Physics-Informed Audio-Geometry-Grid Representation Learning for Universal Sound Source Localization
Authors: Min-Sang Baek
Gyeong-Su Kim
Donghyun Kim
Joon-Hyuk Chang
Venue: ICLR 2026 Poster (2026)
Keywords: Sound Source Localization
Geometry-Invariant
Grid-Flexible
Representation Learning
Physics-Informed Design
Learnable Non-uniform DFT
Relative Microphone Positional Encoding
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: This paper proposes audio-geometry-grid representation learning for grid-flexible and geometry-invariant sound source localization, leveraging learnable non-uniform discrete Fourier transform and relative microphone positional encoding.

Abstract: Sound source localization (SSL) is a fundamental task in spatial audio understanding, yet most deep neural network-based methods are constrained by fixed array geometries and predefined directional grids, limiting generalizability and scalability. To address these issues, we propose _audio-geometry-grid representation learning_ (AGG-RL), a novel framework that jointly learns audio-geometry and grid representations in a shared latent space, enabling both geometry-invariant and grid-flexible SSL. Moreover, to enhance generalizability and interpretability, we introduce two physics-informed components: a _learnable non-uniform discrete Fourier transform_ (LNuDFT), which optimizes the dense allocation of frequency bins in a non-uniform manner to emphasize informative phase regions, and a _relative microphone positional encoding_ (rMPE), which encodes relative microphone coordinates in accordance with the nature of inter-channel time differences. Experiments on synthetic and real datasets demonstrate that AGG-RL achieves superior performance, particularly under unseen conditions. The results highlight the potential of representation learning with physics-informed design towards a universal solution for spatial acoustic scene understanding across diverse scenarios.

Published as a conference paper at ICLR 2026
PHYSICS-INFORMED AUDIO-GEOMETRY-GRID REP- RESENTATION LEARNING FOR UNIVERSAL SOUND
SOURCE LOCALIZATION
Min-Sang Back, Gyeong-Su Kim, Donghyun Kim Joon-Hyuk Chang" Department of Electronic Engineering, Hanyang University. Seoul, Republic of Korea (kng643, r9dt atabboy3522, jchang) @hanyang ac. kr
ABSTRACT
Sound source localization (SSL) is fundamental task in spatial audio understand- ing, yet most deep neural network- -based methods are constrained by fixed array geometries and predefined directional grids, limiting generalizability and scala- bility. To address these issues, we propose mudio-geometry-giie representation learning (AGG-RL), a novel framework that jointly learns audio-geometry and grid representations in shared latent space, enabling both geometry innvriiat and grid-flexible SSL. Moreover, to enhance generalizability and interpretability, introduce two thysics-informee crete Fourier transform (LNuDFT), which optimizes the dense allocation of fre- queney bins in non-uniform manner to emphasize informative phase regions, and relative microphone positional encoding (rMPE), which encodes relative microphone coordinates in accordance with the nature of inter-channel time dif- ferences. Experiments on synthetic and real datasets demonstrate that AGG-RL achieves superior performance, particularly under unseen conditions. The results highlight the potential of representation learning with physics-informed informed design to- wards universal solution for spatial acoustic scene understanding across diverse scenarios.
components: learnable non-uniform dis-
INTRODUCTION
With the growing interest in learning and reasoning about 3D space in machine learning (Mildenhall
al. 2021; Zhang al. 2025 Xie al.) 2025), multichannel audio has emerged promising
modality for capturing spatial cues and enabling spatially aware generation (Ochiai et al., 2017
Simeoni al. 2019 Richard et al. 2021 Leng al. [002 Luo et al. 2022 Huang et 2023
Zheng et al. 2024 Sun et al. 2025
Brunetto et al.] 2025 Li et al.] 2022a Liang et al. 20255] )) A
central task this field sound source localization (SSL), which estimates the direction -f
(DOA) of sound sources. SSL is not only a fundamental building block in spatial audio processing
but also synergizes with applications such as robotics (Gan et al.) 2020) Wang et al., 2021 Do
et al., 2022] Wang et al. (024a)) autonomous vehicles (Furletov et al. 2021: Jeon et al.) (025).
drones (Wang & Cavallaro] 2022; Chevtchenko et al. 2025), and immersive AR/VR systems and
smart devices (Rajguru et al. 2022 Gupta et al. 2022 Lin et al. 2024 Yang al. 2025).
Traditionally, SSL has relied on classical signal processing methods based on the time difference- of-arrival (TDOA) between microphones in microphone array (MA) (Benesty et al. 2008), such as GCC-PHAT (Knapp & Carter 1976). MUSIC (Schmidt] [1966), and SRP-PHAT (Dibiase (000)) which exploit inter-channel phase differences (IPDs) in the frequency domain. The advent of deep neural networks (DNNs) has enabled models to learn robust audio representations, often surpassing
classical methods (Grumiaux al. 2022 Chakrabarty & Habets
2019:
Nguyen al.) 2020 Yang
et al. 202 Diaz-Guerra et al. 202 la He et al. 2021 Back et al.
2023 Zhang et al. 2024 Battula
al. 2025 Li al. 2025b). However, most existing DNN-based methods remain critically limited:
they are highly dependent on specific MA geometries and predefined DOA grids.
"Corresponding author.

