SCRAPL: Scattering Transform with Random Paths for Machine Learning
Authors: Christopher Mitcheltree
Vincent Lostanlen
Emmanouil Benetos
Mathieu Lagrange
Venue: ICLR 2026 Poster (2026)
Keywords: scattering transform
wavelets
stochastic optimization
ddsp
perceptual quality assessment
Primary area: learning on time series and dynamical systems
TL;DR: A stochastic optimization scheme for efficient perceptual quality assessment of deep inverse problems, implemented for differentiable joint time–frequency scattering, with applications to unsupervised sound matching of the Roland TR-808 drum machine.

Abstract: The Euclidean distance between wavelet scattering transform coefficients (known as paths) provides informative gradients for perceptual quality assessment of deep inverse problems in computer vision, speech, and audio processing. However, these transforms are computationally expensive when employed as differentiable loss functions for stochastic gradient descent due to their numerous paths, which significantly limits their use in neural network training. Against this problem, we propose "Scattering transform with Random Paths for machine Learning" (SCRAPL): a stochastic optimization scheme for efficient evaluation of multivariable scattering transforms. We implement SCRAPL for the joint time–frequency scattering transform (JTFS) which demodulates spectrotemporal patterns at multiple scales and rates, allowing a fine characterization of intermittent auditory textures. We apply SCRAPL to differentiable digital signal processing (DDSP), specifically, unsupervised sound matching of a granular synthesizer and the Roland TR-808 drum machine. We also propose an initialization heuristic based on importance sampling, which adapts SCRAPL to the perceptual content of the dataset, improving neural network convergence and evaluation performance. We make our code and audio samples available and provide SCRAPL as a Python package.

Published as a conference paper at ICLR 2026
SCRAPL: SCATTERING TRANSFORM WITH RANDOM PATHS FOR MACHINE LEARNING
Christopher Mitcheltree' Vincent Lostanlen
Emmanouil Benetos'
Mathieu Lagrange
'Centre for Digital Music, Queen Mary University of London, UK {c.mi Sc.mitcheltrees emmanouil
wwwpoocii...eeetooo benetos @mm ac. uk
Nantes Université, Ecole Centrale Nantes, CNRS, LS2N, UMR 6004, France {vincent. lostanlen, mathieu. lagrangee@1s2n.
ABSTRACT
The Euclidean distance between wavelet scattering transform coefficients (known paths) provides informative gradients for perceptual quality assessment of deep inverse problems in computer vision, speech, and audio processing. However, these transforms are computationally expensive when employed as differentiable loss functions for stochastic gradient descent due to their numerous paths, which signifi- cantly limits their use in neural network training. Against this problem, we propose "Scattering transform with Random Paths for machine Learning" (SCRAPL): a stochastic optimization scheme for efficient evaluation of multivariable scattering transforms. We implement SCRAPL for the joint time- frequency scattering trans- form (JTFS) which demodulates spectrotemporal patterns multiple scales and rates, allowing fine characterization of intermittent auditory textures. We apply SCRAPL to differentiable digital signal processing (DDSP), specifically, unsu- pervised sound matching of a granular synthesizer and the Roland TR-808 drum machine. We also propose an initialization heuristic based on importance sampling, which adapts SCRAPL to the perceptual content of the dataset, improving neural network convergence and evaluation performance. We make our code and audio samples available and provide SCRAPL as Python package.
INTRODUCTION
A scattering transform (ST) is a wavelet-based nonlinear operator which decomposes high-resolution input æ into a collection ox of low-resolution coefficients, known as paths (Mallat) (012)). Without loss of generality, let consider a two-layer multivariable ST of time-domain signal a()):
(p(p,r, P (([ (||w L
+ (1)(1.2))
In the equation above, W is wavelet transform; the vertical bars denote complex modulus; the circled asterisk @ denotes a multivariable convolution over time / and wavelet scale 2; v is a multivariable wavelet filterbank which indexed by path pt Vo i.e., VP, with p = 0 is a multivariable low-pass filter; and is a pointwise nonlinearity, e.g., path normalization and logarithmic transformation.
The design of the filterbank V aims tradeoff between three properties: invariance rigid motion, stability to small deformations, and separation of sparse patterns (Mallat) (016). In speech and audio processing, examples of such include "plain" time ST (Andén & Mallat 2014). joint Lime-frequency scattering (JTFS) (Andén & Mallat, (2014), and spiral ST (Lostanlen & Mallat 2016). In computer vision, examples include "plain" " 2-D ST (Bruna & Mallat 2013), joint roto-translation
ST (Sifre & Mallat 2013), and -ooorroto-tranlatiion ST (Oyallon et al. 2014).
The squared Euclidean distance between scattering coefficients, distance for short, is:
P-1T-1A-
(2x(p,t.)) (,) 2
do x) = Σ Σ
(2)
where P is the number of paths; T is the number of time samples; and A is the number of scales. Behavioral studies suggest that ST distance a good predictor of dissimilarity judgments between isolated sounds, for suitably chosen V and (Patil al. 2012 Lostanlen al. 2021 Tian et al.

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Relatedly, neurophysiology studies suggest that JTFS is suitable idealized model of spectrotemporal receptive fields in the auditory cortex of humans Haignere & McDermott 2018) and nonhuman mammals (Kowalski et al. 1996). These findings motivate the use of JTFS as part of a differentiable loss function for neural audio models (Vahidi et al.) 2023).
2025).
As an illustration, let be fixed reference and ã (ww) be its reconstruction by autoencoder F with trainable weights w. Denoting the set of path indices by o = -o.....P .....-1.. 1} and the vector of
all time-frequency entries (2)(,, for each path p E 3 by (2r), the ST loss function writes as:
La i
② where vp P. 2 (z) -
(3)
P
Unfortunately, (x) and its gradient V L are expensive in memory and in operations. Certainly, algorithmic refinements such as FFT-based filtering multirate processing, and depth- first search can reduce the cost of an ST path (Oyallon et al. 2018). Yet. the need to traverse all P paths remains an obstacle to the applicability of multivariable ST for gradient- based learning at scale.
