As machine learning systems are increasingly deployed in settings where correctness, safety, and alignment with domain-specific requirements are critical, ensuring that models satisfy formal properties has become a central challenge. Two main paradigms have emerged to address this problem: a priori design, where logical or structural requirements are integrated directly into the model’s architecture or training process, and a posteriori verification, where trained models are analyzed to determine whether they satisfy desired properties. In this position paper, I argue that these approaches are not competing, but rather complementary. Wherever possible, requirements should be enforced by design, ensuring correctness by construction and reducing the verification burden. Recent advances—–ranging from differentiable requirements-aware layers and loss functions to full neurosymbolic models—–demonstrate the feasibility and benefits of this approach. However, not all requirements are easily expressible in a differentiable or learnable form, and in such cases, verification remains essential for certifying model behavior post hoc. This is particularly relevant for complex global properties, interactions between components, or constraints introduced after training. This paper provides an overview over the progress made on both fronts, while identifying practical trade-offs in expressivity, scalability, and trustworthiness. It is also a call for a unified research agenda that treats verification and design as interdependent tools in the development of reliable learning systems. The position provided in the paper is clear: whatever can be enforced by design, should be—while verification should serve as a safety net where design falls short.

Synthetic tabular data generation has traditionally been a challenging problem due to the high complexity of the underlying distributions that characterise this type of data. Despite recent advances in deep generative models (DGMs), existing methods often fail to produce realistic datapoints that are well-aligned with available background knowledge. In this paper, we address this limitation by introducing Disjunctive Refinement Layer (DRL), a novel layer designed to enforce the alignment of generated data with the background knowledge specified in user-defined constraints. DRL is the first method able to automatically make deep learning models inherently compliant with constraints as expressive as quantifier-free linear formulas, which can define non-convex and even disconnected spaces. Our experimental analysis shows that DRL not only guarantees constraint satisfaction but also improves efficacy in downstream tasks. Notably, when applied to DGMs that frequently violate constraints, DRL eliminates violations entirely. Further, it improves performance metrics by up to 21.4\% in F1-score and 20.9\% in Area Under the ROC Curve, thus demonstrating its practical impact on data generation.

Neurosymbolic AI is growing in popularity thanks to its ability to combine neural perception and symbolic reasoning in end-to-end trainable models. However, recent findings reveal these are prone to shortcut reasoning, i.e., to learning unindented concepts--or neural predicates--which exploit spurious correlations to satisfy the symbolic constraints. In this paper, we address reasoning shortcuts at their root cause and we introduce Prototypical Neurosymbolic architectures. These models are able to satisfy the symbolic constraints (be right) because they have learnt the correct basic concepts (for the right reasons) and not because of spurious correlations, even in extremely low data regimes. Leveraging the theory of prototypical learning, we demonstrate that we can effectively avoid reasoning shortcuts by training the models to satisfy the background knowledge while taking into account the similarity of the input with respect to the handful of labelled datapoints. We extensively validate our approach on the recently proposed rsbench benchmark suite in a variety of settings and tasks with very scarce supervision: we show significant improvements in learning the right concepts both in synthetic tasks (MNIST-EvenOdd and Kand-Logic) and real-world, high-stake ones (BDD-OIA). Our findings pave the way to prototype grounding as an effective, annotation-efficient strategy for safe and reliable neurosymbolic learning.

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding 95% non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to 4.5% improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.

For their outstanding ability of finding hidden patterns in data, deep learning models have been extensively applied in many different domains. However, recent works have shown that, if a set of requirements expressing inherent knowledge about the problem at hand is given, then neural networks often fail to comply with them. This represents a major drawback for deep learning models, as requirements compliance is normally considered a necessary condition for standard software deployment. In this paper, we propose a novel neuro-symbolic framework able to make any neural network compliant by design to a given set of requirements over the output space expressed in full propositional logic. This framework, called CCN+, integrates the requirements into the output layer of the neural network by applying multiple inference rules that ensure compliance with the requirements and adapts the standard binary cross-entropy loss function to the requirement output layer. As a result, not only the outputted predictions are guaranteed to be compliant with the requirements, but the neural network itself learns how to exploit the domain knowledge expressed by the requirements to get better performance. We conduct an extensive experimental evaluation of CCN+ on 19 real-world multi-label classification datasets with propositional logic requirements, including a challenging dataset for autonomous driving. Our experimental analysis confirms that CCN+ is able to outperform both its neural counterparts and the state-of-the-art models.

