Marco Molinari

Riccardo Sven Risuleo, Marco Molinari, Giulio Bottegal et al.

This paper describes a benchmark consisting of a set of synthetic measurements relative to an office environment simulated with the software IDA-ICE. The simulated environment reproduces a laboratory at the KTH-EES Smart Building, equipped with a building management system. The data set contains records collected over a period of several days. The signals to CO$_2$ concentration, mechanical ventilation airflows, air infiltrations and occupancy. Information on door and window opening is also available. This benchmark is intended for testing data-based modeling techniques. The ultimate goal is the development of models to improve the forecast and control of environmental variables. Among the numerous challenges related to this framework, we point out the problem of occupancy estimation using information on CO$_2$ concentration. This can be seen as a blind identification problem. For benchmarking purposes, we present two different identification approaches: a baseline overparametrization method and a kernel-based method.

Davide Ghilardi, Federico Belotti, Marco Molinari et al.

SAEs have recently been employed as a promising unsupervised approach for understanding the representations of layers of Large Language Models (LLMs). However, with the growth in model size and complexity, training SAEs is computationally intensive, as typically one SAE is trained for each model layer. To address such limitation, we propose \textit{Group-SAE}, a novel strategy to train SAEs. Our method considers the similarity of the residual stream representations between contiguous layers to group similar layers and train a single SAE per group. To balance the trade-off between efficiency and performance, we further introduce \textit{AMAD} (Average Maximum Angular Distance), an empirical metric that guides the selection of an optimal number of groups based on representational similarity across layers. Experiments on models from the Pythia family show that our approach significantly accelerates training with minimal impact on reconstruction quality and comparable downstream task performance and interpretability over baseline SAEs trained layer by layer. This method provides an efficient and scalable strategy for training SAEs in modern LLMs.