Original: INRAS: Implicit Neural Representation for Audio Scenes
Revised: INRAS: Implicit Neural Representation for Audio Scenes

Original: [Figure]
Revised: Kun Su ∗†

Revised: Mingfei Chen ∗†

Original: AffiliationAddress email
Revised: Eli Shlizerman ‡†§ INRAS SurfacePoints Binaural Impulse Response

Original: [Figure]
Revised: Source Sound * Spatial Sound Emitter Listener

Original: Abstract
Revised: Abstract

Original: The spatial acoustic information of a scene, i.e., how sounds emitted from a particular location in the scene are perceived in another location, is key for immersivescene modeling.
Revised: The spatial acoustic information of a scene, i.e., how sounds emitted from a particular location in the scene are perceived in another location, is key for immersive scene modeling.

Original: Robust representation of scene’s acoustics can be formulatedthrough a continuous field formulation along with impulse responses varied byemitter-listener locations.
Revised: Robust representation of scene’s acoustics can be formulated through a continuous field formulation along with impulse responses varied by emitter-listener locations.

Original: The impulse responses are then used to render soundsperceived by the listener.
Revised: The impulse responses are then used to render sounds perceived by the listener.

Original: While such representation is advantageous, parameterization of impulse responses for generic scenes presents itself as a challenge.
Revised: While such representation is advantageous, parameterization of impulse responses for generic scenes presents itself as a challenge.

Original: Indeed, traditional acoustic field coding methods  only implement parameteriza- tion at discrete probe points and rely on handcrafted features.
Revised: Indeed, traditional pre-computation methods have only implemented parameterization at discrete probe points and require large storage, while other existing methods such as geometry-based sound simulations still suffer from inability to simulate all wave-based sound effects.

Original: In this work, weintroduce a novel method for  Implicit Neural Representation for Audio Scenes (INRAS) which renders high fidelity time-domain impulse responses at any arbitraryemitter-listener positions using neural network parameterization.
Revised: In this work, we introduce a novel neural network for light-weight Implicit Neural Representation for Audio Scenes (INRAS), which can render a high fidelity time-domain impulse responses at any arbitrary emitterlistener positions by learning a continuous implicit function.

Original: Our experimentalresults show that INRAS outperforms existing approaches for representation andrendering of sounds for varying emitter-listener locations in all aspects, includingthe impulse response quality, inference speed, and storage requirements.
Revised: INRAS disentangles scene’s geometry features with three modules to generate independent features for the emitter, the geometry of the scene, and the listener respectively.

Original: INRASachieves such enhancement in performance by introducing a novel audio scenefeature decomposition, which leads to  efficient reuse of scene-dependent featuresfor any arbitrary emitter-listener positions. Furthermore, such a decompositionallows INRAS to generalize the representation from one scene to another with onlya few additional parameters.
Revised: These lead to an efficient reuse of scene-dependent features and support effective multi-condition training for multiple scenes. Our experimental results show that INRAS outperforms existing approaches for representation and rendering of sounds for varying emitter-listener locations in all aspects, including the impulse response quality, inference speed, and storage requirements.

Original: Submitted to 36th Conference on Neural Information Processing Systems (NeurIPS 2022).Do not distribute.
Revised: Corresponding author: shlizee@uw.edu 36th Conference on Neural Information Processing Systems (NeurIPS 2022).

Original:  Introduction
Revised:  Introduction

Original: There are more than a billion buildings in the world, each of them with unique architecture, interiordesign and activities they are intended for.
Revised: There are more than a billion buildings in the world, each of them with unique architecture, interior design and activities they are intended for.

Original: While vision is the primary sense for overall impressionand navigation through the world’s interior scenes, hearing plays a key role for a full immersion in ascene.
Revised: While vision is the primary sense for overall impression and navigation through the world’s interior scenes, hearing plays a key role for a full immersion in a scene.

Original: Indeed, many of our daily activities in an interior scene, such as having a conversation withsomeone somewhere in the scene, listening to music or watching TV, calling our pets and locatingthem, are dependent on the hearing function.
Revised: Indeed, many of our daily activities in an interior scene, such as having a conversation with someone somewhere in the scene, listening to music or watching TV, calling our pets and locating them, are dependent on the hearing function.

Original: Hearing is the sense that allows us to experience thescene and interact with it, and the sound quality and its synchronization with the scene, completesour audio-visual perception.
Revised: Hearing is the sense that allows us to experience the scene and interact with it, and the sound quality and its synchronization with the scene completes our audio-visual perception.

Original: Indeed, the selection of scene acoustics plays a significant role in theactivities that the scene would be used for.
Revised: Indeed, the selection of scene acoustics plays a significant role in the activities that the scene would be used for.

Original: For example, a dedicated IMAX theater with the latestsurround sound  system will draw audience to watch the latest movies, while educational activitieswill be held in quiet classrooms, and coffee shops with their energetic, but not noisy, environmentwill draw visitors to work on their laptops.
Revised: For example, a dedicated IMAX theater with the latest sound surround system will draw audience to watch the latest movies, while educational activities will be held in quiet classrooms, and coffee shops with their energetic, but not noisy, environment will draw visitors to work on their laptops.

Original: In these examples, spatial sound perception is affectedby the collection of the reflected sounds bounced off the floor,  walls,  ceiling, and other reflectivesurfaces in the scene.
Revised: In these examples, spatial sound perception is affected by the collection of the reflected sounds bounced off the floor, the walls, the ceiling, and other reflective surfaces in the scene.

Original: It is thus imperative to computationally model spatial audio aspects of interior scenes in order toadequately render a scene with spatial audio.
Revised: It is thus imperative to computationally model spatial audio aspects of interior scenes in order to adequately render a scene with spatial audio.

Original: However, computational modeling and representation ofspatial audio in an arbitrary scene is a non-trivial task, and has been an ongoing research theme withlong history in acoustics research [1].
Revised: Computational modeling and representation of spatial audio in an arbitrary scene is a non-trivial task, however, it has been an ongoing research theme with long history in acoustics research [1].

Original: Typically, the relationship between an arbitrary emitter soundand spatial sound can be represented by an impulse response, which is the function of time and thepositions of the emitter and the listener [2].
Revised: Typically, the relationship between an arbitrary emitter sound and spatial sound can be represented by an impulse response, which is the function of time and positions of the emitter and the listener [2].

Original: For a real scene, an impulse response between the emitterand the listener can be usually measured by playing a sine sweep, using a loudspeaker at the emitterand recording the sound pressure with a microphone at the listener  [3].
Revised: For a real scene, an impulse response between the emitter and the listener can be usually measured by playing a sine sweep, using a loudspeaker at the emitter location and recording the sound pressure with a microphone at the listener location [3].

Original: Alternatively, the impulseresponses can be also simulated by computational geometry-based sound propagation techniques fora real or virtualscene [4, 5, 6, 7].
Revised: Alternatively, the impulse responses can be also simulated by computational geometry-based sound propagation techniques for scenes that are real or virtual [4, 5, 6, 7].

Original: In both cases, it is time-consuming and computationally expensiveto render impulse responses in a continuous space, and therefore prohibit more immersive, interactivespatial sound rendering in scenes.
Revised: In both cases, it is time-consuming and computationally expensive to render impulse responses in a continuous space, and therefore prohibit more immersive, interactive spatial sound rendering in scenes.

Original: Classic encoding approaches parameterize the impulse responsesusing a few perceptual parameters that guide reproduction of reverberations [8, 9].
Revised: Classic encoding approaches parameterize the impulse responses using a few perceptual parameters that guide reproduction of reverberations [8, 9].

Original: However, suchfeatures are typically custom and designed specifically for some scenes and therefore are difficult toreproduce impulse responses with high fidelity.
Revised: However, such features are typically custom and designed specifically for some scenes and do not guarantee high fidelity impulse responses for a given novel scene.

Original: In this work, we propose an Implicit Neural Representation for Audio Scenes, INRAS, for efficientrepresentation of spatial audio fields with high fidelity.
Revised: In this work, we propose an Implicit Neural Representation for Audio Scenes, INRAS, for efficient representation of spatial audio fields with high fidelity.

Original: In recent years, neural networks have beenshown to parameterize implicit, continuous representations and achieved remarkable progress incomputer graphics [10].
Revised: In recent years, neural networks have been shown to parameterize implicit, continuous representations and achieved remarkable progress in computer graphics [10].

Original: The infinite resolution property of such representation could be advantageousfor representing the acoustic field as well.
Revised: The infinite resolution property of such representation could be advantageous for representing the acoustic field as well.