In this article, we aim to accelerate the training of an autoencoder F whose loss is the ST distance between reference and reconstruction, and so over finite corpus L = (zo...., Formally:
N-1
w" aig
Le o Fun) (w).
Given the decomposition in Equation 3 naive idea would be to replace each term term. in the equation
above by some per-path loss LLar where the p's would be drawn independently and uniformly at random in the path set P. This is a crude form of stochastic approximation (Benveniste et al., 2012) which is motivated by the tree-like structure of ST: neglecting the overhead of the first layer (Wx)).
the computation of single-path gradient V Led is roughly P times more efficient than that of full ST gradient V La, However, this speedup comes at the detriment of numerical precision: a deterministic quantity has been replaced by an estimator whose variance may be impractically large.
"Seattering transform with Random Paths for machine Learning" (SCRAPL) is our proposed solution to this problem. Acknowledging that each single-path gradient makes for an inexpensive but noisy learning signal, we stabilize it via a combination of three stochastic optimization techniques and apply an architecture-infornel importance sampling heuristic. Our contributions are:
1. Stochastic approximation of scattering transform through uniform sampling of paths.
2. Path-wise adaptive moment estimation (A-Adam for short): an extension of the Adam algorithm (Kingma & Ba 2014) which accounts for the non-i..d. nature of ST paths.
3. Path-wise stochastic average gradient with acceleration (P-SAGA for short): a variant of the SAGA algorithm (Defazio al. 2014) which keeps memory of previous gradient values across all paths p.
4. 6-importance sampling: parallelizable initialization heuristic that supplies auxiliary information to the stochastic optimizer by sampling paths p in proportion to the typical rate of change of the gradient in the optimization landscape.
Our main empirical finding is that SCRAPL. accomplishes a favorable tradeoff between goodness of fit and computational efficiency on unsupervised sound matching, i.e., nonlinear inverse problem in which the forward operator implements an audio synthesizer. In the context of differentiable digital signal processing (DDSP), the state-of-the-art perceptual loss function for this task is multiscale spectral loss (MSS, Yamamoto et al. (2020). Engel et al. (2020)). However, the gradient of MSS is uninformative when input and reconstruction are misaligned or when the synthesizer controls involve spectrotemporal modulations (Vahidi et al. 2023). Taking advantage of the stability guarantees of ITFS, SCRAPI. expands the class of synthesizers which can be effectively decoded via DDSP.
Figure T illustrates one of our experiments: unsupervised sound matching for nondeterministic granular synthesizer. On one hand, models based on MSS and other state-of-the-art perceptual losses are computationally efficient but inaccurate. On the other hand, JTFS-based models are five times more accurate but twenty five times more costly. SCRAPL is a new point on this Pareto front: is within a factor two of JTFS in terms of accuracy while being within factor two of MSS in terms of runtime, making it suitable for large-scale DDSP. Relatedly, SCRAPL is also more memory-efficien than JTFS, thus reducing overhead between CPU/GPU cores and allowing for larger batch size.
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Supervised
JTFS
Relative Error
SCRAPL
4
8-
PANNS
# MS-CLAP
MSS Log + Linear MSS Revisited
16
MSS Linear
1
2
4
8
16
32
Relative Computational Cost
Figure 1: Mean average synthesizer parameter error (y-axis) versus computational cost (x-axis) of unsupervised sound matching models for the granular synthesis task. Both axes are rescaled by the performance of supervised model with the same number of parameters. Whiskers denote 95% CI. estimated over 20 random seeds. Due to computational limitations, JTFS-based sound matching is evaluated only once.
2 RELATED WORK
The guiding intuition behind SCRAPL is that natural signals and images exhibit strong correlations across ST paths. This fact has been observed empirically since the onset of ST research (Bruna & Mallat 2013) Andén & Mallat 2011) and aligns with earlier work on texture modeling based on pairwise correlations between wavelet modulus coefficients (Portilla & Simoncelli, 20000).
Visual and auditory textures, understood as stationary random fields, play a key role in applied ST research. ST features outperform short-term Fourier features (e.g., MSS) in their ability to
characterize intermittency in non-Gaussian textures (Muzy et al. 2015). Texture resynthesis by gradient descent of ST loss has been applied such diverse settings computer music creation
Lostanlen et al.) 2019) and the study of the cosmic microwave background (Delouis et al.) 2022).
The democratization of differentiable programming toolkits (c.g.. TensorFlow, PyTorch, JAX) has greatly advanced the flexibility of gradient backpropagation in "hybrid" scattering -cattering-neural networks involving learnable and non-learnable modules. Angles & Mallat (2018) have built hybrid scattering-
GAN model for image generation, in which ST distance plays the role of a discriminator.
To our knowledge, the closest prior work SCRAPL the pruned graph scattering transform (pGST) of loannidis et al.) (2020). method which reduces the complexity of ST by pruning the path set S down to proper subset Ge C CP,, based on a graph-spectrum-ingee inspired criterion. Although both PGST and SCRAPI. share similar overarching goal, let us point out that PGST is feature selection method: the cardinality of Ge is typically ~ 10% that of S0 and Ge is kept fixed across training examples and across epochs. In comparison, SCRAPL performs more radical pruning, down to a single path (card G' = 1), while harnessing dedicated techniques in stochastic optimization -A--A and G -SAGA) reduce the variance of ST loss during gradient backpropagation.
3 METHODS
3.1
STOCHASTIC APPROXIMATION OF SCATTERING TRANSFORM LOSS GRADIENT
The proposition below, proven in Appendix A shows that if paths are drawn uniformly at random, the stochastic approximation in SCRAPL is unbiased: in other words, the expected value of the stochastic gradient of per-path loss is equal to the gradient full ST loss.
