AAAI 2026

\documentclass[11pt,twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[margin=0.75in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}
\usepackage{booktabs}
\usepackage{enumitem}
\usepackage{xcolor}
\usepackage{times}
\usepackage{natbib}
\usepackage{hyperref}
\usepackage{url}
\usepackage{microtype}
\usepackage{algorithm}
\usepackage{algorithmic}
\usepackage{caption}
\usepackage{multirow}

\setlength{\columnsep}{0.25in}

\title{\Large\bfseries Compositional Neuro-Symbolic Reasoning with\\Learned Abstraction Hierarchies}

\author{
  \textbf{Olivia Hartmann}\textsuperscript{1}\quad
  \textbf{Raj Mehta}\textsuperscript{2}\quad
  \textbf{Chloe Dupont}\textsuperscript{3}\quad
  \textbf{Yifan Liu}\textsuperscript{1}\\[4pt]
  \textsuperscript{1}MIT CSAIL\quad
  \textsuperscript{2}Allen Institute for AI\quad
  \textsuperscript{3}University of Oxford\\[2pt]
  {\small\texttt{\{ohartmann,yfliu\}@mit.edu, [email protected], [email protected]}}
}

\date{}

\begin{document}
\maketitle

\begin{abstract}
Compositional reasoning---the ability to combine known concepts and rules to solve novel problems---remains a fundamental challenge for current AI systems. While neural networks excel at pattern recognition and symbolic systems excel at logical reasoning, neither alone achieves robust compositional generalization. We present \textsc{NeuralAbstract}, a neuro-symbolic architecture that learns hierarchical abstractions from data and performs compositional reasoning over these learned abstractions. Our approach constructs a multi-level abstraction hierarchy where lower levels capture perceptual features and higher levels encode relational and logical structure. A differentiable symbolic reasoning module operates over the hierarchy, combining neural perception with rule-based inference. On CLEVR-CoGenT, SCAN, and a new benchmark for hierarchical planning (HierPlan), \textsc{NeuralAbstract} achieves 98.7\%, 99.2\%, and 87.3\% accuracy respectively, significantly outperforming both pure neural and existing neuro-symbolic baselines. Ablation studies confirm that learned abstraction hierarchies are critical for generalization to novel compositions.
\end{abstract}

\section{Introduction}

Compositionality---the principle that complex meanings are constructed from simpler parts according to structural rules---is a cornerstone of human cognition \citep{fodor1988connectionism}. Humans can understand ``the cat chased the dog'' having only seen cats, dogs, and chasing separately. This compositional generalization remains elusive for deep learning systems, which tend to memorize surface-level patterns rather than learning underlying compositional rules \citep{lake2018generalization}.

Neuro-symbolic approaches aim to combine the perceptual strengths of neural networks with the compositional reasoning abilities of symbolic systems \citep{garcez2019neural}. However, most existing neuro-symbolic systems require hand-designed symbolic representations, limiting their applicability to domains with well-defined ontologies. The key question we address is: \emph{can we learn the symbolic abstractions themselves while maintaining compositional reasoning capabilities?}

We present \textsc{NeuralAbstract}, which answers this question affirmatively. Our system learns a hierarchy of abstractions from raw perceptual input, where each level captures increasingly abstract concepts. A differentiable symbolic reasoning module then performs logical inference over these learned abstractions. The hierarchy provides the structural scaffolding necessary for compositional generalization, while end-to-end learning ensures the abstractions are grounded in perceptual reality.

\paragraph{Contributions.}
\begin{itemize}[nosep,leftmargin=*]
  \item A method for learning hierarchical symbolic abstractions from raw perceptual input through differentiable discretization.
  \item A differentiable reasoning module that performs forward chaining over learned abstraction hierarchies.
  \item State-of-the-art results on compositional reasoning benchmarks.
  \item A new hierarchical planning benchmark (\textsc{HierPlan}) for evaluating multi-level compositional reasoning.
\end{itemize}

\section{Related Work}

\paragraph{Compositional Generalization.}
The SCAN benchmark \citep{lake2018generalization} revealed that sequence-to-sequence models fail at systematic compositional generalization. Subsequent work proposed architectural modifications including equivariant architectures \citep{gordon2020permutation}, meta-learning approaches \citep{lake2019compositional}, and data augmentation strategies. Our approach differs by explicitly constructing symbolic structures that support composition.

