Alessandro Daniele

Alessandro Daniele, Emile van Krieken, Luciano Serafini et al.

Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is discarded after training, even if it is still useful at test time. Instead, we ensure neural network predictions satisfy the knowledge by refining the predictions with an extra computation step. We introduce differentiable refinement functions that find a corrected prediction close to the original prediction. We study how to effectively and efficiently compute these refinement functions. Using a new algorithm called Iterative Local Refinement (ILR), we combine refinement functions to find refined predictions for logical formulas of any complexity. ILR finds refinements on complex SAT formulas in significantly fewer iterations and frequently finds solutions where gradient descent can not. Finally, ILR produces competitive results in the MNIST addition task.

Alessandro Daniele, Tommaso Campari, Sagar Malhotra et al.

Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems rely on continuous relaxation of logical knowledge, and no discrete decisions are made within the model pipeline. Furthermore, these methods assume that the symbolic rules are given. In this paper, we propose Deep Symbolic Learning (DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a (set of) perception functions which map continuous data to discrete symbols, and a symbolic function over the set of symbols. DSL learns simultaneously the perception and symbolic functions while being trained only on their composition (NeSy-function). The key novelty of DSL is that it can create internal (interpretable) symbolic representations and map them to perception inputs within a differentiable NN learning pipeline. The created symbols are automatically selected to generate symbolic functions that best explain the data. We provide experimental analysis to substantiate the efficacy of DSL in simultaneously learning perception and symbolic functions.

Alessandro Daniele, Luciano Serafini

In the recent past, there has been a growing interest in Neural-Symbolic Integration frameworks, i.e., hybrid systems that integrate connectionist and symbolic approaches to obtain the best of both worlds. In this work we focus on a specific method, KENN (Knowledge Enhanced Neural Networks), a Neural-Symbolic architecture that injects prior logical knowledge into a neural network by adding on its top a residual layer that modifies the initial predictions accordingly to the knowledge. Among the advantages of this strategy, there is the inclusion of clause weights, learnable parameters that represent the strength of the clauses, meaning that the model can learn the impact of each rule on the final predictions. As a special case, if the training data contradicts a constraint, KENN learns to ignore it, making the system robust to the presence of wrong knowledge. In this paper, we propose an extension of KENN for relational data. One of the main advantages of KENN resides in its scalability, thanks to a flexible treatment of dependencies between the rules obtained by stacking multiple logical layers. We show experimentally the efficacy of this strategy. The results show that KENN is capable of increasing the performances of the underlying neural network, obtaining better or comparable accuracies in respect to other two related methods that combine learning with logic, requiring significantly less time for learning.

Alessandro Daniele, Tommaso Campari, Sagar Malhotra et al.

Deep Learning (DL) techniques have achieved remarkable successes in recent years. However, their ability to generalize and execute reasoning tasks remains a challenge. A potential solution to this issue is Neuro-Symbolic Integration (NeSy), where neural approaches are combined with symbolic reasoning. Most of these methods exploit a neural network to map perceptions to symbols and a logical reasoner to predict the output of the downstream task. These methods exhibit superior generalization capacity compared to fully neural architectures. However, they suffer from several issues, including slow convergence, learning difficulties with complex perception tasks, and convergence to local minima. This paper proposes a simple yet effective method to ameliorate these problems. The key idea involves pretraining a neural model on the downstream task. Then, a NeSy model is trained on the same task via transfer learning, where the weights of the perceptual part are injected from the pretrained network. The key observation of our work is that the neural network fails to generalize only at the level of the symbolic part while being perfectly capable of learning the mapping from perceptions to symbols. We have tested our training strategy on various SOTA NeSy methods and datasets, demonstrating consistent improvements in the aforementioned problems.

