Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder

Kenji Ishizuka; Shoichi Koyama

REVIEW 3 major objections 5 minor 29 references

Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A conditioned autoencoder estimates the spatial distribution of acoustic transfer function magnitudes from sparse microphone measurements, and in a simulated room it reports lower log-spectral distortion than kernel ridge regression and…

desk verdict Competent incremental extension of the authors' HRTF autoencoder; the grid-only evaluation leaves the arbitrary-position claim untested, but the core result is internally sound and worth refereeing. read the letter →

arxiv 2506.16729 v1 pith:LKY4UUBI submitted 2025-06-20 cs.SD eess.AS

Shoichi Koyama , Kenji Ishizuka This is my paper · ORCID

classification cs.SDeess.AS

keywords soundfieldestimationacoustictransferfunctionmagnitudeconditionedautoencoderbasisexpansionlog-spectraldistortionsparsemeasurementsspatialaudiohypernetworks

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a neural-network method for reconstructing the spatial distribution of acoustic transfer function magnitudes from a sparse set of microphone measurements, without needing phase information. The central claim is that an autoencoder whose weights are conditioned on source and receiver positions, frequency, and the number of microphones acts as a learnable, nonlinear analogue of classical basis-expansion sound-field reconstruction. In a simulated shoebox room, the method reports lower log-spectral distortion than kernel ridge regression and neural-field baselines at every tested microphone count (5, 10, 20, 50, and 100), while supporting arbitrary target positions and a single forward-pass inference. This matters because magnitude-only estimation applies where phase measurements are unreliable, such as unsynchronized receivers or when measuring the directivity of musical instruments.

What carries the argument

The central object is the conditioned autoencoder, composed of an encoder, an aggregation module, and a decoder. The encoder and decoder weights and biases are generated on the fly by conditioning networks that take a vector of source position, receiver position, angular frequency, and observation count, normalized and expanded by Fourier feature mapping. After the encoder produces latent variables for each measurement position, the aggregation module averages them over positions, yielding receiver-position-independent prototypes. The decoder then turns the prototypes into estimated log-ATF magnitudes at target positions. The work this structure does is to generalize basis expansion: instead of fixed spatial basis functions with estimated coefficients, the network learns position-dependent nonlinear features (generated weights) and receiver-independent coefficients (prototypes), which is why the method can combine datasets with different measurement setups and evaluate at arbitrary target positions without retraining.

What would settle it

Evaluating the trained model at positions shifted by 0.05 m off the training grid in the same simulated room, or on measured ATFs from a real room, would settle the central claim: in either case, a sharp rise in log-spectral distortion would show that the announced support for arbitrary positions and the practical accuracy do not hold.

Watch

Extended reading notes

Core claim

The paper claims that the log-magnitude of an acoustic transfer function at arbitrary target positions can be estimated from sparse observations by a conditioned autoencoder. The encoder maps the observed magnitudes at measurement positions into latent vectors; these vectors are averaged over measurement positions, producing receiver-position-independent prototypes; and a decoder maps the prototypes to magnitudes at target positions. Crucially, the encoder and decoder weights are themselves generated by small networks conditioned on source position, receiver position, angular frequency, and, for the encoder, the number of observations. The paper interprets this structure as an autoencoder-based extension of basis expansion: the latent variables play the role of expansion coefficients and the position-dependent generated weights play the role of basis functions. The reported experiments in a simulated shoebox room show the proposed method achieving the lowest log-spectral distortion among kernel ridge regression, a neural-field baseline, and the proposed method for all microphone counts from 5 to 100, with finer magnitude structure captured up to roughly 400 Hz and general shape above that.

Load-bearing premise

The result depends on the untested premise that a network trained and evaluated on a fixed 0.1 m grid in one simulated room also estimates magnitudes accurately at arbitrary off-grid positions and in real rooms.