Proposition 3.1. Let o- (0p) be a scattering transform with P paths. Given a signal or image æ, let F., be an autoencoder operating on æ and let ee be the associated ST reconstruction loss. Let Up be the uniform distribution over 9 {0, ...... ,. P- 1]. One has, for every weight vector w:
F Eg
(w)) v (A o FF (w))
(5)
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Although uniform sampling of paths matches the intuition of approximating the ST gradient in expectation, we will see that this may be suboptimal. The 9-importance sampling method, which we will present in Section 3.4 does not satisfy the hypothesis of Proposition [.1] yet. it consistently outperforms uniform sampling as part of SCRAPI. The design of biased stochastic approximation schemes is active topic in machine learning research (Dieuleveut al. 2023)
3.2
ADAM: PATH- WISE ADAPTIVE MOMENT ESTIMATION
The key idea behind the Adam optimizer is to smooth the successive realizations of the stochastic gradient, here denoted by g. via autoregressive estimates of its first- and second-order element-wise moments, denoted by m and (Kingma & Ba 2014). However, the smoothing technique in Adam is ineffective for SCRAPL because the gradients of path-wise ST losses are not identically distributed. Against this problem, we propose maintain P estimates of path- path-wise
wise moments (9P-Adm)):
m&p -- B1 (k-T Tpp/P
mp + (1- (1- Fp) 1g
Up - B2 (k- 1/p
Up (1- sp) ((g (g
(7)
where is the current iteration number, Tp is the iteration when path p was last drawn; B1 and B2 are hyperparameters; and the circled dot denotes element-wiss multiplication of vectors. The exponent (k - (k- adapts the time constant of smoothing to the recency of the previous estimate.
The second step in -Adam,, following classical Adam, consists of bias correction and the ratio of debiased first-order moment to stable square root of debiased second-order moment:
mp
B
k/P
Jcurrent
(8)
Up
E
+
where we have adapted the original exponents of Adam (B B5) to account for the number of paths.
3.3 -SAAGA: PATH-WISE STOCHASTIC AVERAGE GRADIENT WITH ACCELERATION
The stochastic average gradient (SAG) algorithm has the potential to accelerate stochastic gradient descent in the context of the minimization of finite sums (Schmidt et al. 2017). Although this sum is typically over training examples in neural network training, in SCRAPL, Equation 3 is a sum over paths for a given example æ. With this observation in mind, we propose PSSAGA a pash-wise version of SAG with acceleration (SAGA, Defazio et al. (2014)). We maintain a memory of the last P. Adam updates over each path, denoted by (âp)o /- and the set of paths previously visited, denoted by r. Given learning rate a₁ at iteration k. the -SAGA update is:
Exergy
w <- w Cs Jourrent 9p max carcd))))
Unlike the original SAG and SAGA algorithms. P. -SAGA's additional memory footprint is propor- tional P, not the size of the dataset N, making it suitable for neural network training and real-world optimization tasks like our experiments in Section 4 We also note that AAdam and SSSAA introduce no additional hyperparameters over the standard Adam optimizer. Algorithm summarizes SCRAPL. with both AAdm and -SSGA enabled.
3.4 0 9-MPORTTACEE SAMPLING
We now consider the important special case of differentiable digital signal processing (DDSP, see Section [] in which the autoencoder composes a non-leara decoder, typically synthesizer, with a learned encoder: i.e., F = (D+Eg) with Eg (w) = θ and D(Ø) = ã (Engel et al. 2020). We assume both D and E. to be differentiable with respect their inputs, but D not necessarily deterministic. We denote by U the dimension the parameter space 0; i.c., the output space E and input space of 1).
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Algorithm 1 "Scattering transform with Random Paths for machine Learning" (SCRAPL), The pseudo-code below describes SCRAPL with a batch size equal to one, without loss generality.
Require: (0p) Scattering transform (ST) with P paths
Require: Categorical distribution over the path set P P0
Require: F: Autoencoder with trainable parameters w
Require: un: Neural network weights initialization
Require: B E: Adam hyperparameters
Require: (0x) : Learning rate schedule
r T+0 0
for in {0,
P 1) do
cp + 0
mp
Up 4 0
9r end for
for k in {I,..., K do
f draw an integer uniformly random in (0..... 1}
f draw an integer at random in {O...., }} according to π
{Stochastic approx.)
[(w) (z,)) (0p F (
V VL(w)
m2 + 1 1//p
mp + - spp
/p/ 1
Up + B2 1/
Up + (1 - B2 k // (g
n + mp/( B BkPP
90 -Adam
+-+-0 up/ (1 B2 A/P
Jcurent f m VVEV Ep t- k
9avg max (ardd Σxer gy
ISAGA Icurent 9p 9avg
{--SAGA)
w 4 w OLOSAGA
9p Jeurrent
r - [p(p}
end for return w
A known drawback of DDSP is that the optimization landscape of spectral loss in parameter space (i.e., of L. D) may not coincide with that of supervised parameter loss (i.e., Buclidean distance 0, also known as P-loss) (Hayes et al. 2024). Against this drawback, we propose method named i-importance sampling (e-IS), which constructs categorical distribution over the path space P. The key idea behind 0-IS is to introduce bias in the stochastic approximation of spectral loss so as to bring it closer to P-loss. For lack of supervision, we are unable construct the optimal distribution but provide heuristic of this form:
U-1 Σ 1=0 C.
Cup
T&p
(10)
where, intuitively, Cu.p represents the importance of parameter dimension 6, upon path p. We rescale this importance relative to all paths and average uniformly across parameters u, yielding an importance-weighter categorical distribution π over paths. We then use π instead of a uniform distribution for sampling paths in the SCRAPL algorithm (see Algorithm I
Let Eg. w)) denote the th coordinate of Eg (w). Given w, we measure the sensitivity of each ST path p the parameter control around the input terms of the following partial derivative:
a ( oD) (Emu(t))
Sp.upp' 2
(11)
d0,
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To convert the sensitivity function Sz,u, into relative importance Ca.p. we analyze the curvature of the loss landscape Lzx We multiply Szaa by the gradient of Ez... yielding a linear transformation of neural network parameters. The coordinate-wist gradient of this linear transformation yields a positive definite matrix: we compute its largest eigenvalue. We repeat this process over representative dataset H of Nis unlabeled signals from the training dataset. Formally:
Cup = E 1mmax Vv (s w) V V=n(()))))
(12)
where Amax (M) is the magnitude of the largest eigenvalue of square matrix M; V is the gradient
with respect to w. In practice, we compute Amax ( using a stochastic power iteration with deflation and the Hessian vector product, which has the same asymptotic runtime complexity as a backpropa- gation step _ Crucially, the computation required for 0-IS can be trivially parallelized across p and u, and only needs to be computed once before training.