Original: Since the acoustic wave equation governs the soundpropagation from an emitter in a scene and its solution can be considered as a continuous fieldof impulse responses, the acoustic field can be encoded via a smooth, continuous representationwhich can alleviate the drawbacks of the approaches that encode the impulse response in discretepositions and perform interpolation during rendering [8, 9].
Revised: Since the acoustic wave equation governs the sound propagation from an emitter in a scene and its solution can be considered as a continuous field of impulse responses, the acoustic field can be encoded via a smooth, continuous representation which can alleviate the drawbacks of the approaches that encode the impulse response in discrete positions and perform interpolation during rendering [8, 9].

Original: Furthermore, our approach is motivatedby interactive sound propagation techniques using precomputed acoustic transfer operator for thescene, where the transfer operator is dependent on the scene geometry and decoupled from theemitter and the listener positions to render impulse response efficiently in interactive sound renderingapplications [11, 12].
Revised: Furthermore, our approach is motivated by interactive sound propagation techniques using precomputed acoustic transfer operator for the scene, where the transfer operator is dependent on the scene geometry and decoupled from the emitter and the listener positions to render impulse response efficiently in interactive sound rendering applications [11, 12].

Original: INRAS integrates the benefits of implicit neural representations and interactiveacoustic transfer to render high fidelity impulse responses in an efficient way.

Original: Specifically, INRAS is a light-weighted and efficient neural network model that can produce highfidelity spatial impulse responses at arbitrary emitter-listener positions.
Revised: Specifically, INRAS is a light-weight and efficient neural network model that can produce high fidelity spatial impulse responses at arbitrary emitter-listener positions.

Original: INRAS includes two mainstages.
Revised: INRAS includes two main stages.

Original: In the first stage, it decomposes the  audio scenefeatures into three parallel modules: i ) the
Revised: In the first stage, it decomposes the features of the audio scene into three parallel modules: i ) the

Original: Scatter module, ii ) the Bounce module, and iii ) the Gather module.
Revised: Scatter module, ii ) the Bounce module, and iii ) the Gather module.

Original: Motivated by the disentangledprocedures in the interactive acoustic radiance transfer techniques [11, 12], we design these threemodules to generate independent features for the emitter, scene geometry, and listener, respectively.
Revised: Motivated by the disentangled procedures in the interactive acoustic radiance transfer techniques [11, 12], we design these three modules to generate independent features for the emitter, scene geometry, and listener, respectively.

Original: Indeed, disentangling the  scene geometryfeatures allows our model to generalize to multiple scenesby adding only a few trainable parameters.
Revised: Indeed, disentangling the features of scene geometry allows our model to represent multiple scenes by adding only a few trainable parameters.

Original: In the second stage, the listener module fuses thethree independent features and generates the directional and binaural impulse responses.
Revised: In the second stage, the listener module fuses the independent features and generates the directional and binaural impulse responses.

Original: We show anoverview of INRAS in Figs 1 and 3.
Revised: We show an overview of INRAS in Figs 1 and 3.

Original: In summary, our main contributions in this work are: 1 ) Wepropose a novel approach, INRAS, to learn the implicit neural representation for audio scenes thatproduce high fidelity time-domain impulse responses at arbitrary emitter-listener positions in thescene. 2 ) 
Revised: In summary, our main contributions in this work are: 1 ) We propose a novel light-weight neural network, INRAS, to learn an implicit neural representation for audio scenes that generate high fidelity time-domain impulse responses for arbitrary emitter-listener. 2 ) INRAS disentangles scene’s geometry features to generate independent features for the emitter, the geometry of the scene, and the listener, which leads to efficient reuse of scene-dependent features for arbitrary emitter-listener positions, and supports effective multi-condition training for multiple scenes by adding only a few trainable parameters.

Original:  INRAS outperforms existing approaches on all metrics of audio rendering, including theimpulse response quality, inference speed, and storage requirements.
Revised: 3 ) INRAS outperforms existing approaches on all metrics of audio rendering, including the impulse response quality, inference speed, and storage requirements.

Original: We show that INRAS isrobust and capable of generalizing across multiple scenes with a few additional parameters.

Original:  Related Work
Revised:  Related Work

Original: Scene Acoustics Modeling .
Revised: Scene Acoustics Modeling .

Original: Modeling scene acoustics can be divided into two categories,  1 ) wavebased and, 2 ) geometry-based approaches.
Revised: Modeling scene acoustics can be divided into two categories, approaches of 1 ) wave-based and, 2 ) geometry-based.

Original: The first type of wave-based algorithms aims to solvethe acoustic wave equation using numerical techniques [13, 14, 15, 16].
Revised: The first type of wave-based algorithms aims to solve the acoustic wave equation using numerical techniques [13, 14, 15, 16].

Original: Due to the computationcomplexity of the wave equation, these approaches are typically used for lower frequencies.
Revised: Due to the computation complexity of the wave equation, these approaches are typically used for lower frequencies.

Original: Whilewave methods have become more utilized with advancement of CPU/
Revised: While wave methods have become more utilized with advancement of CPU/

Original: GPU computing power [17,18], this cost directs existing methods to prefer geometric approximations of scene acoustics  [19].
Revised: GPU computing power [17, 18], this cost directs existing methods to prefer geometric approximations of scene acoustics (the second type of acoustic modeling) [19].

Original: This second type of geometry-based approaches assume that the sound travels along a straightline, and determine the path of sound propagation according tothe energy attenuation.
Revised: Geometry-based approaches assume that the sound travels along a straight line, and determine the path of sound propagation according to energy attenuation.

Original: Thesemethods are generally faster than wave-based methods and are suitable for high-frequency soundpropagation.
Revised: These methods are generally faster than wave-based methods and are suitable for high-frequency sound propagation.

Original: However, with such an approach, it is difficult to accurately simulate low-frequencyacoustic phenomena such as edge diffractions and surface scattering of arbitrary order.
Revised: However, with such an approach, it is difficult to accurately simulate low-frequency acoustic phenomena such as edge diffractions and surface scattering of arbitrary order.

Original: The commonlyused geometric approaches are image sources methods [4, 5], ray-tracing [6, 7, 20], radiosity [21],and acoustic radiance transfer [22].
Revised: The commonly used geometric approaches are image sources methods [4, 5], ray-tracing [6, 7, 20], radiosity [21], and acoustic radiance transfer [22].

Original: Furthermore, a general model of geometric room acoustics can be formulated as an integral equation.
Revised: A general model of geometric room acoustics can be formulated as an integral equation.

Original: One of the first equations is the Kuttruff’s integral equation for diffuse reflections in a convexroom [23].
Revised: One of the first equations is the Kuttruff’s integral equation for diffuse reflections in a convex room [23].

Original: Multiple extensions of this mathematical model have been proposed subsequently, suchas the room acoustic rendering equation which provides a framework for most geometric acousticmethods for interiors [24].
Revised: Multiple extensions of this mathematical model have been proposed subsequently, such as the room acoustic rendering equation which provides a framework for most geometric acoustic methods for interiors [24].

Original: These algorithms for sound propagation are limited to static sources and/orlisteners.
Revised: These algorithms for sound propagation are limited to static sources and/or listeners.

Original: Interactive applications are usually achieved by precomputing sound propagation effectssuch as precomputing acoustic radiance transfer from static sources [11, 12, 25].
Revised: Interactive applications are usually achieved by precomputing sound propagation effects such as precomputing acoustic radiance transfer from static sources [11, 12, 25].

Original: While our workaims to represent the scene acoustics instead of performing simulation from scratch, the proposed INRAS model is motivated by the interactive acoustic radiance transfer method [11, 12].
Revised: While our work aims to represent the scene acoustics instead of performing simulation from scratch, the proposed INRAS model is motivated by the interactive acoustic radiance transfer method [11, 12].

Original: Sound Field Encoding.
Revised: Sound Field Encoding.

Original: Classical sound field encoding approaches represent the field around alistener point by capturing the sound from spatially distributed sources.
Revised: Classical sound field encoding approaches represent the field around a listener point by capturing the sound from spatially distributed sources.

Original: For example, Ambisonics [26]represents the sound field around a point using spherical harmonic coefficients and independently ofthe reproduction setup (speakers or headphones).
Revised: For example, Ambisonics [26] represents the sound field around a point using spherical harmonic coefficients and independently of the reproduction setup (speakers or headphones).

Original: Parametric surround approaches, such as MPEGSurround [27], assume a known speaker configuration around the listener.
Revised: Parametric surround approaches, such as MPEGSurround [27], assume a known speaker configuration around the listener.

Original: MPEG-H [28] extends theidea to allow encoding that is agnostic to the reproduction setup and supports higher-order Ambisonicsand binaural rendering.
Revised: MPEG-H [28] extends the idea to allow encoding that is agnostic to the reproduction setup and supports higher-order Ambisonics and binaural rendering.

