When water moves, mollusks open shell and when something touches membrane, then shell closes. Animals are able to coordinate perception with action, which is especially clear during the hunt. In the children cognitive development, the transition from sensorimotor to more abstract representations of reality follow a stagebased principle. Is that the exclusive outcome of biology or is dictated by general principles of optimization, so that stages are nothing else than the natural solution to break the complexity of learning. Most machine learning algorithms relies on simple protocols (supervised, reinforcement, unsupervised, semisupervised schemes), in which a considerable number of relevant interactions are missed. How about the crucial role of the teacher? The clear identification of hierarchical labels in learning environments can be thought of as a sign of intermediate goals for the agent, and the formalization of some constraints might directly give insights on the birth of deep architectures.
Contents
Members of the project
 Marco Gori
 Marco Maggini
 Michelangelo Diligenti
 Stefano Melacci
 Francesco Giannini
 Giuseppe Marra
 Alessandro Betti
 Lisa Graziani
 Gabriele Ciravegna
Former members
 Leonardo Rigutini
 Claudio Saccà
 Salvatore Frandina
 Marco Lippi
 Paolo Nistri
 Stefano Campi
Research Direction and workpackages
 Learning from constraints in singletask learning: Focus on single task learning and reformulation of kernel machines within the framework of learning from constraints. Classification and regression is reformulated by expressing the collection of examples as constraints.In addition, the problem in which the targets are attached on infinite subsets of the domain is investigated. Here is a more detailed list of topics to be faced:
 reformulation of learning from finite collection of examples in the framework of learning from constraints;
 constraints in the input domain expressed in infinite subsets (e.g.: (x,y) is any pair of the input and we impose that the target is “+1” for all x: 0<x<3);
 algorithmic issues
 Learning from convex constraints: Convex constraints in multitask learning is investigated from a general point of view with emphasis on polytopes. Here is a detailed list of topics to be faced:
 the case of linear constraints A f(x) = b
 the case of f(x)>0
 the case of general polytopes
 probabilistic normalization of classifiers
 benchmarks based on artificial examples
 Learning from constraints by quasilocal kernels: Investigation of the role of the kernel in “learning from constraints”. In particular, the emphasis is on the difference between local and global kernels and on how to come up with mixed solutions. Here is a detailed list of topics to be faced:
 why are neither local nor global kernels very appropriate (especially) in the framework of learning from constraints?
 Mixture of kernels and kernel learning issues
 Expansions of local kernels (e.g.: expansion of Gaussian with sigma, 2 sigma, 4 sigma, …)
 benchmarks based on artificial examples
 Bridging logic and kernel machines: How can kernel machines and FOL be bridged in a multitask environment? Here is a detailed list of topics to be faced:
 Learning with constraints by kernel machines
 From FOL clauses to realvalued constraints
 Enforcing constraints by penalties
 Benchmarks based on artificial examples
 Learning from constraints and active teaching: Study of stagebased learning, which starts from induction and continue with higher level constraint satisfaction. Here is a list of topics to be developed:
 Two stagebased learning: perceptual level and abstract level
 Order relations from a set of constraints (the “easy” comes first)
 Gradient methods
 Continuation methods
 Learning of constraints: Analysis on the development of constraints, which are not necessarily given in advance, but are learned just as other functions (from examples and (other given) constraints. Here is a list of topics to be developed:
 General study of the case in which the constraints are just learnable functions;
 Learning of constraints once we give a parametricbased representation of constraints
 The role of phases in learning constraints
 Learning constraints and deep architectures
 Forcing constraints in multilayer networks: Learning from constraints based on multilayered networks instead of the variational approach that originates kernellike machines. Here is a list of topics to be developed:
 Algorithmic issues – backproplike algorithms;
 Experiments for problems of coherent classification from multiview patterns
 Coherent decisionmaking