\paragraph{Neuro-Symbolic AI.}
Neural Theorem Provers \citep{rocktaschel2017end} and DeepProbLog \citep{manhaeve2018deepproblog} integrate neural perception with logical reasoning. Neural Module Networks \citep{andreas2016neural} compose specialized neural modules according to parsed program structures. \textsc{NeuralAbstract} extends these ideas by learning the abstraction hierarchy rather than relying on predefined predicates or module inventories.

\paragraph{Abstraction Learning.}
Concept Bottleneck Models \citep{koh2020concept} learn interpretable intermediate concepts, but require concept annotations. Object-centric learning \citep{locatello2020object} discovers object-level abstractions from images. We generalize beyond objects to multi-level abstractions including relations, properties, and rules.

\section{Method}

\subsection{Overview}

Given an input (image, text, or structured data), \textsc{NeuralAbstract} operates in three phases:
\begin{enumerate}[nosep,leftmargin=*]
  \item \textbf{Perception}: A neural encoder extracts continuous features.
  \item \textbf{Abstraction}: Features are discretized into a multi-level symbolic hierarchy.
  \item \textbf{Reasoning}: A differentiable symbolic engine performs inference over the hierarchy.
\end{enumerate}

\subsection{Hierarchical Abstraction Learning}

We define $L$ abstraction levels. Level 0 consists of continuous neural features $\mathbf{z} = f_\theta(\mathbf{x})$. Each subsequent level $\ell$ discretizes and abstracts the representations from level $\ell - 1$.

\paragraph{Differentiable Discretization.}
At level $\ell$, we maintain a codebook $\mathbf{C}^\ell = \{\mathbf{c}_1^\ell, \ldots, \mathbf{c}_{K_\ell}^\ell\}$ of $K_\ell$ abstract concepts. Continuous representations are mapped to discrete symbols using Gumbel-Softmax:
\begin{equation}
s_i^\ell = \text{GumbelSoftmax}\left(\frac{\text{sim}(\mathbf{z}_i^{\ell-1}, \mathbf{C}^\ell)}{\tau}\right)
\end{equation}
where $\tau$ is a temperature parameter annealed during training.

\paragraph{Relational Abstraction.}
Higher levels capture relations between lower-level symbols. For level $\ell \geq 2$, we compute pairwise interaction scores:
\begin{equation}
r_{ij}^\ell = g_\phi^\ell(s_i^{\ell-1}, s_j^{\ell-1})
\end{equation}
and discretize these into relational symbols that populate level $\ell$.

\subsection{Differentiable Symbolic Reasoning}

Given the abstraction hierarchy, we perform reasoning via differentiable forward chaining. We maintain a set of learned rules $\mathcal{R} = \{R_1, \ldots, R_M\}$, where each rule $R_k$ has a soft attention over possible antecedents and consequents:
\begin{equation}
R_k: \alpha_k^1 \wedge \alpha_k^2 \wedge \cdots \Rightarrow \beta_k
\end{equation}
The rule application uses soft unification:
\begin{equation}
P(\beta_k \mid \mathcal{F}) = \sigma\!\left(\sum_{i} w_i \cdot \text{match}(\alpha_k^i, \mathcal{F})\right)
\end{equation}
where $\mathcal{F}$ is the current set of derived facts and $\sigma$ is the sigmoid function.