Our definition of O-IS inspired by |Schmidt et al. (2017) 7) who propose a variant of the SAG algorithm in which mini-batches are sampled non-uniformly; more precisely, in proportion to the Lipschitz constant of the gradients, which we approximate using Equation for for each p and u. This heuristic relies the argument that gradients which change quickly should be regarded more important than gradients which change slowly.
EXPERIMENTS
We apply SCRAPL to a differentiable implementation of the joint time-frequency scattering transform Muradeli et al., 2022). We conduct three unsupervised sound matching experiments under the DDSP autoencoder paradigm described in Section 3.4] The encoder, Ez. is a convolutional neural network which operates on a constant-Q transform (Cheuk et al.) 2020). We use relatively lightweight neural networks for our experiments, a choice made possible by the strong inductive bias DDSP provides and informed by prior work (Han et al., 2025) indicating that larger networks do not necessarily improve sound matching capabilitiies We choose all hyperparameters in experiments heuristically.
To highlight the new kinds of perceptual quality assessment tasks SCRAPL enables, all three experiments investigate nondeterministic decoders that introduce random time shifts into the resulting reconstructed audio. While our experiments are for a discriminative and generative audio processing task, we emphasize that SCRAPL is general algorithm and can be equally applied to deep inverse problems that leverage other scattering transforms.
4.1 JOINT TIME- -REQUEER SCATTERING TRANSFORM (JTFS)
The joint time time-frequnccy scattering transform (JTFS) is a nonlinear convolutional operator which extracts spectrotemporal modulations over the constant-Q spectrogram (Andén al. 2019). The multivariable filter V comprises two stages: temporal scattering, i.e., 1-D band-pass filtering with Morlet wavelets over the time axis; and frequential scattering, i.e., idem over the boe-freuenncy axis. The center frequencies of band-pass filters for temporal scattering, called rates, are measured in Hertz. The center frequencies for frequential scattering, called scales, are measured in eycles per octave. Thus, in the case of JTFS, the path index is a vate-scale multiindex.
The JTFS has been shown to correlate with human perception (Lostanlen et al., 2021| Tian et al. 2025) and can provide an informative gradient for audio comparisons that are misaligned Vahidi jet al., 2023) or benefit from multi-resolltion analysis like percussive sounds (Han et al. 2024), which is why we select it as the underlying ST of the SCRAPI. algorithm in our unsupervised sound matching experiments. Additionally, due to its computational complexity, until now it has been used almost exclusively precomputed feature instead of loss function for neural network training.
4.2 GRANULAR SYNTH SOUND MATCHING
Granular synthesis is example of SCRAPL and the JTFS, due to its inherently stochastic audio generation process with individual grains being misaligned in time at the micro-level, but still being perceived as single texture. It has been extensively used in the production of electronic music since the late 1950 and played a
class of synths that can be effectively sound matched with
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fundamental role in the creation of contemporary electronic music genres. Our differentiable granular synth produces textures of chirplet grains with random temporal positions, center frequencies, and chirp rates, and has two continuous parameters: density (Qdensity) which controls how many grains are produced, and slope (Qstope which controls their rate of frequency modulation.
We compare four MSS-based losses: linear, log linear (Engel et al. 2020), random (Steinmetz & Reiss 2020), and a SOTA hyperparameter-tunee, revisited MSS loss (Schwär & Müller 2023).
Given their correlation with human perception (Kilgour al. [2019] Tailleur al. (024)) also include the Euclidean distance of MS-CLAP (Elizalde et al. (023) and PANNs Wavegram Logmel embeddings (Kong et al.) 2020). In addition, we train with ordinary (i.e., full-tree) JTFS so as to put the speed and accuracy of SCRAPL into context. Lastly, as an estimate of best achievable performance with our encoder architecture and training configuration, we run a supervised version of sound matching, also known as "parameter loss" or P-loss for short (see Section 3.4 the implementation details in Appendix
We summarize
4.3 CHIRPLET SYNTH SOUND MATCHING
Similar to the unsupervised granular synth sound matching experiment, we evaluate our 0-importance sampling initialization heuristic for SCRAPI, on differentiable chirplet synth (based on the imple- mentation by Vahidi et al. (2023)) with two parameters: 9AM which controls the rate of amplitude modulation (Hz) and FFm which controls the rate of frequency modulation (oct/s). Since the paths in the JTFS correspond to specific wavelet AM and FM center frequencies, given a chirplet synth configuration with bounded AM and 0FM ranges, we know approximately which paths of the JTFS should provide the most informative gradients for the synth parameters. After computing our initial- ization heuristic, we analyze the resulting path probabilities and verify that the paths within the parameter ranges of the synth have been assigned a probability greater than uniform.
We evaluate four different synth configurations:
1. Slow AM (0AM E [1.0, 2100 Hz), slow FM (0FM E [0.5, 1.0] oct/s);
2. Slow AM (9AM E [1.0,2.0] Hz), moderate FM (0FM E [2.0,4.0] oct/s);
3. Fast AM (0AM E [2.8,8.4) Hz), moderate FM (0FM E [2.0,4.0] oct/s);
4. Fast AM (9AM E (..8,8.4 Hz), fast FM (6PM E [4.0, 12.0] oct/s).
We compare SCRAPL training runs using uniform sampling and 0-importance sampling calculated from a single training batch of 32 examples. We summarize the implementation details in Appendix
4.4 ROLAND TR-808 SOUND MATCHING
As a real-world evaluation task, we sound match a DDSP implementation (Shier et al. 2024) of the Roland TR-808 Rhythm Composer drum machine, historically meaningful synthesizer for the creation of Detroit techno, house, and hip-hop music Inharmonic transient sounds like percussion form of non-stationary signal that the JTFS is well suited for perceptual quality assessment (Han) et al. 2024) because of its ability to extract spectrotemporal patterns at multiple scales and rates. Additionally, due the transient nature of drum sounds, they are highly sensitive to even a few milliseconds of misalignment, thus further benefiting from the time invariance of JTFS.