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Published as a conference paper at ICLR 2026
To address these limitations, geometry-Invariant invariant SSL methods (Schwartz et al. 2023 Grinstein iet al. 2024 Wang et al.] 2024b; BBakk et al.] 2025) and grid-flexible approaches Yang et al. 2021 Wang et al. 2024b) have been proposed. Although these methods alleviate some constraints, they still fall short of achieving robust SSL. across arbitrary geometries and grids. Therefore, we pro- pose cudio-ggommery--rrid representation learning (AGG-RL) for robust, universal SSL.. Inspired by representation learning (Bengio et al. 2013] Koyama et al., 2024a; Shi et al. [022] [Dimitriadi) al. 2023 Zhu et al., 2024; Kim al. (025), AGG-RL learns two types of representations. audio- geometry representations (AGRs) and grid representations (GRs). AGRs are derived from audio and MA geometry, while GRs encode candidate DOA grids. Their similarity produces probabilistic spatial spectrum, which is trained with soft labels that represent relationships among neighboring grid points. This enables the model to capture seaiii-gemetty-grii relationships, facilitating uni- versal SSL on arbitrary grids and geometries without retraining.
Furthermore, to enhance generalization, we introduce two components inspired by physics-informet DNNs (Raissi et al. 2019 Karniadakis et al. 2021 Gabrielli et al. 20188] Koyama et al.) 2024bb
Ribeiro et al. 20244; Miotello et al. [024] Karakonstantis et al.] 2024 Damiano et al.] (025):
learnable non-uniform discrete Fourier transform (LNuDFT) and relative microphone positional encoding (rMPE). For the proposed LNuDFT, the gap between adjacent frequency bins is modeled a learnable parameter, allowing the DNN to densely allocate bins in critical frequency regions that convey physically informative phase cues. In addition, based on absolute MPE (aMPE) (Baek al., 2225). IMPE introduced embed microphone coordinates a relative fashion- consistenn with the nature of TDOA, which depends on relative rather than absolute coordinates. Both com- ponents incorporate physics-based structural assumptions into the feature extraction process while still allowing adaptivity through training. This yields physics-informe inductive biases that guide learning toward acoustically meaningful representations.
Experiments on both synthetic and real datasets (Löllmann et al. 2018) demonstrate the effective- ness of the proposed method, showing strong generalization to unseen environments in terms of angular error and accuracy. Moreover, our framework supports flexible grid selection without re- training, enhancing adaptability across diverse scenarios. These results highlight AGG-RL, aug- mented with LNuDFT and rMPE, as a promising step toward 3D acoustic scene understanding.
BACKGROUND
2.1
TIME DIFFERENCE-OF-ANE ARRIVAL AND INTER-CHANNEL PHASE DIFFERENCE
Inteeehoomel plase differennce
0
1k
5k
7k
pdlmi
Frequency (H1x
(a) Sound received by the microphone array.
(b) IPD at r = 0.5 ms, showing phase wrapping and aliasing.
Figure 1: Illustration of (a) signals received by a microphone array and (b) IPD in the frequency domain, where phase wrapping can cause spatial aliasing.
Modeling sound wave as a plane wave in the far-field situation, when the wave reaches spatially separated microphones at different times, a TDOA arises, as shown in Fig. Ta). In the frequency domain, the TDOA Tp.g between channels p and g is related to the IPD AO at frequency f as follows:
A0
2 0.) -000 (((
Tp.q
(1)
2x
where j is the imaginary unit, and 0, and fg denote the phases at channels p and q. respectively. At higher frequencies, phase varies more rapidly, enabling finer resolution of the TDOA. However, since phase is wrapped within [-7, Ø), the same IPD value may correspond multiple TDOAs,
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resulting in spatial aliasing, as illustrated in Fig. Tb). The aliasing condition depends the micro- phone spacing r and the maximum unambiguous frequency fmax:
S fmax
2r
where is the speed of sound, and X is the wavelength corresponding to S. Thus, aliasing can be avoided either by reducing the microphone spacing r below half the wavelength of fmax or by limiting the frequency below fmax. In summary, lower frequencies are alias-free but provide coarse TDOA resolution, while higher frequencies yield finer resolution at the cost of potential aliasing. As MA geometries vary widely across wollw applications, accounting for this trade-off is crucial for geometry-invariant SSL.
2.2 OUTPUT REPRESENTATION PARADIGMS IN DNN-BASED SSL
The outputs of DNN-based SSL can be broadly categorized into regression and classification ap- proaches. Regression methods directly predict source locations in 3D coordinates (Diaz-Guerra et al. 2021a; Grinstein et al.) 2024). They offer theoretically infinite resolution, but suffer from limited interpretability. since they predict only coordinates rather than a spatial spectrum indicating source likelihood across the entire space. Furthermore, their architectures are typically constrained by the maximum number of sources. Classification based methods discretize the 3D space into pre- defined DOA grids (Schwartz et al. 2023 Baek et al. (002).. This yields interpretable spatial spectra without being tied to the number of sources, but performance is bounded by grid resolution, and re- training is required when adopting new grids. To balance these trade-offs, template matching (Yang) al. 2021 Wang al. 2024b) has been explored. This approach enables SSL on arbitrary grids without retraining by comparing outputs with IPD templates from candidate DOAs. However, as the model is optimized for IPD estimation rather than direct DOA prediction, performance can degrade. Moreover, template matching requires pairwise outputs for each microphone pair and a predefined number of sources, leading to increased computational cost. These limitations motivate the pro- posed AGG-RI. framework, which enables flexible-grid SSI. with direct candidate DOA prediction, without relying on handcrafted templates or pairwise computations.
3 PROPOSED FRAMEWORK
Wide Beamwidth
Varying Beamwidth
Narrow Beamwidth
Spatial Spectrum,
Grid Representation. G
Audio Boddio-Geometty Representation. A
AuGeonet
Gridnel
Mic. Pos. Encoding
GCC-PHAT
0.0
Leamable NuDET
IXOA Grid Candidates
Audio Signal
Mic. Army Geometry
Figure 2: Overview of the proposed framework. The model takes audio signals, microphone array geometries, and candidate DOA grids as inputs, and outputs spatial spectra over the grids. Multiple oracle spatial spectra with different beamwidth parameters are also shown. The microphone arry shown (Sphere48 AC Pro by gfai tech GmbH) is reproduced with permission.
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To achieve grid fiii-flexible and geometry-invariinn SSL, propose AGG-RL, illustrated in Fig. The framework consists two networks: the audio-geomeery representation network (AuGeonet), A(-), and the grid representation network (Gridnet), 9(-). AuGeonet integrates two physics-informed cipponents--NuuDDe and rMPF-to extract robust AGRs, while Gridnet produces GRs from can- didate DOA grids. AGRs and GRs projected into shared latent space, and their similarity is measured by an inner product, where larger values indicate higher likelihood of source presence. The models are trained using soft-labeled oracle spatial spectra (shown the top of Fig. 2 as su- pervision, enabling effective learning of audio-geoos geometry-gne relationships.
3.1 LEARNABLE NON-UNIFORM DISCRETE FOURIER TRANSFORM
In contrast the standard DFT, which uses uniformly spaced frequency bins, the NuDFT (Bagchi & Mitra 1996a bj 1999) employs non-uniform frequency bin allocations that can be optimal for
specific applications (Wei & Yang 2022 Wen & Houlihan 2023 de Haan et al. 2002 Chang 2005
Muralishankar et al.] 2020; Lim et al. (024).. While NuDFT can also be defined with non-uniform
sampling along the time axis, here we focus on non-uniformity along the frequency axis. In SSL, NuDFT enables more effective extraction of IPD features by emphasizing physically informative
frequency ranges with densely sampled bins, discussed in Section 2.1
Let X E R denote the -ssmmle signal received at the e-th channel of C-channel MA, which is a mixture of multiple speakers, noise, and reverberation. The trequency-domaln representation X. is obtained by applying the LNuDFT independently to each channel, defined as:
N-1
X [k. 1
Σ m=
X. + w [n]
12 -2 12
(3)
windowed Irame
LNuDFT basis
where e denotes the channel index, k (O...... K 1} the frequency-bin index, and the frame index. N is the frame length, NN the starting sample of the /-th frame, and w[-] is window function. vn denotes the location of the ke-th frequency bin, which maps the physical frequency fxx X fs with sampling frequency fa. When K = N + and V/k = k. Eq. (3) reduces to the standard DFT. For the proposed LNuDFT, 2i is treated as learnable parameter instead of being fixed as in the NuDFT, enabling the model to allocate frequency bins more densely in regions that convey physically informative phase cues for SSL, To ensure monotonic ordering and compliance with the Nyquist limit (0 < P/ as the cumulative sum of positive, learnable increments ag between adjacent bins:
2
N < 1K-1 S 2: the maximum representable frequency), 1x is defined
Vo = 0, 1/2 = 1/-1 ak-1, a > 0 Vk E {1,2..... 1}.
(4)
To ensure effective initialization, risit and inii are assigned using logit-based mapping that allo- cates bins more densely in the mid-frequency range, as follows:
D Estart + Eend Estart
k
(Estarts fend); Ds In
Vk 8k
(5)
K
juit
v0
(K 1),
0k-1
init
jnit
init UK-1:
(6)
vK-1
where 0 < Estart < Cend < 1 are hyperparameters that prevent saturation of the logit function. After each gradient update, the following constraints are applied to preserve monotonicity and the Nyquist limit:
āg min (max (āz, Cmin) Cmux)
N
if Σ
K-1 k=
K k=
2
ag
dg
(8)
otherwise.
where äg is the raw parameter updated by gradient descent, clipped to (Gmin- Emax) to enforce posi- tivity and avoid extreme values. Normalization in Eq. (8) guarantees that v% is bounded by N 2. An illustration of LNuDFT is provided in Appendix A.2 Additionally, LNuDFT can be efficiently im- plemented as 1D convolution (Bagchi & Mitra 1996a b). where basis functions serve as convolution kernels of size N and feature dimension K, with hop size H. This adaptive allocation of frequency bins during training preserves phase information while enhancing robustness and interpretability by focusing on physically informative frequency regions relevant to IPD).
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3.2
RELATIVE PHASE FEATURE AND MICROPHONE POSITIONAL ENCODING
As MA geometries vary widely across applications, numerous geometry-invarian methods have
been explored (Luo al. 2020 Pandey et al. 2022 Yoshioka al. 2022 Mu et. 2024 [024|xuue al. 2025).
In parallel, several geometry-aware approaches have been proposed for SSL (Grinstein et al.
Recognizing that TDOA patterns inherently depend on the MA geometries, GI-DOAEnet (Back et al. 2025) stands as a representative example, explicitly incorporating geometry information via aMPE and channel-wise multi-head self- attention (CW-MHSA) (Vaswani et al.) 2017 Pandey et al.) (022). Here, CW-MHSA computes pairwise channel similarities, while aMPE injects geometry information as positional encodings. This design illustrates how geometry-awen enhance robustness across different MA configurations. Building on this framework, we present AuGeonet, a modified version of GI-DOAEnet that integrates LNuDFT- GCC-PHAT features and rMPEs, aiming to improve generalization to unseen MA configurations.
2024 Schwartz et al. 2023; Wang et al. 2024b Back et at. 2025). 2025) )
features can be directly embedded into the network to
Relative phase features. To better exploit IPDs, instead of raw DFT coefficients, we adopt GCC- PHAT (nnap & Carter 1976) in frequency-domin that emphasizes phase differences while sup- pressing magnitude variations. Computing all pairwise GCC-PHAT features scales as O ) so we employ a reference- based scheme that reduces complexity to OCC). The reference channel ē is chosen as the microphone closest to the MA center, and the LNuDFT-basee GCC-PHAT is defined:
X. [, [ 1 X K 4]
GOC [K, =
(9)
X
X.(k, O]
|-| the magnitude. The resulting feature G E C(C-1)*XXI is split into real and imaginary parts and concatenated along the frequency axis, pro- ducing X E (CC-1)x2Xxx This emphasizes relative phase cues while reducing input dimen- sionality C 1 by excluding the reference channel.
where denotes complex conjugation and
Relative microphone positional encoding. Inspired by the inherently relative nature of IPDs and relative positional encodings (Shaw et al. [2018] Pham et al.) 2020; Su et al. 2024), we introduce rMPE, which encodes each microphone coordinates relative to reference channel. This design di- rectly aligns with the physics of sound propagation, where TDOA and IPD depend solely on relative microphone positions (see Appendix I.I. Let Pe (Ze: Vey ze) denote the Cartesian coordinates of microphone c. The relative coordinates are:
He = Ie.
Dc = Vc ya,
be 2e 22,
(10)
F. = V
22
22
0. atan2 (Ge, tt),
&e n. atan2 &e.
2
where F. E o0), ). 02 E |-T,, R), and p. E [0, т| represent the distance, azimuth, and elevation, respectively. Following aMPE, rMPE encodes these spherical coordinates into sinusoidal encodings:
Q
v(Q) a/
0.
1
(11)
1
PPM = hf De, G. 3.
PPM = hFMaffa De, Fei a, M)
cos (2 vMM + 0.)
cos( i. B (M))
(12)
sin 2n (MM) 0c)
sin 0. 8 v(M) cos @.. vvM) sin( vvM))
= añe
= añ,
cos 2 (M) (M)+ 9.)
sin (2 (M)) (M)+ +.)
where v(Q) uniformly partitions the range [0, into Q elements, and T is a transpose operation. h-M(() and (-) denote the phase-modulated (PM) and frequency-moculateed (FM) rMPE map- ping functions, respectively. a is a scaling factor, ,3 a frequency factor, and M the target feature dimension. Stacking across all non-reference microphones yields P E (C-1)) aligned with the input features and CW-MHSA to provide positional cues. With the proposed LNuDFT-based GCC-PHAT and rMPE integrated into AuGeonet, we obtain AGRs, A:
A A (x, p: θ) E Ox
(13)
where is the AGR dimensionality, O is the number of outputs in the deeply supervised curricu- lum leaming (DSCL) framework (Baek et al. 2023). and O denotes the learnable parameters of
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AuGeonet. The architectural details of AuGeonet provided in Appendix A.3 These AGRs natu- rally capture audio audio-geometry geometry relationships and are later integrated into AGG-RL to estimate spatial spectra over candidate DOAs.
3.3 AUDIO-GEOMETRY GRID REPRESENTATION LEARNING
To overcome the limitations of fixed-grid classification, discussed in Section 2.2
propose AGG- RL. which aligns AGRs with GRs and produces a probabilistic spatial spectrum over arbitrary can- didate DOAs by measuring their similarity. We first encode the d-th candidate DOA, with azimuth angle 0g and elevation angle da. into a G-dimensional sinusoidal vector, analogous to Eq. (12) for
PM-based rMPE:
Coos( v(G) + 0a)
sin (2n v(G) + 0.) cos
G = (aaaaaaaaa.a.. Ed:
ERC
(14)
+ da)
sin 2 + dd)
where (+ria()) denotes the grid encoding function, and modulation frequency. Using Grid- net Go(-). a simple DNN with learnable parameters vr specific to each output index (see Ap-
pendix A.4 G. is transformed into GR:
Gd G. (G.:: RRC
(15)
Given AGRs A E ROOGXL from AuGeonet, the similarity is computed by scaled inner product followed by sigmoid function a(), producing the prohabilistic spatial spectrum:
Sd = o ( (ClloAao)) VG
e00.1].
(16)
