Indaco Biazzo

selected publications

1. The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems

   Biazzo, Indaco

   Communications Physics 2023

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   Autoregressive Neural Networks (ARNNs) have shown exceptional results in generation tasks across image, language, and scientific domains. Despite their success, ARNN architectures often operate as black boxes without a clear connection to underlying physics or statistical models. This research derives an exact mapping of the Boltzmann distribution of binary pairwise interacting systems in autoregressive form. The parameters of the ARNN are directly related to the Hamiltonian’s couplings and external fields, and commonly used structures like residual connections and recurrent architecture emerge from the derivation. This explicit formulation leverages statistical physics techniques to derive ARNNs for specific systems. Using the Curie–Weiss and Sherrington–Kirkpatrick models as examples, the proposed architectures show superior performance in replicating the associated Boltzmann distributions compared to commonly used designs. The findings foster a deeper connection between physical systems and neural network design, paving the way for tailored architectures and providing a physical lens to interpret existing ones.

2. A Bayesian generative neural network framework for epidemic inference problems

   Biazzo, Indaco, Braunstein, Alfredo, Dall’Asta, Luca, and Mazza, Fabio

   Scientific Reports 2022

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   The reconstruction of missing information in epidemic spreading on contact networks can be essential in the prevention and containment strategies. The identification and warning of infectious but asymptomatic individuals (i.e., contact tracing), the well-known patient-zero problem, or the inference of the infectivity values in structured populations are examples of significant epidemic inference problems. As the number of possible epidemic cascades grows exponentially with the number of individuals involved and only an almost negligible subset of them is compatible with the observations (e.g., medical tests), epidemic inference in contact networks poses incredible computational challenges. We present a new generative neural networks framework that learns to generate the most probable infection cascades compatible with observations. The proposed method achieves better (in some cases, significantly better) or comparable results with existing methods in all problems considered both in synthetic and real contact networks. Given its generality, clear Bayesian and variational nature, the presented framework paves the way to solve fundamental inference epidemic problems with high precision in small and medium-sized real case scenarios such as the spread of infections in workplaces and hospitals.

3. General scores for accessibility and inequality measures in urban areas

   Biazzo, Indaco, Monechi, Bernardo, and Loreto, Vittorio

   Royal Society open science 2019

   arXiv HTML
4. Epidemic mitigation by statistical inference from contact tracing data

   Baker, Antoine,  Biazzo, Indaco, Braunstein, Alfredo, Catania, Giovanni, Dall’Asta, Luca, Ingrosso, Alessandro, Krzakala, Florent, Mazza, Fabio, Mézard, Marc, Muntoni, Anna Paola, and others,

   Proceedings of the National Academy of Sciences 2021

   arXiv HTML
5. CityChrone: an Interactive Platform for Transport Network Analysis and Planning in Urban Systems

   Biazzo, Indaco

   In Complex Networks & Their Applications X 2022

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   Urban systems studies in the last decades have greatly benefited from the digital revolution and the accumulation of a massive amount of data. Extracting useful information from these data calls for new and innovative theoretical and computational approaches. This work presents an open-source, modular, and scalable platform for urban planning and transports network analysis, the CityChrone [citychrone.org]. The platform shows, on interactive maps, measures of performances of public transport in cities. The measures are based on the computation of the travel time distance between a large set of points. Thanks to the high efficiency of the routing algorithm developed, the platform allows users to create new public transports networks and showing the effect on mobility in a small amount of time. A preliminary analysis of the user-generated scenarios is presented. All the source code of the CityChrone platform is open-source, and we employ only open data to ensure the reproducibility of results.