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arxiv: 2507.14874 · v2 · submitted 2025-07-20 · 💻 cs.LG · cs.AI

The Tsetlin Machine Goes Deep: Logical Learning and Reasoning With Graphs

Ole-Christoffer Granmo , Youmna Abdelwahab , Per-Arne Andersen , Karl Audun K. Borgersen , Paul F. A. Clarke , Kunal Dumbre , Ylva Gr{\o}nnings{\ae}ter , Vojtech Halenka
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Runar Helin Lei Jiao Ahmed Khalid Rebekka Omslandseter Rupsa Saha Mayur Shende Xuan Zhang
This is my paper

Pith reviewed 2026-05-19 03:44 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords Graph Tsetlin Machinedeep clausesmessage passinginterpretable machine learninggraph representation learningTsetlin automatasub-graph patternslogical reasoning
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The pith

The Graph Tsetlin Machine learns nested deep clauses from graph inputs via message passing to recognize sub-graph patterns with exponentially fewer rules.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Graph Tsetlin Machine to extend the flat, rule-based Tsetlin Machine to graph-structured data. It uses message passing to build nested deep clauses that capture sub-graph patterns, allowing the model to handle sequences, grids, relations, and multimodal inputs. This construction reduces the number of clauses needed while aiming to retain the interpretability and logical reasoning strengths of standard Tsetlin Machines. The authors demonstrate the approach on image classification, action tracking, recommendation systems, and genome sequence analysis, claiming gains in accuracy, noise tolerance, and training speed in several cases.

Core claim

Through message passing, the GraphTM builds nested deep clauses to recognize sub-graph patterns with exponentially fewer clauses, increasing both interpretability and data utilization. This moves the Tsetlin Machine beyond fixed-length flat inputs to support versatile graph representations while preserving its core logical and efficient properties.

What carries the argument

Message passing on graphs to construct nested deep clauses that recognize sub-graph patterns.

Load-bearing premise

Message passing on graphs can reliably construct interpretable deep clauses while preserving the efficiency and accuracy advantages of standard Tsetlin Machines across diverse tasks.

What would settle it

An experiment on a new graph dataset in which the GraphTM requires as many or more clauses as a flat Tsetlin Machine, or loses accuracy relative to standard deep models without a clear gain in interpretability, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2507.14874 by Ahmed Khalid, Karl Audun K. Borgersen, Kunal Dumbre, Lei Jiao, Mayur Shende, Ole-Christoffer Granmo, Paul F. A. Clarke, Per-Arne Andersen, Rebekka Omslandseter, Runar Helin, Rupsa Saha, Vojtech Halenka, Xuan Zhang, Ylva Gr{\o}nnings{\ae}ter, Youmna Abdelwahab.

Figure 1
Figure 1. Figure 1: The GraphTM processes graph-structured input and exploits this structure to build deep clauses through nesting. Reasoning by elimination reduces the number of clauses exponentially, while the processing of graph nodes and clauses is parallel (purple and orange). The GraphTM first evaluates each node’s properties using the layer-zero components C 0 j of the clauses (1.). If C 0 j matches the properties of a… view at source ↗
Figure 2
Figure 2. Figure 2: Encoding images into graphs. The GraphTM and CoTM were trained using identical hyperparameters for 30 epochs, with the average accuracy over the final five epochs presented in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Interpreting the active clauses for a given input from the (a) MNIST and (b) F-MNIST [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Graph structure representation for sentences. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Graph construction for action coreference tracking. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Graph construction for recommendation systems: representing customer, product, category [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test set average accuracy and standard error across five independent trials for the multivalue [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Scalability of GraphTM with increasing data volume and sequence length. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: illustrates the structure of a TA with two actions and 2N states, where N is the number of states for each action. When the TA is in any state between 0 to N − 1, the action “Include" is selected. The action becomes “Exclude" when the TA is in any state between N to 2N − 1. The transitions among the states are triggered by a reward or a penalty that the TA receives from the environment, which, in this case… view at source ↗
Figure 10
Figure 10. Figure 10: Hierarchical message passing structure across layers, from the perspective of Node [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
read the original abstract

Pattern recognition with concise and flat AND-rules makes the Tsetlin Machine (TM) both interpretable and efficient, while the power of Tsetlin automata enables accuracy comparable to deep learning on an increasing number of datasets. We introduce the Graph Tsetlin Machine (GraphTM) for learning interpretable deep clauses from graph-structured input. Moving beyond flat, fixed-length input, the GraphTM gets more versatile, supporting sequences, grids, relations, and multimodality. Through message passing, the GraphTM builds nested deep clauses to recognize sub-graph patterns with exponentially fewer clauses, increasing both interpretability and data utilization. For image classification, GraphTM preserves interpretability and achieves 3.86%-points higher accuracy on CIFAR-10 than a convolutional TM. For tracking action coreference, faced with increasingly challenging tasks, GraphTM outperforms other reinforcement learning methods by up to 20.6%-points. In recommendation systems, it tolerates increasing noise to a great extent, similar to a GCN. Finally, for viral genome sequence data, GraphTM is competitive with BiLSTM-CNN and GCN accuracy-wise, training ~2.5x faster than GCN. The GraphTM's application to these varied fields demonstrates how graph representation learning and deep clauses bring new possibilities for TM learning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the Graph Tsetlin Machine (GraphTM), an extension of the Tsetlin Machine to graph-structured inputs. Using message passing, it constructs nested deep clauses for recognizing sub-graph patterns, claiming exponentially fewer clauses, enhanced interpretability, and improved data utilization. Empirical evaluations are provided on CIFAR-10 image classification, action coreference tracking, recommendation systems, and viral genome sequence data, reporting accuracy gains or competitiveness against baselines such as convolutional TMs, reinforcement learning methods, GCNs, and BiLSTM-CNNs.