where scaling by VG stabilizes optimization by controlling the variance of the inner prod- uct (Vaswani et al., 2017). Through this procedure, AGRs are encouraged to align with GRs at true-source DOAs while diverging from non-source directions. Meanwhile, GRs trained to rep- resent candidate DOAs independently of the audios and MA geometries, enabling flexible-grid SSL.
Candidate DOAs are sampled using Fibonacci sphere points (Saff & Kuijlaars 1997). providing near-uniform coverage over the unit sphere. During training, Fibonacci grids with 7) points are ran- domly rotated for data augmentation. Soft targets are defined as oracle spatial spectra with varying beamwidths (Back et al. 2023) and used in weighted binary cross-entropy (BCE) loss (Nguyen al., 2020). which emphasizes positive samples. At inference, an iterative peak detection algo- rithm (Back et al.. (023) is applied to the final layer output to identify multiple source DOAs. Further details are given in Appendix A.8 In summary, AGG-RL enables flexible-grid and geometry- invariant SSL without retraining, while retaining the interpretability of ilassification-bssee methods.
EXPERIMENTAL SETUP
4.1 MODEL. IMPLEMENTATION AND BASELINES
We compared our method against classical baselines (MUSIC (Schmidt 1986). SRP-PHAT Dibi-
ase 2000)) and recent DNN-based methods (Unet (Schwartz et al. 2023). Neural-SRP (Grinstein al. 2024), GI-DOAEnet (Back et al.) )025)). To ensure fair comparison, all methods were im- plemented in a causal setting with identical DFT parameters (N = 512,
257. !l 128) and Hann window. For classical methods, candidate DOAs were sampled using Fibonacci grids with D 512 and 2048. Unet and Neural-SRF were modified following GI-DOAEnet to produce multi- ple spatial spectra outputs, following Baek et al. (2025). Unet was re-implemented from the original paper, while Neural-SRF a and GI-DOAEne were adapted from public code. Unet used SRP-PHAT input with D 512, whereas Neural-SRP employed time-domain GCC-PHAT features; both were
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adapted output spectra on a Fibonacci grid with D = 2048. For GI-DOAEnet, both PM- and FM- based aMPE variants were evaluated, with an output dimension of D = 2048. We additionally note that IPDnet with template matching (Wang et al. 2024b) was excluded from direct comparison due to its impractical computational cost (23.2 GF.OPs for 2-channel input, making it prohibitive for larger MAs) and incompatible output format (estimates microphone pairwise, requency-dependee IPDs instead of DOAs). For the proposed method, FM-based rMPE was adopted as default, as it slightly outperformed PM-based encoding in preliminary experiments, and D 2048 was used for consistency. For LNuDFT of AuGeonet, initialization was performed with Sturt = 0.15 and Gend 0.95, and constraints were applied with Cmin = 0.01 and Gmax 100. All CONN-based methods followed the same training setup described in Appendix A.9
4.2 DATASET AND EVALUATION METRICS
Table Parameters used for synthetic dataset generation.
Parameter
Interval
Unit
Number of speakers
[1,2]
RT60
[0.2, 1.3]
Room size
[3x3x2,5, 10x8x6]
m
Distance
[0.3, 2.5]
m
Azimuth
[0, 360)
Flevation
[0, 180]
SNR (speech vs. noise)
[-5, 30]
dB
SIR (between speakers)
[-5. 5]
dB
SIR (between noises)
[-15, 15]
dB
Synthetic datasets were used for training, validation, and partial evaluation. The training set was generated on-the-fly to provide diverse conditions, with fixed number of channels per batch. Ta- summarizee the ranges of acoustic and spatial parameters used to generate the synthetic mix- tures, including reverberation time (RT60), signal-to-noise ratio (SNR) between speech and noise, and signal-to-interferenne ratio (SIR) between speakers or between noise sources. For each sample, simulated multichannel room impulse responses (RIRs) using the image source method (Allen & Berkley| 1979) implemented in gpuRIR (Diaz-Gre Guerra et al.) 20215). Speech signals were drawn from peerch (Panayotov et al. 20155) and noise signals from MS-SNSD (Reddy et al.] 2019). each cropped to 4 seconds. Additional implementation details for the synthetic data generation are provided in Appendix A. 1.
Table Evaluation dataset configuration.
Dataset
Real Dataset Microphone Arra
Channels
Training Exposure
NAO robot
NAO robot
12
/ (scen)
Eigenmike
Eigenmike
X (unseen)
Dynamic-S
X
Dynamic
4-12 / (seen)
Dynamic-U U
X
Dynamic
13-16 X (unseen)
After training, the model with the lowest validation loss was selected for evaluation. Evaluation was conducted using four datasets, as shown in Table 2 Real recordings were taken from LO- CATA (Löllmann al., 2018). where NAO rohot and Eigenmike datasets consisted of recordings using the NAO robof and the Eigenmike"] respectively. Only non-moving sources with up to two speakers were used for evaluation, resampled to 16 kHz. Two synthetic datasets, Dynamic-S and Dynamic-U, were constructed to evaluate generalization to seen and unseen numbers of channels, respectively, across a variety of MA geometries. These synthetic datasets were generated with 300 utterances per channel, following the same procedure the training set but using different source material: TIMIT (Garofolo et al. 1993) for speech and ESC-50 (Piczak 2015) for noise. For evalua- tion metries, we used mean absolute error (MAF, 9) and accuracy (ACC1o. %) (see Appendix AT. MAE measured the average angular error; lower values indicate better performance. ACC mea- sured the percentage of predictions within 10" margin; higher values indicate better performance. Both metrics were computed per utterance and averaged over each set.
delleebbaannn /etta::/wwww.albbbrrr..ommm
https://eigenn himm/iggemminn ke
em32 kemm
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5 RESULTS AND DISCUSSION
Table 3: Experimental results with different methods. The best results each dataset in bold.
NAO robor MAR
Eigenmike MAE
Dynamic-S MAR
Dynamic-U MAA
ACC
ACCm
AACO.
AACCs
MUSICs1:
20.63 =2.4
64.95
29.93
+3.09
36,37
30.35
40.3
27.94
27.13 20,89
33.20
MUSIC19s
19.31 12665
69.77
29.78 13,06
36,68
30.24 1063
28.50
26.88 10:90
33.92
PHA-SH
22.36 m1.79
67.95
27.45 +1.73
41,38
43.98 +0.70
24.55
38.64 +1.03
32.13
SRP-PHAT 244
21.77 21:75
67.84
26.88
+1.91
53.22
43.89 +0.70
25.10
38.40 #1.04
32.39
Unet
10.89 11.53
86.25
14.89
1:.7
65.82
19.94 10009
58.88
19.15 20:94
60.57
with AGG-RL
12.79 #3.26
77.33
16.86 +3.26
55.69
21.23 +11.0
53.74
20.11 #0.95
56.08
Neural-SRP
9.72 12228
78.66
52.75
118.61
22.16
19.60
10.74
52.32
21.18 11.01
45.51
with AGG-RL
9.89
72,80
13:25
42.32
37.07
1:0.44
50.56
19.05 11.01
54.13
GI-DOAEnet
11.31 #2254
77.36
93.61
#:13.06
0.00
15.49 +:1.55
64.36
54.81 #:1.3
6.10
GI-DOAEnet"
12.26 1:2.7
72.47
77.09
1:13.32
2.82
17.40
110.59
58.54
79.17 1:1.1
0.58
Proposed
8.25 +1.52
90.78
11.24 1:77
72.17
10.32 +:0.99
77.34
14.12 +0.77
63.17
(i) MMPE-PM
8,38 11.63
89.85
13:42 12200
70.09
11.55
10..50
74.46
12.46 1.0.8
67.97
(ii) DFT
13.24 =2.97
72.32
111.21 =9.86
0.00
16.47 +:0.58
60.88
87.71 #1.89
0.92
(iit) GCC-PHAT
9.17 1344
87.74
16.53
13.97
39.35
1:048
77.56
17,90 :0:71
(iv) LNuDFT Uniform
8.69 #2.97
90.03
15.13 +2.68
40.70
10.44 +:1.7
77.69
23.03 #:0,99
36.05
(V) NoDFT Logit init.
8,96.12.5
89.34
17.34 12.47
28.52
10.64
76.56
11.83 1.066
72.77
(vi) Fixed grid
42.28
87.31
13.58 +2.60
40.82
9.57
81.70
13.84
65.29
(vii) Gridnet with FM Enc.
9.95 +2.36
85.60
12.58
+2.68
50.55
11.10 +:149
75.49
15,24
#:0.88
58.60
(viii) Gridnet with Cartesian
9.08 +22.5
88.17
11.87
#2,80
64.62
10.41
+0.48
77.28
23.10
=0:91
34.26
Table presents the overall results on the evaluation datasets. Rows above the double line corre- spond to baseline methods, while rows below represent the proposed method and its ablation studies. The 95% confidence intervals (CIs) for the MAE are reported using + values, which indicate the corresponding margin of error.
The subscripts 512 and 2048 indicate the number of grids used for SRP-PHAT and MUSIC. Both methods consistently underperformed compared to DNN-based ap- proaches across all datasets. Moreover, increasing the number of grid points did not lead to meaning- ful improvements. Accordingly, Unet adopted SRP-PHAT with D 512 for efficiency, Among the DNN-based baselines, Neural-SRP achieved lower MAE than Unet on the NAO robot and Dynamic- S datasets. while Unet outperformed Neural-SBR -SPP on the remaining datasets and metrics. Notably, Neural-SRP exhibited substantial performance degradation on Eigenmike. When AGG-RL was ap- plied, performance of Unet slightly degraded overall. In contrast, Neural-SRP showed performance drops in seen conditions such as NAO robot and Dynamic-S, but significant improvements under unseen conditions, including Eigenmike and Dynamic-U, U. These results demonstrate that AGG-RL effectively enhanced generalizability for Neural-SRP. GI-DOAEnet variants with different aMPE types outperformed Unet and Neural-SRP on Dynamic-S, which shared the same channel configu- ration as the training set. However, their performance dropped significantly under unseen settings, including Eigenmike and Dynamic-U.
Comparison with baselines.
The proposed method consistently achieved superior performance across all datasets, elearly validat- ing its robustness and effectiveness. However, achieved slightly worse results on unseen conditions compared to the seen conditions. This indicates a performance gap between seen and unseen sce- narios but still outperformed all baselines. To further validate these findings, we provide box and violin plots (Appendix 12) to examine the distribution of errors, results under different acoustic conditions (Appendix A3.13 to assess robustness across diverse environments, and spatial spectrum visualizations (Appendix A.15) to illustrate the interpretability and stability of the proposed method. Additionally, Appendix(A.14 repports results on the STARSS23 dataset (Shimada al. 2023), further demonstrating the effectiveness of the method on real-word world benchmark with different recording conditions. The following ablation studies further clarify the contributions of each component.
Effectiveness of GCC-PHAT and rMPE. Experiment (i) replaced rMPE with PM-based one. This variant showed comparable but slightly inferior performance on most datasets, except for Dynamic-U, indicating that FM was more effective than PM for rMPE. Accordingly, all proposed and subsequent ablation studies adopted FM-based rMPE as the default. In experiment (ii), both GCC-PHAT and rMPE were replaced with the standard DFT and FM- 1M-based, aMPE, respectively. This led to a consistent performance drop across all datasets, underscoring the importance of rel- ative representations introduced by GCC-PHAT and rMPE. In both GI-DOAEnet and AuGeonet,
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CW-MHSA layers were used to capture channel-wise relationships. However, prior works (Kazem- nejad et al. 2023] Zhou et al.] (024) have shown that MHSA performance degrades when extrapo- lating to longer sequences than those encountered during training. We therefore hypothesize that the relative nature of GCC-PHAT and rMPE mitigated this limitation, thereby enhancing generalization
to unseen conditions.
Effectiveness of LNuDFT. Experiments (iii) evaluated the contribution of LNuDFT under different configurations. In experiment (iii), LNuDFT was replaced with the standard DFT while re- taining GCC-PHAT and rMPE. Performance degraded on all datasets except Dynamic-S, validating the effectiveness of LNuDFT. Experiment (iv) initialized LNuDFT with the uniform spacing, iden- tical to the standard DFT and allowed it to be trained. While it achieved comparable results to the proposed method on Dynamic-S and NAO robot, performance decreased on Eigenmike and Dynamic- U. In experiment (v), NuDFT parameters were initialized using a proposed logit-based mapping and then frozen during training. This variant yielded the best performance on Dynamic-U, U, suggest- ing that initializing LNuDFT with an informative frequency distribution benefited generalization to unseen conditions. While logit-based initialization was more effective in practice, the choice of mapping function and hyperparameters was made empirically. Identifying optimal initialization strategies remains an open direction for future research and may further enhance performance. The visualization of trained LNuDFT parameters (Appendix (A.2) reveals that they densely focused on physically informative frequency regions, enhancing both model interpretability and robustness.
Effectiveness of AGG-RL. In experiment (vi), AGG-RL was replaced with a fixed-grid -rid setup (D = 2048), directly predicting spatial spectra as in standard classification models. This variant achieved the best performance on Dynamic-S, which matched the training condition, and slightly outperformed the proposed method on Dynamic-U. However, it degraded real datasets, showing that AGG-RL was crucial for generalization. Experiments (vii) and (vii) replaced Gridnet inputs with FM-based encodings of Eq. (12) and raw Cartesian coordinates, respectively. FM-based encod- ing achieved similar results, but PM-based encoding was slightly superior overall. Raw Cartesian inputs yielded comparable performance on most datasets but dropped on Dynamic-U, suggesting that sinusoidal encodings better captured the candidate DOA grid structure.
Table 4: Experimental results with different numbers of candidate grids D. The best results on each dataset are in bold.
NAO robot
Eigenmike
Dynamie-S
Dynamie-U
D
MAE
ACC,
MAE
ACC,
MAA
ACC,
MAE
ACC,
128
12.69
13.14
68.01
13.60
12.83
58.65
13.84
10.4
60.29
16.34
10.72
45.70
256
10.92
#2.70
81.25
13.51
#3.15
58.20
13.11
#051
69.79
16.32
+0,30
51.33
512
10.19
#2.17
87.51
11.65
12.72
61.05
11.59
10.99
74.60
14.97
10.77
61.27
1024
9.21
#2.5
89.91
12.13
#286
72.66
10.66
=0.49
77.52
14.24
49.76
61.88
2048
8.25
11:52
90.78
11.24
11:36
72.17
10.32
10.49
77.34
14.12
10.77
63.17
4096
9.16
#2.56
89.91
#2.68
73.06
10.14
20.50
77.73
+0.77
63.72
8192
8.91
12.63
89.54
11.52
1:776
75.97
9.91
10.49
78.12
13.85
10.76
63.83
16384
8.79
89.04
11.54
22,80
72.48
9.96
10.50
78.21
13,87
10.77
64.18
Table 4 further reports the results of the proposed method with varying D. When D was too small, performance dropped due to limited spatial resolution. Once D 2 512, performance stabilized across all datasets, confirming the grid-flexibility of AGG-RL. When D exceeded 2048, the trends between the real and synthetic datasets diverged slightly. For the synthetic datasets (Dynamic-S and Dynamic-U), the performance continued to improve mildly with larger D. Since these datasets were closely matched to the simulated training domain, finer angular discretization reduced quantization error and provided consistent, though marginal, improvements. This indicates diminishing returns beyond a certain resolution. In contrast, performance on the real datasets (NAO robot and Eigenmike) showed slight degradation once D exceeded 2048 (except for ACC10 on Eigenmike). Real-worr world recordings inevitably contained small acoustic mismatches- such ufacturing tolerances, and RIR deviations that were not present in synthetic data. With an overly dense grid, the localization decision became more sensitive to these perturbations, increasing esti- mation variance. Overall, the results suggest that increasing 1) beyond a certain threshold yields limited gains, and excessively large D is not necessarily beneficial in practice. t-SNE visualizations of the GRs (Appendix (6. further confirm that Gridnet learned structured spatial embeddings. Overall, AGG-RL enhanced robustness on real recordings and unseen conditions, effectively inte- grating audio-geometry-gee grid information into a shared latent space.
such as sensor noise, microphone man-