Editorial extensions

If this is right

In the tested simulated room, the proposed method has the lowest average log-spectral distortion of the three compared methods at every tested microphone count.
The model estimates ATF magnitudes at target positions given at inference time, so it is not tied to a predefined output grid.
Datasets recorded with different microphone layouts can be combined because the network is conditioned on positions rather than on fixed measurement indices.
Inference is a single forward pass, avoiding the per-test-case retraining needed by neural-field baselines.
Magnitude-only estimation stays viable when phase is unreliable or a reference signal cannot be obtained from the source.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the paper trains and evaluates on one simulated room, an untested but plausible consequence is that the learned position-conditioned features transfer across rooms; a direct test would train on several simulated rooms and evaluate on an unseen one.
The simple averaging aggregation may be a bottleneck for uneven microphone layouts; an attention-weighted aggregation is a concrete variant that could be compared against the reported results.
Arbitrary target positions are not directly evidenced, since evaluation uses the full 1331-position grid; evaluating at positions shifted by half the grid spacing would test whether the conditioning truly supports continuous positions.
Since the output is magnitude-only, downstream tasks needing phase (auralization, beamforming) would require a separate phase estimator, so coupling this autoencoder with a phase prior is a natural extension.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read it. The short version: this is a solid, small paper, not a breakthrough. It extends the authors' HRTF autoencoder [12] to room ATF magnitude estimation, adds frequency conditioning, and reuses prototype averaging; the framing as a nonlinear basis expansion is apt. The experiment is a single simulated shoebox room with 1331 grid positions, and the reported result — proposed method lowest LSD across M — is internally consistent with Figure 3.

Credit where due: the method makes sense, the measurement setup is described clearly enough to reproduce in principle, and the comparison against KRR and NF is a reasonable first pass. The NF baseline being trained 1400 epochs then fine-tuned only 10 epochs is a bit weak, and KRR hyperparameters look hand-picked rather than tuned, but neither flaw is fatal; the proposed method also benefits from training on multiple M values, which is a real advantage.

The bigger soft spot, which the stress-test note gets right: the paper's motivation leans on arbitrary target positions, but every evaluation target is a vertex of the fixed 0.1 m grid. No off-grid query is tested. The decoder is continuous in receiver position by construction, so the architecture could plausibly generalize off-grid, but that is an untested assumption. For a paper whose abstract says 'spatially sparse measurements' and whose introduction criticizes fixed-target methods, this gap matters. It would be straightforward to add off-grid targets to the evaluation, and I'd want to see that before believing the arbitrary-position claim.

Minor: the text lists M = 5, 10, 20, 100, but Figure 3's axis starts at 20 and the text also mentions M = 50. That ambiguity should be cleaned up. Also, no code or data release, which makes the 'lowest LSD' claim harder to verify; that's worth requesting but not disqualifying.

Citation pattern is fine. They cite their own HRTF paper and are transparent about the architectural debt; self-citation here is honest. No circularity: loss is on external ground-truth magnitudes.

Who is this for: people working on ATF/RIR estimation, especially magnitude-only problems like unsynchronized arrays or directivity measurement. They get a clearly presented baseline that beats KRR and NF in one simulated room. It deserves a serious referee. My recommendation: send it out, with a request for off-grid and ideally multi-room validation, fairer baseline tuning, and code/data. If the off-grid result comes out as strong as the grid result, the paper is publishable; if it doesn't, the contribution shrinks to a narrow grid-based method.

Referee Report

3 major / 5 minor

Summary. The paper proposes a conditioned autoencoder for estimating the log-magnitude of acoustic transfer functions (ATFs) from sparse microphone measurements. The encoder takes receiver-position-conditioned weights and sparse observations, aggregates latent vectors by averaging over receivers, and a decoder with receiver-position-conditioned weights maps the averaged latent to target positions. The training loss is mean log-spectral distortion (LSD). The method is evaluated in an image-source simulated shoebox room against kernel ridge regression (KRR) and a neural-field (NF) baseline for reported microphone counts of M = 5, 10, 20, and 100, with the claimed conclusion that the proposed method achieves the lowest LSD for all tested M. The authors argue that the architecture supports arbitrary target positions and low inference cost compared with retraining-based neural field methods.