Original: The Spatial Decomposition Method (SDM) [29] fits an image source modelto responses measured with a microphone array, approximating it at a point with multiple delayedspherical wavefronts.
Revised: The Spatial Decomposition Method (SDM) [29] fits an image source model to responses measured with a microphone array, approximating it at a point with multiple delayed spherical wavefronts.

Original: In Directional Audio Coding (DiRaC) [30], the input is the directional soundsignal at a listener, which is a superposition of all sound source signals in a scene convolved with thecorresponding directional impulse responses.
Revised: In Directional Audio Coding (DiRaC) [30], the input is the directional sound signal at a listener which is a superposition of all sound source signals in a scene convolved with the corresponding directional impulse responses.

Original: DiRaC computes direction and a diffuseness parameterfor each of many time-frequency bins.
Revised: DiRaC computes direction and the diffuseness parameter for each of many time-frequency bins.

Original: These approaches are static and do not allow the listener tonavigate the scene and experience the change in sound while doing so.
Revised: These approaches are static and do not allow the listener to navigate the scene and experience the changes in sound while doing so.

Original: Several works for interactivesound field encoding propose to extract important features from precomputed impulse responses andsynthesize them back using digital signal processing techniques [8, 31, 9].
Revised: Several works for interactive sound field encoding propose to extract important features from precomputed impulse responses and synthesize them back using digital signal processing techniques [8, 31, 9].

Original: However, these encodingstypically cannot reproduce impulse responses with high fidelity.
Revised: However, these encodings typically cannot reproduce impulse responses with high fidelity.

Original: Deep Acoustics.
Revised: Deep Acoustics.

Original: In recent years, deep learning approaches have beenapplied and developed forvarious acoustics applications.
Revised: In recent years, deep learning approaches have been developed for various audio applications, especially in speech [32, 33, 34, 35, 36] and music [37, 38, 39, 40].

Original: These include neural sound spatialization from a mono audio [32],estimation of room geometry and reflection coefficients from impulse response [33], reverberationtime and direct-to-reverberation ratio prediction [34, 35], and learning the head-related transferfunctions (HRTFs) [36].
Revised: In acoustics, these include neural sound spatialization from a mono audio [41], estimation of room geometry and reflection coefficients from impulse response [42], reverberation time and direct-to-reverberation ratio prediction [43, 44], and learning the head-related transfer functions (HRTFs) [45].

Original: In relation to scene modeling, deep neural networks modeling room impulse responses (RIR) have been studied extensively.
Revised: In relation to scene modeling, deep neural networks which model room impulse responses (RIR) have been extensively studied.

Original: A convolutional neural network model has beenproposed to estimate room impulse response from reverberant speech [37].
Revised: A convolutional neural network model has been proposed to estimate room impulse response from reverberant speech [46].

Original: Deep generative modelssuch as IR-GAN [38] and fast-RIR [39] have been proposed to generate new realistic impulseresponses.
Revised: Deep generative models such as IR-GAN [47] and fast-RIR [48] have been proposed to generate new realistic impulse responses.

Original: Recently, the emergence of implicit neural representations has shown great success inrepresenting 3D geometry [40] and the appearance[10] of a scene.
Revised: Recently, the emergence of implicit neural representations has shown great success in representing 3D geometry [49] and the appearance of a scene [10].

Original: Such representation approachcould be generalized to represent images, videos, and sounds[41] by learning a continuous mappingcapable of capturing data at an "infinite resolution".
Revised: Such representation approach could be generalized to represent images, videos, and sounds by learning a continuous mapping capable of capturing data at an "infinite resolution" [50].

Original: Indeed, very recently, it has been proposed to learn an implicit neural function to represent the roomimpulse responses [42, 43].
Revised: Indeed, very recently, it has been proposed to learn an implicit neural function to represent the impulse responses of interior scenes such as rooms [51, 52].

Original: The Impulse Response Multi-layer perceptrons (IR-MLP) approachpredicts impulse responses from spatio-temporal coordinates using an MLP but it does not supportboth moving sources and moving listeners scenarios [42].
Revised: The Impulse Response Multi-layer perceptrons (IR-MLP) proposes to predict impulse responses from spatio-temporal coordinates using an MLP. However, this approach does not support both moving sources and moving listeners scenarios [51].

Original: Such a problem has been approached by Neural Acoustic Fields (NAF) [43], which proposes to learn a continuously map from all emitterand listener location pairs to a neural impulse response function using the magnitude component ofthe frequency-time spectrogram representation after applying Short-time-Fourier-Transform.
Revised: Such a problem has been addressed by Neural Acoustic Fields (NAF) [52], which proposes to learn a continuous map from all emitter and listener location pairs to a neural impulse response function using the magnitude component of the frequency-time spectrogram representation after applying Short-time-Fourier-Transform.

Original: Whilethe smooth nature of the time-frequency spectrogram can be beneficial for training deep neuralnetworks, the smoothness and entanglement of the time-frequency representation prediction alsoleads to imprecise modeling of high peaks that appear less frequently.
Revised: While the smooth nature of the time-frequency spectrogram can be beneficial for training deep neural networks, the smoothness and entanglement of the time-frequency representation prediction also leads to imprecise modeling of high peaks that appear less frequently.

Original: For example, the sparse highpeaks in the early reflection part of impulse response play a dominant role in our perceptual feelingsfor sound source directions and clarity.
Revised: For example, the sparse high peaks in the early reflection part of impulse response play a dominant role in our perceptual feelings for sound source directions and clarity.

Original: Moreover, modeling using the spectrogram magnitude ignoresthe phase information and adding  random phase which may distort the audio signal significantly.
Revised: Moreover, modeling using the spectrogram magnitude ignores the phase information and adding a random phase which may distort the audio signal.

Original: In our approach, we learn the neural representation of the sound field for both moving listenersand moving sources scenarios.
Revised: In our approach, we learn the neural representation of the sound field for both moving listeners and moving sources scenarios.

Original: We aim to learn such implicit neural representation for renderingtime-domain impulse responses instead of spectrograms.
Revised: We aim to learn such implicit neural representation for rendering time-domain impulse responses instead of spectrograms.

Original: Our results show that INRAS can generatehigher fidelity impulse responses with even fewer trainable parameters.
Revised: Our results show that INRAS can generate higher fidelity impulse responses with even fewer trainable parameters.

Original:  Methods
Revised:  Methods

Original: Problem Setup.
Revised: Problem Setup.

Original: INRAS implements several deep neural networks to model the continuous implicitfunction that maps scene’s coordinates  to the corresponding time-domain directional and binauralimpulse responses of the sound field.
Revised: INRAS implements several deep neural networks to model the continuous implicit function that maps the coordinates of the scene to the corresponding time-domain directional and binaural impulse responses of the sound field.

Original: More formally, for a given 3D scene D , we denote the soundemitter locations as s ∈ R 3 , the listener locations as l ∈ R 3 , and the listener head orientationθ ∈ R 2 .
Revised: More formally, for a given 3D scene D , we denote the sound emitter locations as s ∈ R 3 , the listener locations as l ∈ R 3 , and the listener head orientation θ ∈ R 2 .

Original: Then ∀ ( s, l, θ ) ∈ R 8 in the scene, there would be corresponding binaural impulse responsesh ∈ R 2 × T where T indicates the time length.
Revised: Then ∀ ( s, l, θ ) ∈ R 8 in the scene, there would be corresponding binaural impulse responses h ∈ R 2 × T where T indicates the time length.

Original: We model the continuous function f ( s, l, θ ) −→ hparameterized by a deep neural network that pairs s, l, θ with appropriate impulse response h .
Revised: We model the continuous function f ( s, l, θ ) −→ h parameterized by a deep neural network that pairs s, l, θ with appropriate impulse response h .

Original: Whilethe idea seems straightforward, training the network to learn the time domain impulse response fromgiven coordinate inputs is challenging due tothe typical long temporal length of impulse responses,and highly oscillating amplitude at different time samples, all which increase the training difficulty.
Revised: While the idea seems straightforward, training the network to learn the time domain impulse response from given coordinate inputs is challenging due to typical long temporal length of impulse responses, and highly oscillating amplitude at different time samples, all which increase the difficulty of training.

Original: One key insight  is that while thescene geometry  determines the impulse responses in the scene, itis always static no matter how emitter and listener positions vary and therefore the geometry basedinformation could be shared with an arbitrary emitter and listener positions.
Revised: A key insight to assist with training is that while the geometry of the scene determines the impulse responses, it is always static no matter how emitter and listener positions vary and therefore the geometry based information could be shared with an arbitrary emitter and listener positions.

