Robert Hoehndorf

Fernando Zhapa-Camacho, Robert Hoehndorf

A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $σ$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two $σ$-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Replacing the underlying sets by types, in the sense of homotopy type theory, preserves this information, and turns this functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts. The payoff is concrete: the shortcut-aware concept posterior that recent methods reach by ensembling or expressive density estimation is the only symmetry-invariant point of the confusion-set simplex, computable in closed form by averaging a single model over the symmetry group. On MNIST reasoning-shortcut benchmarks this single-model wrapper is better calibrated than a diversity-trained ensemble, while leaving label accuracy and identifiable concepts untouched. Code is freely available at https://github.com/bio-ontology-research-group/hott-nesy.

Mohammad Ashhad, Robert Hoehndorf, Ricardo Henao

Survival analysis is complicated by censored data, high-dimensional features, and non-linear interactions. Classical models offer interpretability and superior calibration but are restricted to linear or predefined functional forms, while deep learning models are flexible and achieve strong discriminative performance, but tend to produce poorly calibrated survival estimates. To address this trade-off, we propose GRAFT (Gated Residual Accelerated Failure Time), a novel AFT model that decouples prognostic ranking from survival calibration. GRAFT's hybrid architecture combines a linear AFT model with a non-linear residual neural network, and it also integrates stochastic gates for automatic feature selection. The model is trained by optimizing a differentiable, C-index-aligned ranking loss using stochastic conditional imputation from local Kaplan-Meier estimators, while calibrated survival estimates are obtained through simple post-training calibration. In public benchmarks, GRAFT outperforms baselines in discrimination and calibration, while remaining robust and sparse in high-noise settings.