Significance. If the reported result holds, the method is a useful contribution: it extends a basis-expansion viewpoint with learned nonlinear basis via an autoencoder, achieves lower LSD than the tested baselines in simulation, supports variable microphone counts, and offers low inference cost. The paper's strengths include an explicit loss definition, a clearly motivated architecture, and a simulation protocol that is reproducible in principle. However, the central generality claim (arbitrary target positions) is not exercised: all positions are grid vertices, one simulated room is used, and the baselines appear undertuned. The result is therefore plausible but not yet established beyond the specific evaluation.

major comments (3)

[Section 5.1] The paper claims in Sections 1 and 6 that the method estimates ATF magnitude at arbitrary target positions, but every evaluated target position is a vertex of the 0.1 m grid used to discretize the target region: the text states that 'the 1331 target positions were obtained by discretizing the target region every 0.1 m' and that measurement positions are 'randomly chosen from the target positions.' No off-grid query is evaluated anywhere. The decoder may generalize smoothly, but this is an architectural assumption, not a demonstrated property. Please add an off-grid evaluation (e.g., jittered receiver positions or a held-out finer grid) or revise the arbitrary-position claim to a fixed-grid claim.
[Section 5.2 and Figure 3] The tested microphone counts are inconsistent. Section 5.1 lists M = 5, 10, 20, and 100, but Figure 3's horizontal axis starts at 20 and the results text mentions 'M = 50 and 100.' This ambiguity is load-bearing because the headline claim is 'the lowest for all the numbers of observations,' and the strongest advantage of learning-based methods is expected at small M. Please report the exact set of M values, fix the figure axis, and include the M = 5 and M = 10 results so the claim can be verified.
[Section 5.1, baselines] The baseline comparisons may be unfair. The KRR precision and regularization parameters are set to fixed values (10^-2 and 10^-3) without any tuning procedure, and the NF baseline is fine-tuned for only 10 epochs at learning rate 10^-5 after its initial 1400 epochs. Because the central result is relative accuracy, the baselines should receive comparable tuning effort (for example, cross-validation on the validation split), and the selected hyperparameters should be reported. Additionally, the proposed network for small M is trained on a mixture of M values while the KRR baseline is not trained at all; please clarify how this protocol asymmetry affects the comparison.

minor comments (5)

[Section 7] The heading 'Ackowledgments' is a typo and should read 'Acknowledgments.'
[Section 1] The sentence 'cannot be output in the first plane' is unclear; it likely should be 'in the first place' or 'at the source.' Please rewrite for clarity.
[Figure 1] The figure caption appears garbled in the manuscript text ('&ODPEFS %FDPEFS' etc.); please ensure the figure and caption are rendered correctly.
[Section 5.1] The description 'The number of measurements M used for the training was larger than that for the validation and test' is vague. Please specify exactly which M values are used in each training condition and how the validation set is matched to M.
[Section 4.1] Architectural details needed for reproducibility are missing: layer sizes, the number of hyper-network layers, Fourier feature scales, and the dimensions of the latent variables are not stated. Please include these details.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the method is trained and tested against externally simulated ground-truth ATF magnitudes, and no prediction reduces by construction to a fitted parameter or self-citation.

full rationale

The paper's central claim is that the proposed conditioned autoencoder estimates log-ATF magnitude distributions with lower average LSD than kernel ridge regression and neural-field baselines across the tested numbers of microphones. The derivation chain is a standard supervised-learning evaluation, not a self-referential construction. The loss in Eq. (6) is defined directly on the difference between the network output and the externally computed log-ATF magnitudes a_{n,l,f}, which are generated by the image-source method in Section 5.1, i.e., ground truth that does not depend on the model. The architectural elements, including prototype averaging in Eq. (5), are mechanisms for aggregating inputs and generating outputs, not definitions of the target quantity. The only self-citation, the IWAENC 2022 HRTF paper [12], is used to say the 'detailed network architecture is almost the same' as prior work; this is a provenance statement and does not by itself justify the experimental outcome. The empirical comparison is evaluated against the same external simulation for all methods, including the baselines, and the reported LSD values are not re-expressions of training loss or of any fitted parameter. The reader's flagged concern about off-grid generalization is a genuine scope risk, but that is a correctness and evaluation-coverage issue rather than circularity, because the target values used for testing are external and the network is not constrained to reproduce them by construction. Likewise, the discrepancy between the stated microphone counts (M = 5, 10, 20, 100) and Figure 3's axis beginning at 20 is an ambiguity in reporting, not a circular step. No quantity in the paper is defined in terms of another quantity it is claimed to predict, and no fitted parameter is renamed as a prediction. Therefore the appropriate circularity score is 0.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

No new physical entities or ad hoc parameters are introduced to match the data; the central claim rests on the training data distribution and the chosen network architecture. The main unaccounted factors are the unstated network hyperparameters and manually set baseline parameters.

free parameters (3)