Alessandro Daniele, Emile van Krieken

Deep learning has achieved remarkable success across various domains, largely thanks to the efficiency of backpropagation (BP). However, BP's reliance on differentiability poses challenges in neurosymbolic learning, where discrete computation is combined with neural models. We show that applying BP to Godel logic, which represents conjunction and disjunction as min and max, is equivalent to a local search algorithm for SAT solving, enabling the optimisation of discrete Boolean formulas without sacrificing differentiability. However, deterministic local search algorithms get stuck in local optima. Therefore, we propose the Godel Trick, which adds noise to the model's logits to escape local optima. We evaluate the Godel Trick on SATLIB, and demonstrate its ability to solve a broad range of SAT problems. Additionally, we apply it to neurosymbolic models and achieve state-of-the-art performance on Visual Sudoku, all while avoiding expensive probabilistic reasoning. These results highlight the Godel Trick's potential as a robust, scalable approach for integrating symbolic reasoning with neural architectures.

Davide Bizzaro, Alessandro Daniele

Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of Goedel fuzzy logic and the recently developed Goedel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on the Visual Tic-Tac-Toe NeSy task, while producing interpretable decision rules.

Filippo Ziliotto, Jelin Raphael Akkara, Alessandro Daniele et al.

Recent advances in Embodied AI have enabled agents to perform increasingly complex tasks and adapt to diverse environments. However, deploying such agents in realistic human-centered scenarios, such as domestic households, remains challenging, particularly due to the difficulty of modeling individual human preferences and behaviors. In this work, we introduce PersONAL (PERSonalized Object Navigation And Localization, a comprehensive benchmark designed to study personalization in Embodied AI. Agents must identify, retrieve, and navigate to objects associated with specific users, responding to natural-language queries such as "find Lily's backpack". PersONAL comprises over 2,000 high-quality episodes across 30+ photorealistic homes from the HM3D dataset. Each episode includes a natural-language scene description with explicit associations between objects and their owners, requiring agents to reason over user-specific semantics. The benchmark supports two evaluation modes: (1) active navigation in unseen environments, and (2) object grounding in previously mapped scenes. Experiments with state-of-the-art baselines reveal a substantial gap to human performance, highlighting the need for embodied agents capable of perceiving, reasoning, and memorizing over personalized information; paving the way towards real-world assistive robot.

Riccardo Andreoni, Andrei Buliga, Alessandro Daniele et al.

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only existing approach relies on an explicit representation of a finite-state automaton corresponding to the temporal specification. Instead, we aim at proposing a neurosymbolic framework designed to incorporate temporal logic specifications, expressed in Linear Temporal Logic over finite traces (LTLf), directly into deep learning architectures for sequence-based tasks. We extend the Iterative Local Refinement (ILR) neurosymbolic algorithm, leveraging the recent introduction of fuzzy LTLf interpretations. We name this proposed method Temporal Iterative Local Refinement (T-ILR). We assess T-ILR on an existing benchmark for temporal neurosymbolic architectures, consisting of the classification of image sequences in the presence of temporal knowledge. The results demonstrate improved accuracy and computational efficiency compared to the state-of-the-art method.

Alessandro Daniele, Luciano Serafini

In the recent past, there has been a growing interest in Neural-Symbolic Integration frameworks, i.e., hybrid systems that integrate connectionist and symbolic approaches to obtain the best of both worlds. In a previous work, we proposed KENN (Knowledge Enhanced Neural Networks), a Neural-Symbolic architecture that injects prior logical knowledge into a neural network by adding a new final layer which modifies the initial predictions accordingly to the knowledge. Among the advantages of this strategy, there is the inclusion of clause weights, learnable parameters that represent the strength of the clauses, meaning that the model can learn the impact of each clause on the final predictions. As a special case, if the training data contradicts a constraint, KENN learns to ignore it, making the system robust to the presence of wrong knowledge. In this paper, we propose an extension of KENN for relational data. To evaluate this new extension, we tested it with different learning configurations on Citeseer, a standard dataset for Collective Classification. The results show that KENN is capable of increasing the performances of the underlying neural network even in the presence relational data, outperforming other two notable methods that combine learning with logic.