\subsection{Training}

The full model is trained end-to-end with:
\begin{equation}
\mathcal{L} = \mathcal{L}_{\text{task}} + \lambda_1 \mathcal{L}_{\text{commit}} + \lambda_2 \mathcal{L}_{\text{sparse}}
\end{equation}
where $\mathcal{L}_{\text{commit}}$ is the VQ-VAE commitment loss for codebook learning, and $\mathcal{L}_{\text{sparse}}$ encourages sparse rule activations to promote interpretability.

\section{Experiments}

\subsection{Benchmarks}

\begin{itemize}[nosep,leftmargin=*]
  \item \textbf{CLEVR-CoGenT} \citep{johnson2017clevr}: Visual question answering requiring compositional reasoning about object properties and spatial relations.
  \item \textbf{SCAN} \citep{lake2018generalization}: Mapping natural language commands to action sequences, testing systematic generalization.
  \item \textbf{HierPlan} (ours): Hierarchical planning tasks requiring multi-level reasoning (e.g., planning a multi-course meal given ingredient constraints, dietary restrictions, and taste preferences).
\end{itemize}

\subsection{Results}

\begin{table}[t]
\centering
\caption{Accuracy (\%) on compositional reasoning benchmarks.}
\label{tab:main}
\small
\begin{tabular}{@{}lccc@{}}
\toprule
\textbf{Method} & \textbf{CLEVR} & \textbf{SCAN} & \textbf{HierPlan} \\
\midrule
LSTM Seq2Seq & 73.2 & 13.8 & 24.1 \\
Transformer & 78.5 & 42.3 & 35.7 \\
NS-VQA & 96.2 & -- & -- \\
NMN & 95.8 & -- & 51.3 \\
LANE & -- & 96.4 & -- \\
DeepProbLog & 94.1 & 84.7 & 62.8 \\
\midrule
\textbf{NeuralAbstract} & \textbf{98.7} & \textbf{99.2} & \textbf{87.3} \\
\bottomrule
\end{tabular}
\end{table}

Table~\ref{tab:main} shows that \textsc{NeuralAbstract} achieves strong performance across all benchmarks. The gains are most dramatic on SCAN and HierPlan, which specifically test compositional generalization to unseen combinations. On HierPlan, the 24.5\% improvement over the best baseline demonstrates the advantage of learned abstraction hierarchies for multi-level reasoning.

\subsection{Ablation Study}

\begin{table}[t]
\centering
\caption{Ablation study on CLEVR-CoGenT and HierPlan.}
\label{tab:ablation}
\small
\begin{tabular}{@{}lcc@{}}
\toprule
\textbf{Configuration} & \textbf{CLEVR} & \textbf{HierPlan} \\
\midrule
Full model (3 levels) & \textbf{98.7} & \textbf{87.3} \\
2 abstraction levels & 97.4 & 78.1 \\
1 abstraction level & 95.1 & 64.2 \\
No discretization & 82.3 & 41.8 \\
No learned rules & 94.6 & 58.7 \\
Fixed (hand-designed) rules & 96.8 & 72.4 \\
\bottomrule
\end{tabular}
\end{table}

Table~\ref{tab:ablation} demonstrates that: (1) multiple abstraction levels are critical, especially for HierPlan; (2) discretization is essential for compositional reasoning; (3) learned rules outperform hand-designed rules, showing the value of end-to-end learning.

\subsection{Interpretability}

We qualitatively examine the learned abstractions. On CLEVR, Level 1 learns object-level concepts (shape, color, size), Level 2 captures spatial relations (left-of, behind), and Level 3 encodes compositional queries (e.g., ``same shape as the object left of the red cube''). This emergent hierarchy closely mirrors the human-designed predicate vocabulary, validating that meaningful abstractions can be learned from data.

\section{Conclusion}

\textsc{NeuralAbstract} demonstrates that hierarchical symbolic abstractions can be learned from data while supporting robust compositional reasoning. By combining differentiable discretization, relational abstraction, and learned symbolic rules, our approach achieves state-of-the-art compositional generalization across visual reasoning, language grounding, and hierarchical planning tasks. The learned abstraction hierarchies are interpretable and align with human conceptual structure, suggesting a promising path toward AI systems with human-like compositional reasoning abilities.