We use a high fidelity, 100% analog datase of 681 bass drum, snare, tom, and hi-hat one-shot recordings of the TR-808 and repeat experiments 40 times on different train/validation/tes splits and random seeds. Since the transient of analog drum recordings rarely perfectly aligned, and no two analog TR-808 drum synths produce the same signal, we investigate both perfectly aligned (labeled micro) and unaligned (labeled meso) sound matching by up to 1:46 ms (+:2048 samples at 44. kHz). Given its correlation with human perception,
employ the JTFS and Fréchet Audio Distance (FAD) (Kilgour et al. 2019; Défossez et al. 2023) as evaluation metrics. We also include MSS and mean frame-by-frame perceptual loudness and
perceptually-sealed spectral centroid and flatness for both the transient and decay portions of reconstructed signals (nine metrics in total).
Additional context for these last six metrics can be found in Shier et al. 20024. We summarize the implementation details in Appendix E
https: https::/saampestt romma rs. htt.a//rrooomeetee//r/rrrrr/rr/a tr- tr-808/ 808/
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Table 1: Evaluation results for the unsupervised granular synth sound matching task with two
continuous 0 0yynth parameters: Odensity and Ostope (more details in Section 4.2). Uncertainties are 95% CI for 20 training runs using different random seeds. Due to computational limitations, the JTFS method is only evaluated once.
Method
synth Lı %0o
Odensity
L1 %0c
Oslope Lı %00
JTFS
42.4
65.8
19.0
SCRAPL (no 0-1S)
73.8
+ 13
70.4
+ 8.8
77.2
19
SCRAPI.
65.7
+ 4.2
72.6
+ 6.3
58.7
+ 7.5
MSS Linear
370
- 0.52
499
0.84
241
0.28
MSS Log Linear
259
- 1.7
277
- 3.2
241
- 0.42
MSS Revisited
311
+1
376
+40
246
3.0
MSS Random
195
+ 4.2
149
+ 7.8
242
+ 1.0
MS-CLAP
166
+ 8.2
81.9
+ 9.0
250
8.2
PANNs Wavegram-Logmel
159
+ 4.4
80.3
+ 4.2
238
+ 5.5
P-loss
20.5
- 0.20
24.7
- 0.31
16.3
+ 0.31
5 RESULTS
5.1 GRANULAR SYNTH SOUND MATCHING
We benchmark all loss function computational costs (see Appendix Table 5 and plot them in Figure against their evaluation accuracy (see Table 1 on Synth L1 relative to supervised training (i.e., P-Joss). We observe that SCRAPL comes within factor two of JTFS in terms of accuracy, and within factor two of MSS in terms of runtime, striking notable balance between them. The significant difference in runtime and convergence between JTFS and SCRAPL is further illustrated in Figure where we plot validation accuracy against wall-clock time, instead of optimization steps. We also note that MSS is unable to sound match the synth at all, and the SOTA embedding losses are only able to optimize ddesiiyy albeit not as well as SCRAPL and JTFS. Validation accuracy curves for all methods are also provided in Figure We provide variation of Figure plotting the test JTFS audio distance on the y-axis in Appendix
Figure
0.25
0.4
JTFS
MSS Linear
0.20
SCRAPL
0.3
MSS Revisited
8gmm 4
MSS Log + Lin.
MSS Random
MS CLAP
0.10
0.1
PANNs
SCRAPL
0.0
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
0
5000
10000
15000
Clock (hours)
Steps
Figure 2: Left: JTFS vs. SCRAPL. wall-clock training times on single NVIDIA RTX A5000 GPU. Due to computational limitations, the JTFS method is only evaluated once. Right: Validation convergence graphs for the unsupervised granular synth sound matching task. Both: Shaded areas are 95% CI for 20 training runs using different random seeds.
Table 2 summarizes the results of ablation of SCRAPL and its P-Adam. S-SAA and 0-IS optimization techniques for the granular synth sound matching task, with Appendix B Table 6 pro- viding additional information about statistical significance. There is clear monotonic improvement in accuracy and convergence time for each technique, as well as a reduction in variance provided by SAAAA and O-IS. We emphasize that SCRAPL without any extra optimization techniques still outperforms all other non-JTFF methods in terms of accuracy, demonstrating its ability to optimize new class of problems and making just stochastic sampling of scattering transforms a viable approach if the additional memory and computational requirements of --Ammmm SASAA and 0-IS are undesirable. Finally, from Table]] I uniform sampling (despite Qdensity now being slightly worse), which is consistent with our hypothesis from Section that that 0-IS results more balanced convergence all synth parameters. Validation accuracy curves for all ablations provided in Appendix B Figure
we see that 9-IS results a better overall accuracy of 6synth than
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Table 2: Ablation table for SCRAPL with test results and validation synth L1 total variation and convergence steps for the unsupervised granular synth sound matching task. Convergence is defined as yynth L < 100 %c. Statistical significance results for each additional optimization technique are Uncertainties are 95% CI for 20 training runs using different random seeds. Due to computational limitations, the JTFS method is only evaluated once.
presented in Appendix B Table O
Method
0-IS
Test
Validation
Adam
SAGA
0 synth L %0c +
Total Var. +
Conv. Steps +
SCRAPL
99.7
- 8.2
5.30 0.25
10906 = 1170
87.4
- 15
6.98 = 0.25
8006 = 697
73.8
+
3.46 0.15
7296 + 683
/
65.7
+ 4.2
3.27 = 0.12
6014 + 642
JTFS P-loss
42.4
5.66
1442
20.5 = 0.20
1.83= 0.025
672
23
In summary, this experiment demonstrates that the variance of the gradient elicited by the stochastic approximation of a ST with the SCRAPL algorithm is manageably small the context of deep neural network (DNN) training, resulting in favorable tradeoff between computational speed and convergence rate when compared to full-tree scattering (i.e., the JTFS). Training with SCRAPL is nearly equivalent training with the gradient of full-tree scattering in terms of JTFS loss on unseen test data: see Appendix B Figure [3] In terms of synthesizer parameter error, training with SCRAPL not as accurate as training with full-tree ST. but outperforms prior work: see Table []] This SOTA result paves the way towards new kind of DNN training for deep inverse problems, in which the forward operator (synth) produces nondeterministic time-freyuency patterns.
