Neural Interpretable Reasoning

We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of variables of the system, we show that this complexity can be mitigated by treating interpretability as a Markovian property and employing neural re-parametrization techniques. Building on these insights, we propose a new modeling paradigm -- neural generation and interpretable execution -- that enables scalable verification of equivariance. This paradigm provides a general approach for designing Neural Interpretable Reasoners that are not only expressive but also transparent.

Interpretable Concept-Based Memory Reasoning

The lack of transparency in the decision-making processes of deep learning systems presents a significant challenge in modern artificial intelligence (AI), as it impairs users' ability to rely on and verify these systems. To address this challenge, Concept Bottleneck Models (CBMs) have made significant progress by incorporating human-interpretable concepts into deep learning architectures. This approach allows predictions to be traced back to specific concept patterns that users can understand and potentially intervene on. However, existing CBMs' task predictors are not fully interpretable, preventing a thorough analysis and any form of formal verification of their decision-making process prior to deployment, thereby raising significant reliability concerns. To bridge this gap, we introduce Concept-based Memory Reasoner (CMR), a novel CBM designed to provide a human-understandable and provably-verifiable task prediction process. Our approach is to model each task prediction as a neural selection mechanism over a memory of learnable logic rules, followed by a symbolic evaluation of the selected rule. The presence of an explicit memory and the symbolic evaluation allow domain experts to inspect and formally verify the validity of certain global properties of interest for the task prediction process. Experimental results demonstrate that CMR achieves comparable accuracy-interpretability trade-offs to state-of-the-art CBMs, discovers logic rules consistent with ground truths, allows for rule interventions, and allows pre-deployment verification.

Explainable Malware Detection with Tailored Logic Explained Networks

Malware detection is a constant challenge in cybersecurity due to the rapid development of new attack techniques. Traditional signature-based approaches struggle to keep pace with the sheer volume of malware samples. Machine learning offers a promising solution, but faces issues of generalization to unseen samples and a lack of explanation for the instances identified as malware. However, human-understandable explanations are especially important in security-critical fields, where understanding model decisions is crucial for trust and legal compliance. While deep learning models excel at malware detection, their black-box nature hinders explainability. Conversely, interpretable models often fall short in performance. To bridge this gap in this application domain, we propose the use of Logic Explained Networks (LENs), which are a recently proposed class of interpretable neural networks providing explanations in the form of First-Order Logic (FOL) rules. This paper extends the application of LENs to the complex domain of malware detection, specifically using the large-scale EMBER dataset. In the experimental results we show that LENs achieve robustness that exceeds traditional interpretable methods and that are rivaling black-box models. Moreover, we introduce a tailored version of LENs that is shown to generate logic explanations with higher fidelity with respect to the model's predictions.

Multitask Kernel-based Learning with Logic Constraints

This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which the learner operates, that is exploited by the learning algorithm together with the information available in the supervised examples. In particular, we consider a multi-task learning scheme, where multiple unary predicates on the feature space are to be learned by kernel machines and a higher level abstract representation consists of logic clauses on these predicates, known to hold for any input. A general approach is presented to convert the logic clauses into a continuous implementation, that processes the outputs computed by the kernel-based predicates. The learning task is formulated as a primal optimization problem of a loss function that combines a term measuring the fitting of the supervised examples, a regularization term, and a penalty term that enforces the constraints on both supervised and unsupervised examples. The proposed semi-supervised learning framework is particularly suited for learning in high dimensionality feature spaces, where the supervised training examples tend to be sparse and generalization difficult. Unlike for standard kernel machines, the cost function to optimize is not generally guaranteed to be convex. However, the experimental results show that it is still possible to find good solutions using a two stage learning schema, in which first the supervised examples are learned until convergence and then the logic constraints are forced. Some promising experimental results on artificial multi-task learning tasks are reported, showing how the classification accuracy can be effectively improved by exploiting the a priori rules and the unsupervised examples.

Multitask Kernel-based Learning with First-Order Logic Constraints

In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task learning scheme where multiple predicates defined on a set of objects are to be jointly learned from examples, enforcing a set of FOL constraints on the admissible configurations of their values. The predicates are defined on the feature spaces, in which the input objects are represented, and can be either known a priori or approximated by an appropriate kernel-based learner. A general approach is presented to convert the FOL clauses into a continuous implementation that can deal with the outputs computed by the kernel-based predicates. The learning problem is formulated as a semi-supervised task that requires the optimization in the primal of a loss function that combines a fitting loss measure on the supervised examples, a regularization term, and a penalty term that enforces the constraints on both the supervised and unsupervised examples. Unfortunately, the penalty term is not convex and it can hinder the optimization process. However, it is possible to avoid poor solutions by using a two stage learning schema, in which the supervised examples are learned first and then the constraints are enforced.

Relational Concept Based Models

The design of interpretable deep learning models working in relational domains poses an open challenge: interpretable deep learning methods, such as Concept-Based Models (CBMs), are not designed to solve relational problems, while relational models are not as interpretable as CBMs. To address this problem, we propose Relational Concept-Based Models, a family of relational deep learning methods providing interpretable task predictions. Our experiments, ranging from image classification to link prediction in knowledge graphs, show that relational CBMs (i) match generalization performance of existing relational black-boxes (as opposed to non-relational CBMs), (ii) support the generation of quantified concept-based explanations, (iii) effectively respond to test-time interventions, and (iv) withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.

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.

Concept Embedding Models

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.

Learning Representations for Sub-Symbolic Reasoning

Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real world applications. This paper presents Relational Reasoning Networks (R2N), a novel end-to-end model that performs relational reasoning in the latent space of a deep learner architecture, where the representations of constants, ground atoms and their manipulations are learned in an integrated fashion. Unlike flat architectures like Knowledge Graph Embedders, which can only represent relations between entities, R2Ns define an additional computational structure, accounting for higher-level relations among the ground atoms. The considered relations can be explicitly known, like the ones defined by logic formulas, or defined as unconstrained correlations among groups of ground atoms. R2Ns can be applied to purely symbolic tasks or as a neuro-symbolic platform to integrate learning and reasoning in heterogeneous problems with both symbolic and feature-based represented entities. The proposed model bridges the gap between previous neuro-symbolic methods that have been either limited in terms of scalability or expressivity. The proposed methodology is shown to achieve state-of-the-art results in different experimental settings.

Discrete solution pools and noise-contrastive estimation for predict-and-optimize

Numerous real-life decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. There is a growing interest in decision-focused learning methods, where the loss function used for learning to predict the uncertain input uses the outcome of solving the combinatorial problem over a set of predictions. Different surrogate loss functions have been identified, often using a continuous approximation of the combinatorial problem. However, a key bottleneck is that to compute the loss, one has to solve the combinatorial optimisation problem for each training instance in each epoch, which is computationally expensive even in the case of continuous approximations. We propose a different solver-agnostic method for decision-focused learning, namely by considering a pool of feasible solutions as a discrete approximation of the full combinatorial problem. Solving is now trivial through a single pass over the solution pool. We design several variants of a noise-contrastive loss over the solution pool, which we substantiate theoretically and empirically. Furthermore, we show that by dynamically re-solving only a fraction of the training instances each epoch, our method performs on par with the state of the art, whilst drastically reducing the time spent solving, hence increasing the feasibility of predict-and-optimize for larger problems.