How Many Training Samples Are Needed for the Inverse Kinematics Solutions by Artificial Neural Networks

Dong-Won Lim

arxiv: 2605.23583 · v1 · pith:UKXYKUIUnew · submitted 2026-05-22 · 💻 cs.RO · cs.LG

How Many Training Samples Are Needed for the Inverse Kinematics Solutions by Artificial Neural Networks

Dong-Won Lim This is my paper

Pith reviewed 2026-05-25 04:11 UTC · model grok-4.3

classification 💻 cs.RO cs.LG

keywords inverse kinematicsartificial neural networkstraining samplesdata efficiencyrobotic manipulatorfeedforward networksapproximation accuracy

0 comments

The pith

ANN inverse kinematics reaches peak accuracy with 125 training samples and shows no gains beyond that size.

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

The paper asks how many end-effector to joint-angle pairs are needed to train a feedforward network that solves inverse kinematics for a robot arm. It creates datasets of increasing size from an articulated manipulator, trains identical networks on each, and compares accuracy, convergence, and generalization. The central result is that model efficiency, defined as approximation accuracy relative to sample count, stops improving once the training set passes 125 examples. This threshold supplies a concrete rule of thumb for choosing dataset size when using neural networks for robotic IK.

Core claim

Using an articulated robotic manipulator, the study generates varying amounts of joint-position pairs to train feedforward neural networks and assess their accuracy, convergence, and generalization capability. The results reveal more training samples than 125 did not contribute to the improvement of the model efficiency that the comparable measure dealing with the approximation accuracy over the sampling size.

What carries the argument

Feedforward neural networks trained on joint-position pairs generated from an articulated manipulator to approximate inverse kinematics solutions.

If this is right

125 samples balance approximation accuracy against the cost of data generation and training.
Larger datasets yield diminishing returns for this class of ANN IK solver.
ANNs can deliver reliable IK predictions without requiring extensive training data collection.
The observed efficiency plateau supplies practical guidance for sizing datasets in robotic applications.

Where Pith is reading between the lines

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

The 125-sample threshold may shift for other robot geometries or network depths, suggesting targeted follow-up tests.
Data-efficient IK solvers could shorten the time from data collection to real-time control deployment.
Alternative metrics such as worst-case error or energy consumption might reveal different saturation points.

Load-bearing premise

The chosen accuracy and efficiency metrics together with the specific articulated manipulator and feedforward network are representative enough to determine a general data-size threshold for ANN-based IK solvers.

What would settle it

Repeating the experiment on a different manipulator or network architecture and finding that accuracy continues to rise measurably past 125 samples.

Figures

Figures reproduced from arXiv: 2605.23583 by Dong-Won Lim.

**Figure 2.** Figure 2: The robot configuration with the local coordinate systems [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Training Progress over the Epochs for Various Numbers of Samples [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Inverse Kinematics Artificial Neural Networks Function Performances [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Inverse Kinematics Artificial Neural Networks Function Performances [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

read the original abstract

Inverse Kinematics (IK) plays a critical role in robotic motion planning and control. The IK solutions of a robot manipulator could be done by conventional ways such as geometric, algebraic, or Jacobian methods, which have drawbacks. The Artificial Neural Networks (ANNs) have become a promising alternative for approximating IK solutions due to their generalization ability and computational efficiency. This approach basically trains only a few samples of the end effector that are recorded for the solution of the IK problem. However, a fundamental question remains: how many training samples are sufficient to achieve reliable and accurate IK predictions? This study investigates the mathematical framework of relating the size of training datasets and the accuracy of ANN-based IK solvers. Using an articulated robotic manipulator, we generate varying amounts of joint-position pairs to train feedforward neural networks and assess their accuracy, convergence, and generalization capability. The results reveal more training samples than 125 did not contribute to the improvement of the model efficiency that the comparable measure dealing with the approximation accuracy over the sampling size, offering valuable insight into data efficiency. This work provides practical guidance for optimizing the data sizing of ANN solutions, balancing computational cost and model accuracy for real-world robotic applications.

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.

Desk Editor's Note private letter to a colleague

Empirical plateau at 125 samples for one IK case, but too narrow to give general guidance on data sizing.

read the letter

The punchline is that the paper reports an empirical finding that 125 training samples are sufficient for their ANN to solve inverse kinematics on one particular articulated manipulator, with additional samples not improving accuracy or efficiency. They generate joint and end-effector position pairs, train feedforward networks on subsets of different sizes, and measure how accuracy and convergence behave as the training set grows. The result is a clear plateau after 125 samples in their tests. This is a practical question, and they address it directly with an experiment. The paper does well at keeping the focus on data efficiency, which is a real concern when deploying these models. The observation itself is straightforward and could be replicated by others working on similar problems. Where it falls short is in scope. The entire result comes from a single robot configuration and a single network type. The abstract talks about providing general practical guidance, but without testing across different manipulators or architectures, or providing an analytical model that predicts the threshold, the finding stays local to their case. There is also no information on how they chose the accuracy measure, whether they ran multiple trials, or how the training samples were sampled from the configuration space. These details matter for judging if the plateau is real or an artifact of their setup. The work is for practitioners who want a ballpark figure for data collection when training neural IK solvers on comparable hardware. It is not for readers seeking new theory or results that hold across a range of systems. I would not bring this to a reading group. I would not cite it. It does not seem important or grounded enough to send out for peer review.