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Published as a conference paper at ICLR 2026
Table 5: Number of parameters and FLOPs under different configurations.
(a) Models with varying numbers of channels
(b) Gridnet with varying grid sizes
Model
Params (M)
FLOPs (G)
Gridnet Params (M)
GR Params
FLOPs
C
C=8 8
C
1024
1.19
0.26
0.27
Unet
L.4
1.49
2.10
SRP
1.13
1.86
8.54
20.08
2048
1.19
0.52
0.54
GI-DOAEact
2.32
0.49
0.89
1.29
4096
1.19
1.04
1.07
AuGeonet
with Fixed Grid
2.32
0.42
0.82
1,22
with AGGGRL
0.83
1.23
Computational resource comparison. We measured inference complexity using fvcord with 1- second inputs, defaulting to G = 256 and D 2048. Table (] compares parameters and FLOPs across different numbers of channels, while Table ()) reports Gridnet results with varying grid sizes. Unet had the largest parameter count and Neural the highest FLOPs, with FLOPs of both models being scaled quadratically with C due to pairwise features. GI-DOAEnet and AuGeonet with fixed grid shared the same parameters, but AuGeonet achieved lower FLOPs with reference-based GCC-PHAT, also ensuring linear scaling in C. With AGG-RL, AuGeonet further reduced parame- ters by replacing direct D 2048 mapping with G 256 representation; FLOPs increased only slightly from the similarity computation Eq. (6). For Gridnet with GRs, FLOPPs scaled linearly with D, and both FLOPs and parameter counts were the same order AuGeonet, contributing to the overall computational complexity. Nevertheless, FLOPs remained lower than those of baselines and IPDnet (Wang et 2024b). In practice, the overhead from Gridnet manageable: GRs can be cached for static environments, or D can be reduced with minimal performance loss. Further studies on efficiency improvements, including lightweight design alternatives, are left for future work.
CONCLUSION
In this paper. we proposed AGG-RL, novel framework for grid-flexible and geometry-invane invariant SSL that jointly learns complementary representations from audio-geometry-grinn inputs. To improve generalization and interpretability, we introduced two physics-informed components: LNNDFT, which enables adaptive frequency analysis to enhance IPD) distinguishability. and rMPE, which encodes relative microphone position cues. Extensive experiments across multiple datasets demon- strated that our framework achieved superior generalizability and robustness, particularly under un- seen geometries and real-world recordings. We believe that AGG-RL provides solid foundation for advancing 3D acoustic scene understanding in practical environments. For future work, we plan to extend AGG-RL to multimodal scenarios and broader spatial sensing tasks that require scalable grid or geometry configurations. We also aim to theoretically analyze the generalization properties of LNuDFT-based representations, providing a stronger foundation for physics-informed DNNs.
REPRODUCIBILITY STATEMENT
In this paper, we rely on publicly available datasets and open-source toolkits to ensure repro- ducibility. Detailed descriptions of the datasets, libraries, and implementation details are pro- vided in the main text and the Appendix. The source code is publicly available at https: 7/github. com BaekMS Bae.aaaaekasaiiiooa Audio Gew.erry-meeeeeeee Grid Representationn Learning
ACKNOWLEDGMENTS
This work was partly supported by the National Research Foundation of Korea(NRF) grant funded by the Korea (SSI) (RS-2025-00557944) and Institute Information & communi- cations Technology Planning & Evaluation (IITP) under the artificial intelligence semiconductor support program to nurture the best talents LUTP-22226-SS-20230055555 grant funded by the Korea govermmen((MSIT).
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REFERENCES
Jont B Allen and David A Berkley, Image method for efficiently simulating small-room acoustics. The Journal of the Acoustical Society of America, (5(4))943-955) 1979.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv: 2016
Min-Sang Back, Joon-Young Young Yang, and Joon-Hyuk Chang. Deeply supervised curriculum learning for deep neural network- sound source localization. Proceedings of the Interspeech, pp- 3744-3748, 2023.
Min-Sang Back, boon-Hyuk Chang, and Israel Cohen. DNN-based geometry-invariant DOA esti- mation with microphone positional encoding and complexity gradual training. IEEE Transactions on Audio, Speech, and Language Processing, 33:2360-233 -376,, 2025.
Sonali Bagchi and Sanjit K Mitra. The nonuniform discrete Fourier transform and its applications in filter design. I. I-D. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 43(6):422-433, 1996a.
Sonali Bagchi and Sanjit K Mitra. The nonuniform discrete Fourier transform and its applications in filter design. II. 2-D. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 43(6):434 444, 1996b.
Sonali Bagchi and Sanjit K Mitra. The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing. Academic Publishers, Norwell, MA, USA, 1999.
Shanmukha Srinivas Battula, Hassan Taherian, Ashutosh Pandey, Daniel Wong, Buye Xu, and DeLiang Wang. Robust frame-level speaker localization in reverberant and noisy environments by exploiting phase difference losses. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1-5, 2025.
Jacob Benesty, Jingdong Chen, and Yiteng Huang. Microphone Array Signal Processing. Springer, Germany, 2008.
Yoshua Bengio, Aaron Courville, and Pascal Vincent. Representation learning: A review and new perspectives. IEEE Transactions Pattern Analysis and Machine Intelligence,35(8)))) 1788- 2013.
Amandine Brunetto, Sascha Hornauer, and Fabien Moutarde. NeRAF: 3D scene infused neural radiance and acoustic fields. Proceedings of the International Conference on Representation Learning (ICLR), pp. 92876-92899, 2025.
Soumitro Chakrabarty and Emanuël A Habets. Multi-speaker DOA estimation using deep convolu- tional networks trained with noise signals. IEEE Journal of Selected Topics in Signal Processing, 13(1):8-21) 2019.
Joon-Hyuk Chang. Warped discrete cosine transform- noisy speech enhancement. IEEE Trans- actions on Circuits and Systems II: Express Briefs, 52(9))535-533) 2005.
Sérgio F Chevtchenko, Belman Jahir Rodríguez, Rafaella Vale, Abishek Soti, Yeshwanth Bethi, Naqib Ibnul, Alexandre Marcireau, Mostafa Rahimi Azghadi, Andrew Wabnitz, and Saeed Af- shar. Drone-based sound source localization: systematic literature review. IEEE Access, 13: 94256-94274, 2025.
Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Hol- ger Schwenk, and Yoshua Bengio. Learning phrase representations using RNN encoder-decodee for statistical machine translation. Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP). pp. 1724-1734, 2014.
Jeonghwan Choi and Joon -yuk Chang. Supervised learning approach for explicit spatial filtering of speech. IEEE Signal Processing Letters, 19:1412-1416, 2022.

