Statistical Mechanics of Learning Machines: from algorithmic and information theoretical limits to new biologically inspired paradigms

Funded by the Italian Ministry of University and Research (MUR) under the PRIN 2002 (cod. 20229T9EAT) in the framework of European Union - Next Generation EU (CUP: J53D2300364001)

Project Duration: 2023-2025

National Coordinator: Daniele Tantari. Head of local unit: Fabrizio Durante (former head: Adriano Barra). 

Local Research Team: Linda Albanese (01/02/2024 - 31/01/2025), Adriano Barra, Fabrizio Durante, Silvio Franz, Maria Longobardi.

Other Institutions: University of Bologna (head of research unit: Daniele Tantari), Università "Luigi Bocconi" (head of the research unit: Enrico Maria Malatesta).

Reasearch Output from the Unisalento Unit

1. E. Agliari, A. Alessandrelli, A. Barra, M.S. Centonze, F. Ricci-Tersenghi.  Generalized hetero-associative neural networks.  Arxiv manuscript (2024). 

2. E. Agliari, A. Alessandrelli, A. Barra, M.S. Centonze, F. Ricci-Tersenghi. Networks of neural networks: the more is different. Arxiv manuscript (2025).

3. E. Agliari, A. Barra, P. Bianco, A. Fachechi, D. Pallara. The thermodynamic limit of mean field neural networks.  Arxiv manuscript (2024). 

4. M. S. Centonze, A. Treves, E. Agliari, A. Barra. Guerra interpolation for place cells. Arxiv manuscript (2024). 

5. L. Albanese. About the AT line in Replica Symmetry Breaking assumption for spin glasses. J. Math. Phys. 66, 073301 (2025). Arxiv manuscript.

6. L. Albanese, A. Alessandrelli. Boolean SK model. Boll. Unione Mat. Ital., in press (2025). Arxiv manuscript.

7. L. Albanese, A. Alessandrelli, A. Barra, P. Sollich. Yet another exponential model. Arxiv manuscript (2025).

8. L. Albanese, A. Barra, P. Bianco, F. Durante, D. Pallara. Hebbian learning from first principles. J. Math. Phys. 65, 113302 (2024). Arxiv manuscript.

9. L. Albanese, A. Alessandrelli, A. Annibale, A. Barra. Replica Symmetry Breaking is supervised and unsupervised Hebbian networks.  J. Phys. A: Math. & Theor.  57(16):165003. Arxiv manuscript (2024). 

10. L. Albanese, A. Barra, E.N.M. Cirillo. Guerra Interpolation for inverse freezing. Arxiv manuscript (2025).

11. A. Alessandrelli, A. Barra, A. Ladiana, A. Lepre, F. Ricci-Tersenghi. Supervised and unsupervised protocols for heteroassociative neural networks. Physica A  676, 130871 (2025). Arxiv manuscript (2025).

12. E. Agliari, F. Alemanno, A. Barra, M. Castellana, D. Lotito, M. Piel. Inverse modeling of time-delayed interactions via the dynamic-entropy formalism.  Phys. Rev. E  110, 024301. Arxiv manuscript  (2024). 

13. E. Agliari, A. Alessandrelli, A. Barra, F. Ricci-Tersenghi. Parallel learning in multitasking neural networks. Journal of Statistical Mechanics  113402.  Arxiv manuscript (2023).

14. L. Anzilli, F. Durante. The average rectangular volume induced by supermodular aggregation functions. J. Math. Anal. Appl. 555:130137, 2026. Open access.

15. M. Aquaro, F. Alemanno, I. Kanter, F. Durante,  A. Barra, E. Agliari. Hebbian Dreaming for small datasets. Neural Networks 173, 106174, webpage SSRN (2024). 

16. M. R. Irshad, K. Archana, R. Maya, M. Longobardi. Estimation of Weighted Extropy with Focus on Its Use in Reliability Modeling. Entropy, 26(2), 160 (2024). 

17. M. Longobardi. Unified Formulations of Entropy and Extropy. In: Quesada-Arencibia, A., Affenzeller, M., Moreno-Díaz, R. (eds) Computer Aided Systems Theory – EUROCAST 2024. EUROCAST 2024. Lecture Notes in Computer Science, vol 15174. Springer, Cham.