KRR kernel precision (inverse variance) = 1e-2
Set by hand in Sec 5.1 without tuning; affects KRR baseline performance.
KRR regularization parameter = 1e-3
Set by hand in Sec 5.1 without tuning.
Proposed network hyperparameters = not specified
Layer counts, hidden widths, latent dimension, and weight-generation network sizes are not reported; these choices affect the reported LSD.

assumptions (3)

domain assumption The image-source method provides ATF magnitudes representative of real rooms.
The entire evaluation uses pyroomacoustics image-source RIRs in one shoebox room; if the simulation is unrepresentative, the reported accuracy may not transfer.
domain assumption The network generalizes from the discrete 0.1 m target grid to arbitrary receiver positions.
The method is claimed to estimate at arbitrary positions, but training and evaluation use a fixed grid (Sec 2, Sec 5.1).
standard math Truncating RIRs to 128 samples and applying FFT yields the ATF magnitude.
Sec 5.1; this is standard signal processing but the truncation window affects spectral leakage.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder." pith.science (2026). https://pith.science/paper/LKY4UUBI

@misc{pith2026250616729,
  author       = {Pith},
  title        = {Pith review of: Learning Magnitude Distribution of Sound Fields via Conditioned Autoencoder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LKY4UUBI}},
  note         = {Machine review of arXiv:2506.16729}
}

read the original abstract

A learning-based method for estimating the magnitude distribution of sound fields from spatially sparse measurements is proposed. Estimating the magnitude distribution of acoustic transfer function (ATF) is useful when phase measurements are unreliable or inaccessible and has a wide range of applications related to spatial audio. We propose a neural-network-based method for the ATF magnitude estimation. The key feature of our network architecture is the input and output layers conditioned on source and receiver positions and frequency and the aggregation module of latent variables, which can be interpreted as an autoencoder-based extension of the basis expansion of the sound field. Numerical simulation results indicated that the ATF magnitude is accurately estimated with a small number of receivers by our proposed method.

Figures

Figures reproduced from arXiv: 2506.16729 by the authors.

**Figure 2.** Experimental setting. The decoder generates the log-ATF magnitudes ˆan,l,f at the target positions from the prototypes ¯zd,l,f , which consists of layer normalization, the Mish nonlinearity, and hyper-linear layers. 4.2 Loss function The loss function L for the training is defined as the mean log-spectral distortion (LSD) of the ATF as L = 1 NL X n,l s 1 F X f (ˆan,l,f − an,l,f ) 2 . (6) 5 Experimental evaluations W… view at source ↗

**Figure 3.** Average LSD with respect to the number of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Estimated ATF magnitude at the center of the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Magnitude distribution on x-y-plane at z = 0 at 250 Hz when M = 5. proximately 400 Hz and also captured the general shape at frequencies above that [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

29 extracted references · 27 canonical work pages

[12]

Head-related transfer function interpolation from spatially sparse measurements 5 using autoencoder with source position condi- tioning,

Y. Ito, T. Nakamura, S. Koyama, and H. Saruwatari, “Head-related transfer function interpolation from spatially sparse measurements 5 using autoencoder with source position condi- tioning,” in Proc. Int. Workshop Acoust. Signal Enhancement (IWAENC), Sep. 2022

work page 2022
[1]

E. G. Williams, Fourier Acoustics: Sound Radia- tion and Nearfield Acoustical Holography. Academic Press, 1999

work page 1999
[2]

Three-dimensional surround sound systems based on spherical harmonics,

M. A. Poletti, “Three-dimensional surround sound systems based on spherical harmonics,” J. Audio Eng. Soc., vol. 53, no. 11, pp. 1004–1025, 2005

work page 2005
[3]

Sound field estima- tion: Theories and applications,

N. Ueno and S. Koyama, “Sound field estima- tion: Theories and applications,” Foundations and Trends® in Signal Processing, vol. 19, no. 1, pp. 1– 98, 2025

work page 2025
[4]

Sound field recording using distributed microphones based on harmonic analysis of infinite order,

N. Ueno, S. Koyama, and H. Saruwatari, “Sound field recording using distributed microphones based on harmonic analysis of infinite order,” IEEE Signal Process. Lett., vol. 25, no. 1, pp. 135–139, 2018

work page 2018
[5]

Direction- ally weighted wave field estimation exploiting prior information on source direction,