Abstract Neural networks have proven to be very powerful at computer vision tasks. However, they often exhibit unexpected behaviors, acting against background knowledge about the problem at hand. This calls for models (i) able to learn from requirements expressing such background knowledge, and (ii) guaranteed to be compliant with the requirements themselves. Unfortunately, the development of such models is hampered by the lack of real-world datasets equipped with formally specified requirements. In this paper, we introduce the ROad event Awareness Dataset with logical Requirements (ROAD-R), the first publicly available dataset for autonomous driving with requirements expressed as logical constraints. Given ROAD-R, we show that current state-of-the-art models often violate its logical constraints, and that it is possible to exploit them to create models that (i) have a better performance, and (ii) are guaranteed to be compliant with the requirements themselves.

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be compliant with the background knowledge itself, e.g., for safety-critical applications. In this survey, we retrace such works and categorize them based on (i) the logical language that they use to express the background knowledge and (ii) the goals that they achieve.

Visual question answering (VQA) is a challenging problem in machine perception, which requires a deep joint understanding of both visual and textual data. Recent research has advanced the automatic generation of high-quality scene graphs from images, while powerful yet elegant models like graph neural networks (GNNs) have shown great power in reasoning over graph-structured data. In this work, we propose to bridge the gap between scene graph generation and VQA by leveraging GNNs. In particular, we design a new model called Conditional Enhanced Graph ATtention network (CE-GAT) to encode pairs of visual and semantic scene graphs with both node and edge features, which is seamlessly integrated with a textual question encoder to generate answers through question-graph conditioning. Moreover, to alleviate the training difficulties of CE-GAT towards VQA, we enforce more useful inductive biases in the scene graphs through novel question-guided graph enriching and pruning. Finally, we evaluate the framework on one of the largest available VQA datasets (namely, GQA) with ground-truth scene graphs, achieving the accuracy of 77.87%, compared with the state of the art (namely, the neural state machine (NSM)), which gives 63.17%. Notably, by leveraging existing scene graphs, our framework is much lighter compared with end-to-end VQA methods (e.g., about 95.3% less parameters than a typical NSM).

Multi-label classification (MC) is a standard machine learning problem in which a data point can be associated with a set of classes. A more challenging scenario is given by hierarchical multi-label classification (HMC) problems, in which every prediction must satisfy a given set of hard constraints expressing subclass relationships between classes. In this article, we propose C-HMCNN(h), a novel approach for solving HMC problems, which, given a network h for the underlying MC problem, exploits the hierarchy information in order to produce predictions coherent with the constraints and to improve performance. Furthermore, we extend the logic used to express HMC constraints in order to be able to specify more complex relations among the classes and propose a new model CCN(h), which extends C-HMCNN(h) and is again able to satisfy and exploit the constraints to improve performance. We conduct an extensive experimental analysis showing the superior performance of both C-HMCNN(h) and CCN(h) when compared to state-of-the-art models in both the HMC and the general MC setting with hard logical constraints.

Nearly all existing techniques for automated video annotation (or captioning) describe videos using natural language sentences. However, this has several shortcomings: (i) it is very hard to then further use the generated natural language annotations in automated data processing, (ii) generating natural language annotations requires solving the hard subtask of generating semantically precise and syntactically correct natural language sentences, which is actually unrelated to the task of video annotation, (iii) it is difficult to quantitatively measure performance, as standard metrics (e.g., accuracy and F1-score) are inapplicable, and (iv) annotations are language-specific. In this paper, we propose the new task of knowledge graph extraction from videos, i.e., producing a description in the form of a knowledge graph of the contents of a given video. Since no datasets exist for this task, we also include a method to automatically generate them, starting from datasets where videos are annotated with natural language. We then describe an initial deep-learning model for knowledge graph extraction from videos, and report results on MSVD* and MSR-VTT*, two datasets obtained from MSVD and MSR-VTT using our method.

Hierarchical multi-label classification (HMC) is a challenging classification task extending standard multi-label classification problems by imposing a hierarchy constraint on the classes. In this paper, we propose C-HMCNN(h), a novel approach for HMC problems, which, given a network h for the underlying multi-label classification problem, exploits the hierarchy information in order to produce predictions coherent with the constraint and improve performance. We conduct an extensive experimental analysis showing the superior performance of C-HMCNN(h) when compared to state-of-the-art models.

Behavior Trees (BTs) are gaining acceptance in robotics to specify action policies at the deliberative level. Their advantages include modularity, ease of use and increasing tool support. In this paper, we define Conditional Behavior Trees (CBTs) as an extension of BTs wherein actions are decorated considering pre- and post-conditions. CBTs improve on basic BTs in that they enable monitoring the execution of single actions by checking pre- and post-conditions, respectively. Since there might exist action sequences wherein some preconditions are violated, CBT executability may depend on the success/failure of specific actions. We developed an encoding of CBT executability into satisfiability of propositional formulas to be checked off-line in a publicly-available tool that computes the encoding for generic CBTs. For the kind of application scenarios and related behavior specifications that we consider, we show that our approach is effective and yields formal guarantees about the executability of deliberative policies designed as CBTs.