Original: Such an idea has beenapplied to interactive sound propagation based on acoustic radiance transfer [11, 12].
Revised: Such an idea has been applied to interactive sound propagation based on acoustic radiance transfer [11, 12].

Original: For traininga neural network model, the approach would be to leverage the static scene geometry by learningreusable scene-dependent features, and associate  with the emitter and the listener.
Revised: For training a neural network model, the approach would be to leverage the static scene geometry by learning reusable scene-dependent features, and associate them with the emitter and the listener.

Original: This allows themodel to realize that the differences between impulse responses at various emitter-listener locationsare dependent on the scene geometry.
Revised: This allows the model to realize that the differences between impulse responses at various emitter-listener locations are dependent on the scene geometry.

Original: Motivated by this approach, we propose two stage model.
Revised: Motivated by this approach, we propose a two-stage model.

Original: Thefirst stage performs  audio scenes featuredecomposition to learn the independent scene geometricfeatures and associate the emitter and listener to the scene.
Revised: The first stage performs decomposition of the audio scenes feature to learn the independent scene geometric features and associate the emitter and listener to the scene.

Original: The second stage fuses these features torender the binaural impulse responses.
Revised: The second stage fuses these features to render the binaural impulse responses.

Original: In the following sections, we review the background of theinteractive acoustic radiance transfer and then describe our model in detail.
Revised: In the following sections, we review the interactive acoustic radiance transfer and then describe our model in detail.

Original: Background on Interactive Acoustic Radiance Transfer.
Revised: Background on Interactive Acoustic Radiance Transfer.

Original: The acoustic radiance transfer is a classicalapproach to model sound propagation in complex room models and it can be derived from the acousticrendering equation [24]
Revised: The acoustic radiance transfer is a classical approach to model sound propagation in complex room models and it can be derived from the acoustic rendering equation [24]

Original: [Equation]
Revised: [Equation]

Original: [Figure] where S is the set of all surface points in the scene, L is the total outgoing acoustic radiance, L 0 isthe emitted acoustic radiance, Ω is the final radiance direction at x ; the incident radiance direction atx is implicit in the specification of x ′ , and R is the reflection kernel, which describes how radianceat point x ′ influences radiance at point x .
Revised: where S is the set of all surface points in the scene, L is the total outgoing acoustic radiance, L 0 is the emitted acoustic radiance, Ω is the final radiance direction at x ; the incident radiance direction at x is implicit in the specification of x ′ , and R is the reflection kernel, which describes how radiance at point x ′ influences radiance at point x .

Original: The equation describes that the outgoing time-dependentradiance at any surface point is a combination of the reflected time-dependent radiance and theemitted time-dependent radiance.
Revised: The equation describes that the outgoing time-dependent radiance at any surface point is a combination of the reflected time-dependent radiance and the emitted time-dependent radiance.

Original: The acoustic radiance transfer algorithm can be summarized in three steps (See Fig. 2).
Revised: The acoustic radiance transfer algorithm can be summarized in three steps (See Fig. 2).

Original: In the firststep, the scene’s boundary is divided into N bounce points, and energy is scattered from the emitterto all bounce points.
Revised: In the first step, the scene’s boundary is divided into N bounce points, and energy is scattered from the emitter to all bounce points.

Original: In the second step, sound energy is emitted in all directions from a givenbounce point.
Revised: In the second step, sound energy is emitted in all directions from a given bounce point.

Original: It propagates through the scene until the propagation is finally terminated upon anincidence at some other bounce point.
Revised: It propagates through the scene until the propagation is finally terminated upon an [Figure] incidence at some other bounce point.

Original: The energy-time curve on each bounce point can be storedas an echogram.
Revised: The energy-time curve on each bounce point can be stored as an echogram.

Original: In the final step, the listener gathers energy responses from all bounce points.
Revised: In the final step, the listener gathers energy responses from all bounce points.

Original: In interactive extensions [11, 12], a linear acoustic transfer operator is precomputed to model thepropagation of acoustic radiance between bounce points distributed over the surface of the scene.
Revised: In interactive extensions [11, 12], a linear acoustic transfer operator is precomputed to model the propagation of acoustic radiance between bounce points distributed over the surface of the scene.

Original: Inother words, the acoustic transfer operator can be seen as the scene-dependent features that are sharedwith all emitter-listener locations.
Revised: In other words, the acoustic transfer operator can be seen as the scene-dependent features that are shared with all emitter-listener locations.

Original: Such disentanglement efficiently updates the impulse response atvarious emitter-listener positions by computing the propagation delay based on the relative distanceto the bounce points.
Revised: Such disentanglement efficiently updates the impulse response at various emitter-listener positions by computing the propagation delay based on the relative distance to the bounce points.

Original: This motivates us to design a neural network model with similar decoupledmodules to satisfy that the scene geometry information can be realized and reused by an arbitraryemitter and listener.
Revised: This motivates us to design a neural network model with similar decoupled modules to satisfy that the scene geometry information can be realized and reused by an arbitrary emitter and listener.

Original: Implicit Neural Representation for Audio Scenes.
Revised: Implicit Neural Representation for Audio Scenes.

Original: INRAS includes two main components: ( a ) audioscenes feature decomposition, and ( b ) spatial binaural impulse response prediction.
Revised: INRAS includes two main components: ( a ) audio scenes feature decomposition, and ( b ) spatial binaural impulse response prediction.

Original: In ( a ) , there arethree parallel modules: 1) the Scatter module  learns features to associate the emitter with bouncepoints; 2) the Bounce module  learns the scene-dependent features shared by all emitter and listenerpositions; 3) the Gather module  learns features to associate the listener with the bounce points.
Revised: In ( a ) , there are three parallel modules: 1) the Scatter module which learns features to associate the emitter with bounce points; 2) the Bounce module which learns the scene-dependent features shared by all emitter and listener positions; 3) the Gather module which learns features to associate the listener with the bounce points.

Original: In( b ) , we fuse the output features of the three parallel modules and render the directional and binauralimpulse responses.
Revised: In ( b ) , we fuse the output features of the three parallel modules and render the directional and binaural impulse responses.

Original: A system overview is shown in Fig.
Revised: System overview is shown in Fig.

Original: Scatter Module.
Revised: Scatter Module.

Original: Similar to computing the initial radiance scattering from the emitter to all bouncepoints in acoustic radiance transfer, the Scatter module is dependent on the relative distance betweenthe emitter position and every bounce point position.
Revised: Similar to computing the initial radiance scattering from the emitter to all bounce points in acoustic radiance transfer, the Scatter module is dependent on the relative distance between the emitter position and every bounce point position.

Original: We divide the surface of the scene into Nbounce points with 3 D locations { b i } Ni =1 ∈ R 3 .
Revised: We divide the surface of the scene into N uniform bounce points with 3 D locations { b i } Ni =1 ∈ R 3 .

Original: We compute the relative distance between theemitter position s to all bounce points { d sb i } Ni =1 .
Revised: We compute the relative distance between the emitter position s to all bounce points { d sb i } Ni =1 .

Original: Using relative distance as input instead of absoluteposition enables the emitter to be aware of thescene geometry  and allows the model to learn smoothcontinuous features for various emitter positions.
Revised: Using relative distance as input instead of absolute position enables the emitter to be aware of the geometry of the scene and allows the model to learn smooth continuous features for various emitter positions.

Original: We usethe sinusoidal encoding to map the input{ d sb i } Ni =1 to a higher dimension, as also used in graphical implicit neural representation [10].
Revised: We use sinusoidal encoding to map the input { d sb i } Ni =1 to a higher dimension. This encoding is similar to the encoding used in graphical implicit neural representation [10].

Original: Welearn a function F Θ parameterized by a fully connected network.
Revised: We learn a function F Θ parameterized by a fully connected network.

Original: We denote the output feature as I = F Θ ( { d sb i } Ni
Revised: We denote the output feature as I = F Θ ( { d sb i } Ni

Original: =1 ) ∈ R N × D , where D indicates the feature dimension.
Revised: =1 ) ∈ R N × D , where D indicates the feature dimension.

Original: In our experiments, we findthat it is sufficient to use 40 to 60 bounce points to cover the scene structure.
Revised: In our experiments, we find that it is sufficient to use 40 to 60 bounce points to cover the structure of the scene.

Original: We perform moreinvestigations of bounce points selection in ablation studies.
Revised: We perform more investigations of bounce points selection in ablation studies Results section.

Original: Bounce Module.
Revised: Bounce Module.

Original: We design the bounce module to generate features representing the geometry ofstatic scenes shared with arbitrary  emitter and listener locations.
Revised: We design the bounce module to generate features representing the geometry of static scenes shared with arbitrary locations of emitter and listener.

