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arxiv: 2511.17578 · v2 · submitted 2025-11-15 · 💻 cs.RO

Implicit Neural Field-Based Process Planning for Multi-Axis Manufacturing: Direct Control over Collision Avoidance and Toolpath Geometry

Neelotpal Dutta , Tianyu Zhang , Tao Liu , Yongxue Chen , Charlie C.L. Wang This is my paper

Pith reviewed 2026-05-17 22:15 UTC · model grok-4.3

classification 💻 cs.RO
keywords implicit neural fieldsmulti-axis manufacturingprocess planningcollision avoidancetoolpath generationadditive manufacturingsubtractive manufacturingneural networks
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The pith

Sinusoidally activated neural networks represent layers and toolpaths as implicit fields for direct collision avoidance and joint optimization in multi-axis manufacturing.

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

The paper introduces an implicit neural field-based framework for process planning in multi-axis manufacturing. Traditional methods handle collisions indirectly and design toolpaths separately after layer optimization. By using sinusoidally activated neural networks to model both layers and toolpaths as implicit fields, the approach creates a single differentiable pipeline. This allows direct evaluation of field values and derivatives at any point for explicit collision avoidance and simultaneous optimization. The method is shown effective for both additive and subtractive manufacturing examples.

Core claim

Representing manufacturing layers and toolpaths as implicit fields using sinusoidally activated neural networks enables direct evaluation of field values and derivatives at arbitrary spatial points, which in turn permits explicit collision avoidance and joint optimization within a unified differentiable pipeline.

What carries the argument

Sinusoidally activated neural networks representing layers and toolpaths as implicit fields, allowing point-wise queries of values and derivatives for optimization.

If this is right

  • Collisions are avoided explicitly during the optimization process instead of indirectly or post hoc.
  • Layers and toolpaths are optimized jointly rather than sequentially.
  • Network hyperparameters can be used to regularize and control singularities and topology transitions.
  • The framework applies across additive and subtractive manufacturing tasks.
  • Toolpath geometry is controlled directly during planning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This representation might allow easier integration with simulation or feedback control loops in robotic manufacturing systems.
  • If the implicit fields generalize well, the method could reduce the need for manual intervention in complex part geometries.
  • Extensions could include incorporating material properties or thermal effects into the same field representations.

Load-bearing premise

Sinusoidally activated neural networks can accurately and stably represent complex manufacturing geometries such that the joint optimization converges without singularities or unwanted topology changes.

What would settle it

Demonstration of a manufacturing geometry where the neural field representation leads to collision during planned paths or fails to produce valid toolpaths despite optimization.

Figures

Figures reproduced from arXiv: 2511.17578 by Charlie C.L. Wang, Neelotpal Dutta, Tao Liu, Tianyu Zhang, Yongxue Chen.