---

Published as a conference paper at ICLR 2026
Djork-Amé Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network learning by exponential linear units (ELUs). In Proceedings of the International Conference on Learning Representations (ICLR), 2016.
Stefano Damiano, Federico Miotello, Mirco Pezzoli, Alberto Berarrdini, Fabio Antonacci, Augusto Sarti, and Toon van Waterschoot. A zero-shot physies-informed dictionary learning approach for sound field reconstruction. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1-5, 2025.
Jan Mark de Haan, Nedelko Grbié, Ingvar Claesson, and Sven Nordholm. Design and evaluation of nonuniform DFT filter banks in subband microphone arrays. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 11-1173- 11-1176, 2002.
David Diaz-Guerra, Antonio Miguel, and Jose R Beltrán. Robust sound source tracking using SRP- PHAT and 3D convolutional neural networks. IEEE/ACM Transactions on Aulio, Speech, and Language Processing, 29:300-311 2021a.
David Diaz-Guerra, Antonio Miguel, and Jose R Beltrán. gpuRIR: A Python library for room impulse response simulation with GPU acceleration. Multimedia Tools and Applications, 80(4): 5653-5671, 2021b.
Joseph Dibiase. A high-accuracy, low-latency technique for talker localization reverberant environments using microphone arrays. Ph.D. Thesis, Brown University, 2000.
Antoni Dimitriadis, Siqi Pan, Vidhyasaharan Sethu, and Beena Ahmed. Spatial HuBERT: Self- supervised spatial speech representation learning for a single talker from multi-channel audio. arXiv preprini arXiv:2310.1092. 2023.
Ha Manh Do, Karla Conn Welch, and Weihua Sheng. SoHAM: A sound-based human activity monitoring framework for home service robots. IEEE Transactions Automation Science and Engineering, 19(3):2369 2280-2233322200 2022.
Nicholas I Fisher, Toby Lewis, and Brian Embleton. Statistical analysis of spherical data.
Cambridge university press, 1993.
Yury Furletov, Volker Willert, and Jürgen Adamy. Auditory scene understanding for autonomous driving. In Proceedings of the IEEE Intelligent Vehicles Symposium (IV), pp. 697-702, 2021.
Leonardo Gabrielli, Stefano Tomassetti, Carlo Zinato, and Francesco Piazza. End-to-end learning for physics-basee based acoustic modeling. IEEE Transactions on Emerging Topics in Computational Intelligence, 2(2):160-170. 2018.
Chuang Gan, Yiwei Zhang, Jiajun Wu, Boqing Gong, and Joshua B Tenenbaum. Look, listen, and act: Towards audio-visude embodied navigation. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 9701-9707, 2020.
John S Garofolo, Lori Lamel, William M Fisher, Jonathan G Fiscus, and David S Pallett. DARPA TIMIT acoustic-phonetic continuous speech corpus CD-ROM. NIST speech disc 1-1.1. NASA STI/Recon technical report 93:27403, 1993.
Eric Grinstein, Christopher M Hicks, Toon van Waterschoot, Mike Brookes, and Patrick A Naylor. The Neural-SRP method for universal robust multi-source tracking. IEEE Open Journal of Signal Processing, 5:19-28, 2024.
Pierre-Amaury Grumiaux, Srdan Kitić, Laurent Girin, and Alexandre Guérin. A survey of sound the Acoustical Society of America, source localization with deep learning methods. The Journal the 157 2022.
Rishabh Gupta, Jianjun He, Rishabh Ranjan, Woon-Seng Gan, Florian Klein, Christian Schneider- wind, Annika Neidhardt, Karlheinz Brandenburg, and Vesa Välimäki. Augmented/Mixed reality audio for hearables: Sensing, control, and rendering. IEEE Signal Processing Magazine, 39(3): 63-89, 2022.
12