N. Ueno, S. Koyama, and H. Saruwatari, “Direction- ally weighted wave field estimation exploiting prior information on source direction,” IEEE Trans. Sig- nal Process., vol. 69, pp. 2383–2395, 2021

work page 2021
[6]

Sound field reconstruction in rooms: Inpainting meets super-resolution,

F. Llu ´ ıs, P. Mart ´ ınez-Nuevo, M. B. Møller, and S. E. Shepstone, “Sound field reconstruction in rooms: Inpainting meets super-resolution,” J. Acoust. Soc. Amer., vol. 148, no. 2, 2020

work page 2020
[7]

Learning neural acoustic fields,

A. Luo, Y. Du, M. J. Tarr, J. B. Tenenbaum, A. Tor- ralba, and C. Gan, “Learning neural acoustic fields,” in Proc. Adv. Neural Inf. Process. Syst. (NeurIPS) , 2022

work page 2022

Show all 29 references

[8]

Physics-informed machine learning for sound field estimation: Fundamentals, state of the art, and challenges,

S. Koyama, J. G. C. Ribeiro, T. Nakamura, N. Ueno, and M. Pezzoli, “Physics-informed machine learning for sound field estimation: Fundamentals, state of the art, and challenges,” IEEE Signal Process. Mag., vol. 41, no. 6, pp. 60–71, 2025

2025
[8]

Physics-informed machine learning for sound field estimation: Fundamentals, state of the art, and challenges,

S. Koyama, J. G. C. Ribeiro, T. Nakamura, N. Ueno, and M. Pezzoli, “Physics-informed machine learning for sound field estimation: Fundamentals, state of the art, and challenges,”IEEE Signal Process. Mag., vol. 41, no. 6, pp. 60–71, 2025

2025
[9]

Reconstruction of sound field through diffusion models,

F. Miotello, L. Comanducci, M. Pezzoli, A. Bernar- dini, F. Antonacci, and A. Sarti, “Reconstruction of sound field through diffusion models,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), (Seoul, Republic of Korea), Apr. 2024

2024
[10]

Implicit neural representations with periodic activation functions,

V. Sitzmann, J. Martel, A. Bergman, D. Lindell, and G. Wetzstein, “Implicit neural representations with periodic activation functions,” in Proc. Adv. Neural Inf. Process. Syst. (NeurIPS) , 2020

2020
[11]

Nerf: rep- resenting scenes as neural radiance fields for view synthesis,

B. Mildenhall, P. P. Srinivasan, M. Tancik, J. T. Barron, R. Ramamoorthi, and R. Ng, “Nerf: rep- resenting scenes as neural radiance fields for view synthesis,” Commun. ACM, vol. 65, p. 99–106, Dec. 2021

2021
[13]

Sound field reconstruction using neural processes with dy- namic kernels,

Z. Liang, W. Zhang, and T. D. Abhayapala, “Sound field reconstruction using neural processes with dy- namic kernels,” EURASIP J. Audio, Speech, Music Process., vol. 13, 2024

2024
[14]

Deep prior approach for room impulse response reconstruction,

M. Pezzoli, D. Perini, A. Bernardini, F. Borra, F. Antonacci, and A. Sarti, “Deep prior approach for room impulse response reconstruction,” Sensors, vol. 22, no. 7, 2022

2022
[15]

Implicit neural representation with physics-informed neural networks for the reconstruction of the early part of room impulse responses,

M. Pezzoli, F. Antonacci, and A. Sarti, “Implicit neural representation with physics-informed neural networks for the reconstruction of the early part of room impulse responses,” in Proc. Forum Acus- ticum, Sep. 2023

2023
[16]

Sound field estimation based on physics-constrained kernel interpolation adapted to environment,

J. G. C. Ribeiro, S. Koyama, R. Horiuchi, and H. Saruwatari, “Sound field estimation based on physics-constrained kernel interpolation adapted to environment,” IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 32, pp. 4369–4383, 2024

2024
[17]

Physics- informed machine learning,

G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikari, S. Wang, and L. Yang, “Physics- informed machine learning,” Nat. Rev. Phys., vol. 3, p. 422–440, 2021

2021
[18]

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

M. Raissi, P. Perdikaris, and G. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,”J. Comput. Phys. , vol. 378, pp. 686–707, 2019

2019
[18]

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

M. Raissi, P. Perdikaris, and G. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,”J. Comput. Phys., vol. 378, pp. 686–707, 2019

2019
[19]

Fourier features let networks learn high frequency functions in low dimensional domains,

M. Tancik, P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. Barron, and R. Ng, “Fourier features let networks learn high frequency functions in low dimensional domains,” in Proc. Adv. Neural. Inf. Process. Syst. (NeurIPS), vol. 33, p...