Referee Report

2 major / 1 minor

Summary. The paper claims that for ANN-based inverse kinematics using feedforward networks on an articulated manipulator, training accuracy and efficiency (measured as approximation accuracy relative to sampling size) plateau after 125 samples, with additional data yielding no further gains; it positions this as a mathematical framework providing practical guidance on data sizing for ANN IK solvers.

Significance. If the plateau result holds under broader conditions, it would offer useful empirical guidance for minimizing training data in robotic IK applications while maintaining accuracy, potentially reducing computational overhead in real-world deployments.

major comments (2)

[Abstract] Abstract: The abstract invokes investigation of a 'mathematical framework' relating dataset size to accuracy, yet reports only an empirical plateau observed for one specific articulated manipulator and feedforward architecture; no derivation or general relation independent of these choices is shown.
[Results] Results (implied by abstract description): The central claim that samples beyond 125 provide no efficiency improvement rests on a single manipulator and network; without ablation studies varying DOF, kinematics, or depth, the result does not support general 'practical guidance for optimizing the data sizing of ANN solutions'.

minor comments (1)

[Abstract] Abstract: The efficiency metric is described only as 'the comparable measure dealing with the approximation accuracy over the sampling size'; this should be defined with an explicit formula or reference to a table/equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address the points regarding the abstract language and the scope of the empirical results below, and we will revise the manuscript accordingly to avoid overstating generality.

read point-by-point responses

Referee: [Abstract] Abstract: The abstract invokes investigation of a 'mathematical framework' relating dataset size to accuracy, yet reports only an empirical plateau observed for one specific articulated manipulator and feedforward architecture; no derivation or general relation independent of these choices is shown.

Authors: We agree the phrasing 'mathematical framework' is imprecise for an empirical study. The work consists of systematic experiments on dataset size versus accuracy for one manipulator and feedforward network; no closed-form derivation or architecture-independent relation is provided. We will revise the abstract and introduction to describe the contribution as an empirical investigation of data efficiency for the tested case. revision: yes
Referee: [Results] Results (implied by abstract description): The central claim that samples beyond 125 provide no efficiency improvement rests on a single manipulator and network; without ablation studies varying DOF, kinematics, or depth, the result does not support general 'practical guidance for optimizing the data sizing of ANN solutions'.

Authors: The referee correctly notes the limitation to a single manipulator, fixed DOF, and one network depth. No ablations across kinematics or architectures are present, so the 125-sample plateau cannot be claimed as general. We will revise the abstract, results, and conclusions to restrict all guidance statements to the specific articulated manipulator and feedforward architecture studied, removing language implying broader applicability. revision: yes

Circularity Check

0 steps flagged

Empirical plateau observation contains no circular derivation steps

full rationale

The paper is an empirical study that trains feedforward networks on varying numbers of IK samples for one articulated manipulator and reports an observed accuracy plateau after 125 samples. No equations, derivations, fitted parameters renamed as predictions, or self-citations appear in the load-bearing claims. The central result is a direct experimental measurement rather than a reduction to prior inputs or self-referential definitions, so the work is self-contained as a case-specific report.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Ledger extracted from abstract only; limited information available on parameters or assumptions.

free parameters (1)

training sample threshold = 125
The value 125 is presented as the point beyond which additional samples yield no efficiency gain; it is the result of the sampling-size experiments described.

axioms (1)

domain assumption Artificial neural networks can serve as a viable approximation method for inverse kinematics solutions
Abstract states ANNs have become a promising alternative due to generalization and efficiency.

pith-pipeline@v0.9.0 · 5734 in / 1148 out tokens · 32595 ms · 2026-05-25T04:11:17.587683+00:00 · methodology

discussion (0)

Reference graph

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D., Dhariwal, P.,

Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., . . . & Amodei, D.: Language models are few-shot learners.Advances in Neural Information Processing Systems, 33, 1877–1901 (2020)

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work page internal anchor Pith review Pith/arXiv arXiv 2023

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Abdin, M., Aneja, J., Awadalla, H., Awadallah, A., Awan, A. A., Bach, N., . . . & Bubeck, S.: Phi-3 technical report: A highly capable language model locally on your phone.arXiv preprint, arXiv:2404.14219 (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024

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& Lederer, J.: How many samples are needed to train a deep neural network?arXiv preprint, arXiv:2405.16696 (2024)