---

Published as a conference paper at ICLR 2026
Yuhang He, Niki Trigoni, and Andrew Markham. SoundDet: Polyphonie moving sound event detection and localization from raw waveform. In Proceedings of the International Conference on Machine Learning (ICML), pp.
2021.
Xiaoyang Huang. Yanjun Wang, Yang Liu, Bingbing Ni, Wenjun Zhang, Jinxian Liu, and Teng Li. AudioEar: Single-view ear reconstruction for personalized spatial audio. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 944-952, 2023.
Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift, In Proceedings of the International Conference on Machine Learning (ICML), pp. 448-456, 2015.
Mingu Jeon, Kyung Cho, Hee- Kim, Byeonggyu Park, Seung-Woo Seo, and Seong-Wor Woo Kim. Non-line-of-sight vehicle localization based on sound. IEEE Transactions on Intelligent Transportation Systems, 26(2):2321-2335 2025.
Xenofon Karakonstantis, Diego Caviedes-Norza Antoine Richard, and Efren Fernandez- Grande. Room impulse response reconstruction with physics-informed deep learning. The Journal of the Acoustical Society of America, 155(2):1048-100) 2024.
George Em Karniadakis, Ioannis Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nature Reviews Physics, 3(6):422-440, 2021.
Amirhossein Kazemnejad, Inkit Padhi, Karthikeyan Natesan Ramamurthy, Payel Das, and Siva Reddy. The impact of positional encoding on length generalization in Transformers. In Proceed- ings of the Advances in Neural Information Processing Systems (NeurIPS), pp. 24892-24928, 2023.
Sungnyun Kim, Sungwoo Cho, Sangmin Bac, Kangwook Jang, and Se-Young Yun. Multi-task corrupted prediction for learning robust audio-visual speech representation. In Proceedings of the International Conference on Representation Learning (ICLR). pp. 65598-65619, 2025.
Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Proceedings of the International Conference on Learning Representations (ICLR), pp. 1-15, 2014.
Charles H Knapp and G Clifford Carter. The generalized correlation method for estimation of time delay. IEEE Transactions on Acousties, Speech, and Signal Processing. 24(4):320-32 1976.
Masanori Koyama, Kenji Fukumizu, Kohei Hayashi, and Takeru Miyato. Neural Fourier transform: A general approach to equivariant representation learning. In Proceedings of the International Conference on Learning Representations (ICLR), pp. 6759,,759, 2024a.
Shoichi Koyama, Juliano G C Ribeiro, Tomohiko Nakamura, Natsuki Ueno, and Mirco Pezzoli. Physics-informed machine learning for sound field estimation: Fundamentals, state of the art, and challenges. IEEE Signal Processing Magazine, 41(6):60-711 2024b.
Yichong Leng, Zehua Chen, Junliang Guo, Haohe Liu, Jiawei Chen, Xu Tan, Danilo Mandic, Lei He, Xiangyang Li, Tao Qin, sheng zhao, and Tie-Yan Liu. BinauralGrad: A two-stage conditional diffusion probabilistic model for binaural audio synthesis. In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), pp. 23689-23700, 2022.
Kai Li, Wendi Sang, Chang Zeng, Runxuan Yang. Guo Chen, and Xiaolin Hu. SonicSim: A cus- tomizable simulation platform for speech processing in moving sound source scenarios. In Pro- ceedings of the International Conference on Representation Learning (ICLR), pp. 67379-67405, 2025a.
Zixuan Li. Shulin He, and Xueliang Zhang. Robust target speaker direction of arrival estimation. In Proceedings of the IEEE International Conference Acoustics, Speech and Signal Processing (ICASSP), pp. 1-5, 2025b.
Susan Liang, Dejan Markovic, Israel D Gebru, Steven Krenn, Todd Keebler, Jacob Sandakly, Frank Yu, Samuel Hassel, Chenliang Xu, and Alexander Richard. BinauralFlow: A causal and stream- able approach for high-quality binaural speech synthesis with flow matching models. In Proceed- ings of the International Conference on Machine Learning (ICML), pp. 37281-37298, 2025.
13

---

Published as a conference paper at ICLR 2026
Hyungseob Lim, Jihyun Lee, Byeong Hyeon Kim, Inseon Jang, and Hong- Goo Kang. Perceptual neural audio coding with modified discrete cosine transform. IEEE Journal of Selected Topics in Signal Processing, ((8)):440-15055 2024.
Ju Lin, Niko Moritz, Yiteng Huang, Ruiming Xie, Ming Sun, Christian Fuegen, and Frank Seide. AGADIR: Towards urray-geometyy agnostic directional speech recognition. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp.
11951-11955, 2024.
Andrew Luo, Yilun Du, Michael Tarr, Josh Tenenbaum, Antonio Torralba, and Chuang Gan. Learn- ing neural acoustic fields. In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), pp. 3165-3177, 2022.
Yi Luo, Zhuo Chen, Nima Mesgarani, and Takuya Yoshioka. End-to-end microphone permutation and number invariant multi-channel speech separation. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 6394 6398, 2020.
Heinrich W Löllmann, Christine Evers, Alexander Schmidt, Heinrich Mellmann, Hendrik Barfuss, Patrick A Naylor, and Walter Kellermann. The LOCATA challenge data corpus for acoustic source localization and tracking. In Proceedings of the IEEE Sensor Arruy and Multichannel Signal Processing Workshop (SAM), pp. 410-414, 2018.
Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021.
Federico Miotello, Ferdinando Terminiello, Mirco Pezzoli, Alberto Bernardini, Fabio Antonacci, and Augusto Sarti. A tthysics-informer neural network- approach for the spatial upsampling of spherical microphone arrays. In Proceedings of the IEEE International Workshop on Acoustic Signal Enhancement (/WAENC), pp. 215-219, 2024.
Bingshen Mu, Pengcheng Guo, Dake Guo, Pan Zhou, Wei Chen, and Lei Xie. Automatic channel selection and spatial feature integration for multi-channel speech recognition across various array topologies. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 11396-1 1400, 2024.
Rangarao Muralishankar, Debayan Ghosh, and Sanjeev Gurugopinath. A novel modified mel-DCT filter bank structure with application to voice activity detection. IEEE Signal Processing Letters, 27:1 07:1240-1244, 2020.
Thi Ngoc Tho Nguyen, Woon-Seng Gan, Rishabh Ranjan, and Douglas L Jones. Robust source counting and DOA estimation using spatial pseudo-spectrum and convolutional neural network. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 28:2626 2637, 2020.
Tsubasa Ochiai, Shinji Watanabe. Takaaki Hori, and John R Hershey. Multichannel end-to- end speech recognition. In Proceedings of the International Conference on Machine Learning (ICML). pp. 2632 2641, 2017.
Vassil Panayotov, Guoguo Chen, Daniel Povey, and Sanjeev Khudanpur. Librispeech: An ASR corpus based public domain audio books. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5206-5210, 2015.
Ashutosh Pandey, Buye Xu, Anurag Kumar, Jacob Donley, Paul Calamia, and Del.iang Wang- TPARN: Triple-path attentive recurrent network for time-domain multichannel speech enhance- ment. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 6497-6501, 2022.
Mgoc-Quan Pham, Thanh-Le Ha, Tuan-Nam Nguyen, Thai-Son Nguyen, Elizabeth Salesky, Sebas- tian Stüker, Jan Niehues, and Alex Waibel. Relative positional encoding for speech recognition and direct translation. In Proceedings of the Interspeech, pp. 31-35, 2020.
Karol Piczak. ESC:
Dataset for environmental sound classification. In Proceedings of the ACM International Conference Multimedia, pp. 1015-1018, 2015.
14

---

Published as a conference paper at ICLR 2026
Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-ine inffore- neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics. 378:686-707, 2019. 2019.
Chinmay Rajguru, Giada Brianza, and Gianluca Memoli. Sound localization in web-based 3D environments. Scientific Reports, 12(1):12107, 2022.
Chandan K A Reddy, Ebrahim Beyrami, Jamie Pool, Ross Cutler, Sriram Srinivasan, and Johannes Gehrke. A scalable noisy speech dataset and online subjective test framework. In Proceedings of the Interspeech, pp. 1816-1820, 2019.
Juliano G C Ribeiro, Shoichi Koyama, Ryosuke Horiuchi, and Hiroshi Saruwatari. Sound field estimation based physics-constrained kernel interpolation adapted to environment. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 32:4369-4383, 2024.
Alexander Richard, Dejan Markovic, Israel Gebru, Steven Krenn, Gladstone Alexander Butler, Fernando Torre, and Yaser Sheikh. Neural synthesis of binaural speech from mono audio. In Proceedings of the International Conference on Learning Representations (ICLR), 2021.
Edward Saff and Amo B Kuijlaars. Distributing many points a sphere. The Mathematical Intelligencer, 19(1):5-11, 1997.
Ralph O Schmidt. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagution, 34(3):276-280, 1986.
Ayal Schwartz, Elior Hadad, Sharon Gannot, and Shlomo E Chazan. Array configuration mismatch in deep DOA estimation: Towards robust training. In Proceedings of the IEFE Workshop Applications of Signal Processing to Audio and Acoustics (WASPAA), pp. 1-5, 2023.
Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position represen- tations. In Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics (NAACL), pp. 464 468, 2018
Bowen Shi, Wei-Ning Hsu, Kushal Lakhotia, and Abdelrahman Mohamed. Learning audio-visua speech representation by masked multimodal cluster prediction. In Proceedings of the Interna- tional Conference on Learning Representations (ICLR), 2022.
Kazuki Shimada, Archontis Politis, Parthasaarathy Sudarsanam, Daniel A Krause, Kengo Uchida, Sharath Adavanne, Aapo Hakala, Yuichiro Koyama, Naoya Takahashi. Shusuke Takahashi, Tuo- mas Virtanen, and Yuki Mitsufuji. STARSS23: An audio-visun dataset of spatial recordings of real scenes with spatiotemporal annotations of sound events. In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), pp. 72931-72957, 2023.
Matthieu Simeoni, Sepand Kashani, Paul Hurley, and Martin Vetterli. DeepWave: A recurrent neural-network for real-time acoustic imaging. In Proceedings the Advances in Neural Infor- mation Processing Systems (NeurIPS), pp. 15300-15312, 2019.
Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, and Yunfeng Liu. RoFormer: En- hanced Transformer with rotary position embedding. Neurocomputing. 167:127063, 2024.
Peiwen Sun, Sitong Cheng, Xiangtai Li, Zhen Ye, Huadai Liu, Honggang Zhang, Wei Xue, and Yike Guo. Both ears wide open: Towards language-driven spatial audio generation. In Proceedings of the International Conference on Representation Learning (ICLR), pp. 42606-42649, 2025.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proceedings of the Advances in Neurul Information Processing Systems (NeurIPS), pp. 1998-6008, 2017.
Jiadong Wang, Xinyuan Qian, Zihan Pan, Malu Zhang, and Haizhou Li. GCC-PHAT with speech- oriented attention for robotic sound source localization. In Proceedings of the IEEE International Conference Robotics and Automation (ICRA), pp. 5876-5883, 2021.
15