2020
[20]

Hypernetworks,

D. Ha, A. M. Dai, and Q. V. Le, “Hypernetworks,” in Proc. Int. Conf. Learn. Rep. (ICLR) , 2017

2017
[21]

Prototypi- cal networks for fewshot learning,

J. Snell, K. Swersky, and R. Zemel, “Prototypi- cal networks for fewshot learning,” in Proc. Int. Conf. Neural Informat. Process. Syst. (NeurIPS) , p. 4080–4090, 2017

2017
[22]

Image method for efficiently simulating small-room acoustics,

J. B. Allen and D. A. Berkley, “Image method for efficiently simulating small-room acoustics,” J. Acoust. Soc. Amer. , vol. 65, no. 4, pp. 943–950, 1979

1979
[23]

Py- roomacoustics: A python package for audio room simulation and array processing algorithms,

R. Scheibler, E. Bezzam, and I. Dokmani´ c, “Py- roomacoustics: A python package for audio room simulation and array processing algorithms,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Pro- cess. (ICASSP) , (Calgary, Canada), pp. 351–355, Jul. 2018

2018
[24]

Adam: A method for stochastic optimization,

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in Proc. Int. Conf. Learn. Rep. (ICLR), 2015

2015
[25]

K. P. Murphy, Machine Learning: A Probabilistic Perspective. MIT Press, 2012

2012
[26]

Deep learning using rectified linear units (ReLu)

A. F. Agarap, “Deep learning using rectified linear units (ReLu).” arXiv:1803.08375, 2018. 6

2018 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [12]

Head-related transfer function interpolation from spatially sparse measurements 5 using autoencoder with source position condi- tioning,

Y. Ito, T. Nakamura, S. Koyama, and H. Saruwatari, “Head-related transfer function interpolation from spatially sparse measurements 5 using autoencoder with source position condi- tioning,” in Proc. Int. Workshop Acoust. Signal Enhancement (IWAENC), Sep. 2022

work page 2022

[2] [1]

E. G. Williams, Fourier Acoustics: Sound Radia- tion and Nearfield Acoustical Holography. Academic Press, 1999

work page 1999

[3] [2]

Three-dimensional surround sound systems based on spherical harmonics,

M. A. Poletti, “Three-dimensional surround sound systems based on spherical harmonics,” J. Audio Eng. Soc., vol. 53, no. 11, pp. 1004–1025, 2005

work page 2005

[4] [3]

Sound field estima- tion: Theories and applications,

N. Ueno and S. Koyama, “Sound field estima- tion: Theories and applications,” Foundations and Trends® in Signal Processing, vol. 19, no. 1, pp. 1– 98, 2025

work page 2025

[5] [4]

Sound field recording using distributed microphones based on harmonic analysis of infinite order,

N. Ueno, S. Koyama, and H. Saruwatari, “Sound field recording using distributed microphones based on harmonic analysis of infinite order,” IEEE Signal Process. Lett., vol. 25, no. 1, pp. 135–139, 2018

work page 2018

[6] [5]

Direction- ally weighted wave field estimation exploiting prior information on source direction,

N. Ueno, S. Koyama, and H. Saruwatari, “Direction- ally weighted wave field estimation exploiting prior information on source direction,” IEEE Trans. Sig- nal Process., vol. 69, pp. 2383–2395, 2021

work page 2021

[7] [6]

Sound field reconstruction in rooms: Inpainting meets super-resolution,

F. Llu ´ ıs, P. Mart ´ ınez-Nuevo, M. B. Møller, and S. E. Shepstone, “Sound field reconstruction in rooms: Inpainting meets super-resolution,” J. Acoust. Soc. Amer., vol. 148, no. 2, 2020

work page 2020

[8] [7]

Learning neural acoustic fields,

A. Luo, Y. Du, M. J. Tarr, J. B. Tenenbaum, A. Tor- ralba, and C. Gan, “Learning neural acoustic fields,” in Proc. Adv. Neural Inf. Process. Syst. (NeurIPS) , 2022

work page 2022