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REVIEW 2 major objections 14 references

Vectorization and caching speed up NeurASP probability and gradient calculations by multiple orders of magnitude.

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2026-06-27 13:20 UTC pith:D72JKIQI

load-bearing objection The paper speeds up NeurASP via vectorization, batching, and caching with claimed large gains, but does not confirm the new version matches the original on probabilities and gradients. the 2 major comments →

arxiv 2606.10787 v2 pith:D72JKIQI submitted 2026-06-09 cs.AI cs.LO

Accelerating NeurASP with vectorization and caching

Alexander Philipp Rader , Alessandra Russo This is my paper
classification cs.AI cs.LO
keywords NeurASPNeurosymbolic AIAnswer Set ProgrammingVectorizationCachingGradient ComputationScalability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes that vectorizing, batching, and caching the probability and gradient computations needed to backpropagate through answer set programming rules makes NeurASP training feasible on larger problems. This change leaves the training objective and final predictions unchanged while reducing computation time dramatically. A new dataset of card-playing tasks is introduced to measure the effect on tasks that were previously too slow. Readers care because the original bottleneck had limited neurosymbolic systems to small-scale examples despite their promise for combining neural perception with symbolic reasoning.

Core claim

By replacing the original non-vectorized probability and gradient calculations with vectorized, batched, and cached versions, the enhanced NeurASP implementation produces identical numerical results yet runs multiple orders of magnitude faster on larger tasks.

What carries the argument

Vectorized and cached probability and gradient calculations over answer set programming rules during backpropagation.

Load-bearing premise

The vectorized and cached versions produce exactly the same numerical probabilities and gradients as the original implementation.

What would settle it

Run both the original and accelerated code on the same card-game input and check whether the computed probabilities and gradients differ by more than floating-point noise.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 0 minor

Summary. The paper claims that vectorization, batch processing, and caching of probability and gradient calculations in NeurASP yield speedups of multiple orders of magnitude on larger tasks while preserving training validity, demonstrated via comparisons on a new playing-card dataset.

Significance. If the optimized implementation is numerically equivalent to the original, the work would meaningfully improve scalability of NeurASP for neurosymbolic tasks that rely on expensive ASP reasoning, directly addressing the computational bottleneck noted in the abstract.

major comments (2)
  1. [Abstract] Abstract: the headline claim of 'speedups of multiple orders of magnitude for larger tasks' while 'keeping training valid' is load-bearing on the unstated assumption that vectorized/batched probability and gradient computations produce identical numerical outputs (including gradients) to the scalar original; no side-by-side numerical verification, error analysis, or equivalence checks are described.
  2. [Abstract] Abstract and described experiments: wall-clock timings are reported without accompanying tables of per-epoch loss values, gradient norms, or final accuracies on identical inputs, leaving open the possibility that floating-point re-association or cache invalidation alters results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for highlighting the need to explicitly verify numerical equivalence between the original and optimized NeurASP implementations. This is a substantive point that strengthens the paper. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of 'speedups of multiple orders of magnitude for larger tasks' while 'keeping training valid' is load-bearing on the unstated assumption that vectorized/batched probability and gradient computations produce identical numerical outputs (including gradients) to the scalar original; no side-by-side numerical verification, error analysis, or equivalence checks are described.

    Authors: We agree that the validity claim requires explicit confirmation that the vectorized, batched, and cached computations produce outputs and gradients identical to the scalar version (within floating-point tolerance). The optimizations were implemented to preserve mathematical equivalence, but we did not include verification experiments in the submitted version. In the revision we will add a dedicated subsection (and corresponding appendix) reporting side-by-side comparisons of probability tensors, gradient values, per-epoch losses, and final accuracies on identical inputs, together with an error analysis showing that discrepancies remain at machine precision. revision: yes

  2. Referee: [Abstract] Abstract and described experiments: wall-clock timings are reported without accompanying tables of per-epoch loss values, gradient norms, or final accuracies on identical inputs, leaving open the possibility that floating-point re-association or cache invalidation alters results.

    Authors: We acknowledge that wall-clock timings alone are insufficient without evidence that training dynamics and outcomes are unchanged. The revised manuscript will include tables (and plots) that directly compare per-epoch loss, gradient norms, and final task accuracies between the original and optimized implementations on the same card-game dataset and random seeds. These will be placed alongside the timing results to demonstrate that the reported speedups do not come at the cost of altered numerical behavior. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical implementation speedup with no derivation chain

full rationale

The paper reports measured wall-clock speedups from vectorization, batching, and caching applied to NeurASP probability/gradient calculations. No equations derive a result from inputs by construction, no parameters are fitted then renamed as predictions, and no self-citation chain supports a uniqueness or ansatz claim. The contribution is purely engineering and benchmarking; the implicit numerical-equivalence assumption is a correctness concern, not a circular reduction of any claimed derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivations, free parameters, or new entities are introduced; the paper reports an engineering optimization whose correctness rests on the unstated assumption that vectorized ASP probability calculations are numerically identical to the scalar version.

pith-pipeline@v0.9.1-grok · 5688 in / 1000 out tokens · 13970 ms · 2026-06-27T13:20:39.659232+00:00 · methodology