Understanding the convergence properties of algorithms like SCRAPL for convex and non-convex tasks is an active area of research (Reddi et al. 2016 2018 Défossez et al., 2022 Kim & Ohl 2025). Our proof of Proposition 3.1 in Appendix A that SCRAPL without any additional optimization techniques an unbiased estimator of full-tree ST is an important first step this direction. We believe that further convergence analysis of SCRAPL remains a promising avenue for future work.
5.2 CHIRPLET SYNTH SOUND MATCHING
Table summarizes the chirplet synth evaluation results, with Appendix C Figure 5 showing validation accuracy curves for uniform and i-importance sampling on the four synth configurationss O-IS improves the prediction of AAM by 25-55% and of 0FM by 14 14-80%, while reducing time to convergence by 23-50%: see Appendix C Table 7 Of course, these improvements are for synth configurations that have been designed to showcase the benefit of nonuniform sampling of paths; however, this overall trend remains true, albeit not as pronounced, for the granular synth (Table and real-world sound matching task (Ta Finally, we plot the path O-IS probabilities in Appendix C Figure 6 and observe that indeed, a unique distribution is learned for each synth, and the greater than uniform probabilities appear to roughly correspond to each configuration' 's limited AM/ / FM range.
5.3 ROLAND TR-808 SOUND MATCHING
Table and Appendix D Tables g and summarize the unsupervised Roland TR-808 synth sound matching audio distance, transient, and decay perceptual similarity results. Overall, we observe that JTFS dominates almost all metrics in both micro and meso environments. showcasing its suitability for transient percussive sounds and temporal invariance. After JTFS, MSS performs best when samples are perfectly aligned (micro), but performs worse in the unaligned (meso) setting and is unable to match the transient, which is the most salient part of a drum hit. In contrast, SCRAPL shows consistent sound matching performance in both miero and meso environments and is able to preserve the transient even when audio is misaligned. However, SCRAPL fails to recover the less audible decay portion of the signal. We hypothesize this is due informative, low-frequency paths for the decay being sparse and underrepresented in the categorical distribution over paths, even after accounting for O-IS. We provide listening samples the accompanying website and encourage readers to evaluate the results directly.
S Companion website: https:://chtt stw.trrsttttteeeeeeee http:t/tttttttissttteeeeeeeettee io/ 1tt.sgtttthiii..aaaaaa.

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Published as a conference paper at ICLR 2026
Table Evaluation results for SCRAPL with and without the d-importance sampling initialization heuristic on unsupervised sound matching of four different AM FM chirplet synths with two
continuous 4yythh parameters: AM and FFm (more details in Section 4.3) Uncertainties are 95% CI for 20 training runs using different random seeds.
Sampling Method
Synth Configuration
0AM L, %cc
OμM L, %6c +
(xt
AM (Hz)
FFm (oct/s)
Uniform
124
+ 10
155
+ 18
1.0 1.0 2.0
0.5 1.0
0-IS
77.7
- 6.7
78.4
- 11
Uniform
111
+0
68.6
+11
1.0 1 2.0
2.0 4.0
0-IS
55.5
+ 4.1
44.4
= 2.8
Uniform 0-IS
122
+
238
+ 21
2.8 8.4
2.0-4.0 - 4.0
54.9
+ 3.5
48.5
+ 4.7
Uniform 0-IS
108
+ 12
95.6
+ 20
2.8 8.4
4.0
12.0
81.5
+
82.1
= 11
Table 4: Audio distance evaluation results for the unsupervised Roland TR-808 DDSP synth sound matching task with 14 continuous 0yyuth parameters (more details in Section Uncertainties 95% CI for 40 training runs using different random seeds and dataset splits. Due to computational limitations, the JTFS method is only trained and evaluated for 4 random seeds.
Method
MSS Log. + Linear
JTFS &
FAD (EnCodec)
Micro
Meso
Micro
Meso
Micro
Meso
JTFS
617 46
622 45
490 28
523 + 17
0.781 0.069
1.04
SCRAPL
(no 0-IS)
862 36
944 48
1140 48
1250 +1
2.75 = 0.39
2.85
SCRAPL
857 42
879
+22
1050 =0
1110
+52
2.43 = 0.22
2.22
MSS Lin.
611 15
724
3:77
779
+31
1470
+
1.22 = 0.082
0.46
MSS L+L
596 19
615 18
1260 +58
1390
+:49
2.14 0.39
3.04
MSS Rev.
637 16
797 20
870 233
1250
4:27
2.02 0.37
2.31
MSS Rand.
682 25
700 26
1410 87
1500
55
7.03 =22
6.7
CONCLUSION
Differentiable similarity measures have the potential to enhance the perceptual quality of generative models and deep inverse problem solvers. In spite of their mathematical guarantees and neuro- physiological plausibility, scattering transforms (ST) have not been able to realize this potential, for lack of tractable optimization algorithms. To fill this gap. SCRAPL takes advantage of the computation each backward pass. Our numerical simulations
tree-like structure of ST show the value of SCRAPL. for unsupervised sound matching, particularly when the synthesizer of interest nondeterministic. Although our ST architecture of choice is joint time-frequency scattering (JTFS), we stress that SCRAPL is agnostic to the specifics of multivariable filterbank design: beyond wavelet scattering, it extends learnable scattering- like architectures (Lattner al. 2019 Cotter & Kingsbury 2019: Gauthier et al., 2022). We consider investigating SCRAPL's generalizability to other ST architectures, different audio tasks such as speech enhancement and automatic mixing, and additional modalities like adversarial image generation and texture synthesis as promising directions future work. As a longer-term perspective, the success our trehtecture-iifooredd importance sampling heuristic highlights the opportunity to meta-learn the relative importance of each ST path for the task at hand over the course of neural network training (Yamaguchi et al. 2023).