 Semanticbased regularization applied to COIL
 Enforcing linear constraints in portfolio asset allocation
 Semanticbased regularization applied to Wikipedia document classification
Integrating logic and learning
The integration of deep learning and logic reasoning is still an openresearch problem and it is considered to be the key for the development of real intelligent agents. From one side, deep learning obtained amazing results in many applications like computer vision, natural language processing and so on. On the other hand, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higherlevel symbolic inference.
Click here for more details on this research topic.
Seminars at SAILab, Siena
 Gabriele Ciravegna, 03 July 2019, A Constraintbased Approach to Learning and Explanation —
 Giuseppe Marra, 12 June 2019, Neural Markov logic networks
 Francesco Giannini, 13 March 2019, Integrating Learning and Reasoning with Deep Logic Models
 Alessandro Betti, 05 February 2019, From architectural constraints to neural subsidiary conditions
 Marco Gori, 09 January 2019, Developmental Learning with Constraints
 Francesco Giannini, 24 October 2018, Some Approaches to Learning of Logical Constraints
 Alessandro Betti, 11 October 2018, Perfect Neuron Building
 Alessandro Betti, 28 June 2018, Learning with Architectural Constraints
 Francesco Giannini, 21 June 2018, Loss functions generation by means of fuzzy aggregators
 Giuseppe Marra, 07 June 2018, Probabilistic Soft Logic
 Fabrizio Riguzzi, 18 April 2018, Deep Probabilistic Logic Programming
 Francesco Giannini, 29 March 2018, LogSCM – Logical Support Constraint Machines
 Giuseppe Marra, 15 March 2018, CLARE: a Constrained Learning And Reasoning Environment
 Francesco Giannini, 23 June 2017, Learning and reasoning under Łukasiewitcz logic
 Francesco Giannini, 25 May 2017, Support constraints and logical deduction
 Francesco Giannini, 18 May 2017, The convex Łukasiewicz fragment
 Marco Gori, 18 April 2011, Constraint verification — In this talk, I discuss how to use the theory for constraint verification. Some links are established with manifold regularization and more general insights are given on how to handle dynamic structures. An example of model checking in logic is also shown.
 Marco Gori, 11 April 2011, Semanticbased regularization — In this talk, I show that a kernelbased solution can also be given in case of quadratic isoperimentric constraints and of holonomic constraints, whenever an appropriate approximation is adopted that is based on the knowledge of the unsupervised examples.
 Marco Gori, 4 April 2011, Constraint quantization — In this talk, I give guidelines for approaching any problem of learning from constraints thanks to the quantization of the constraints on the set of unsupervised/supervised data. It is shown that a kernelbased solution exists and that the classic kernel machine mathematical apparatus can be fully reused.
 Marco Gori, 28 March 2011, Exact penalties and support domains — In this talk, I discuss the cases in which exact penalties can replace the Lagrangian approach and present the emergence of constraint domains (support vectors as a special case) and show the consequent reduction of the representer theorems.
 Marco Gori, 21 March 2011, Representer theorems in learning from constraints — In this talk, I present the general representer theorems in both cases of (universal quantifier)based and (existentially quantifier)based constraints using the Lagrangian approach. I show some properties of the Lagrange multipliers and discuss primal/dual solutions, including links with path following primaldual methods.
 Marco Gori, 14 March 2011, An introduction to learning from constraints — In this talk, I give an introduction to learning from constraints by presenting examples in different contexts. Universal and existential constraints are introduced and a general formulation of the learning problem is given within the framework of variational calculus. Links with learning from examples and classic constraint satisfaction – including logic – are given.
 Marco Gori, 7 March 2011, Pseudodifferential operators, kernels, boundary conditions, and wellposedness — In this talk, I focus attention on pseudodifferential operators and to their connection with kernels, including their spectral interpretation. I discuss the role of boundary conditions for the existence and uniqueness of the solution and, finally, make some heuristic comment on the choice of the kernel. In particular, the discussion will focus on local vs global kernels and related literature by showing the connection with classic results on selfadjoint operators and boundedness. Finally I give some insights on the relaxation of the regularity assumptions on the solution by showing some interesting examples of optimality.
 Marco Gori, 28 February 2011, Where do kernel machines come from? Not, yet another model! — In this talk, I discuss the simplest problem the agent is expected to face: learn from a collection of supervised pairs. I prove that the results are strictly related to kernel machines and that, in particular, many significant links can be established with the theory of RKHS. A Bayesian interpretation of learning is also given.
 Marco Gori, 21 February 2011, An introduction to constrained variational calculus — In this talk, I introduce the solution to classic variational problems with subsidiary conditions by using the Lagrangian approach. The subject is presented with applicative perspectives to machine learning.
Talks
 LYRICS: a unified framework for learning and inference with constraints – IDA – Czech Technical University – Prague – January 2019
 Integrating deep learning and reasoning with First Order Fuzzy Logic – DTAI – KU Leuven – Leuven – September 2018
 Characterization of the Convex Łukasiewicz Fragment for Learning from Constraints, AAAI2018, New Orleans, USA, January 2018
 Learning Łukasiewicz Logic Fragments by Quadratic Programming, ECMLPKDD2017, Skopje, Macedonia, September 2017
 Learning from Logical Constraints by Quadratic Optimization, Fondazione Bruno Kessler FBK, Trento, June 2017
 Learning from constraints, Academy of Sciences of Czech Republic, Prague June 2012
 Learning from constraints, WU, Wien, June 2012
 Learning from constraints, KAIST, Seoul, February 2012
 Support Constraints machines, SIMBAD2011, September 2011
 Support constraint machines, Boston Neuro Talks MIT, September 2011
 Support constraint machines, in “Collective Learning and Inference in Structured Data”, invited talk, ECML2011, Athens, September 2011
 Learning from constraints (keynote speech) ECML2011, Athens, September 2011
 Learning from constraints, Naple, June 2011
 Natural laws of stagebased learning in humans and machines, Naturalization of mind, Siena, May 2011
 Knowledgebased parsimonious agents, Mind Force, Siena October 2010
 On the puzzle of inductiondeduction: Bridging perception and symbolic reasoning, Katholieke Universiteit Leuven, May 2010
 On the puzzle of inductiondeduction: Bridging perception and symbolic reasoning, Technical Univ. of Auckland, New Zealand, February 2010
 On the puzzle of inductiondeduction: Bridging perception and symbolic reasoning, Univ. of Waikato, New Zealand, February 2010
 On the puzzle of inductiondeduction: Bridging perception and symbolic reasoning, Monash Univ., Melbourne, February 2010
 On the puzzle of inductiondeduction: Bridging perception and symbolic reasoning, Trento, December 2009
 Semanticbased regularization: insights into deep learning (b), Erice, December 2009
 Semanticbased regularization: insights into deep learning (a), Erice, December 2009
 On the puzzle of inductiondeduction, Erice, December 2009
 Semanticbased regularization and Piaget’s cognitive stages, FIRB Intelligent Technologies for Cultural Visits and Mobile Education,Trento, September 2009
 Semanticbased regularization: insights into deep learning, Ulm, 13 July 2009
 On the birth of cognitive stages: Beyond sensimotor based agents in machine learning, Certosa di Pontignano, RutgersJoint Workshop on Mind and Culture, Certosa di Pontignano, Siena, June 2009
 Semanticbased regularization: learning from rules and examples, Modena, April 2009
 Semanticbased regularization, Genova, February 2009
 University of Florence, January 2009
 Semanticbased regularization, UPMC, Paris, December 2008
 Diffusion learning by prior and acquired links, keynote speech, Varna, September 2008
Publications
 Marra, G., Giannini, F., Diligenti, M., Maggini, M., & Gori, M. (2019). Learning and TNorms Theory. arXiv preprint arXiv:1907.11468. (submitted to TNNLS)
 Giannini, F., Marra, G., Diligenti, M., Maggini, M., & Gori, M. (2019). On the relation between Loss Functions and TNorms. arXiv preprint arXiv:1907.07904. (to appear in ILP 2019)
 Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2019). LYRICS: a General Interface Layer to Integrate Logic and Deep Learning. arXiv preprint arXiv:1903.07534. (to appear in ECML 2019)
 Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2019). Integrating Learning and Reasoning with Deep Logic Models. arXiv preprint arXiv:1901.04195. (to appear in ECML 2019)

Teso, S., Masera, L., Diligenti, M., & Passerini, A. (2019). Combining learning and constraints for genomewide protein annotation. BMC bioinformatics, 20(1), 338.

Graziani, L., Melacci, S., & Gori, M. (2019). Coherence constraints in facial expression recognition. Intelligenza Artificiale, 13(1), 7992.
 Giannini, F., Diligenti, M., Gori, M., & Maggini, M. (2018). On a convex logic fragment for learning and reasoning. IEEE Transactions on Fuzzy Systems.
 Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2018). ConstraintBased Visual Generation. arXiv preprint arXiv:1807.09202. (to appear in ICANN 2019)

Graziani, L., Melacci, S., & Gori, M. (2018, November). The Role of Coherence in Facial Expression Recognition. In International Conference of the Italian Association for Artificial Intelligence (pp. 320333). Springer, Cham.

Zugarini, A., Morvan, J., Melacci, S., Knerr, S., & Gori, M. (2018, September). Combining deep learning and symbolic processing for extracting knowledge from raw text. In IAPR Workshop on Artificial Neural Networks in Pattern Recognition (pp. 90101). Springer, Cham.

Roychowdhury, S., Diligenti, M., & Gori, M. (2018, June). Image Classification Using Deep Learning and Prior Knowledge. In Workshops at the ThirtySecond AAAI Conference on Artificial Intelligence.
 Giannini, F., Diligenti, M., Gori, M., & Maggini, M. (2018, April). Characterization of the Convex Łukasiewicz Fragment for Learning From Constraints. In ThirtySecond AAAI Conference on Artificial Intelligence.
 Giannini, F., Diligenti, M., Gori, M., & Maggini, M. (2017, September). Learning Łukasiewicz Logic Fragments by Quadratic Programming. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 410426). Springer, Cham.

Diligenti, M., Roychowdhury, S., & Gori, M. (2017, December). Integrating prior knowledge into deep learning. In 2017 16th IEEE International Conference on Machine Learning and Applications (ICMLA) (pp. 920923). IEEE.

Rossi, A., Montefoschi, F., Rizzo, A., Diligenti, M., & Festucci, C. (2017, October). Autoassociative recurrent neural networks and long term dependencies in novelty detection for audio surveillance applications. In IOP Conference Series: Materials Science and Engineering (Vol. 261, No. 1, p. 012009). IOP Publishing.
 Marco Gori, Marco Maggini, and Alessandro Rossi, The Principle of Cognitive Action: Experimental Analysis,” Technical Report, University of Siena, 2017

Diligenti, M., Gori, M., & Sacca, C. (2017). Semanticbased regularization for learning and inference. Artificial Intelligence, 244, 143165.

Diligenti, M., Gori, M., & Scoca, V. (2016, September). Learning efficiently in semantic based regularization. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 3346). Springer, Cham.

Diligenti, M., Gori, M., & Saccà, C. (2016). Learning in VariableDimensional Spaces. IEEE transactions on neural networks and learning systems, 27(6), 13221332.
 Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti: ” Foundations of Support Constraint Machines “. Neural Computation (MIT Press), 2015
 Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti: ” Learning as Constraint Reactions “. In KoprinkovaHristova, Petia and Mladenov, Valeri and Kasabov, Nikola (eds.): Artificial Neural Networks – Methods and Applications in Bio and Neuroinformatics, Springer Series in BioNeuroinformatics, Volume 4, 245270 (2015) DOI: 10.1007/9783319099033_12

Saccà, C., Diligenti, M., & Gori, M. (2014). Experimental Guidelines for SemanticBased Regularization. In Recent Advances of Neural Network Models and Applications (pp. 1523). Springer, Cham.

Sacca, C., Teso, S., Diligenti, M., & Passerini, A. (2014). Improved multilevel protein–protein interaction prediction with semanticbased regularization. BMC bioinformatics, 15(1), 103.
 Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti: ” Learning with Mixed Hard/Soft Pointwise Constraints “. IEEE Transactions on Neural Networks and Learning Systems, to appear (2014)
 Giorgio Gnecco, Marco Gori, Stefano Melacci, and Marcello Sanguineti, “ A theoretical framework for supervised learning from regions ”, Neurocomputing (129): 2532, 2014
 Giorgio Gnecco, Marco Gori, and Marcello Sanguineti, “ Learning with boundary conditions “, Neural Computation (25): 10291106, 2013
 Stefano Melacci, Marco Gori: ” Learning with Box Kernels “. IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 35, Issue 11, 26802692 (2013)
 Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti, ” Learning with hard constraints “, In Proceedings of the 23rd International Conference on Artificial Neural Networks (ICANN), Lecture Notes in Computer Science, LNCS 8131, Springer Berlin Heidel berg (2013), 146–153
 S. Frandina, M. Gori, M. Lippi, M. Maggini, S. Melacci ” Inference, Learning, and Laws of Nature “, Ninth International Workshop on NeuralSymbolic Learning and Reasoning at IJCAI 2013.
 Frandina, Salvatore, et al. ” Variational foundations of online backpropagation “, Artificial Neural Networks and Machine Learning–ICANN 2013. Springer Berlin Heidelberg, 2013. 8289.
 S. Frandina, M. Gori, M. Lippi, M. Maggini, S. Melacci ” On–Line Laplacian One–Class Support Vector Machines “, Artificial Neural Networks and Machine Learning–ICANN 2013. Springer Berlin Heidelberg, 2013. 186193.
 Claudio Saccà, Michelangelo Diligenti, Marco Gori, “ Graph and Manifold CoRegularization “, In Proceedings of the 12th International Conference on Machine Learning Applications (ICMLA 2013)
 Claudio Saccà, Michelangelo Diligenti, Marco Gori, ” Collective Classification using Semantic Based Regularization “, In Proceedings of the 12th International Conference on Machine Learning Applications (ICMLA 2013)
 Marco Gori, Stefano Melacci, ” Constraint Verification with Kernel Machines “, IEEE Trans. on Neural Networks and Learning Systems (24): 825831, 2013
 Claudio Saccà, Salvatore Frandina, Michelangelo Diligenti, Marco Gori, “ Constraintbased Learning for Text Categorization “, CoCoMile Workshop (ECAI), 2012
 Stefano Melacci, Marco Gori, “ Unsupervised Learning by Minimal Entropy Encoding “, IEEE Trans. on Neural Networks and Learning Systems (12): 18491861, 2012
 Michelangelo Diligenti, Marco Gori, Marco Maggini, “Learning to Tag Text from Rules and Examples” , In Proceedings of AI*IA 2011, Palermo, Italy, September 1518, 2011
 Claudio Saccà, Michelangelo Diligenti, Marco Gori, Marco Maggini, “Learning to Tag from Logic Constraints in Hyperlinked Environments” , Proceedings of the 10th International Conference on Machine Leraning Applications (ICMLA 2011) Honululu, USA, 2011
 Claudio Saccà, Michelangelo Diligenti, Marco Gori, Marco Maggini, “ Integrating Logic Knowledge into Graph Regularization: an application to image tagging ”, In Proceedings of the 9^{th} Workshop on Mining and Learning with Graphs (MLG 2011), San Diego, CA (USA), August 2021, 2011
 Michelangelo Diligenti, Marco Gori, Marco Maggini, Leonardo Rigutini, “ Bridging Logic and Kernel Machines”, Machine Learning , DOI: 10.1007/s109940115243x, (online First), May 2011
 Stefano Melacci, Marco Gori, “Kernel Methods for Minimum Entropy Encoding” , In Proceedings of the 10th International Conference on Machine Leraning Applications (ICMLA 2011), Honululu, USA, 2011
 Marco Gori, Stefano Melacci, “Support Constraint Machines” , In Proceedings of the 18th International Conference on Neural Information Processing (ICONIP 2011), Shanghai, China, November 1317, 2011.
 Stefano Melacci, Marco Gori, “Learning with Box Kernels” , In Proceedings of the 18th International Conference on Neural Information Processing (ICONIP 2011), Shanghai, China, November 1317, 2011.
 Stefano Melacci, Marco Gori, “SemiSupervised Multiclass Kernel Machines with Probabilistic Constraints“, In Proceedings of the 12th International Conference on Advances in Artificial Intelligence (AI*IA 2011), September 2011.
 Marco Gori, Stefano Melacci, ” Learning with convex constraints “, In Proceedings of the 19th International Conference on Artificial Neural Networks (ICANN 2010), September 2010.
 Michelangelo Diligenti, Marco Gori, Marco Maggini, Leonardo Rigutini, ” Multitask Kernelbased Learning with Logic Constraints “, In Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010), August 2010.
 Michelangelo Diligenti, Marco Gori, Marco Maggini, Leonardo Rigutini, “Multitask Kernelbased Learning with FirstOrder Logic Constraints“, In Proceedings of the 20th International Conference on Inductive Logic Programming (ILP 2010) , June 2010.
 Stefano Melacci, Marco Maggini, Marco Gori,” Semi–supervised learning with constraints for multi–view object recognition “, In Proceedings of the 18th International Conference on Artificial Neural Networks (ICANN 2009), September 2009.
 Marco Gori, ” Semanticbased regularization and Piaget’s cognitive stages “, Neural Networks, vol. 22, no 7, September 2009, pp. 10351039.