---

Published as a conference paper at ICLR 2026
Jiang Wang, Yuanzheng He, Daobilige Su, Katsutoshi Itoyama, Kazuhiro Nakadai, Junfeng Wu, Shoudong Huang, Youfu Li, and He Kong. SLAM-based joint calibration of multiple asyn- chronous microphone arrays and sound source localization. IEEE Transactions on Robotics, 40: 4024 4044, 2024a.
Lin Wang and Andrea Cavallaro. Deep-learming-assitted sound source localization from a flying drone. IEEE Sensors Journal, 22(21):20828-2883 2022.
Yabo Wang. Bing Yang. and Xiaofei Li. IPDnet: universal direct-path, IPD estimation network for sound source localization. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 32:5051-5064, 2024b.
Deyun Wei and Jun Yang. Non-uniform sparse Fourier transform and its applications. IEEE Trans- actions Signal Processing, 70:4468 4482, 2022.
Muqian Wen and John Houlihan. Application of the non-uniform Fourier transform to non-
uniformly sampled Fourier transform spectrometers. Optics Communications 540:129491, 2023.
Jiajian Xie, Shengyu Zhang, Mengze Li, chengfei Iv, Zhou Zhao, and Fei Wu. EcoFace: Audio- visual emotional co-disentanglement speech-driven 3D talking face generation. In Proceedings of the International Conference Learning Representations (ICLR), pp. 101625-101643, 2025.
Zhongweiyang Xu, Xulin Fan, Zhong-Qune Wang, Xilin Jiang, and Romit Roy Choudhury. Array- DPS: Unsupervised blind speech separation with a diffusion prior. In Proceedings of the Interna- fional Conference on Machine Learning (ICMI., pp. 69160-69188, 2025.
Bing Yang, Hong Liu, and Xiaofei Li. Learning deep direct-path relative transfer function for binaural sound source localization. 1EEE/ACM Transactions on Audio, Speech, and Language Processing, 29:3491-35053 2021.
Yufeng Yang, Desh Raj. Ju Lin, Niko Moritz, Junteng Jia, Gil Keren, Egor Lakomkin, Yiteng Huang, Jacob Donley, Jay Mahadeokar, and Ozlem Kalinli. M-BEST-RQ: A multi-channel speech foun- dation model for smart glasses. In Proceedings of the IEEE International Conference on Acous- fics, Speech and Signal Processing (ICASSP), pp. 1-5, 2025.
Takuya Yoshioka, Xiaofei Wang, Dongmei Wang, Min Tang, Zirun Zhu, Zhuo Chen, and Naoyuki Kanda. VarArray: Atray-geometry agnnstsiic continuous speech separation. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp- 2022.
Dehao Zhang, Shuai Wang, Ammar Belatreche, Wenjie Wei, Yichen Xiao, Haorui Zheng, Zijian Zhou, Malu Zhang, and Yang Yang. Spike-based neuromorphic model for sound source localiza- tion. In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), pp- 113911-113936 2024.
Yue Zhang, Zhiyang Xu, Ying Shen, Parisa Kordjamshidi, and Lifu Huang. SPARTUN3D: Situated spatial understanding of 3D world in large language model. In Proceedings of the International Conference on Learning Representations (ICLR), pp. 73388-73406 2025.
Zhisheng Zheng, Puyuan Peng. Ziyang Ma, Xie Chen, Eunsol Choi, and David Harwath. BAT:
Learning to reason about spatial sounds with large language models. In Proceedings of the Inter- national Conference on Machine Learning (ICML), pp. 61454-61469, 2024.
Yongchao Zhou, Uri Alon, Xinyun Chen, Xuezhi Wang. Rishabh Agarwal, and Denny Zhou. Trans- formers can achieve length generalization but not robustly. In Proceedings of the International Conference on Learning Representations Workshop on Mathematical and Empirical Understand- ing of Foundation Models, 2024.
Qiushi Zhu, Jie Zhang, Yu Gu, Yuchen Hu, and Lirong Dai. Multichannel AV-wa22ee22 A frame- work for learning multichannel multi-modal speech representation. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 19768-19776, 2024.
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A APPENDIX
A.1
RELATIONSHIP BETWEEN TDOA AND RELATIVE MICROPHONE POSITIONS
We derive here the relationship between the TDOA and relative microphone positions under the stan- dard plane-waye assumption. Assuming a far-field source, the time of arrival T(-) at a microphone position p R33 is given by
u
T())
(17)
where Ty is the reference arrival time at the origin of the coordinates, u E IR is the unit direction vector of the incoming wave, and is the speed of sound. Let Pm and Pn denote the positions of the m-th and n-th microphones, respectively. Their TDOA ATm,n is
(pn. Pm) u'Apm.n
Amm, = T(pm) - (Pp.)
(18)
V where Apm,n := Pr. Pm is the relative microphone position vector. This result shows that the TDOA depends solely on the relative microphone positions Apm.x. which is analogous to Eq. (10). not their absolute coordinates. As the IPD is given by (f) 2T ATm the same property holds for IPDs as well. Therefore, encoding microphone geometry in a relative form, as done in the proposed rMPE, is directly grounded in the underlying physies of wave propagation.
A.2 LNUDFT PARAMETER VISUALIZATION
8k
Uniform init. & Frozen
Prequency fr (Hz)
6k
Uniform init. & Trained
Logit init. & Frozen
Logit init, & Trained
4k
2k
0
192
256
Index k
Figure 3: Frequency response of LNuDFT parameters.
Figure 3 shows the frequency response of the LNuDFT parameters with fa " Sa. where the kHz. The horizontal axis represents the indices of the LNuDFT parameters, k. and the vertical axis represents the frequency fü in Hz. The standard DFT was initialized with uniformly spaced bins, which after training evolved into a non-uninee non-uniform spacing that allocates higher resolution to the 1.5-7.5 kHz range. In contrast, the proposed logit-based initialization already placed parameters densely within the 2-6 kHz region at initialization, and they tended to evolve toward more uniform spacing after training. This behavior indicates that the model tended to attenuate resolution at too low and high frequencies, concentrating more bins in the mid- frequency range. It denotes that the proposed initialization and the results of LNuDFT were well aligned with the spectral characteristics of speech signals, which are primarily concentrated in this frequency range, and provides informative IPD cues crucial for SSL and TDOA estimation.
sampling frequency was S.
The selected values of 6aun 0.15 and Cend = 0.95 for the logit-based initialization were chosen to assign denser sampling to the low- and mid-frequency regions, while sparsely covering the high- frequency region to avoid spatial aliasing. As shown in Fig. this initialization results in frequency allocations that concentrate primarily on the mid-frequency bins where IPD cues are most reliable. Furthermore, the initialization also assigned slightly denser sampling in the low-frequency bins than in the high- high-frequency bins, ensuring stable IPD information while avoiding aliasing effects. We performed grid search Eaunt and Cend and observed that small perturbations around the selected values did not significantly affect performance. The chosen configuration provided the most consistent and robust results across experiments.
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A.3 AUGEONET ARCHITECTURE
Rep. Mapping Block #3
A
Rep. Mapping Block #2
A₂
Rep. Mapping Block #1
A
Audio- Audio-Geomeetyy R Representation
Frame-wise GRU
x4
Channl-wise MHSA
Mic. Pos. Encoding
Residual ConvBlock 4
Init ConvBlock
Init Batch Norm
GCC-PHAT
LNuDFT
2, y
Mic, Arry Geometry
Audio Signal
Figure 4: AuGeonet architecture.
The overall structure of AuGeonet is modified from GI-DOAEnet (Back et al.) 2025). with detailed architecture available in the original paper. The default settings of the AuGeonet were M = 128, 7, 4, O 3, and G = 256. Other hyperparameters followed those of GI-DOAEnet. Figure illustrates the modified AuGeonet architecture, and the key modifications are summarized below:
Input feature. The input is replaced with LNuDFT-based GCC-PHAT features.
Integrating the geometry information. Each channel of the input GCC-PHAT features is treated as a batch. These features are first processed with ID batch normalization (BN) [loff & Szegedy) 2015). and relative microphone coordinates in both Cartesian and sinusoidal spherical forms (Gt,, De: &e, fc. sin He,, cos de, sin Ge, cos &e) from Eq. (10) concatenated along the frequency dimension to provide comprehensive geometry information. Then, an initial ConvBlock (CB), consisting of ID convolution layer, an ELU (Clevert et al., (0166) activation, and BN, projects the frequency dimension from 2K +88 to feature size M. A stack of Residual ConvBlock (RCBs), each composed of two CBs with residual connection, follows the initial CB to extract local fea- tures. rMPE is added to the input of each RCB, and a total of 4 RCBs are used.
cos
After the RCBs, four spatio-temporal dual-path blocks (STDPBs) sists of a CW-MHSA with rMPE, which captures spatial dependencies by applying MHSA across the channel dimension for each time frame, and frame-wise wiiee GRU (Cho et al. 2014). which models temporal dependencies.
applied. Each STDPB con-
Output representation. Finally, O representation mapping blocks (RMBs) are used instead the spatial spectrum mapping blocks in GI-DOAEnet. Each RMB consists of an RCB, which applies layer normalization (LN) (Ba et al. 2016) instead of BN, followed by a linear layer that projects the features to size G. The output of RCB each RMB is also passed to the subsequent one.
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A.4
GRIDNET ARCHITECTURE
Layer
Layer Norn
ELU
xB
Lince Layer
6,6
Candidate DOA
Figure 5: Gridnet architecture.
Gridnet consists of sequential blocks, each composed of linear layer that preserves the feature dimension G, followed by ELU activation (Clevert al. (016) and an LN layer, illustrated in Fig. [] A final linear layer produces the output, GR. All candidate DOAs are modulated with sinusoidal encoding before being input Gridnet. These modulated candidate DOAs are processed in batch, allowing Gridnet to efficiently handle varying numbers of candidates D without retraining. B was and the frequency modulation factor & was set our experiments.
A.5 FIBONACCI SPHERE SAMPLING
Algorithm 1: Fibonacci sphere point generation
Input: Number of DOA grids D
Output: Set of 3D points T ) Va (I.ds yas za, 0d da) the unit sphere
1+yB
1 +- 2x
P
for d 0 to D
do
1- 2d+1
D
r - V-=2
< d
X ー r COS w
Ч rsin
0 - atan2(y,
6 < atan2(z, x22 + y2)
Add point w'u = (x, y/, z, 0, ②) to
end
return
(a) Fibonacci sphere sampling.
(b) Equiangular sphere sampling.
Figure 6: Examples of (a) Fibonacci sphere sampling and (b) equiangular sphere sampling.
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Fibonacci sphere sampling generates nearly uniform points the unit sphere using the golden angle, thereby avoiding the pole clustering problem latiude-longitude grids (Saff Kuijlaars 1997]. Algorithm[[ summarizes the procedure, with yp denoting the golden ratio. Figure a shows an example with 1) = 512 points, while Fig. bb) illustrates equiangular sampling (32 azimuth x 16 elevation), which suffers from dense clustering at the poles. This method efficiently approximates uniform sampling without complex computations.
A.6 ORACLE SPATIAL SPECTRUM GENERATION
The oracle spatial spectrum S R2
Dxxxx is generated as: if | > 0,
x(Tx)(cox (8(sa.b)) -1) }
}
max WE
Sd
(19)
0,
otherwise,
8(5, 1b) arccos (I. + MeYl 2x 2
(20)
In v2 008 1'
<(>)
(21)
where V is the set of ground ground-truth truth DOAs at the 1-th frame, and Su is the d-th DOA candidate. The angular distance between candidate and ground-truth DOA computed by 8(-), and 7o controls the beamwidth (Choi & Chang (022) for the o-th output. A smaller %o yields narrower beams with sharper peaks but weaker relationships across neighboring DOAs, while a larger %o produces wider beams with smoother transitions.
A.7 LOss FUNCTION
The weighted BCE loss is defined as:
L
C(S,S) 1 L.
ΣEΣ {o Sd,ott log Sa.o1 + (1 Sd,o,) log (1-8)
(22)
where p is a weighting factor to balance the loss between positive (ground-truth DOAs) and negative samples (Nguyen et al. 2020). In experiments, set 2.
A.8 ITERATIVE MAX-PEAK SELECTION AL.GORITHM
Algorithm 2: Iterative max-peak selection from spatial spectrum
Input: Predicted spatial spectrum So,1. number of active speakers Ti angular distance margin L
Output: Set of estimated DOAs V
Initialize 1 < 0
while 1 < Ti do
Find index d' arg max, Sa.0.1
Add DOA candidate via- V Suppress $a,01 0 for all d within angular distance of d' (computed using Eq. (20)).
return V
Algorithm 2 outlines the iterative max-peak selection method for estimating DOAs (Bak et al.
2023 from the predicted spatial spectrum Sa,1 E TR.", where the number of candidate points at the (-th frame and o-th output. The number of active speakers Ti is assumed to be known priori, and T. is an angular distance margin to avoid selecting multiple peaks from the same source, which was set to 10 in our experiments.
A.9 MODEL TRAINING DETAILS
Every DNN-based method used similar training settings. The batch size was set to for most models, except Neural-SRP which reduced to due to memory constraints of GPU. All models
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were implemented in PyTorch and trained single NVIDIA RTX 3090/ 4090 GPU. We used the weighted BCE loss in Eq. (22), and the Adam optimizer (Kingma & Ba 2014), gradient clipping within 1, and adaptive learning rate schedule that decayed by 0.9 if the validation loss did not improve for two consecutive epochs. To facilitate robust SSL. learning, we employed complexity gradual training (CGT) strategy (Baek al. 2025), consisting of multi-stage geometry learning (MSGL) and DSCL.
Table 6: Multi-stage geometry learning (MSGL) hyperparameters.
Stage
Microphone Array
Number of channels
Learning Rate
Weight Decay
Epoch
1
Tetrahedron (4 cm)
4
2.5x 10
1.0x 10*
1-10
2
Dynamic
4
5.0 10
1.0x 10
11-20
3
Dynamic
4-12
1.0x 10
1.0x 10
21-300
Table summarizes the MSGL setup. The training complexity was gradually increased: from fixed dynamic MAs, and from a fixed to variable number of channels. with stage-specific learning rates and weight decay for stable convergence. Each epoch contained 800 utterances for training, and validation was conducted after every epoch (2.000 samples in stages 1-2, and 300 samples per channel in stage 3). DSCL employed multiple outputs with varying beamwidth targets, starting coarse and gradually refining them. Beamwidth parameters % were initialized as [32", 12", 5*] and decreased linearly to [5 5", 5 between epochs 35-60. This coarse-to-fine fone scheme first captures broad spatial patterns and then sharpens them into accurate spatial spectra for SSL.
A.10 SYNTHETIC DATASET GENERATION
Algorithm 3: Synthetic dataset generation.
Input: Anechoic speech dataset, noise dataset, number of channels C' Output: Synthetic mixtures, oracle voice activity detection (VAD) labels, ground-truth DOAs foreach utterance do
Speech selection: Randomly select speakers and utterances, resample 16 kHz, trim/pad to 4 s, and obtain oracle VAD labels using WebRTC VAD
Noise generation: Select one coherent noise, resample 16 kHz, generate channel-wise Gaussian white noise, and trim/pad to 4s.
Spatial setup: Randomly configure room size, RT60, and C-channel 3D geometry with inter-microphone distances constrained by Eq. (23). Place speakers with at least 10 angular separation, with coherent noise placed at least 2.5 m away, and ensure the microphone array is at least 0.1 from walls.
RIR generation: Generate synthetic RIRs using gpuRIR (Diaz-Guerra et al. 202 with the image source method (Allen & Berkley, 1979) and diffuse modeling. Signal construction: Convolve signals with RIRs, mix speech with random SIR, mix noises with random SIR, and combine speech and noise with random SNR.
Rmin [mxx (1, 4 - 3 - 6] cm,
(23)
Rmax
[7, max (7, 9 9444-0 Gxt) cm.
This section details the process of generating the synthetic dataset, following the procedure of Baek et al. (222)). SeoortthmBoutlieee the steps, while Eq. (23) defines the minimum Rmin and maximum Rmax inter-microphone distances as function of the number of channels C. Table summarizes the ranges of acoustic parameters used in Algorithm 3 for generating the synthetic dataset. Each parameter was randomly sampled from a uniform distribution within the specified interval, except for the elevation angle. The elevation 1993), given by f. where ip ~ vMF x) with = т and k = 2, favoring positions near the horizontal plane while restricting the range to [0, m..
drawn from von Mises Fisher distribution (Fisher al.)
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For training and validation, anechoic utterances were taken from LibriSpeech (Panayotov et al. 2013), where the train-clean-IDe and test-clean sets were used, respectively, and noises were taken from MS-SNSD (Reddy et al., 2019), where the train and test sets were used, respectively. Anechoic speech for evaluation was taken from TIMIT (Garofolo et al. 1993). and noises from ESC-50 (Piczak 2015).
A.11 EVALUATION METRICS
MAE (9) and 1CC (%) are defined as:
Tt
MAE (*) 180
min PEP.
Σ sml
(Se. (p(s))
(24)
Lactl
Ti
LE
[
1CC
100,
(25)
Laac
where| |- denotes the cardinality of set, and List is the set of active speaker labels in the utterance. Ti is the number of sources for the (-th frame, Pi is the set of all permutations of [; sources, is the ground-truth DOA of source Wp(s) is the estimated DOA assigned to source s under permutation and 6(-) is the angular distance between two directions computed using Eq. (20). MAE computes the mean angular eπror between ground-trute and estimated DOAs, considering all possible source permutations to resolve permutation ambiguity in multi-source scenarios. Lage is the subset of Laat whose angular error is less than 10
12
BOX AND VIOLIN PLOTS OF THE RESULTS
.....
Mielion
MAR
30
Propesed
Newra-SRP
Unet
Figure Box and violin plots of MAE for Dynamic-S with 4-12 channels.
90
Mtean
Mesian
MAR (*)
60
Propesed
Neura-SRP
Unet
Figure 8: Box and violin plots of MAE for Dynamic-U with 13-16 channels.
Figures and present the box and violin plots of MAE results for Dynamic-S with 4-12 channels and Dynamic-U U with 13-16 channels, respectively. Box plots show the interquartile range (IQR) and whiskers, where the black solid lines denote whiskers within 1.5 times the IQR. The dotted and dashed lines inside box plots indicate the median and mean of each method, respectively. Violin plots illustrate the kernel density estimation of the distribution. The proposed method exhibited a more pronounced peak around the median values with narrower distribution, indicating that the results were more concentrated and consistent compared to the baselines, Unet and Neural-SRP. both equipped with AGG-RI..
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A.13
ANALYSIS ACROSS ENVIRONMENTAL CONDITIONS
40
Prepwal Neuaal
Prppesl NeraalS10 SIt?
Une
30
ACC,a (25)
60
MAB
20
10
-5
10
15
20
25
30
-5
10
20
25
30
SNR (dB)
SNR (dB)
SNR vs. MAE
(b) SNR ACC1o
Propuee
25
Nound SRP
Uinsi
a (75)
MAB (1)
-0
80
15
Propoced Noural
30-
10
Unet
0.2
0.4
0.6
0.8
1.0
1.2
0.2
0.4
0.6
0.8
1.0
1.2
RTW (8)
RT6O (8)
(c) RT60 MAE
(d) RT60 vs. ACC10
Figure 9: MAE and 1C results of the proposed method and baselines (Unet, Neural-SRP, both with AGG-RL) on the Dynamic-S and Dynamic-U datasets across different SNR and RT60 condi- tions.
To assess the impact of environmental conditions SSL performance, we analyzed the results across varying SNRs and RT60s using the synthetic datasets. Figure P illustrates the MAE and ACC10 results for Dynamic-S and Dynamic-U, comparing the proposed method with the baselines (Unet and Neural-SRR -RRr,, both equipped with AGG-RL. The two datasets were combined to provide a comprehensive overview of performance tendencies under varying environmental conditions. The combined datasets were divided into 10 equally sized bins for each SNR and RT60 range, and the nearest values to the bin centers were averaged. All methods showed improved performance with increasing SNR and decreasing RT60, as easier acoustic conditions inherently facilitate more accu- rate SSL. Notably, the proposed method consistently outperformed the baselines across all SNR and RT60 ranges, demonstrating strong robustness under both low-SNR and highly reverberant condi- tions.
Table 7: Experimental results under different numbers of active speakers across all datasets.
NAO robot
Eigenmike
Dynamic-S MAE
Dynamic-U U
MAE
ACC,
MAE
ACC.,
ACC,,
MAE
ACCio
Unet
speaker
11.59 #3.43
93.00
16.14 43,69
68.49
16.92
10.91
62.74
13.52 =1.20
71.68
speakers
19.78
24.41
23.29
44.75
12.14
32.46
29.76
30.06
=1.14
33.98
Neural-SRP
speaker
7.28 42.62
90.21
10.77
4:228
79.08
12.77
1:084
63.65
9.73 10.97
73.21
2 spcakers
13.28 #5.31
33.74
17.89
43.67
17.24
33.55
+:093
20.92
31.22 #1.30
26.47
Proposed
speaker
7.48
96.06
9.77
+1.42
81.13
20:52
85.95
9.51 4092
74.09
speakers
10.71 13354
73.90
15.93
1:3.5
43.50
17.93
1:0.33
58.84
21.17
21.0
39.58
Table 7 summarizes the experimental results under different numbers of active speakers across all datasets. All methods showed degradation when moving from one to two speakers, which reflects the increased difficulty of SSL in multi-source scenarios. However, except for the MAE in the single-speaker condition of the NAO robot dataset-wih Neural-SRP showed marginally better performance- the proposed method consistently outperformed both baselines across all datasets and speaker configurations, demonstrating its strong ability to handle both single- and mulli-sppalee spatial scenes.
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A.14 RESULTS WITH STARSS23 DATASET
Table 8: Experimental results on STARSS23 with different methods. The best results on each dataset are bold.
Total
Speaker
2 Speakers MAR
MAR:
ACC0p
MĀK
ACCC
AACC
Unet
43.91 =4.07
23.55
38.37
28.55
35.71
46.03 #5.96
18.90
Neural-SRP
55.54 27.55
5.74
50.11
#16.56
10.12
57.62 28.35
4.07
Proposed
27.32
#5.50
36.09
18.67
#6.15
56.58
30.63 #6.96
28.25
For further validation, evaluated the proposed method using the STARSS23 dataset (Shimada ct al. 2023), which consists of real recorded multi-speaker reverberant mixtures originally recorded with 32-channel Eigenmike MA. The official dataset provides downmixed versions using 6-, 10-, 26-, and 22-th channel subsets, corresponding to a 4-channel tetrahedral-shaped configuration. Al- though the dataset was developed for sound event localization and detection (SELD), focused exclusively on the speech localization aspect. Speech-only segments were selected based on the provided annotations. The results in Table [
show noticeable degradation compared Table 3 This is expected because STARSS23 involves low SNR conditions with various sound events, highly dynamic scenes with moving speakers, and acoustic characteristics that differ significantly from our static, synthetic training data. Despite these challenges, the proposed method consistently outper- formed the baselines across all evaluation settings, demonstrating strong generalization capability to real-world and dynamic recording conditions.
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A.15
SPATIAL SPECTRUM VISUALIZATION
Oracle
Proposer
1.0
1.0
O1
0.8
120FP
B0
Elension
120
1F
20
0.6
90
90
0.1
0.2
0.2
120
120
Azimuth
0.0
Asimuth
0.0
Neural-SBP SRP
Unet
1.0
20
Elevation
0.6
Elevadion
0.6
90
90P
0.4
0.4
0.2
0.2
120
120F
Azimuth
Aximuth
0.0
Figure 10: Spatial spectra averaged across frames for utterance with active speakers from the NAO robot dataset, visualized in Mollweide projection. Peaks correspond to estimated DOAs on the unit sphere.
Oracle
Proposed
2000
2000
Grd Index
1500
0.75
1500
0.75
1000
0.50
1000
0.50
500
0.25
500
0.25
0.00
0.00
200
400
600
800
200
400
600
800
Frame
Frame
Neural-SRP
Unet
2000
2000
Grid Indox
1500
00.55
Gril Iadox
1500
1000
0.50
1000
0.50
500
0.25
500
0.25
0.00
0.00
200
400
600
800
0
200
400
600
800
Frame
Frame
Figure 11: Frame wise spatial spectra for the same utterance as Fig.
10 shown in 2D where the
T-axis represents time frames and the y-axis denotes grid indices.
Figure 10 illustrates the spatial spectra of the oracle, the proposed method, Neural-SRP, and Unet on utterance with two active speakers from the NAO robot dataset. For visualization, frame-level spectra were averaged and projected onto the Mollweide map. The proposed method produced sharp and distinct peaks exactly both ground-truth DOAs, elosely resembling the oracle. In contrast, Neural-SRP yielded a broad peak that failed to clearly separate the two speakers, while Unet gen- erated less distinctive peaks. Figure TT illustrates the spatial spectra in 2D, where and y-axes represent frame and DOA index d, respectively. The proposed method consistently produced sta- ble peaks aligned with ground truth DOAs and accurate VAD estimation, whereas Neural-SRP and Unet exhibited less consistent activations and unreliable VAD distinction.
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Published as a conference paper at ICLR 2026
Oracle
Proposed
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Figure 12: Spatial spectra averaged across frames for an utterance with a single active speaker from the Eigenmike dataset, visualized in Mollweide projection. Peaks correspond to estimated DOAs the unit sphere.
Orscle
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Figure 13: Frame-wiss wise spatial spectra for the same utterance Fig.
12 shown in 2D where the
r-axis represents time frames and the y-axis denotes grid indices.
Figures 12 and 13 show the spatial spectra of the oracle, proposed method, Neural-SRP, and Unet on an utterance with a single active speaker from the Eigenmike dataset, using Mollweide projection and 2D frame-wise view, respectively. In the Mollweide projection (Fig. 12] the proposed method produced a distinct and sharp peak at the ground-truth DOA. By contrast, Neural-SRP yielded broad peak that did not clearly indicate the source location, while Unet produced multiple non- ground-truth peaks (e.g., near -90" azimuth), demonstrating less reliable estimation. In the 2D representation (Fig. 13), the proposed method consistently localized the source with sharp peaks and reliable VAD, closely matching the oracle. Neural-SRP again exhibited a wide, ambiguous peak, and Unet generated less sharp peaks along with spurious responses. Overall, the proposed method yielded sharper and more stable spatial spectra than the baselines, highlighting its robustness for unseen MA geometries.
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Published as a conference paper at ICLR 2026
A.16 VISUALIZATION OF GRID REPRESENTATIONS
1-NNE2
2048
1024
Figure 14: Grid representations visualized with t-SNE, Fibonacci grid points with 4096 used as input candidates.
1812
Asinmth
Elevation
S-N
180
50'
45"
1-8NR1
1-SNE
(a) t-SNE with varying azimuth
(b) t-SNE with varying elevation
Figure 15: Grid representations visualized with t-SNE for azimuth and elevation candidates.
Figure 14 visualizes the output with Fibonacci grid points with D 4096. Nearby directions in 3D space were embedded closely, whereas opposite directions were mapped farther apart, demon- strating that the GRs preserved directional similarity in the latent space. Figure 15 a) illustrates the case of varying azimuth while fixing elevation at 90" with D = 2048. The t-SNE output formed circular pattern consistent with azimuthal changes, indicating smooth representation of angular vari- ation. Figure b))b) shows the case of varying elevation while fixing azimuth at O* with D = 2048. The t-SNE output formed an S-shaped pattern aligned with elevation changes, demonstrating that the Gridnet consistently encodes variations in elevation. These results indicate that Gridnet cap- tured and preserved the relationships of candidate DOAs in the latent space, supporting flexible and interpretable candidate DOA representation.
A.17 THE USE OF LARGE LANGUAGE MODELS
The authors used large language models (LLMs) to assist in writing the manuscript, including refin- ing language and ensuring clarity and coherence.
27


