# Loss Function Considering Dead Zone for Neural Networks

arXiv: https://arxiv.org/abs/2402.00393 · HTML: https://mlsanity.com/paper/2402.00393/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Encoding Physical Constraints in Differentiable Newton-Euler Algorithm](https://mlsanity.com/paper/2001.08861/) (2020)
- [Imitation Learning for Object Manipulation Based on Position/Force Information Using Bilateral Control](https://mlsanity.com/paper/1811.03759/) (2018)
- [Imitation Learning for Variable Speed Contact Motion for Operation up to Control Bandwidth](https://mlsanity.com/paper/2102.10283/) (2021)
- [An Independently Learnable Hierarchical Model for Bilateral Control-Based Imitation Learning Applications](https://mlsanity.com/paper/2203.08619/) (2022)
- [Imitation Learning for Nonprehensile Manipulation through Self-Supervised Learning Considering Motion Speed](https://mlsanity.com/paper/2206.10289/) (2022)
- [A New Autoregressive Neural Network Model with Command Compensation for Imitation Learning Based on Bilateral Control](https://mlsanity.com/paper/2103.08879/) (2021)
- [Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview](https://mlsanity.com/paper/1902.09032/) (2019)

## Built on by (most cited first, 2 of 2)

- [FACTR 2: Learning External Force Sensing for Commodity Robot Arms Improves Policy Learning](https://mlsanity.com/paper/2606.12406/) (2026)
- [FWBC-VLA: Force-Aware Whole-Body Compensation for Contact-Rich Loco-Manipulation](https://mlsanity.com/paper/2609.03889/) (2026)

## Abstract (arXiv)

It is important to reveal the inverse dynamics of manipulators to improve control performance of model-based control. Neural networks (NNs) are promising techniques to represent complicated inverse dynamics while they require a large amount of motion data. However, motion data in dead zones of actuators is not suitable for training models decreasing the number of useful training data. In this study, based on the fact that the manipulator joint does not work irrespective of input torque in dead zones, we propose a new loss function that considers only errors of joints not in dead zones. The proposed method enables to increase in the amount of motion data available for training and the accuracy of the inverse dynamics computation. Experiments on actual equipment using a three-degree-of-freedom (DOF) manipulator showed higher accuracy than conventional methods. We also confirmed and discussed the behavior of the model of the proposed method in dead zones.