0 comments
read the original abstract

Neurosymbolic AI combines neural networks with symbolic programs to create robust and explainable predictions. One such framework is NeurASP, which trains a neural network to predict concepts and reasons over them using rules written in answer set programming (ASP) to solve downstream tasks. Crucially, labels are only provided for the downstream prediction produced by the symbolic rules, not for the latent concepts themselves. Backpropagation through the non-differentiable ASP component requires expensive probability and gradient calculations, which has hindered scalability to more sophisticated tasks. In this paper, we address the current limitations of NeurASP by improving its computational performance through vectorization, batch processing and caching of intermediate computations during training. We compare computation speeds between the original and our new implementation of NeurASP and report speedups of multiple orders of magnitude for larger tasks. To this end, we propose a new dataset of difficult tasks involving playing cards, which we use to test the capabilities of NeurASP's enhanced learning function.

Figures

Figures reproduced from arXiv: 2606.10787 by Alessandra Russo, Alexander Philipp Rader.

Figure 1
Figure 1. Figure 1: The inference procedure of NeurASP exemplified with an MNIST addition exam [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The learning procedure of NeurASP exemplified with an MNIST addition example. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: NeurASP probability calculation function [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The computation times (seconds) for the probability and gradient calculations [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Differences between downstream and latent validation accuracies for Card prod [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 1 canonical work pages · 1 internal anchor

  1. [1]

    InNeural-Symbolic Learning and Reasoning: 18th International Conference, NeSy 2024, Barcelona, Spain, September 9–12, 2024, Proceedings, Part I2024, 195–218, Berlin, Heidelberg

    Aspis, Y.,Albinhassan, M.,Lobo, J.,and Russo, A.Embed2rule scalable neuro-symbolic learning via latent space weak-labelling. InNeural-Symbolic Learning and Reasoning: 18th International Conference, NeSy 2024, Barcelona, Spain, September 9–12, 2024, Proceedings, Part I2024, 195–218, Berlin, Heidelberg. Springer-Verlag

    2024

  2. [2]

    Ffnsl: Feed-forward neural-symbolic learner,112, 2, 515–569

    Cunnington, D.,Law, M.,Lobo, J.,and Russo, A.2023. Ffnsl: Feed-forward neural-symbolic learner,112, 2, 515–569

    2023

  3. [3]

    The mnist database of handwritten digit images for machine learning research, 29, 6, 141–142

    Deng, L.2012. The mnist database of handwritten digit images for machine learning research, 29, 6, 141–142

    2012

  4. [4]

    and Lamb, L.Neurosymbolic ai: the 3rd wave

    Garcez, A. and Lamb, L.Neurosymbolic ai: the 3rd wave. InArtificial Intelligence Review 2023, volume 56, pp. 1–20

    2023

  5. [5]

    Multi-shot ASP solving with clingo

    Gebser, M.,Kaminski, R.,Kaufmann, B.,and Schaub, T.Multi-shot ASP solving with clingo. InCoRR2017, volume abs/1705.09811

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Llm-arc: Enhancing llms with an automated reasoning critic

    Ferrucci, D.2024. Llm-arc: Enhancing llms with an automated reasoning critic

    2024

  7. [7]

    and Hinton, G.2009

    Krizhevsky, A. and Hinton, G.2009. Learning multiple layers of features from tiny images. Technical Report 0, University of Toronto, Toronto, Ontario

    2009

  8. [8]

    InReason- ing Web

    Law, M.,Russo, A.,and Broda, K.Logic-based learning of answer set programs. InReason- ing Web. Explainable Artificial Intelligence: 15th International Summer School 2019, Bolzano,

    2019

  9. [9]

    196–231, Cham

    Italy, September 20–24, 2019, Tutorial Lectures2019, pp. 196–231, Cham. Springer Interna- tional Publishing

    2019

  10. [10]

    Springer Publishing Company, Incorporated, 1st edition

    Lifschitz, V.2019.Answer Set Programming. Springer Publishing Company, Incorporated, 1st edition

    2019

  11. [11]

    Neural probabilistic logic programming in deepproblog,298, 103504

    Manhaeve, R.,Duman ˇci´c, S.,Kimmig, A.,Demeester, T.,and De Raedt, L.2021. Neural probabilistic logic programming in deepproblog,298, 103504

    2021

  12. [12]

    S.,and Kersting, K.2024

    Skryagin, A.,Ochs, D.,Dhami, D. S.,and Kersting, K.2024. Scalable neural-probabilistic answer set programming,78. 16Rader and Russo

    2024

  13. [13]

    S.,and Kersting, K.2022

    Skryagin, A.,Stammer, W.,Ochs, D.,Dhami, D. S.,and Kersting, K.2022. Neural- Probabilistic Answer Set Programming,19, 463–473

    2022

  14. [14]

    Dspy-based neural-symbolic pipeline to enhance spatial reasoning in llms

    Wang, R.,Sun, K.,and Kuhn, J.2024. Dspy-based neural-symbolic pipeline to enhance spatial reasoning in llms

    2024