\section*{Ethical Considerations}

Our work addresses fundamental reasoning capabilities without direct application to sensitive domains. The HierPlan benchmark uses synthetic tasks without personal data. We acknowledge that improved AI reasoning capabilities could have dual-use implications and encourage responsible development of such technologies.

{\small
\bibliographystyle{plainnat}
\begin{thebibliography}{15}
\bibitem[Andreas et~al.(2016)]{andreas2016neural}
J.~Andreas, M.~Rohrbach, T.~Darrell, and D.~Klein.
\newblock Neural module networks.
\newblock In \emph{Proc.\ CVPR}, 2016.

\bibitem[Fodor and Pylyshyn(1988)]{fodor1988connectionism}
J.~Fodor and Z.~Pylyshyn.
\newblock Connectionism and cognitive architecture: A critical analysis.
\newblock \emph{Cognition}, 28(1-2):3--71, 1988.

\bibitem[Garcez et~al.(2019)]{garcez2019neural}
A.~d'Avila~Garcez, M.~Gori, L.~Lamb, L.~Serafini, M.~Spranger, and S.~Tran.
\newblock Neural-symbolic computing: An effective methodology for principled integration of machine learning and reasoning.
\newblock \emph{J.\ Applied Logics}, 6(4):611--631, 2019.

\bibitem[Gordon et~al.(2020)]{gordon2020permutation}
J.~Gordon, D.~Lopez-Paz, M.~Baroni, and D.~Bouchacourt.
\newblock Permutation equivariant models for compositional generalization in language.
\newblock In \emph{Proc.\ ICLR}, 2020.

\bibitem[Johnson et~al.(2017)]{johnson2017clevr}
J.~Johnson, B.~Hariharan, L.~van~der~Maaten, L.~Fei-Fei, C.~L. Zitnick, and R.~Girshick.
\newblock {CLEVR}: A diagnostic dataset for compositional language and elementary visual reasoning.
\newblock In \emph{Proc.\ CVPR}, 2017.

\bibitem[Koh et~al.(2020)]{koh2020concept}
P.~W. Koh, T.~Nguyen, Y.~S. Tang, S.~Mussmann, E.~Pierson, B.~Kim, and P.~Liang.
\newblock Concept bottleneck models.
\newblock In \emph{Proc.\ ICML}, 2020.

\bibitem[Lake and Baroni(2018)]{lake2018generalization}
B.~Lake and M.~Baroni.
\newblock Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks.
\newblock In \emph{Proc.\ ICML}, 2018.

\bibitem[Lake(2019)]{lake2019compositional}
B.~Lake.
\newblock Compositional generalization through meta sequence-to-sequence learning.
\newblock In \emph{Proc.\ NeurIPS}, 2019.

\bibitem[Locatello et~al.(2020)]{locatello2020object}
F.~Locatello, D.~Weissenborn, T.~Unterthiner, A.~Mahendran, G.~Heigold, J.~Uszkoreit, A.~Dosovitskiy, and T.~Kipf.
\newblock Object-centric learning with slot attention.
\newblock In \emph{Proc.\ NeurIPS}, 2020.

\bibitem[Manhaeve et~al.(2018)]{manhaeve2018deepproblog}
R.~Manhaeve, S.~Dumancic, A.~Kimmig, T.~Demeester, and L.~De~Raedt.
\newblock {DeepProbLog}: Neural probabilistic logic programming.
\newblock In \emph{Proc.\ NeurIPS}, 2018.

\bibitem[Rockt\"aschel and Riedel(2017)]{rocktaschel2017end}
T.~Rockt\"aschel and S.~Riedel.
\newblock End-to-end differentiable proving.
\newblock In \emph{Proc.\ NeurIPS}, 2017.
\end{thebibliography}
}

\end{document}