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REPRODUCIBILITY STATEMENT
Appendix E contains hyperparameters and training details for each the three experiments this paper. We also provide listening samples, source code, configuration files, instructions to reproduce our experiments, and the SCRAPL algorithm Python package the companion website:
https::/chrisst sthetrreteeeeeeeeee gi git.ub..... wttiibi.oosccrrrr io/scrapl/
ACKNOWLEDGMENTS
Christopher Mitcheltree is research student the UKRI Centre for Doctoral Training in Artificial In- telligence and Music, supported jointly by UK Research and Innovation (grant number EP/S022694/1) and Queen Mary University of London. This research was funded in part by the French National Research Agency (ANR) under the project MuReNN "ANR-23- SEER-2--CE2---2 1---CE2--0000"
C.M. would like to thank Jordie Shier for his help with the differentiable Roland TR-808 synthe- sizer implementtiion and the insightful conversations about applying and evaluating the SCRAPL. algorithm.
REFERENCES
Joakim Andén and Stéphanc Mallat. Multiscale scattering for audio classification. In Proceedings of the International Society for Music Information Retrieval Conference (ISMIR), 2011.
Joakim Andén and Stéphane Mallat. Deep scattering spectrum. IEEE Transactions Signal Processing, 62 (16):41 4128, 2014.
Joakim Andén, Vincent Lostanlen, Stéphane Mallat. Joint frequenyy scattering. IEEE Transactions on Signal Processing, 67(14):3704-3718 2019.
Tomás Angles and Stéphane Mallat. Generative networks inverse problems with scattering transforms. In Proceedings of the International Conference on Learning Representations (ICLR), 2018.
Albert Benveniste. Michel Métivier, and Pierre Priouret. Adaptive algorithms and stochastic approximations. volume 22. Springer Science & Business Media, 2012.
Joan Bruna and Stéphane Mallat. Invariant scattering convolution networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3888):1872-1886, 2013.
Kin Wai Cheuk, Hans Anderson, Kat Agres, and Dorien Herremans. nnAudio: An on-the- GPU audio to spectrogram conversion toolhox using ID convolutional neural networks. IEEE Access, 8: 8:161981-162003, 2020.
Fergal Cotter and Nick Kingsbury. A leamable ScatterNet: Locally invariant convolutional layers. Proceedings of the IEEE International Conference on Image Processing (ICIP), 2019.
Aaron Defazio, Francis Bach, and Simon Lacoste-Julien. SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives. In Advances in Neural Information Processing Systems (NeurIPS), 2014.
Alexandre Défossez, Lcon Bottou, Francis Bach, and Nicolas Usunier. A simple convergence proof of Adam and AdaGrad. Transuctions on Machine Learning Research, 2022, ISSN 2835-8856.
Alexandre Défossez, Jade Copet, Gabriel Synnaeve, and Yossi Adi High fidelity neural audio compression. Transactions on Machine Learning Research, 2023. ISSN 2835-8856.
J.-M. Delouis, Erwan Allys, Edouard Gauvrit, and François Boulanger. Non-gaussian modelling and statistical denoising of Planck dust polarisation full-sky maps using scattering transforms. Astronomy Astrrophysics 668:A122, 2022.
Aymeric Dieuleveut, Gersende Fort, Eric Moulines, and Hoi-To Stochastic approximation beyond gradient for signal processing and machine learning. IEEE Transactions on Signal Processing, 71:3117-3148 2023.
Benjamin Elizalde, Soham Deshmukh, Mahmoud Al Ismail, and Huaming Wang. CLAP: Learning audio concepts from natural language supervision. In Proceedings of the IEFE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2023.

---

Published as a conference paper at ICLR 2026
Jesse Engel, Lamtharn Hantrakul, Chenjie Gu, and Adam Roberts. DDSP: Differentiable digital signal processing. Proceedings of the International Conference on Learning Representations (ICLR), 2020.
Shanel Gauthier, Benjamin Thérien, Laurent Alsene-Racicot, Muawiz Chaudhary, Irina Rish, Eugene Belilovsky,
Michael Fickenherg, and Guy Wolf, Parametric scattering networks. In Proceedings of the IEF.F. International Conference on Computer Vision and Pottern Recognition (CVPR), 2022.
Han Han, Vincent Lostanlen, and Mathieu Lagrange. Learning to solve inverse problems for perceptual sound matching, JEEE/ACM Transactions on Audio, Speech, and Language Processing, 32:2605-2611 2024.
Han Han, Vincent Lostanlen, and Mathieu Lagrange. Gradient clipping improves neural network optimization for perceptual sound matching. In Proceedings of the European Signal Processing Conference (EUSIPCO), September 2025.
Ben Hayes, Jordie Shier, György Fazekas, Andrew McPherson, and Charalampos Saitis. A review of differen- tiable digital signal processing for music and speech synthesis. Frontiers in Signal Processing, 3. 2024, ISSN 2673-8198.
Vassilis N. loannidis, Siheng Chen, and Georgios B. Giannakis. Pruned graph scattering transforms. In Proceedings of the International Conference on Learning Representations (ICLR), 2020.
Kevin Kilgour, Mauricio Zuluaga, Dominik Roblek, and Matthew Sharifi. Fréchet audio distance: A reference- free metric for evaluating music enhancement algorithms. In Proceedings of the International Speech Communication Association Conference (Interspeech), pp. 2350 2354, 2019.
Gyu Ycol Kim and Min-hwan Oh. ADAM optimization with adaptive batch selection. In Proceedings of the International Conference on Learning Representations (ICLR), 2025.
Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Proceedings of the International Conference on Learning Representations (ICLR), 2014.