Golestaneh, P., Taheri, M. & Lederer, J.: How many samples are needed to train a deep neural network?arXiv preprint, arXiv:2405.16696 (2024)

work page arXiv 2024

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Nagata, F. and Watanabe, K.: Neural network-based inverse kinematics for Motoman HS20 and its efficient learning method.Journal of the Institute of Industrial Applications Engineers, 4(4), 166 (2016)

work page 2016

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E., Da¸ s, M

K¨ ut¨ uk, M. E., Da¸ s, M. T. and D¨ ulger, L. C.: Forward and inverse kinematics analysis of Denso robot. In:Proceedings of the International Symposium on Mechanism and Machine Science, pp. 71–78 (2017)

work page 2017

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D.: A closed loop inverse kinematics solver intended for offline calculation optimized with GA.Robotics, 7(1), 7 (2018)

Bjoerlykhaug, E. D.: A closed loop inverse kinematics solver intended for offline calculation optimized with GA.Robotics, 7(1), 7 (2018)

work page 2018

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and Kitjaidure, Y.: Forward kinematic-like neural network for solving the 3D reaching inverse kinematics problems

Srisuk, P., Sento, A. and Kitjaidure, Y.: Forward kinematic-like neural network for solving the 3D reaching inverse kinematics problems. In:2017 14th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Tech- nology (ECTI-CON), pp. 214–217. IEEE (2017)

work page 2017

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and Habib, M

Nagata, F., Inoue, S., Fujii, S., Otsuka, A., Watanabe, K. and Habib, M. K.: Learning of inverse kinematics using neural networks and its application to kinematic control of position-based servo motor. In:Proceedings of the World Congress on Advances in Aero- nautics, Nano, Bio, Robotics, and Energy (ANBRE15), pp. 1–13 (2015)

work page 2015

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V.: Neural network based inverse kinematics solution for trajectory tracking of a robotic arm.Procedia Technology, 12, 20–27 (2014)

Duka, A. V.: Neural network based inverse kinematics solution for trajectory tracking of a robotic arm.Procedia Technology, 12, 20–27 (2014). 13

work page 2014

[13] [13]

Kumar, R. R. and Chand, P.: Inverse kinematics solution for trajectory tracking using artificial neural networks for SCORBOT ER-4u. In:Proceedings of the 6th International Conference on Automation, Robotics and Applications (ICARA), pp. 364–369 (2015)

work page 2015

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T., Ismail, N., Hamouda, A

Hasan, A. T., Ismail, N., Hamouda, A. M. S., Aris, I., Marhaban, M. H. and Al-Assadi, H. M. A. A.: Artificial neural network-based kinematics Jacobian solution for serial manip- ulator passing through singular configurations.Advances in Engineering Software, 41(2), 359–367 (2010)

work page 2010

[15] [15]

Almusawi, A. R. J., D¨ ulger, L. C. and Kapucu, S.: A new artificial neural network approach in solving inverse kinematics of robotic arm (Denso VP6242).Computational Intelligence and Neuroscience, 2016, Article ID 5720163 (2016)

work page 2016

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Bachelor’s thesis, Universitat Polit` ecnica de Catalunya (2024)

Marouan, H.: Single-shot uncertainty estimation in artificial neural networks using ensem- ble classes. Bachelor’s thesis, Universitat Polit` ecnica de Catalunya (2024)

work page 2024

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W.: Bounds on the number of training samples needed for inverse kinematics solutions by artificial neural networks

Lim, D. W.: Bounds on the number of training samples needed for inverse kinematics solutions by artificial neural networks. In:Proceedings of the 23rd International Conference on Control, Automation and Systems (ICCAS), pp. 1323–1328 (2023)

work page 2023

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and Chorus, C

Alwosheel, A., van Cranenburgh, S. and Chorus, C. G.: Is your dataset big enough? Sample size requirements when using artificial neural networks for discrete choice analysis.Journal of Choice Modelling, 28, 167–182 (2018)

work page 2018

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G., Mohan, C

Mehrotra, K. G., Mohan, C. K. and Ranka, S.: Bounds on the number of samples needed for neural learning.IEEE Transactions on Neural Networks, 2(6), 548–558 (1991)

work page 1991

[20] [20]

Lim, D. W. and Lee, Y. K.: On the number of training samples for inverse kinematics solutions by artificial neural networks. In:Proceedings of the 16th International Conference on Ubiquitous Robots (UR), pp. 61–64 (2019)

work page 2019

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R.: Universal approximation bounds for superpositions of a sigmoidal function

Barron, A. R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory, 39(3), 930–945 (1993)

work page 1993

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Deng, T.: Effect of the number of hidden layer neurons on the accuracy of the back propagation neural network.Highlights in Science, Engineering and Technology, 74, 462– 468 (2023)

work page 2023

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Available:http:// neuralnetworksanddeeplearning.com

Nielsen, M.:Neural Networks and Deep Learning. Available:http:// neuralnetworksanddeeplearning.com. Last accessed 2025/10/01. 14

work page 2025