Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.01519

Auto-Formalizing Neuro-Symbolic Predictors

Samuele Bortolotti·Weixin Chen·Han Zhao·Andrea Passerini·Stefano Teso·Antonio Vergari
View original source ↗Read source document ↗Export metadata ↓

Abstract

Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified constraints, making them particularly suitable for high-stakes applications where compliance with domain knowledge is essential. A key bottleneck in this paradigm is the acquisition of symbolic constraints: encoding domain knowledge into logical formulas remains a manual and expert-intensive process. In this work, we investigate the extent to which auto-formalization via LLMs can systematically translate textual knowledge into symbolic knowledge that can be plugged into NeSy predictors. To this end, we introduce auto-nesy-bench, a new benchmark for evaluating constraint formalization and its impact on downstream accuracy of NeSy predictors. Through an extensive evaluation across several domains, we find that LLMs can formalize constraints to a meaningful extent, generating formulas that are often similar to those provided by human experts. Moreover, when the generated formulas are syntactically valid, they can lead to high-quality downstream predictions. The code and benchmark are available at https://unitn-sml.github.io/auto-nesy-bench/.

Explore related subjects

cs.LGcs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Samuele Bortolotti, Weixin Chen, Han Zhao, Andrea Passerini, Stefano Teso, Antonio Vergari. 2026-10-01. Auto-Formalizing Neuro-Symbolic Predictors. https://arxiv.org/abs/2610.01519

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric graphs}$, $\textit{i.e.}$, graphs with nodes positioned in the Euclidean space given an $\textit{arbitrarily}$ chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as $\textit{Galilean invariance}$. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

cs.LG↗
arXiv2026

Geometry-Aware Adaptation for Pretrained Models

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fréchet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

cs.LG↗
arXiv2026

Information propagation dynamics in Deep Graph Networks

Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can effectively process and learn such structured information. However, learning effective information propagation patterns within DGNs remains a critical challenge that heavily influences the model capabilities, both in the static domain and in the temporal domain (where features and/or topology evolve). Given this challenge, this thesis investigates the dynamics of information propagation within DGNs for static and dynamic graphs, focusing on their design as dynamical systems. Throughout this work, we provide theoretical and empirical evidence to demonstrate the effectiveness of our proposed architectures in propagating and preserving long-term dependencies between nodes, and in learning complex spatio-temporal patterns from irregular and sparsely sampled dynamic graphs. In summary, this thesis provides a comprehensive exploration of the intersection between graphs, deep learning, and dynamical systems, offering insights and advancements for the field of graph representation learning and paving the way for more effective and versatile graph-based learning models.

cs.LG↗