Reviews:
[{"review_id": "inIORM9Ln3", "reviewer": "Reviewer_aRq1", "summary": "This paper introduces AGG-RL, a novel framework for sound source localization (SSL). It aims to achieve SSL with geometric invariance and grid flexibility by jointly learning audio-geometric representations and grid representations in a shared latent space. To achieve this, the approach proposes a learnable non-uniform discrete Fourier transform (LNuDFT) that assigns frequency bins based on physical informativeness, and a relative microphone position encoding (rMPE) aligned with TDOA. Experiments were conducted on synthetic and real datasets, demonstrating improved performance over baselines.", "questions": "1. Experiment (v) still outperforms the proposed one on the Dynamic-U data and performs on par with the proposed one for NAO robot, but significantly degrades on the Eigenmike. Please expand on this discrepancy?\n\n2. In L70, “Both components facilitate the extraction of spatial representations with physics-based inductive biases”: Why are LNuDFT and rMPE considered as imposing (physics-based) inductive biases? To me, these are perceived as a process that introduces and makes learnable parameters for feature extraction more flexible, and I see it as a process that relieves the inductive bias.\n\n3. Can the LNuDFT initialization or update scheme get stuck in poor local minima, e.g., if the initial frequency allocation is far from optimal? Have the authors tried more physically motivated or data-driven initializations beyond logit-based mapping?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- **Originality**: The integration of physics-informed design (LNuDFT, rMPE) with a unified latent space for audio, geometry, and grid is original and is well-motivated by known limitations of geometry-specific and fixed-grid methods in SSL.\n- **Quality**: The experimental design is thorough: ablation studies, varied datasets (including real recordings), and consistent baselines provide credible evidence for claims of generalization and robustness. The efficiency analysis (parameter count, FLOPs) is also useful.\n- **Clarity**: The paper is mostly well written, with helpful architectural diagrams and clear mathematical formulations. The method and its motivation are explained coherently, and appendices include implementation details and sample code links.\n- **Significance**: The experimental results demonstrate that this framework provides substantial improvements to SSL in real-world environments where array and grid conditions may vary.", "weaknesses": "1. **(Lack of justification for the claim on being physics-informed)** The paper mentions LNuDFT and rMPE as two main components proposed as ‘physics-informed components’ in the abstract, but the reason why these are ‘physics-informed’ was not explained.\n    - Although Appendix A.1 supports that LNuDFT's ‘trainable manner’ emphasizes informative phase regions/causes to some extent, but the way of drawing the claim that 'it emphasizes informative regions' was limited to the common sense about speech signals. (For example, would the frequency response of LNuDFT parameters become different for the other signals, e.g., bird chirps or ambient wind noise etc?)\n    - Similarly, for rMPE, it was not demonstrated that using this method actually captures “inter-channel time differences” more effectively.\n\n    Performing DFT non-uniformly and encoding information relatively can be done independently of physics; connecting it to physical phenomena seems to require more detailed justification.\n\n2. **(Difficulty in result analysis)** While it is commendable that comparisons were made on both real and synthetic datasets, the fact that all microphone arrays in the synthetic data were selected as dynamic microphones complicates result analysis.\n    - Particularly, examining the results in Table 3 reveals a noticeable trend of performance differences, but it is unclear whether this stems from differences between real and synthetic data or from differences in dynamic microphones. The authors also did not draw a clear conclusion on this point.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tNHoThGSyq", "reviewer": "Reviewer_LRbg", "summary": "This paper presents AGG-RL (Audio Geometry Grid Representation Learning), a family of algorithms to estimate direction-of-arrival in a way that is invariant to the geometry of the microphone array and adaptable to different grids.\n\nTo achieve this, AGG-RL relies on two innovations: i) using a DFT where the width of the frequency bins is learnt alongside the training (allowing for higher resolution on the frequencies that are most relevant for direction-of-arrival estimation), and ii) use of relative position encoding to describe the microphone geometry.\n\nTo train AGG-RL a network (AuGeonet)  encodes the sound field (conditioned on the microphone array geometry), whereas another network (Gridnet) encodes a grid of query points where the sources in the sound-field may be localised. The final output logits are obtained by combining the outputs of AuGeonet and Gridnet (essentially an inner product), with each logic representing the probability of a source being present at the corresponding query point. Binary cross-entropy is used to compute the loss.\n\nEvaluations on the LOCATA dataset show AGG-RL achieving ~11° mean-absolute error on direction-of-arrival estimation on a microphone array and dataset not seen during training.", "questions": "* **Q1**: In eq 14, are the grid points $\\\\theta_d$ and $\\\\phi_d$ obtained by linearly spacing the azimuth and elevation ranges by $\\\\frac{G}{2}$ points respectively?\n* **Q2**: How many synthetic samples were used during training? Can the performance of AGG-RL be further improved by adding further training samples?\n* **Q3** Appendix A.9 contains really important information that it is not hinted at in the main text (acoustics characteristics of the simulations, utterances and noise datasets, SNRs, duration of the audio segments) that should be summarised in the main text.\n* **Q4**: What does it mean exactly that the NAO dataset has training exposure? Was the dataset used during training?\n* **Q5**: In table 2, could you report the spread of the mean-absolute-error of the direction-of-arrival errors?\n* **Q6**:  How do you train AuGeonet to accept more/fewer microphones in an array? Is there a \"not present\" encoding?\n* **Q7**: Could you breakdown the results in table 2 by number of speakers present in the sound-field?\n* **Q8**: Could you breakdown the results in table 2 by SNR and T60?\n*  **Q9**: Can AGG-RL model different directional sensitivities in microphones? If not, could you hypothesise if this would be possible with an extension?  Relatedly, would it be possible to input ideal ambisonics to AGG-RL?\n* **Q10**: What microphone array geometry information is provided to AuGeonet? The main manuscript seems to indicate it is the relative encodings just the relative angles, but Appendix A.3 indicates the geometry is given in cartesian and polar coordinates.\n* **Q11**: Could you evaluate AGG-RL against other datasets for direction-of-arrival estimation in the literature (eg. TUT Sound Events 2018[1], Spatial LibriSpeech [2], STARSS'23 [3]?\n* **Q12**: In table 11, why does the performance decay as the number of points in the grid increases.\n\n\n-----\n\n### Nitpicks (do not affect rating, no need to follow up on these during rebuttal)\n\n* **N1**: I found the notation for $\\bf{v}$ very confusing and for a few minutes could not understand what $\\bf{v}_M$ and $\\bf{v}_G$ were. These would be easier to parse if they were expressed as a function $v(Q) = \\frac{4}{Q}\\[0, 1, \\dots, \\frac{Q}{4} -1\\]$\n* **N2**: Similarly I find it would be easier if you indicated the function parameters in  equations 12, 14,15 and 16.\n* **N3**: I would suggest explicitly mentioning in equation 1 that $c, k, l$ refer to the channel, frequency, and time indices respectively.\n\n\n-------\n[1] Adavanne et al. (2019) “Sound Event Localization and Detection of Overlapping Sources Using Convolutional Recurrent Neural\nNetworks”. Journal of Selected Topics in Signal Processing.\n\n[2] Sarabia et al. (2023) “Spatial LibriSpeech: An Augmented Dataset for Spatial Audio Learning” Interspeech.\n\n[3] Shimada et al. (2023) \"STARSS23: An Audio-Visual Dataset of Spatial Recordings of Real Scenes with Spatiotemporal Annotations of Sound Events\" NeurIPS Track on Datasets and Benchmarks.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The paper is well written and easy to follow (though see nitpicks below for possible improvements).\n* The contributions (learnable DFT widths, relative positions for microphone array embeddings, and flexible grids) are elegant, inspired by physics, and well described in the manuscript.\n* The paper contains a useful introduction to direction-of-arrival estimation, allowing non-acoustics-experts to follow the paper.\n* The evaluation ablates all the components of AGG-RL and presents very strong results.\n* Device-independent direction-of-arrival estimation is an important problem for acoustics: many consumer devices nowadays need to perform direction-of-arrival estimation, but each tends to have their own configuration. A single network that generalises over all devices is genuinely useful.", "weaknesses": "* **W1**: Some details of the training and evaluation procedures are missing in the manuscript (see questions below)\n* **W2**: More ablations are needed to fully characterise the behaviour of AGG-RL (eg. SNR, number of sources in the sound-field, see questions below for specifics).\n* **W3**: Evaluating against other datasets with different microphone array geometries would help definitely establish generalisation to any microphone array.\n\n_Overall_, this is a strong submission held back by a relatively short evaluation that leaves many questions unanswered. It is my hope many of these issues are resolved during rebuttal.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WdOZVuhPXG", "reviewer": "Reviewer_ZXmA", "summary": "The paper introduces the Audio-Geometry-Grid Representation Learning (AGG-RL) framework designed to achieve universal sound source localization (SSL) that is flexible regarding Direction-of-Arrival (DOA) grids and invariant to microphone array (MA) geometries. This is achieved by learning shared latent representations for audio-geometry information and DOA grid candidates, allowing the model to predict a probabilistic spatial spectrum without requiring retraining for new grid resolutions or MA configurations.\nThe primary technical contributions include two physics-informed components integrated into the framework: a Learnable Non-uniform Discrete Fourier Transform (LNuDFT), which adaptively allocates frequency bins to emphasize informative phase cues, and a relative Microphone Positional Encoding (rMPE), which encodes microphone coordinates relative to a reference channel, aligning with the nature of inter-channel time differences (TDOA). Experiments on synthetic and real datasets demonstrated that AGG-RL achieves better performance and stronger generalization to unseen microphone geometries and environments where traditional methods struggle.", "questions": "- Could the authors elaborate on the empirical tuning process that led to the specific values chosen $\\epsilon_{start}=0.15, \\epsilon_{end}=0.95, \\epsilon_{min}=0.01, \\epsilon_{max} =100$, and how sensitive the final performance is to small variations in these constraints?\n- While AGG-RL achieved good performance in general, the results still indicated a performance gap between seen and unseen conditions. What specific architecture or training configurations do the authors believe offer the most potential to further minimize this performance gap under diverse, unseen MA geometries?\n-  In the ablation study, experiment (vi) (Fixed Grid) achieved the best performance on the Dynamic-S dataset (seen training conditions), and surprisingly, slightly outperformed the proposed AGG-RL method on the Dynamic-U dataset (unseen channels) in terms of ACC10. Why did the AGG-RL framework exhibit a degradation compared to the fixed-grid approach in this specific unseen synthetic channel configuration?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper integrates two novel, physics-informed components to enhance generalizability and interpretability. The LNuDFT optimizes frequency bin allocation to emphasize physically informative phase cues (IPDs) crucial for SSL. The rMPE encodes microphone coordinates relatively and improves generalization to unseen MA configurations.\n- AGG-RL demonstrates better performance and robustness across experiments, showing strong generalization to unseen MA geometries, unseen numbers of channels (Dynamic-U), and real-world recordings.\n- I like the visualization of the interpretable probabilistic spatial spectrum over candidate DOAs. It confirms that the proposed method yields sharper, more stable, and more distinct peaks closely aligned with ground-truth DOAs compared to baselines, even under unseen geometries.\n- The paper is well-written, and I really enjoy reading it.", "weaknesses": "- The concept of the NuDFT itself is not new, having been explored in prior signal processing literature since the 1990s. The novelty lies in making the frequency bin locations $\\nu_k$ learnable parameters within a deep neural network. While effective and physics-informed, this is an adaptation and optimization of an existing signal processing technique to maximize the extraction of IPDs.\n- While the logit-based initialization strategy for LNuDFT proved effective in practice and benefited generalization to unseen conditions, the choice of mapping function and hyperparameters was made empirically", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)