Original: To model such scene dependentfeatures, we learn a function U Φ parameterized by a multi-layer perceptron (MLP) with residual 𝒅 𝒃 𝒊 𝒍 : (𝒙 𝒍 − 𝒙 𝒃 𝒊 ,𝒚 𝒍 −𝒚 𝒃 𝒊 ) 
Revised: To model such scene dependent features, we learn a function U Φ parameterized by a multi-layer perceptron (MLP) with residual connections that takes all bounce points positions { b i } Ni =1 ∈ R 3 as input and outputs the features Q = U Φ ( { b i } Ni =1 ) ∈ R N × D . Gather Module. This module is similar to the Scatter module.

Revised: We aim to associate the listener with the bounce points in the scene.

Revised: We compute the relative distance between the listener position l to all bounce points: { d lb i } Ni =1 , and use sinusoidal encoding to learn a function G Ψ parameterized by a fully connected network to generate the output feature O = G Ψ ( { d lb i }

Original: GatherModule 𝒃 𝒊 : (𝒙 $ 𝒊 ,𝒚 $ 𝒊 ) 
Revised: Ni =1 ) ∈ R N × D . Spatial-Time Feature Composition. The three modules in Feature Decomposition described above do not incorporate time-dependencies. Adding time to every module could significantly slow down the training procedure.

Revised: Motivated by the acoustic operator decomposition in the interactive sound propagation [12], the energy-time echogram for a specific bounce point

Revised: b i ( t ) can be represented by a set of time domain basis functions { τ k ( t ) } Kk =1 via a linear combination: b i ( t ) = (cid:80)

Revised: Kk

Original: {+=
+}
Revised: {+=
+}

Revised: α k τ k ( t ) , where α ’s are coefficients in the basis space.

Revised: We follow this representation and learn a function 𝒅 𝒃 𝒊 𝒍 : (𝒙 𝒍 − 𝒙 𝒃 𝒊 ,𝒚 𝒍 −𝒚 𝒃 𝒊 )

Revised: GatherModule 𝒃 𝒊 : (𝒙 $ 𝒊 ,𝒚 $ 𝒊 )

Original: BounceModule 𝒅 𝒃 𝒊 𝒔 : (𝒙 𝒔 − 𝒙 𝒃 𝒊 ,𝒚 𝒔 − 𝒚 𝒃 𝒊 )
Revised: BounceModule 𝒅 𝒃 𝒊 𝒔 : (𝒙 𝒔 − 𝒙 𝒃 𝒊 ,𝒚 𝒔 − 𝒚 𝒃 𝒊 )

Original: ScatterModule
Revised: ScatterModule

Original: Time 𝑻 𝑭 𝜣 𝑼 𝚽 𝑮 𝚿
Revised: Time 𝑻 𝑭 𝜣 𝑼 𝚽 𝑮 𝚿

Original: Decomposed Feature 𝑬 𝒃 𝒊 (a)Audio Scenes Feature
Revised: Decomposed Feature 𝑬 𝒃 𝒊 (a)Audio Scenes Feature

Original: Decomposition
Revised: Decomposition

Original: MLP
Revised: MLP

Original: Head Orientation 𝜽
Revised: Head Orientation 𝜽

Original: Left/Right Ear
Revised: Left/Right Ear

Original: ListenerModule
Revised: ListenerModule

Original: Binaural IR (b) Spatial Binaural IR Prediction 𝑽 𝚪 {𝑬 𝒃 𝒊 } 𝒊*𝟏𝑵 …
Revised: Binaural IR (b) Spatial Binaural IR Prediction 𝑽 𝚪 {𝑬 𝒃 𝒊 } 𝒊*𝟏𝑵 …

Original: Bounce 𝒃 𝒊 (𝒙 " 𝒊 ,𝒚 " 𝒊 )
Revised: Bounce 𝒃 𝒊 (𝒙 " 𝒊 ,𝒚 " 𝒊 )

Original: Listener 𝒍 (𝒙 𝒍 ,𝒚 𝒍 ) Emitter 𝒔 (𝒙 𝒔 ,𝒚 𝒔 ) 𝒅 𝒃 𝒊 𝒍
Revised: Listener 𝒍 (𝒙 𝒍 ,𝒚 𝒍 ) Emitter 𝒔 (𝒙 𝒔 ,𝒚 𝒔 ) 𝒅 𝒃 𝒊 𝒍

Original: 𝒅 𝒃 𝒊 𝒔 connections that takes all bounce points positions { b i } Ni =1 ∈ R 3 as input and outputs the features

Original: [Equation]

Original: Gather Module.

Original: This module is similar to the scatter module.

Original: We aim to associate the listener withthe bounce points in the scene.

Original: We compute the relative distance between the listener position l to allbounce points: { d lb i } Ni =1 .

Original: We also use sinusoidal encoding and learn a function G Ψ parameterized bya fully connected network to generate the output feature O = G Ψ ( { d lb i }

Original: Ni =1 ) ∈ R N × D .

Original: Spatial-Time Feature Composition. The modules do not incorporate the time-dependencies. Addingthe time dimension in every module could significantly slow down the training procedure. Motivatedby the acoustic operator decomposition in the interactive sound propagation [12], the energy-timeechogram for a specific bounce point
Revised: 𝒅 𝒃 𝒊 𝒔

Original: b i ( t ) can be represented by a set of time domain basis functions{ τ k ( t ) } Kk =1 via a linear combination: b i ( t ) = (cid:80)

Original: [-Kk =
 α k τ k ( t ) , where α ’s are coefficients in thebasis space. Similarly, we learn a function-] P τ through a fully connected network to obtain a setof time-domain basis functions which can be reused by all spatial features.
Revised: [-Kk =
 α k τ k ( t ) , where α ’s are coefficients in thebasis space. Similarly, we learn a function-] P τ through a fully connected network to obtain a set of time-domain basis functions which can be reused by all spatial features.

Original: We encode the timesamples { t j } Tj =1 using  sinusoidal encoding.
Revised: We encode the time samples { t j } Tj =1 using the sinusoidal encoding.

Original: The output is denoted as M = P τ ( { t j } Tj =1 ) ∈ R T × D .
Revised: The output is denoted as M = P τ ( { t j } Tj =1 ) ∈ R T × D .

Original: We then perform fast matrix multiplication to obtain spatial-time features ˆ I = MI ⊤ , ˆ Q = MQ ⊤and ˆ O = MO ⊤ .
Revised: We then perform fast matrix multiplication to obtain spatial-time features ˆ I = MI ⊤ , ˆ Q = MQ ⊤ and ˆ O = MO ⊤ .

Original: Listener Module.
Revised: Listener Module.

Original: In the stage of spatial binaural impulse response prediction, the listener modulefirst performs feature fusions by concatenating the three features together E
Revised: In the stage of spatial binaural impulse response prediction, the listener module first performs feature fusions by concatenating the three features together E

Original: = {
Revised: = {

Original: ˆ I, ˆ Q, ˆ O } ∈ R T × 3 N ,where { E b i } Ni =1 ∈ R T × 3 represents fused spatial-time features for l and s associated with the bouncepoint b i .
Revised: ˆ I, ˆ Q, ˆ O } ∈ R T × 3 N , where { E b i } Ni =1 ∈ R T × 3 represents fused spatial-time features for l and s associated with the bounce point b i .

Original: We feed E as input to the listener module and further takes care of the head orientationconditions θ  encoded by a learnable embedding matrix.
Revised: We feed E as input to the Listener module which combines it with the orientation of the head given by θ and encoded by a learnable embedding matrix.

Original: We model the listener module via MLP andgenerate binaural impulse responses in time-domain h = V Γ ( E, θ ) .
Revised: We model the listener module via MLP and generate binaural impulse responses in time-domain h = V Γ ( E, θ ) .

Original: Training and Rendering.
Revised: Training and Rendering.

Original: All components and modules of INRAS are trained jointly.
Revised: All components and modules of INRAS are trained jointly.

Original: We use acombination of mean square error loss L mse =
Revised: We use a combination of mean square error loss L mse =

Original: ∥
Revised: ∥

Original: h − ˆ h ∥ 22 and multi-resolution STFT loss L mr_stft whichhas been shown effective in modeling audio signals in the time domain [44].
Revised: h − ˆ h ∥ 22 and multi-resolution STFT loss L mr_stft which has been shown effective in modeling audio signals in the time domain [53].

Original: The multi-resolution
Revised: The multi-resolution

Original: STFT loss first converts the impulse response into frequency-time domain H = STFT ( h ) andcomputes the spectral convergence loss L sc = ∥|
Revised: STFT loss first converts the impulse response into frequency-time domain H = STFT ( h ) and computes the spectral convergence loss L sc = ∥|

Original: H |−|
Revised: H |−|

Original: ˆ H |∥ 2 ∥| H |∥, the magnitude loss L mag =
Revised: ˆ H |∥ 2 ∥| H |∥, the magnitude loss L mag =

Original: ∥| H | − | ˆ H |∥ 1and the phase loss L phase =
Revised: ∥| H | − | ˆ H |∥and the phase loss L phase =

Original: ∥ ϕ ( H ) − ϕ
Revised: ∥ ϕ ( H ) − ϕ

Original: ( ˆ H ) ∥ , our total loss can be summarized as follow:
Revised: ( ˆ H ) ∥ , our total loss can be summarized as follow:

Original: [Equation]
Revised: [Equation]

Original: Once we obtain the impulse response h , we can render sounds perceived at the listener location byconvolving the impulse response with a sound source y .
Revised: Once we obtain the impulse response h , we can render sounds perceived at the listener location by convolving the impulse response with a sound source y .

Original: The final sound is denoted as ˆ y = h ⊛ y .
Revised: The final sound is denoted as ˆ y = h ⊛ y .

Original: Generalization to Multiple Scenes.
Revised: Multi-condition Training with Multiple Scenes.

Original: The design of INRAS enables the emitter and the listener tobe aware of scene geometry by computing the relative distance to the bounce points in scatter and gather modules andthe bounce module provides a static scene-dependent feature.
Revised: The design of INRAS enables the emitter and the listener to be aware of scene geometry by computing the relative distance to the bounce points in Scatter and Gather modules and provides a static scene-dependent features.

Original: Intuitively, we caninclude the collection of bounce points from multiple scenes and let the emitter and listener realizewhich scene they are in to achieve the generalization goal.
Revised: This concept could be generalized to multiple scenes, since one can include bounce points from multiple scenes and let the emitter and listener to predict which scene they are in to achieve a multi-condition representation goal.

Original: Specifically, we normalize the coordinatespace of multiple scenes and adapt the total number of bounce points N total
Revised: Specifically, we normalize the coordinate space of multiple scenes and adapt the total number of bounce points N total

Original: =
Revised: =

Original: (cid:80)
Revised: (cid:80)

Original: Ki =
Revised: Ki =

Original: 1 N i for K scenes.
Revised: 1 N i for K scenes.

Original: When computing the relative distance and bounce points features for the emitter/listener in a specificscene, we mask the other irrelevant bounce points.
Revised: When computing the relative distance and bounce points features for the emitter/listener in a specific scene, we mask the other irrelevant bounce points.

Original: Since all other components and feature dimensionare kept the same, such operation adds a handful of trainable parameters due to the increased bouncepoints number and in turn enables the generalization from scene to scene.
Revised: Since all other components and feature dimension are kept the same, such operation adds a handful of trainable parameters due to the increased bounce points number and in turn enables the multi-condition representation over multiple scenes.

Original:  Experiments
Revised:  Experiments

Original: Datasets.
Revised: Datasets.

Original: To evaluate our method, we use the Soundspaces dataset which consists of dense pairs ofimpulse responses generated by geometric sound propagation methods [45].
Revised: To evaluate our method, we use the Soundspaces dataset which consists of dense pairs of impulse responses generated by geometric sound propagation methods [54].

Original: All scenes have  the sameheight and providethe binaural impulse responses for four different head orientations ( 0 , 90 , 180 , 270degrees).
Revised: All scenes have [Figure] the same ceiling height and provide binaural impulse responses for four different head orientations ( 0 , 90 , 180 , 270 degrees).

Original: For a fair comparison tothe previous work [43], we re-sample all impulses responsesto 22050 sampling rate and use the same 6 scenes including 2 multi-room layouts, 2 rooms withnon-rectangular walls, and 2 single rooms with rectangular walls.
Revised: For a fair comparison to previous work [52], we re-sample all impulses responses to 22050 sampling rate and use the same 6 scenes, including 2 multi-room layouts, 2 rooms with non-rectangular walls, and 2 single rooms with rectangular walls.

Original: For each scene, we use 90% datafor training and hold 10% data for testing.
Revised: For each scene, we use 90% data for training and hold 10% data for testing.

Original: Implementation Details.
Revised: Implementation Details.

Original: We use Pytorch to implement all INRAS models.
Revised: We use Pytorch to implement all INRAS models.

Original: For all scenes, we extractthe bounce points from the mesh boundary, ( 40 to 60 , depending on the scene).
Revised: For all scenes, we extract the bounce points from the mesh boundary, ( 40 to 60 , depending on the scene).

Original: We encode therelative distance from emitter/listener to bounce points using sinusoidal encoding with 10 frequenciesof sin and cos functions.
Revised: We encode the relative distance from emitter/listener to bounce points using sinusoidal encoding with 10 frequencies of sin and cos functions.

Original: We use a fully connected layer in the scatter module and gather module.
Revised: We use a fully connected layer in the Scatter module and Gather module.

Original: Inthe bounce module, we use a 4 -layer residual MLP.
Revised: In the Bounce module, we use a 4 -layer residual MLP.

Original: In the listener module, we use a 6 -layer residual
Revised: In the Listener module, we use a 6 -layer residual

Original: MLP.
Revised: MLP.

Original: In all MLPs, we use 256 neurons and set PreLU as the activation function.
Revised: In all MLPs, we use 256 neurons and set PreLU as the activation function.

Original: We use AdamWoptimizer [46] to train all models on a Tesla T4 GPU for 100 epochs with a batch size of 64 .
Revised: We use AdamW optimizer [55] to train all models on a Tesla T4 GPU for 100 epochs with a batch size of 64 .

Original: Theinitial learning rate is set as 5e-4 and is gradually decreased by a factor of 0 .
Revised: The initial learning rate is set as 5e-4 and it gradually decreases by a factor of 0 .

Original: Baseline Methods.
Revised: Baseline Methods.

Original: We compare our method to existing learning-based and classical approaches.
Revised: We compare our method to existing learning-based and classical approaches.

Original: For learning-based approaches, we compare INRAS with NAF [43].
Revised: For learning-based approaches, we compare INRAS with NAF [52].

Original: We also compare  two audiocoding methods Advanced Audio Coding (AAC) and Xiph Opus by applying both linear and nearestneighbor interpolation to the coded acoustic fields.
Revised: Since INRAS is effectively a novel encoding method to compress the acoustic field of a scene, we also compare INRAS with two audio encoding methods: Advanced Audio Coding (AAC) and Xiph Opus by applying both linear and nearest neighbor interpolation to the coded acoustic fields.

Original: Evaluation Metrics.
Revised: Evaluation Metrics.

Original: We evaluate all methods on three aspects:the impulse response quality, thestorage requirements and inference speed.
Revised: We evaluate all methods on three aspects: impulse response quality, storage requirements and inference speed.

Original: We first compute acoustic parameters to evaluate theimpulse response quality.
Revised: We first compute acoustic parameters to evaluate the impulse response quality.

Original: We use acoustic parameter Clarity (C50) to quantify the part of earlyreflections of the impulse response which is associated with music loudness, speech intelligibility,and clarity.
Revised: We use acoustic parameter Clarity (C50) to quantify the part of early reflections of the impulse response which is associated with music loudness, speech intelligibility, and clarity.

Original: To study the effects ofthe late reverberation parts, we use reverberation (T60) and earlydecay time (EDT) to illustrate the statistical portion of the impulse response.
Revised: To study the effects of late reverberation parts, we use reverberation (T60) and early decay time (EDT) to illustrate the statistical portion of the impulse response.

Original: The reverberationtime (T60) measures how long it takes for the acoustic energy to decay by 60 dB. EDT is closelyrelated to the listener’s perception of reverberation but it is also affected by the early reflections of theimpulse responses.
Revised: The reverberation time (T60) measures how long it takes for the acoustic energy to decay by 60 dB. EDT is closely related to the listener’s perception of reverberation but it is also affected by the early reflections of the impulse responses.

Original: We illustrate for the acoustic metrics can be found in Fig.
Revised: Illustration for these acoustic metrics can be found in Fig.

Original: In addition, we alsocompute the storage requirements for saving audio scenes representations and the inference speed forrendering a binaural impulse response in the scene.
Revised: In addition, we also compute the storage requirements for saving audio scenes representations and the inference speed for rendering a binaural impulse response in the scene.

Original: For fair comparison, we test inference speed forall methods consistently on a  Telsa T4 GPU. 
Revised: For fair comparison, we test inference speed for all methods consistently on a same Telsa T4 GPU. [Table] [Table] [Figure]

Revised: [Table]

Original:  Results.
Revised: [Figure] [Table] [Figure] Results.

Original: The quantitative evaluation results are shown in Table 1.
Revised: Quantitative evaluation results are shown in Table 1.

