arXiv subjects

Sandro Preto

Publications and source records attributed to Sandro Preto.

3 recordsLinked to original sources

arXiv2026

A polynomial-size logical twin for neural networks

A logical twin of a neural network is a logical representation that mimics the computation of the network through logical formulas. We revisit two earlier proposals for constructing logical twins of feedforward neural networks in Łukasiewicz logic, both of which are susceptible to exponential blow-up in running time and representation size. Building on ideas from both approaches, we present a new construction that directly yields logical twins in Łukasiewicz logic. We show that this construction can be computed in polynomial time and produces polynomial-size logical twins. Finally, we report an empirical evaluation of the three methods, showing that the new proposal substantially outperforms the other two.

cs.LO↗

arXiv2025

Regional, Lattice and Logical Representations of Neural Networks

A possible path to the interpretability of neural networks is to (approximately) represent them in the regional format of piecewise linear functions, where regions of inputs are associated to linear functions computing the network outputs. We present an algorithm for the translation of feedforward neural networks with ReLU activation functions in hidden layers and truncated identity activation functions in the output layer. We also empirically investigate the complexity of regional representations outputted by our method for neural networks with varying sizes. Lattice and logical representations of neural networks are straightforward from regional representations as long as they satisfy a specific property. So we empirically investigate to what extent the translations by our algorithm satisfy such property.

cs.LO↗

arXiv2022

Coherence of probabilistic constraints on Nash equilibria

Observable games are game situations that reach one of possibly many Nash equilibria. Before an instance of the game starts, an external observer does not know, a priori, what is the exact profile of actions that will occur; thus, he assigns subjective probabilities to players' actions. However, not all probabilistic assignments are coherent with a given game. We study the decision problem of determining if a given set of probabilistic constraints assigned a priori by the observer to a given game is coherent, which we call the Coherence of Probabilistic Constraints on Equilibria, or PCE-Coherence. We show several results concerning algorithms and complexity for PCE-Coherence when only pure Nash equilibria are considered. In this context, we also study the computation of maximal and minimal probabilistic constraints on actions that preserves coherence. Finally, we study these problems when mixed Nash equilibria are allowed.

cs.GT↗