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Neural Network-assisted Analysis of Tube Vocal Tract Models

Summary

The paper introduces DeepVocalTube (DVT), a methodological pipeline that uses neural networks to study how the shape of a segmented acoustic tube, a classic simplified model of the vocal tract, determines its resonances (formants). The authors simulated a 16 cm open-to-closed tube built from sixteen 1 cm cylinders. They randomly varied the cross-sectional area of each cylinder and computed F1–F3 with the Liljencrants and Fant (1975) circuit-theory algorithm. They also added an internal end correction for abrupt narrow-to-wide transitions. A multiple linear regression baseline fit the resulting data poorly, which showed that the area-to-formant relationship is strongly nonlinear. They then trained a multilayer perceptron and used SHAP to estimate how much each tube segment contributes to each predicted formant, both for single configurations such as a vowel [a] and across the whole dataset. The framework is not tied to one simulation method and can work with any segment-based tube model. This makes it a reusable, interpretable tool for exploring articulatory-acoustic relations in phonetics research and teaching.

Key points

  • Synthetic dataset: 40,000 random 16-segment configurations with segment areas between 0.1 and 10 cm². A sensitivity check compared training sets of 1,000, 5,000, 10,000, 20,000 and 40,000 samples.
  • Linear baseline: the linear regression reached R² below 0.32 for all three formants, and its residuals showed clear nonlinear structure.
  • MLP setup: a scikit-learn MLPRegressor with 16 standardized inputs and hidden layers of 64 and 32 ReLU units. Training used Adam (learning rate 0.001, batch size 200), MSE loss with L2 α = 1e-4, 500 epochs and random seed 42. XGBoost was set aside because earlier work (Song, 2025) found it consistently weaker than the MLP.
  • End correction: applied when a narrow section is less than 0.16 of the adjoining wider area, following Ingard (1953) and Fant (1971). The original Fant program lacked this correction.
  • Interpretability: SHAP waterfall, beeswarm and bar plots rank the influence of each segment on F1, F2 and F3.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Linguistics & languages

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.63317/3qp8kma6ohov

@inproceedings{song2026neural,
  title = {{Neural Network-assisted Analysis of Tube Vocal Tract Models}},
  author = {Song, Runhui and Sjons, Johan and Ekstrom, Axel G.},
  booktitle = {Proceedings of the Fifteenth Language Resources and Evaluation Conference},
  year = {2026},
  doi = {10.63317/3qp8kma6ohov},
  url = {https://doi.org/10.63317/3qp8kma6ohov}
}

References

31 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. H. Akaike. 2003. A new look at the statistical model identification. IEEE transactions on automatic control, 19(6):716–723. find
  2. S. Arlot and A. Celisse. 2009. A survey of cross validation procedures for model selection. Statistics Surveys, 4. find
  3. J. Ba and R. Caruana. 2014. Do deep nets really need to be deep? Advances in neural information processing systems, 27. find
  4. P. Badin and G. Fant. 1984. Notes on vocal tract computation. STL QPSR, 2(3):53–108. find
  5. J. Bergstra and Y. Bengio. 2012. Random search for hyper-parameter optimization. The journal of machine learning research, 13(1):281–305. find
  6. L. Breiman, J. Friedman, R. A. Olshen, and C. J. Stone. 2017. Classification and regression trees. Routledge. find
  7. R. Carré, P. Divenyi, and M. Mrayati. 2017. Speech: A dynamic process. Walter de Gruyter GmbH & Co KG. find
  8. T. Chen and C. Guestrin. 2016. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, pages 785–794. find
  9. J. Dang, C. H. Shadle, Y. Kawanishi, K. Honda, and H. Suzuki. 1998. An experimental study of the open end correction coefficient for side branches within an acoustic tube. The Journal of the Acoustical Society of America, 104(2):1075– 1084. find
  10. P. Delattre. 1951. The physiological interpretation of sound spectrograms. Pmla, 66(5):864–875. find
  11. H. K Dunn. 1950. The calculation of vowel resonances, and an electrical vocal tract. The Journal of the Acoustical Society of America, 22(6):740– 753. find
  12. G. Fant. 1971. Acoustic Theory of Speech Production: With Calculations Based on X-Ray Studies of Russian Articulations. Mouton. find
  13. J. H. Friedman. 2001. Greedy function approximation: a gradient boosting machine. Annals of statistics, pages 1189–1232. find
  14. Figure 3: Waterfall plots of SHAP values for predicting F1 (top), F2 (middle), and F3 (bottom) for an example vowel [a], highlighting the contribution of each tube segment in a single example. find
  15. T. Fushiki. 2011. Estimation of prediction error by using k-fold cross-validation. Statistics and Computing, 21:137–146. find
  16. Xavier Glorot and Yoshua Bengio. 2010. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249–256. JMLR Workshop and Conference Proceedings. find
  17. I. Goodfellow, Y. Bengio, and A. Courville. 2016. Deep learning. Adaptive computation and machine learning. MIT Press, Cambridge, MA. find
  18. M. Halle. 1983. On distinctive features and their articulatory implementation. Natural language and linguistic theory, 1(1):91–105. find
  19. S. Harper, L. Goldstein, and Shrikanth Narayanan. 2020. Variability in individual constriction contributions to third formant values in american english/r/. The Journal of the Acoustical Society of America, 147(6):3905–3916. find
  20. W. L. Henke. 1966. Dynamic articulatory model of speech production using computer simulation. Ph.D. thesis, Massachusetts Institute of Technology. find
  21. U. Ingard. 1953. On the theory and design of acoustic resonators. The Journal of the Acoustical Society of America, 25(6):1037–1061. find
  22. IPA International Phonetic Association. 1999. Handbook of the International Phonetic Association: A guide to the use of the International Phonetic Alphabet. Cambridge University Press. find
  23. R. Jakobson, C. G. Fant, and M. Halle. 1951. Preliminaries to speech analysis: The distinctive features and their correlates. MIT press. find
  24. G. James, D. Witten, T. Hastie, and R. Tibshirani. 2021. An introduction to statistical learning : with applications in R, second edition edition. Springer texts in statistics. Springer, New York. find
  25. K. Johnson. 2012. Acoustic and auditory phonetics, 3. ed. edition. Wiley-Blackwell, Malden, MA. find
  26. D. P. Kingma and J. Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980. find
  27. P. Ladefoged and I. Maddieson. 1996. The sounds of the world’s languages. Phonological theory. Blackwell, Oxford. find
  28. J. Lee, S. Shaiman, and G. Weismer. 2016. Relationship between tongue positions and formant frequencies in female speakers. The Journal of the Acoustical Society of America, 139(1):426– 440. find
  29. J. Liljencrants and G. Fant. 1975. Computer program for vt-resonance frequency calculations. STL-QPSR, 16:15–21. find
  30. B. Lindblom, J. Sundberg, P. Branderud, and H. Djamshidpey. 2007. On the acoustics of spread lips. Proceedings of Fonetik, 50(1):13– 16. find
  31. B. E. F. Lindblom and J. E. F. Sundberg. 1971. Acoustical consequences of lip, tongue, jaw, and larynx movement. The Journal of the Acoustical Society of America, 50(4B):1166–1179. find

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