Sebastiano Stramaglia

Kenzo Clauw, Sebastiano Stramaglia, Daniele Marinazzo

This paper studies emergent phenomena in neural networks by focusing on grokking where models suddenly generalize after delayed memorization. To understand this phase transition, we utilize higher-order mutual information to analyze the collective behavior (synergy) and shared properties (redundancy) between neurons during training. We identify distinct phases before grokking allowing us to anticipate when it occurs. We attribute grokking to an emergent phase transition caused by the synergistic interactions between neurons as a whole. We show that weight decay and weight initialization can enhance the emergent phase.

Kenzo Clauw, Sebastiano Stramaglia, Daniele Marinazzo

Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.e. concepts). Finally, we show the O-information can be used for multi-neuron importance. This can be demonstrated by re-training a synergistic sub-network, which results in a minimal change in performance. These results suggest our method can be used for pruning and unsupervised representation learning.

Ivan Lazic, Chiara Barà, Marta Iovino et al.

Understanding the contribution of individual features in predictive models remains a central goal in interpretable machine learning, and while many model-agnostic methods exist to estimate feature importance, they often fall short in capturing high-order interactions and disentangling overlapping contributions. In this work, we present an information-theoretic extension of the High-order interactions for Feature importance (Hi-Fi) method, leveraging Conditional Mutual Information (CMI) estimated via a k-Nearest Neighbor (kNN) approach working on mixed discrete and continuous random variables. Our framework decomposes feature contributions into unique, synergistic, and redundant components, offering a richer, model-independent understanding of their predictive roles. We validate the method using synthetic datasets with known Gaussian structures, where ground truth interaction patterns are analytically derived, and further test it on non-Gaussian and real-world gene expression data from TCGA-BRCA. Results indicate that the proposed estimator accurately recovers theoretical and expected findings, providing a potential use case for developing feature selection algorithms or model development based on interaction analysis.

Sebastiano Stramaglia, Tomas Scagliarini, Yuri Antonacci et al.

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the 'local Granger causality', i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation.