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Francesco Giannini

Publications and source records attributed to Francesco Giannini.

34 records · Page 2Linked to original sources
arXiv2023

Interpretable Neural-Symbolic Concept Reasoning

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

cs.AI↗
arXiv2023

Interpretable Graph Networks Formulate Universal Algebra Conjectures

The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the foundations of modern mathematics -- is still completely unexplored. This work proposes the first use of AI to investigate UA's conjectures with an equivalent equational and topological characterization. While topological representations would enable the analysis of such properties using graph neural networks, the limited transparency and brittle explainability of these models hinder their straightforward use to empirically validate existing conjectures or to formulate new ones. To bridge these gaps, we propose a general algorithm generating AI-ready datasets based on UA's conjectures, and introduce a novel neural layer to build fully interpretable graph networks. The results of our experiments demonstrate that interpretable graph networks: (i) enhance interpretability without sacrificing task accuracy, (ii) strongly generalize when predicting universal algebra's properties, (iii) generate simple explanations that empirically validate existing conjectures, and (iv) identify subgraphs suggesting the formulation of novel conjectures.

cs.LG↗
arXiv2023

Enhancing Embedding Representations of Biomedical Data using Logic Knowledge

Knowledge Graph Embeddings (KGE) have become a quite popular class of models specifically devised to deal with ontologies and graph structure data, as they can implicitly encode statistical dependencies between entities and relations in a latent space. KGE techniques are particularly effective for the biomedical domain, where it is quite common to deal with large knowledge graphs underlying complex interactions between biological and chemical objects. Recently in the literature, the PharmKG dataset has been proposed as one of the most challenging knowledge graph biomedical benchmark, with hundreds of thousands of relational facts between genes, diseases and chemicals. Despite KGEs can scale to very large relational domains, they generally fail at representing more complex relational dependencies between facts, like logic rules, which may be fundamental in complex experimental settings. In this paper, we exploit logic rules to enhance the embedding representations of KGEs on the PharmKG dataset. To this end, we adopt Relational Reasoning Network (R2N), a recently proposed neural-symbolic approach showing promising results on knowledge graph completion tasks. An R2N uses the available logic rules to build a neural architecture that reasons over KGE latent representations. In the experiments, we show that our approach is able to significantly improve the current state-of-the-art on the PharmKG dataset. Finally, we provide an ablation study to experimentally compare the effect of alternative sets of rules according to different selection criteria and varying the number of considered rules.

cs.AI↗
arXiv2023

T-Norms Driven Loss Functions for Machine Learning

Neural-symbolic approaches have recently gained popularity to inject prior knowledge into a learner without requiring it to induce this knowledge from data. These approaches can potentially learn competitive solutions with a significant reduction of the amount of supervised data. A large class of neural-symbolic approaches is based on First-Order Logic to represent prior knowledge, relaxed to a differentiable form using fuzzy logic. This paper shows that the loss function expressing these neural-symbolic learning tasks can be unambiguously determined given the selection of a t-norm generator. When restricted to supervised learning, the presented theoretical apparatus provides a clean justification to the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures. However, the proposed learning formulation extends the advantages of the cross-entropy loss to the general knowledge that can be represented by a neural-symbolic method. Therefore, the methodology allows the development of a novel class of loss functions, which are shown in the experimental results to lead to faster convergence rates than the approaches previously proposed in the literature.

cs.AI↗
arXiv2023

Extending Logic Explained Networks to Text Classification

Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly favour the generation of global explanations, while local ones tend to be noisy and verbose. For these reasons, we propose LENp, improving local explanations by perturbing input words, and we test it on text classification. Our results show that (i) LENp provides better local explanations than LIME in terms of sensitivity and faithfulness, and (ii) logic explanations are more useful and user-friendly than feature scoring provided by LIME as attested by a human survey.

cs.CL↗
arXiv2022

Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off

Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an intermediate level of human-like concepts. This enables human interventions which can correct mispredicted concepts to improve the model's performance. However, existing concept bottleneck models are unable to find optimal compromises between high task accuracy, robust concept-based explanations, and effective interventions on concepts -- particularly in real-world conditions where complete and accurate concept supervisions are scarce. To address this, we propose Concept Embedding Models, a novel family of concept bottleneck models which goes beyond the current accuracy-vs-interpretability trade-off by learning interpretable high-dimensional concept representations. Our experiments demonstrate that Concept Embedding Models (1) attain better or competitive task accuracy w.r.t. standard neural models without concepts, (2) provide concept representations capturing meaningful semantics including and beyond their ground truth labels, (3) support test-time concept interventions whose effect in test accuracy surpasses that in standard concept bottleneck models, and (4) scale to real-world conditions where complete concept supervisions are scarce.

cs.LG↗
arXiv2022

Entropy-based Logic Explanations of Neural Networks

Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage human-understandable symbols (i.e. concepts) to predict class memberships. However, most of these approaches focus on the identification of the most relevant concepts but do not provide concise, formal explanations of how such concepts are leveraged by the classifier to make predictions. In this paper, we propose a novel end-to-end differentiable approach enabling the extraction of logic explanations from neural networks using the formalism of First-Order Logic. The method relies on an entropy-based criterion which automatically identifies the most relevant concepts. We consider four different case studies to demonstrate that: (i) this entropy-based criterion enables the distillation of concise logic explanations in safety-critical domains from clinical data to computer vision; (ii) the proposed approach outperforms state-of-the-art white-box models in terms of classification accuracy and matches black box performances.

cs.AI↗
arXiv2021

Logic Explained Networks

The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations in which the machine is expected to support the decision of human experts, providing a comprehensible explanation is a feature of crucial importance. The language used to communicate the explanations must be formal enough to be implementable in a machine and friendly enough to be understandable by a wide audience. In this paper, we propose a general approach to Explainable Artificial Intelligence in the case of neural architectures, showing how a mindful design of the networks leads to a family of interpretable deep learning models called Logic Explained Networks (LENs). LENs only require their inputs to be human-understandable predicates, and they provide explanations in terms of simple First-Order Logic (FOL) formulas involving such predicates. LENs are general enough to cover a large number of scenarios. Amongst them, we consider the case in which LENs are directly used as special classifiers with the capability of being explainable, or when they act as additional networks with the role of creating the conditions for making a black-box classifier explainable by FOL formulas. Despite supervised learning problems are mostly emphasized, we also show that LENs can learn and provide explanations in unsupervised learning settings. Experimental results on several datasets and tasks show that LENs may yield better classifications than established white-box models, such as decision trees and Bayesian rule lists, while providing more compact and meaningful explanations.

cs.LG↗
arXiv2020

Relational Neural Machines

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these reasons, combining deep architectures and probabilistic logic reasoning is a fundamental goal towards the development of intelligent agents operating in complex environments. This paper presents Relational Neural Machines, a novel framework allowing to jointly train the parameters of the learners and of a First--Order Logic based reasoner. A Relational Neural Machine is able to recover both classical learning from supervised data in case of pure sub-symbolic learning, and Markov Logic Networks in case of pure symbolic reasoning, while allowing to jointly train and perform inference in hybrid learning tasks. Proper algorithmic solutions are devised to make learning and inference tractable in large-scale problems. The experiments show promising results in different relational tasks.

cs.AI↗
arXiv2019

Conditions for Unnecessary Logical Constraints in Kernel Machines

A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors. In a similar way, in the general scheme of learning from constraints, where possibly several constraints are considered, some of them may turn out to be unnecessary with respect to the learning optimization, even if they are active for a given optimal solution. In this paper we extend the definition of support vector to support constraint and we provide some criteria to determine which constraints can be removed from the learning problem still yielding the same optimal solutions. In particular, we discuss the case of logical constraints expressed by Lukasiewicz logic, where both inferential and algebraic arguments can be considered. Some theoretical results that characterize the concept of unnecessary constraint are proved and explained by means of examples.

cs.LO↗
arXiv2019

Constraint-Based Visual Generation

In the last few years the systematic adoption of deep learning to visual generation has produced impressive results that, amongst others, definitely benefit from the massive exploration of convolutional architectures. In this paper, we propose a general approach to visual generation that combines learning capabilities with logic descriptions of the target to be generated. The process of generation is regarded as a constrained satisfaction problem, where the constraints describe a set of properties that characterize the target. Interestingly, the constraints can also involve logic variables, while all of them are converted into real-valued functions by means of the t-norm theory. We use deep architectures to model the involved variables, and propose a computational scheme where the learning process carries out a satisfaction of the constraints. We propose some examples in which the theory can naturally be used, including the modeling of GAN and auto-encoders, and report promising results in problems with the generation of handwritten characters and face transformations.

cs.LG↗
arXiv2019

LYRICS: a General Interface Layer to Integrate Logic Inference and Deep Learning

In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a clear need for the definition of a general and tight integration between low-level tasks, processing sensorial data that can be effectively elaborated using deep learning techniques, and the logic reasoning that allows humans to take decisions in complex environments. This paper presents LYRICS, a generic interface layer for AI, which is implemented in TersorFlow (TF). LYRICS provides an input language that allows to define arbitrary First Order Logic (FOL) background knowledge. The predicates and functions of the FOL knowledge can be bound to any TF computational graph, and the formulas are converted into a set of real-valued constraints, which participate to the overall optimization problem. This allows to learn the weights of the learners, under the constraints imposed by the prior knowledge. The framework is extremely general as it imposes no restrictions in terms of which models or knowledge can be integrated. In this paper, we show the generality of the approach showing some use cases of the presented language, including model checking, supervised learning and collective classification.

cs.LG↗
arXiv2019

On the relation between Loss Functions and T-Norms

Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures. While the cross-entropy loss is usually justified from a probabilistic perspective, this paper shows an alternative and more direct interpretation of this loss in terms of t-norms and their associated generator functions, and derives a general relation between loss functions and t-norms. In particular, the presented work shows intriguing results leading to the development of a novel class of loss functions. These losses can be exploited in any supervised learning task and which could lead to faster convergence rates that the commonly employed cross-entropy loss.

cs.LG↗
arXiv2019

Integrating Learning and Reasoning with Deep Logic Models

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learning and logic reasoning is still an open-research problem and it is considered to be the key for the development of real intelligent agents. This paper presents Deep Logic Models, which are deep graphical models integrating deep learning and logic reasoning both for learning and inference. Deep Logic Models create an end-to-end differentiable architecture, where deep learners are embedded into a network implementing a continuous relaxation of the logic knowledge. The learning process allows to jointly learn the weights of the deep learners and the meta-parameters controlling the high-level reasoning. The experimental results show that the proposed methodology overtakes the limitations of the other approaches that have been proposed to bridge deep learning and reasoning.

cs.LG↗
arXiv2018

On a Convex Logic Fragment for Learning and Reasoning

In this paper we introduce the convex fragment of Łukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any learning framework involving logical constraints. The method is of particular interest since the fragment guarantees to deal with convex constraints, which are shown to be equivalent to a set of linear constraints. Within this framework, we are able to formulate learning with kernel machines as well as collective classification as a quadratic programming problem.

cs.LO↗