Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts

Neuro-Symbolic (NeSy) predictive models hold the promise of improved compliance with given constraints, systematic generalization, and interpretability, as they allow to infer labels that are consistent with some prior knowledge by reasoning over high-level concepts extracted from sub-symbolic inputs. It was recently shown that NeSy predictors are affected by reasoning shortcuts: they can attain high accuracy but by leveraging concepts with unintended semantics, thus coming short of their promised advantages. Yet, a systematic characterization of reasoning shortcuts and of potential mitigation strategies is missing. This work fills this gap by characterizing them as unintended optima of the learning objective and identifying four key conditions behind their occurrence. Based on this, we derive several natural mitigation strategies, and analyze their efficacy both theoretically and empirically. Our analysis shows reasoning shortcuts are difficult to deal with, casting doubts on the trustworthiness and interpretability of existing NeSy solutions.

Egocentric Hierarchical Visual Semantics

We are interested in aligning how people think about objects and what machines perceive, meaning by this the fact that object recognition, as performed by a machine, should follow a process which resembles that followed by humans when thinking of an object associated with a certain concept. The ultimate goal is to build systems which can meaningfully interact with their users, describing what they perceive in the users' own terms. As from the field of Lexical Semantics, humans organize the meaning of words in hierarchies where the meaning of, e.g., a noun, is defined in terms of the meaning of a more general noun, its genus, and of one or more differentiating properties, its differentia. The main tenet of this paper is that object recognition should implement a hierarchical process which follows the hierarchical semantic structure used to define the meaning of words. We achieve this goal by implementing an algorithm which, for any object, recursively recognizes its visual genus and its visual differentia. In other words, the recognition of an object is decomposed in a sequence of steps where the locally relevant visual features are recognized. This paper presents the algorithm and a first evaluation.

Interval Logic Tensor Networks

In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy logic, event durations using trapezoidal fuzzy intervals, and fuzzy temporal relations using relationships between the intervals' areas. We propose Interval Logic Tensor Networks (ILTN), a neuro-symbolic system that learns by propagating gradients through IRL. In order to support effective learning, ILTN defines smoothened versions of the fuzzy intervals and temporal relations of IRL using softplus activations. We show that ILTN can successfully leverage knowledge expressed in IRL in synthetic tasks that require reasoning about events to predict their fuzzy durations. Our results show that the system is capable of making events compliant with background temporal knowledge.

Neuro-Symbolic Reasoning Shortcuts: Mitigation Strategies and their Limitations

Neuro-symbolic predictors learn a mapping from sub-symbolic inputs to higher-level concepts and then carry out (probabilistic) logical inference on this intermediate representation. This setup offers clear advantages in terms of consistency to symbolic prior knowledge, and is often believed to provide interpretability benefits in that - by virtue of complying with the knowledge - the learned concepts can be better understood by human stakeholders. However, it was recently shown that this setup is affected by reasoning shortcuts whereby predictions attain high accuracy by leveraging concepts with unintended semantics, yielding poor out-of-distribution performance and compromising interpretability. In this short paper, we establish a formal link between reasoning shortcuts and the optima of the loss function, and identify situations in which reasoning shortcuts can arise. Based on this, we discuss limitations of natural mitigation strategies such as reconstruction and concept supervision.

Enhancing SMT-based Weighted Model Integration by Structure Awareness

The development of efficient exact and approximate algorithms for probabilistic inference is a long-standing goal of artificial intelligence research. Whereas substantial progress has been made in dealing with purely discrete or purely continuous domains, adapting the developed solutions to tackle hybrid domains, characterised by discrete and continuous variables and their relationships, is highly non-trivial. Weighted Model Integration (WMI) recently emerged as a unifying formalism for probabilistic inference in hybrid domains. Despite a considerable amount of recent work, allowing WMI algorithms to scale with the complexity of the hybrid problem is still a challenge. In this paper we highlight some substantial limitations of existing state-of-the-art solutions, and develop an algorithm that combines SMT-based enumeration, an efficient technique in formal verification, with an effective encoding of the problem structure. This allows our algorithm to avoid generating redundant models, resulting in drastic computational savings. Additionally, we show how SMT-based approaches can seamlessly deal with different integration techniques, both exact and approximate, significantly expanding the set of problems that can be tackled by WMI technology. An extensive experimental evaluation on both synthetic and real-world datasets confirms the substantial advantage of the proposed solution over existing alternatives. The application potential of this technology is further showcased on a prototypical task aimed at verifying the fairness of probabilistic programs.

Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities

Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static) graph-structured data. However, many real-world systems are dynamic in nature, since the graph and node/edge attributes change over time. In recent years, GNN-based models for temporal graphs have emerged as a promising area of research to extend the capabilities of GNNs. In this work, we provide the first comprehensive overview of the current state-of-the-art of temporal GNN, introducing a rigorous formalization of learning settings and tasks and a novel taxonomy categorizing existing approaches in terms of how the temporal aspect is represented and processed. We conclude the survey with a discussion of the most relevant open challenges for the field, from both research and application perspectives.

Neuro Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal

We introduce Neuro-Symbolic Continual Learning, where a model has to solve a sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to high-level concepts and compute predictions by reasoning consistently with prior knowledge. Our key observation is that neuro-symbolic tasks, although different, often share concepts whose semantics remains stable over time. Traditional approaches fall short: existing continual strategies ignore knowledge altogether, while stock neuro-symbolic architectures suffer from catastrophic forgetting. We show that leveraging prior knowledge by combining neuro-symbolic architectures with continual strategies does help avoid catastrophic forgetting, but also that doing so can yield models affected by reasoning shortcuts. These undermine the semantics of the acquired concepts, even when detailed prior knowledge is provided upfront and inference is exact, and in turn continual performance. To overcome these issues, we introduce COOL, a COncept-level cOntinual Learning strategy tailored for neuro-symbolic continual problems that acquires high-quality concepts and remembers them over time. Our experiments on three novel benchmarks highlights how COOL attains sustained high performance on neuro-symbolic continual learning tasks in which other strategies fail.

Explaining the Explainers in Graph Neural Networks: a Comparative Study

Following a fast initial breakthrough in graph based learning, Graph Neural Networks (GNNs) have reached a widespread application in many science and engineering fields, prompting the need for methods to understand their decision process. GNN explainers have started to emerge in recent years, with a multitude of methods both novel or adapted from other domains. To sort out this plethora of alternative approaches, several studies have benchmarked the performance of different explainers in terms of various explainability metrics. However, these earlier works make no attempts at providing insights into why different GNN architectures are more or less explainable, or which explainer should be preferred in a given setting. In this survey, we fill these gaps by devising a systematic experimental study, which tests ten explainers on eight representative architectures trained on six carefully designed graph and node classification datasets. With our results we provide key insights on the choice and applicability of GNN explainers, we isolate key components that make them usable and successful and provide recommendations on how to avoid common interpretation pitfalls. We conclude by highlighting open questions and directions of possible future research.

Global Explainability of GNNs via Logic Combination of Learned Concepts

While instance-level explanation of GNN is a well-studied problem with plenty of approaches being developed, providing a global explanation for the behaviour of a GNN is much less explored, despite its potential in interpretability and debugging. Existing solutions either simply list local explanations for a given class, or generate a synthetic prototypical graph with maximal score for a given class, completely missing any combinatorial aspect that the GNN could have learned. In this work, we propose GLGExplainer (Global Logic-based GNN Explainer), the first Global Explainer capable of generating explanations as arbitrary Boolean combinations of learned graphical concepts. GLGExplainer is a fully differentiable architecture that takes local explanations as inputs and combines them into a logic formula over graphical concepts, represented as clusters of local explanations. Contrary to existing solutions, GLGExplainer provides accurate and human-interpretable global explanations that are perfectly aligned with ground-truth explanations (on synthetic data) or match existing domain knowledge (on real-world data). Extracted formulas are faithful to the model predictions, to the point of providing insights into some occasionally incorrect rules learned by the model, making GLGExplainer a promising diagnostic tool for learned GNNs.