Figure 1
Figure 1. Figure 1: This figure summarizes our work. In the computational domain defined by an [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The figure illustrates our unified representation of both layers and toolpaths in [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Pipeline of the algorithm for neural field-based process planning: (a) illustrates [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the proposed collision detection scheme. The shaded gray region [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: An illustration of our inter-layer distance control strategy. The blue and green [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the total loss function framework used across different applications. [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Figure showing our neural approximation of the signed distance field (SDF) for [PITH_FULL_IMAGE:figures/full_fig_p029_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Evaluation of the signed distance field network ( [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: This figure presents the tool-geometry used in collision avoidance within our [PITH_FULL_IMAGE:figures/full_fig_p034_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Illustration of the multi-axis additive manufacturing (printing) setup. A 6-DoF [PITH_FULL_IMAGE:figures/full_fig_p035_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Layers for the Fertility model obtained using our method (by minimizing [PITH_FULL_IMAGE:figures/full_fig_p037_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: This figure presents a comparison of the Fertility model layers generated using [PITH_FULL_IMAGE:figures/full_fig_p038_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: This figure presents an additional comparison with the results of Neural Slicer. [PITH_FULL_IMAGE:figures/full_fig_p039_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Results and comparisons for the 4C model (d), which we attempt to print [PITH_FULL_IMAGE:figures/full_fig_p040_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of gradient–norm control strategies for generating support-free [PITH_FULL_IMAGE:figures/full_fig_p041_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Results and analysis for the Fork model. (a) Model geometry with applied [PITH_FULL_IMAGE:figures/full_fig_p043_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: This figure presents our result for Toolpath–Geometry–driven optimization [PITH_FULL_IMAGE:figures/full_fig_p044_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: This figure provides a comparison between our method and the High-Density [PITH_FULL_IMAGE:figures/full_fig_p045_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Results for the S-Curve model. The colored layers indicate different layers, [PITH_FULL_IMAGE:figures/full_fig_p047_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Rough-milling planning for the Cup model. (a) Target geometry with stock ma [PITH_FULL_IMAGE:figures/full_fig_p049_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: This figure illustrates the necessity of singularities in the gradient of the tool [PITH_FULL_IMAGE:figures/full_fig_p050_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Effect of the frequency-scaling factor ( [PITH_FULL_IMAGE:figures/full_fig_p052_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Figure illustrating the need for our toolpath curvature filtering method. (a) [PITH_FULL_IMAGE:figures/full_fig_p055_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: In this figure we illustrate the effect of the weight of the layer curvature loss [PITH_FULL_IMAGE:figures/full_fig_p056_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: This figure illustrates the effect of directly using Eq.(16) (normalized version) [PITH_FULL_IMAGE:figures/full_fig_p057_25.png] view at source ↗
read the original abstract

Existing curved-layer-based process planning methods for multi-axis manufacturing address collisions only indirectly and generate toolpaths in a post-processing step, leaving toolpath geometry uncontrolled during optimization. We present an implicit neural field-based framework for multi-axis process planning that overcomes these limitations by embedding both layer generation and toolpath design within a single differentiable pipeline. Using sinusoidally activated neural networks to represent layers and toolpaths as implicit fields, our method enables direct evaluation of field values and derivatives at any spatial point, thereby allowing explicit collision avoidance and joint optimization of manufacturing layers and toolpaths. We further investigate how network hyperparameters and objective definitions influence singularity behavior and topology transitions, offering built-in mechanisms for regularization and stability control. The proposed approach is demonstrated on examples in both additive and subtractive manufacturing, validating its generality and effectiveness.

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 proposes an implicit neural field-based framework for multi-axis manufacturing process planning in both additive and subtractive contexts. Layers and toolpaths are represented as implicit fields using sinusoidally activated neural networks (SIRENs), enabling a single differentiable pipeline for joint optimization with explicit collision avoidance via direct field and derivative evaluation at arbitrary points. The work includes analysis of network hyperparameters and objective definitions to control singularities and topology transitions, and demonstrates the approach on example parts.

Significance. If the central claims hold with accurate geometry representation and stable optimization, the method would advance the field by replacing indirect or post-processing collision handling with integrated, differentiable control over both layer geometry and toolpath shape. This could yield more efficient plans and better handling of complex multi-axis constraints. The built-in regularization mechanisms for stability are a practical strength.

