Rik Adriaensen

Robin Manhaeve, Stefano Colamonaco, Vincent Derkinderen et al.

DeepLog is an operational neurosymbolic framework that unifies logic and deep learning within standard PyTorch workflows. While existing neurosymbolic systems focus on a particular paradigm and semantics, DeepLog serves as a universal backend that can emulate many systems in the neurosymbolic alphabet soup. By treating diverse neurosymbolic languages as high-level specifications, the DeepLog software automatically compiles them into optimized arithmetic circuits. This design lowers the barrier for machine learning practitioners by treating logic as composable modules, while providing neurosymbolic developers with a shared, high-performance basis for prototyping new integration strategies. The code is available here: https://github.com/ML-KULeuven/deeplog

Rik Adriaensen, Lucas Van Praet, Jessa Bekker et al.

Operationalizing definitions of fairness is difficult in practice, as multiple definitions can be incompatible while each being arguably desirable. Instead, it may be easier to directly describe algorithmic bias through ad-hoc assumptions specific to a particular real-world task, e.g., based on background information on systemic biases in its context. Such assumptions can, in turn, be used to mitigate this bias during training. Yet, a framework for incorporating such assumptions that is simultaneously principled, flexible, and interpretable is currently lacking. Our approach is to formalize bias assumptions as programs in ProbLog, a probabilistic logic programming language that allows for the description of probabilistic causal relationships through logic. Neurosymbolic extensions of ProbLog then allow for easy integration of these assumptions in a neural network's training process. We propose a set of templates to express different types of bias and show the versatility of our approach on synthetic tabular datasets with known biases. Using estimates of the bias distortions present, we also succeed in mitigating algorithmic bias in real-world tabular and image data. We conclude that ProbLog4Fairness outperforms baselines due to its ability to flexibly model the relevant bias assumptions, where other methods typically uphold a fixed bias type or notion of fairness.

Vincent Derkinderen, Robin Manhaeve, Rik Adriaensen et al.

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational mechanisms used in neurosymbolic AI. DeepLog can represent and emulate a wide range of neurosymbolic systems. It consists of two key components. The first is the DeepLog language for specifying neurosymbolic models and inference tasks. This language consists of an annotated neural extension of grounded first-order logic, and makes abstraction of the type of logic, e.g. boolean, fuzzy or probabilistic, and whether logic is used in the architecture or in the loss function. The second DeepLog component is situated at the computational level and uses extended algebraic circuits as computational graphs. Together these two components are to be considered as a neurosymbolic abstract machine, with the DeepLog language as the intermediate level of abstraction and the circuits level as the computational one. DeepLog is implemented in software, relies on the latest insights in implementing algebraic circuits on GPUs, and is declarative in that it is easy to obtain different neurosymbolic models by making different choices for the underlying algebraic structures and logics. The generality and efficiency of the DeepLog neurosymbolic machine is demonstrated through an experimental comparison between 1) different fuzzy and probabilistic logics, 2) between using logic in the architecture or in the loss function, and 3) between a standalone CPU-based implementation of a neurosymbolic AI system and a DeepLog GPU-based one.