Original: INRAS outperforms both traditionalaudio coding and learning-based methods in all metrics.
Revised: INRAS outperforms both traditional audio coding and learning-based methods in all metrics.

Original: In particular, C50 and EDT errors  outperform NAF by 43% and 39% , indicating that the early reflection part of our rendered impulse responses ismuch closer to the ground truth.
Revised: In particular, C50 and EDT errors for INRAS outperform NAF by 43% and 39% , indicating that the early reflection part of INRAS rendered impulse responses is much closer to the ground truth.

Original: Fig.
Revised: Fig.

Original: 4 illustrates  comparison of two examples of rendered impulseresponses waveforms of AAC-linear, NAF and INRAS method.
Revised: 4 illustrates a comparison of two examples of rendered impulse responses waveforms by AAC-linear, NAF and INRAS method.

Original: On the top left of the figure, wevisualize the impulse responses loudness map of INRAS where colors indicate the loudness amplitude.
Revised: On the top left of the figure, we visualize the impulse responses loudness map of INRAS where colors indicate the loudness amplitude.

Original: In the two right columns, the comparison shows that the AAC-linear results have large gaps fromthe ground truth.
Revised: In the two right columns, the comparison shows that the AAC-linear waveforms have large gaps from the ground truth.

Original: While NAF is able to capture the exponentially decay pattern for reverberation,it cannot capture thethe early reflection part of  impulse responses which include the high peaksthat are important for clarity. In comparison, INRAS can render both the early reflections and late [Figure] [Table]
Revised: While NAF is able to capture the exponential decay pattern of reverberation, it cannot capture the early reflection part of both impulse responses that are shown.

Original: Parameters [Table] [Table] [Table]
Revised: This part includes high peaks important for clarity.

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: nearest

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table] 37.86 INRAS [Table] Ours) 0.
Revised: In comparison, INRAS can render both the early reflections and the late reverberation.

Original: [Table]

Original: reverberation much closer to the ground truth impulse responses.

Original: For more qualitative visualizationon loudness maps and waveforms, please refer to Suppl.
Revised: We show more qualitative visualization on loudness maps and waveforms in the Suppl.

Original: Materials.
Revised: Materials.

Original: Moreover,our INRAS modelonly takes about 0 .
Revised: Moreover, INRAS model takes only ∼ 0 .

Original: 65 million trainable parameters which results in less than 3 MB storage and 4 msinference speed, indicating the INRAS is significantly light-weighted and efficient.
Revised: 65 million trainable parameters which results in less than 3 MB storage and 4 ms inference speed, indicating the INRAS is significantly more light-weight and efficient model.

Original: Generalization to Multiple Scenes.
Revised: Multi-condition Training on Multiple Scenes.

Original: As discussed in the method section, the effective audio scenefeature decomposition allows us to train a single INRAS  to generalize from scene to scene.
Revised: As discussed in the method section, the effective audio scene feature decomposition allows us to train a single INRAS model to represent multiple scenes.

Original: Weinvestigated this property by traininga single INRASmodel on three scenes with different typesof layouts.
Revised: We investigated this property by training INRAS on three scenes with different types of scene layouts.

Original: We selected one multi-room layout, one room with non-rectangular walls, and oneroom with rectangular walls (See Fig. 5).
Revised: We selected one multi-room layout, one room with non-rectangular walls, and one room with rectangular walls (See Fig. 5).

Original: As expected, INRAS can learn continuous implicit neuralrepresentations for all three scenes.
Revised: As expected, INRAS can learn continuous implicit neural representations for all three scenes.

Original: We illustrate the loudness maps for all three scenes learned byone single model  and in Table 2. We show quantitative results of the multi-scene model.
Revised: We illustrate the loudness maps for all three scenes learned by such single model in Fig. 5 and in Table 2, where we show quantitative results of the multi-scene model.

Original: For othermethods, we compute the average values for the three scenes.

Original: In addition to the acoustic parametersthat evaluate the impulse response quality, we further evaluate the quality of the final rendered audiosignal after convolving the impulse response with a sound source.
Revised: In addition to the acoustic parameters that evaluate the impulse response quality, we further evaluate the quality of the final rendered audio signal after convolving the impulse response with a sound source.

Original: Specifically, we compute the Signal-to-Noise ratio (SNR) and audio Peak Signal to Noise Ratio (PSNR).
Revised: Specifically, we compute the Signal-to-Noise ratio (SNR) and audio Peak Signal to Noise Ratio (PSNR).

Original: The results in Table 2clearly shows that ourgeneralized model  can achieve high-quality results and better overall accuracythan NAF.
Revised: The results in Table 2 clearly show that our model after multi-condition training can achieve high-quality results and better overall accuracy than average of other models applied to each scene.

Original: Notably, the number of trainable parameters in INRAS increases  by 0 .
Revised: Notably, the number of trainable parameters in INRAS increases only by 0 .

Original: 1 M to extend thesingle-scene to multi-scenes thus keeping the storage requirement less than 3 MB.
Revised: 1 M to extend the single-scene to multi-scenes thus keeping the storage requirement less than 3 MB.

Original: In comparison,other approaches have increased the storage size linearly. 
Revised: In comparison, other approaches have increased the storage size linearly. [Table]

Original: Ablation Studies.
Revised: Ablation Studies.

Original: To show the effectiveness of INRAS v.s. similar variants, we use a representativescene to perform ablation studies.
Revised: To show the effectiveness of INRAS v.s. similar variants, we use a representative scene to perform ablation studies.

Original: Table 3 shows comparison results of INRAS and its ablated variants.[Figure] [Figure] [Table]
Revised: Table 3 shows comparison results of INRAS and its ablated variants.

Original: We first implement a brute-force model (Simple INRAS) using a residual MLP like NAF architectureand provide the normalized emitter and listener positions as input to predict the time domain impulseresponse using MSE loss only.
Revised: We first implement a brute-force model (Simple INRAS) using a residual MLP like NAF architecture and provide the normalized emitter and listener positions as input to predict the time domain impulse response using MSE loss only.

Original: The result turns out to be unsuccessfully in all metrics.
Revised: The result turns out to be unsuccessful in all metrics.

Original: We furthershow that adding the multi-resolution STFT loss can improvethe T60 error but still  fails to capturethe early reflection part.
Revised: We further show that adding a multi-resolution STFT loss can improve T60 error but still the model fails to capture the early reflection part.

Original: Next, we show that without using the relative distance impairs the resultssince the emitter and the listener could not realize the scene geometry.
Revised: Next, we show that not including the relative distance impairs the results since the emitter and the listener could not realize the scene geometry.

Original: Besides, removing the bouncemodule eliminates the static scene feature and therefore impairs the performance.
Revised: Also, removing the bounce module eliminates the static scene feature and therefore impairs the performance.

Original: We also investigateto the importance of bounce point selection.
Revised: We also investigate the importance of bounce point selection.

Original: We sample two types of bounce points that both havethe same total number as the original setting but they do not cover the whole scene, i.e., missingsome boundaries.
Revised: We sample two types of bounce points that both have the same total number as the original setting but they do not cover the whole scene, i [Table] e., missing some boundaries.

Original: The results show that only using bounce points covered the full scene geometrycan achieve the best performance in all results.
Revised: The results show that only using bounce points cover that the full scene geometry can achieve the best performance in all metrics.

Original: [Table]
Revised: [Table]

Revised: Bounce Points Sampling.

Revised: We uniformly sample bounce points on the boundaries of obstacles appearing in the scene.

Revised: In the Soundspace dataset, the only obstacles are walls that block sound propagation.

Revised: Thus we uniformly sample the points on the surface of each room.

Revised: The number of bounce points is dependent on the room size and the sampling rate.

Original: Conclusion
Revised: We performed experiments with various sampling rates to evaluate which selection to use. For example, one room has a perimeter of about 24 meters and the total number points of the mesh boundary is around 2400 . Our experiments indicated that uniform sampling of the bounce points every 0 . 5 m (sample rate: 1 / 50 , 48 bounce points) is optimal.

Revised: Notably, the impulse response data has the same spatial resolution.

Revised: A higher sampling rate does not necessarily achieve better performance since noise and redundant features could be induced with higher sampling resolution.

Revised: We compare different sampling rates for bounce points for the room mesh in Table

Revised: [Table]

Revised: Multi-conditioned Representation for Various Reflection Coefficients.

Revised: To test whether INRAS can be conditioned on various reflection coefficients, we create a 3 m x 5 m room using the available open source Python package (pyroomacoustics) [56] to simulate impulse responses using Image Source +

Revised: Ray tracing method.

Revised: We use spatial resolution of 0 .

Revised: 5 m to sample both impulse responses and bounce points.