major comments (2)
  1. [§4 and §3.2] §4 (Experiments) and §3.2 (Implicit Field Representation): The central claim of 'direct control' via derivative-based collision avoidance rests on SIREN fields producing accurate zero-level sets and normals for complex manufacturing geometries. However, no quantitative evaluation of representation error (e.g., Hausdorff distance, normal deviation, or comparison to ground-truth CAD distance fields) is provided for parts containing sharp edges or thin features. SIREN ringing or smoothing artifacts in such regimes would distort the collision loss, undermining the advantage over post-processing methods. The hyperparameter study addresses singularities but does not quantify this representation fidelity.
  2. [§3.3] §3.3 (Joint Optimization): The joint optimization of layers and toolpaths assumes convergence without problematic topology transitions or local minima induced by field artifacts. The manuscript should report convergence statistics, failure rates across trials, and sensitivity to initialization, as these directly affect whether the pipeline delivers reliable manufacturing plans.
minor comments (2)
  1. [Abstract and §1] The abstract and introduction would benefit from a brief comparison table contrasting the proposed pipeline with prior curved-layer methods on the dimensions of collision handling and toolpath control.
  2. [§3] Notation for the implicit field functions (e.g., layer field vs. toolpath field) should be introduced with explicit definitions and consistent usage across equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and have incorporated revisions to enhance the clarity and rigor of our claims regarding the accuracy and reliability of the proposed framework.

read point-by-point responses

  1. Referee: [§4 and §3.2] §4 (Experiments) and §3.2 (Implicit Field Representation): The central claim of 'direct control' via derivative-based collision avoidance rests on SIREN fields producing accurate zero-level sets and normals for complex manufacturing geometries. However, no quantitative evaluation of representation error (e.g., Hausdorff distance, normal deviation, or comparison to ground-truth CAD distance fields) is provided for parts containing sharp edges or thin features. SIREN ringing or smoothing artifacts in such regimes would distort the collision loss, undermining the advantage over post-processing methods. The hyperparameter study addresses singularities but does not quantify this representation fidelity.

    Authors: We agree that quantitative metrics for representation fidelity are important to substantiate the central claims. Although the hyperparameter study in the original manuscript provides indirect evidence through successful manufacturing outcomes, we acknowledge the value of direct error quantification. In the revised manuscript, we have added quantitative evaluations including Hausdorff distances and average normal deviations for the implicit representations against ground-truth CAD models for all demonstrated parts. These results are now reported in a new table in §4, showing that representation errors remain within acceptable manufacturing tolerances even for geometries with sharp edges and thin features. revision: yes

  2. Referee: [§3.3] §3.3 (Joint Optimization): The joint optimization of layers and toolpaths assumes convergence without problematic topology transitions or local minima induced by field artifacts. The manuscript should report convergence statistics, failure rates across trials, and sensitivity to initialization, as these directly affect whether the pipeline delivers reliable manufacturing plans.

    Authors: We recognize that reporting optimization reliability metrics would better demonstrate the robustness of the joint optimization pipeline. The original manuscript focused on the formulation and qualitative results, but to address this, we have performed additional experiments with multiple random initializations and report the convergence statistics, including success rates (defined as achieving collision-free plans without topology issues), average iterations, and sensitivity analysis in the revised §4. These additions confirm stable convergence in the tested scenarios due to the proposed regularization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard neural implicit properties

full rationale

The paper presents a new application of sinusoidally activated neural networks (SIREN) to represent manufacturing layers and toolpaths as implicit fields within a differentiable pipeline. Direct evaluation of field values and derivatives for collision avoidance follows from the established differentiability of such networks rather than any self-definitional reduction, fitted input renamed as prediction, or load-bearing self-citation chain. Hyperparameter investigation and regularization are described as empirical controls on singularities, not as justifications that loop back to the inputs. The central claims retain independent content as an engineering framework for joint layer/toolpath optimization in additive and subtractive manufacturing.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests primarily on the domain assumption that implicit neural fields with sinusoidal activations can represent and optimize manufacturing layers and toolpaths differentiably; no explicit free parameters or invented entities with independent evidence are detailed in the abstract.

axioms (1)
  • domain assumption Sinusoidally activated neural networks can represent layers and toolpaths as implicit fields suitable for direct derivative evaluation and optimization
    Invoked as the core representation enabling the differentiable pipeline.
invented entities (1)
  • Implicit neural fields for joint layer and toolpath representation no independent evidence
    purpose: To allow direct spatial evaluation and collision avoidance within optimization
    Introduced as the key modeling choice in the framework

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