Significance. Should the proposed mechanism for building interpretable nested clauses via message passing prove sound, this could represent a meaningful advance in interpretable AI by integrating graph-based learning with the logical, automata-driven framework of Tsetlin Machines. The reported performance improvements across diverse tasks highlight potential for more efficient and versatile logical reasoning systems.

major comments (2)
  1. The central claim that message passing builds 'nested deep clauses' to recognize sub-graph patterns with exponentially fewer clauses requires a concrete example or formal definition showing how messages are mapped to literals while preserving the conjunction structure and Tsetlin automata feedback. Without this, it is unclear if the resulting rules remain flat AND-rules or if interpretability guarantees carry over. This is load-bearing for the interpretability and efficiency advantages asserted in the abstract.
  2. Specific accuracy figures are reported (e.g., 3.86%-points improvement on CIFAR-10), but the manuscript appears to lack full details on experimental setups, error bars, hyperparameter choices, and statistical tests. This makes it difficult to assess the reliability of the performance claims and the assertion of better data utilization.
minor comments (2)
  1. Consider adding a short illustrative example of a deep clause or the clause reduction factor to make the 'exponentially fewer clauses' claim more tangible for readers.
  2. Ensure consistent notation for graph elements (nodes, edges, messages) and how they relate to Tsetlin literals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline the revisions we will incorporate to strengthen the presentation.

read point-by-point responses

  1. Referee: The central claim that message passing builds 'nested deep clauses' to recognize sub-graph patterns with exponentially fewer clauses requires a concrete example or formal definition showing how messages are mapped to literals while preserving the conjunction structure and Tsetlin automata feedback. Without this, it is unclear if the resulting rules remain flat AND-rules or if interpretability guarantees carry over. This is load-bearing for the interpretability and efficiency advantages asserted in the abstract.

    Authors: We agree that a concrete example and explicit formal mapping are needed to make the mechanism fully transparent. In the revised manuscript we will add a new subsection that walks through a small illustrative graph, showing the exact mapping of each message to literals, the preservation of conjunction at every nesting level, and the extension of Tsetlin automata feedback to the resulting deep clauses. This addition will demonstrate that the rules remain logical AND-rules while the nesting enables sub-graph pattern recognition, thereby supporting the claimed interpretability and efficiency gains. revision: yes

  2. Referee: Specific accuracy figures are reported (e.g., 3.86%-points improvement on CIFAR-10), but the manuscript appears to lack full details on experimental setups, error bars, hyperparameter choices, and statistical tests. This makes it difficult to assess the reliability of the performance claims and the assertion of better data utilization.

    Authors: We acknowledge that the current experimental reporting is insufficient for full reproducibility and statistical assessment. In the revision we will expand the experimental section with complete hyperparameter tables for every dataset and baseline, error bars computed over multiple independent runs, and appropriate statistical tests (e.g., paired t-tests) for the reported accuracy differences, including the 3.86%-point CIFAR-10 gain and the data-utilization claims. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on new graph message-passing construction and empirical results

full rationale

The paper defines GraphTM by extending standard TM clause learning with message passing on graphs to produce nested clauses. This is presented as a novel architectural choice rather than a derivation that reduces to prior fitted parameters or self-citations by construction. Central claims about exponential clause reduction and preserved interpretability are tied to experimental outcomes on CIFAR-10, action tracking, recommendations, and genomes, not to any self-referential equation or uniqueness theorem imported from the authors' prior work. No load-bearing step equates a 'prediction' to an input fit or renames an existing result. Self-citations to base TM are normal background and do not carry the new graph-specific results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are detailed in the provided text.

pith-pipeline@v0.9.0 · 5841 in / 910 out tokens · 25880 ms · 2026-05-19T03:44:06.508879+00:00 · methodology

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Reference graph

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    Guidelines: • The answer NA means that the abstract and introduction do not include the claims made in the paper

    Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? Answer: [Yes] Justification: The main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope, which is further validated by experiments in Section 3. Guidelines: • The answer NA mean...

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    Limitations

    Limitations Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: Limitations of the proposed architecture with regards to different datasets are discussed along side the experimental results. Computational efficiency is reported where applicable. Guidelines: • The answer NA means that the pape...

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    Guidelines: • The answer NA means that the paper does not include theoretical results

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  32. [32]

    Guidelines: • The answer NA means that the paper does not include experiments

    Experimental Result Reproducibility Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)? Answer: [Yes] Justification: Code will be provided as p...

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    Open access to data and code 29 Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: Anonymized code for experiments will be provided in the supplemental material, and details for open acce...

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    Experimental run wise details are added in supplemental material

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    Guidelines: • The answer NA means that the paper does not include experiments

    Experiments Compute Resources Question: For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: Compute resources are elaborated in Section 3. Guidelines: • The answer NA means that the paper does no...

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    Guidelines: • The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics

    Code Of Ethics Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? Answer: [Yes] Justification: This work maintains strict adherence to the NeurIPS Code of Ethics. Guidelines: • The answer NA means that the authors have not reviewed the NeurIPS Code of Et...

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    Guidelines: • The answer NA means that there is no societal impact of the work performed

    Broader Impacts Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [NA] Justification: This work proposes a novel architecture for the Tsetlin Machine and its applicability on smaller datsets, thus wider applications and further societal impact is beyond the scope of this ...

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