# Recursive querying of neural networks via weighted structures

arXiv: https://arxiv.org/abs/2601.03201 · HTML: https://mlsanity.com/paper/2601.03201/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 14 of 14)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Expressiveness and Approximation Properties of Graph Neural Networks](https://mlsanity.com/paper/2204.04661/) (2022)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)
- [Foundations of Symbolic Languages for Model Interpretability](https://mlsanity.com/paper/2110.02376/) (2021)
- [On the expressive power of query languages for matrices](https://mlsanity.com/paper/1709.08359/) (2017)
- [Convergence of Datalog over (Pre-) Semirings](https://mlsanity.com/paper/2105.14435/) (2021)
- [Learning Concepts Described by Weight Aggregation Logic](https://mlsanity.com/paper/2009.10574/) (2020)
- [A Uniform Language to Explain Decision Trees](https://mlsanity.com/paper/2310.11636/) (2023)
- [Aggregate Queries on Sparse Databases](https://mlsanity.com/paper/1912.12338/) (2019)
- [Juggling Functions Inside a Database](https://mlsanity.com/paper/1703.03147/) (2017)
- [Query languages for neural networks](https://mlsanity.com/paper/2408.10362/) (2024)
- [SQL4NN: Validation and expressive querying of models as data](https://mlsanity.com/paper/2502.14745/) (2025)

## Built on by (most cited first, 2 of 2)

- [Query Languages for Machine-Learning Models](https://mlsanity.com/paper/2601.09381/) (2026)
- [Neuro-Relational Programs: Unifying Queries and Neural Computation over Structured Data](https://mlsanity.com/paper/2606.11946/) (2026)

## Abstract (arXiv)

Expressive querying of machine learning models - viewed as a form of intentional data - enables their verification and interpretation using declarative languages, thereby making learned representations of data more accessible. Motivated by the querying of feedforward neural networks, we investigate logics for weighted structures. In the absence of a bound on neural network depth, such logics must incorporate recursion; thereto we revisit the functional fixpoint mechanism proposed by Gr"adel and Gurevich. We adopt it in a Datalog-like syntax; we extend normal forms for fixpoint logics to weighted structures; and show an equivalent "loose" fixpoint mechanism that allows values of inductively defined weight functions to be overwritten. We propose a "scalar" restriction of functional fixpoint logic, of polynomial-time data complexity, and show it can express all PTIME model-agnostic queries over reduced networks with polynomially bounded weights. In contrast, we show that very simple model-agnostic queries are already NP-complete. Finally, we consider transformations of weighted structures by iterated transductions.