions should equal the forecast for the total. The forecasts are incoherent if they do not satisfy such constraints. Temporal hierarchies are another application of hierarchical time series, in which the same variable is predicted at different scales (e.g., monthly, quarterly and yearly) and coherence across the different temporal scales is needed. Reconciliation is the process of adjusting forecasts which are created independently for each time series, so that they become coherent. I will discuss the state-of-the-art of reconciliation algorithms.*Room B1.17 East Campus USI-SUPSI*