Revised: For the same room, we create 225 sets of impulse responses with various absorption and

Revised: Sampling Rate\Metric

Revised: [Equation]

Revised: [Table]

Revised: [Table]

Revised: [Table]

Revised: Our results show that INRAS outperforms geometry-based simulation in all metrics and obtains significant improvement in accuracy.

Revised: scattering coefficients on the walls.

Revised: We use 90% sets of coefficients for training and 10% for testing.

Revised: For the coefficients seen in the training, we also hold 10% spatial points for testing.

Revised: To incorporate the coefficient condition in our model, we adapt our model by adding a coefficient embedding using sinusoidal embedding similar to coordinate inputs.

Revised: An addition operation is performed to add the coefficient embedding to the decomposed features.

Revised: In this experiment, as shown in Table 5, INRAS model achieves testing T60 error of 3 . 83% , C50 error of 1 . 13 dB and EDT error of 0 .

Revised: 03 second, which is not far from the performance on the training set.

Revised: These results show that INRAS can perform well even when absorption and scattering coefficients are unseen and vary.

Original: In conclusion, here we present INRAS, a novel implicit neural representation for audio scenes.
Revised: In conclusion, here we present INRAS, a novel implicit neural representation for audio scenes.

Original: INRASis a light-weight, fast model that effectively renders high fidelity impulse responses for multiple audioscenes.
Revised: INRAS is a light-weight, fast model, that effectively renders high fidelity impulse responses for multiple audio scenes.

Original: We achieve such function by leveraging a novel reusable representation of scene-dependentfeatures and associate them with  emitter and  listener.
Revised: We achieve such function by leveraging a novel reusable representation of scene-dependent features and associate them with the emitter and the listener.

Original: Experimental results demonstrate that INRASoutperforms other methods in all metrics and we further show that INRAS generalizes across scenes.
Revised: Experimental results demonstrate that INRAS outperforms other methods in all metrics and we further show that INRAS can represent multiple scenes after multi-condition training.

Revised: In summary, there are multiple benefits of an implicit neural representation of acoustic fields by

Revised: INRAS.

Revised: The first benefit is that in comparison to previous pre-computation approaches, an implicit neural representation of INRAS can learn a continuous compact representation for pre-computed impulse responses in a scene which significantly decreases the storage requirement and provides fast inference in run-time.

Revised: Indeed some state-of-the-art geometry-based sound simulations can be made real-time.

Revised: However, these approaches still have the common drawback of geometric-based methods, such as inaccuracy at low frequency and inability to simulate complete wave-based sound effects.

Original: Checklist
Revised: In comparison, an implicit neural representation of INRAS is not limited to these drawbacks at run-time because conceptually it can learn to map input coordinates to infinite-high fidelity impulse responses which can be pre-computed ahead of time. In other words, the complexity of the sound simulation will not be a bottleneck for the quality of the real-time rendering. Furthermore, implicit neural representations can fit real world data, on which it is challenging for an interactive geometric-based simulation to reach the same quality. To further investigate this aspect, we train INRAS on S 1 -M 3969 subset of meshRIR dataset [57] which includes dense real impulse responses recordings in a room with approximate dimensions of 7 m x 6 . 4 m. We sample the bounce point every 0 .

Revised: 5 m. Since the recording is a single channel, we remove the head orientation conditions at the listener module and output a single channel.

Revised: We use 90 % data for training and 10 % data for testing.

Revised: For a fair comparison, we faithfully tuned material parameters of the room model to best match the ground truth recordings.

Revised: Our results show that INRAS outperforms geometry-based simulation in all metrics and obtains large gains in accuracy, as shown in Table 6.

Original: The checklist follows the references.
Revised: The checklist follows the references.

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Revised: Please read the checklist guidelines carefully for information on how to answer these questions.

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Revised: For each question, change the default [TODO] to [Yes] , [No] or [N/A] .

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Revised: You are strongly encouraged to include a justification to your answer , either by referencing the appropriate section of your paper or providing a brief inline description.

Original: For example:
Revised: For example:

Original: • Did you include the license to the code and datasets?
Revised: • Did you include the license to the code and datasets?

Original: [Yes] See Section ?? .•
Revised: [Yes] We include the license in the supplementary material.

Original:  Did you include the license to the code and datasets?
Revised: • Did you include the license to the code and datasets?

Original: [No] The code and the data areproprietary.•
Revised: [No] The code and the data are proprietary.

Original:  Did you include the license to the code and datasets?
Revised: • Did you include the license to the code and datasets?

Original: [N/A]
Revised: [N/A]

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Revised: Please do not modify the questions and only use the provided macros for your answers.

Original: Note that the
Revised: Note that the

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Revised: In your paper, please delete this instructions block and only keep the Checklist section heading above along with the questions/answers below.

Original: For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper’scontributions and scope?
Revised: For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?

Original: [Yes] The sections of Methods and Experiments clearlydescribe the claims we made.(b)
Revised: [Yes] The sections of Methods and Experiments clearly describe the claims we made.

Original:  Did you describe the limitations of your work?
Revised: (b) Did you describe the limitations of your work?

Original: [Yes] We describe the limitations ofour work in the supplementary material.
Revised: [Yes] We describe the limitations of our work in the supplementary material.

Original: (c) Did you discuss any potential negative societal impacts of your work?
Revised: (c) Did you discuss any potential negative societal impacts of your work?

Original: [Yes] Wedescribe such impacts in the supplementary material.(d)
Revised: [Yes] We describe such impacts in the supplementary material.

Original:  Have you read the ethics review guidelines and ensured that your paper conforms tothem?
Revised: (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?

Original: [Yes]2.
Revised: [Yes] 2.

Original: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?
Revised: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A](b) Did you include complete proofs of all theoretical results?
Revised: [N/A] (b) Did you include complete proofs of all theoretical results?

Original: [N/A]3.
Revised: [N/A] 3.

Original: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
Revised: If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?

Original: [Yes] The inference code is available in the supplementary material.
Revised: [Yes] The inference code is available in the supplementary material.

Original: The full code will be available in the Github after the review process.
Revised: The full code will be available in the Github after the review process.

Original: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they[Table] were chosen)?
Revised: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Original: [Yes] We describe the training details in the implementation details section and more details can be found in the supplementary material.
Revised: [Yes] We describe the training details in the implementation details section and more details can be found in the supplementary material.

Original: (c) Did you report error bars (e.g., with respect to the random seed after running exper- iments multiple times)?
Revised: (c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?

Original: [No] No.
Revised: [No] No.

Original: We fix the random seed for reproduction purpose.
Revised: We fix the random seed for reproduction purpose.

Original: The errors bars are not reported because it would be too computationally expensive.
Revised: The errors bars are not reported because it would be too computationally expensive.

Original: (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?
Revised: (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?

Original: [Yes] We describe resources in the implementation details section.
Revised: [Yes] We describe resources in the implementation details section.

Original: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...[Table] (a) If your work uses existing assets, did you cite the creators?
Revised: If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] We cite all the[Table] existing assets used in our work.[Table]
Revised: [Yes] We cite all the existing assets used in our work.

Original: (b) Did you mention the license of the assets?
Revised: (b) Did you mention the license of the assets?

Original: [Yes] we mention the license of the assets in the supplementary material.[Table]
Revised: [Yes] we mention the license of the assets in the supplementary material.

Original: (c) Did you include any new assets either in the supplemental material or as a URL?
Revised: (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [N/A] [Table]
Revised: [N/A] (d) Did you discuss whether

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’re[Table] using/curating?[N/A]
Revised: and how consent was obtained from people whose data you’re using/curating?

Original: [Table] (e) Did you discuss whether the data you are using/curating contains personally identifiable[Table] information or offensive content?
Revised: [N/A] (e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?

Original: [Yes] We discuss it in the supplementary material.
Revised: [Yes] We discuss it in the supplementary material.

Original: [Table] If you used crowdsourcing or conducted research with human subjects...[Table] (a) Did you include the full text of instructions given to participants and screenshots,if applicable?
Revised: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?

Original: [Yes] The human evaluation is fully described in the supplementary[Table] material.
Revised: [Yes] The human evaluation is fully described in the supplementary material.

Original: [Table] (b) Did you describe any potential participant risks, with links to Institutional Review[Table] Board (IRB) approvals, if applicable?
Revised: (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?

Original: [N/A] there is no potential risk in our human[Table] evaluation.
Revised: [N/A] there is no potential risk in our human evaluation.

Original: [Table] (c) Did you include the estimated hourly wage paid to participants and the total amount[Table] spent on participant compensation?
Revised: (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?

Original: [Yes] we include these material in the supplemen- [Table] tary material.[Table]
Revised: [Yes] we include these material in the supplementary material.