Qiuqiang Kong. Yin Cao, Turab lqbal, Yuxuan Wang, Wenwu Wang, and Mark Plumbley. PANNs: Large- scale pretrained audio neural networks for audio pattern recognition. IEEF/ACM Transactions on Audio, Speech, and Language Processing, 28:2880-288 2894, November 2020. ISSN 2329-9290.
Nina Kowalski, Didier A. Depireux, and Shihab A. Shamma. Analysis of dynamic spectra in ferret primary audi- tory cortex. I. Characteristics of single-unit responses to moving ripple spectra. Journal of Neurophysiology. 76(5):3503-3523, 1996.
Stefan Lattner, Monika Dörfler, and Andreas Arzt. Leamning complex basis functions for invariant representations of audio. In Proceedings of the International Society for Music Information Retrieval Conference (ISMIR), 2019.
Vincent Lostanlen and Stéphane Mallat. Wavelet scattering on the pitch spiral. In Proceedings of the International Conference on Digital Audio Effects (DAFx), 2016.
Vincent Lostanlen, Joakim Andén, and Mathieu Lagrange. Fourier at the heart of computer music: From harmonic sounds to texture. Comptes Rendus. Physique, 20(5):461-44 1473, 2019.
Vincent Lostanlen, Christian El-Hajj, Mathias Rossignol, Grégoire Lafay, Joakim Andén, and Mathicu Lagrange. frequecyy scattering accurately models auditory similarities between instrumental playing techniques. EURASIP Journal on Audio, Speech, and Music Processing, 2021(1):3, 2021.
Stéphane Mallat. Group invariant scattering. Communications on Pure and Applied Mathematics, 65(10):
1331-1398. 2012.
Stéphane Mallat. Understanding deep convolutional networks. Philosophical Transactions of the Royal Society A: Mathmatical, Physical and Engineering Sciences, 374(2065):0110203 2016.
John Muradeli, Cyrus Vahidi, Changhong Wang, Han Han, Vincent Lostanlen, Mathieu Lagrange, and György Fazekas. Differentiable time-frequency scattering on GPU. In Proceedings of the International Conference on Digital Audio Effects (DAFx). 2022.
Jean-François Muzy, Emmanuel Bacry, Stéphane Mallat, and Joan Bruna. Intermittent process analysis with scattering moments. Annals of Statistics, 43(1):323, 2015.
Sam V. Norman- Nornnn-Haignere and Josh H. McDermott. Neural responses to natural and model-matched stimuli reveal distinct computations in primary and nonprimary auditory cortex. PLOS Biology, 16(12):1-46, 2018.
12

---

Published as a conference paper at ICLR 2026
Edouard Oyallon, Stéphane Mallat, and Laurent Sifre. Generic deep networks with wavelet scattering. In Proceedings of the International Conference on Learning Representations (ICLR) Workshop Track, 2014.
Edouard Oyallon, Sergey Zagoruyko. Gabriel Huang, Nikos Komodakis, Simon Lacoste-Juie Julien, Matthew Blaschko, and Eugene Belilovsky. Scattering networks hybrid representation learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(9)) 2221, 2018.
Kailash Patil, Daniel Pressnitzer, Shihab Shamma, Mounya Elhilali, Music our ears: The biological bases of musical timbre perception. PLOS Computational Biology. 8(11):1 2012.
Javier Portilla and Eero Simoncelli. parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, (0:4999-77 70, 2000.
Sashank Reddi, Suvrit Sra, Barnabás Póczos, and Alex Smola. Fast incremental method for smooth nonconvex optimization. In Proceedings of the IEEE Conference on Decision and Control (CDC), pp. 19717 2016.
Sashank Reddi, Satyen Kalc, and Sanjiv Kumar. On the convergence of Adam and beyond. In Proceedings of the International Conference on Learning Representations (ICLR), 2018.
Mark Schmidt, Nicolas Le Roux, and Francis Bach. Minimizing finite sums with the stochastic average gradient. Mathematical Progrumming, (2011-2):331122 March 2017. ISSN 0025-5610.
Simon Schwär and Meinard Müller. Multi-scale spectral loss revisited. IEEE Signal Processing Letters, 30: 1712-1716 2023.
Jordie Shier, Charalampos Saitis, Andrew Robertson, and Andrew McPherson. Real-time timbre remapping with diffcrentiable DSP. In Proceedings of the International Conference on New Interfaces for Musical Expression (NIME), 2024.
Laurent Sifre and Stéphane Mallat. Rotation. scaling and deformation invariant scattering for texture discrimi- nation. In Proceedings of the IEEE Conference Computer Vision and Puttern Recognition (CVPR), pp. 1233-1240, 2013.
Christian J. Steinmetz and Joshua D. Reiss. auraloss: Audio focused loss functions in PyTorch. In Digital Music Research Network One-day Workshop (DMRN+15), 2020.
Modan Tailleur, Junwon Lee, Mathieu Lagrange. Keunwoo Choi, Laurie M. Heller, Keisuke Imoto, and Yuki Okamoto. Correlation of Fréchet audio distance human perception of environmental audio is embedding dependant, In Proceedings of the European Signal Processing Conference (EUSIPCO), 2024.
Haokun Tian, Stefan Lattner, and Charalampos Saitis. Assessing the alignment audio representations with timbre similarity ratings. Proceedings of the International Society for Music Information Retrieval Conference (ISMIR), 2025.
Cyrus Vahidi, Han Han, Changhong Wang. Mathicu Lagrange, György Fazekas, and Vincent Lostanlen. Mesostructures; Beyond spectrogram loss in differentiable time-frreueee frequency analysis. Journal of the Audio Engineering Society. 710))5777585, 2023.
Shin'ys ya Yamaguchi, Daiki Chijiwa, Sekitoshi Kanai, Atsutoshi Kumagai, and Hisashi Kashima. Regularizing neural networks with meta-learning generative models, Advances in Neural Information Processing Systems (NeurIPS), 36:27315-27331, 2023.
Ryuichi Yamamoto, Eunwoo Song, and Jac-Min Kim. Parallel Wavegan: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram. Proceedings of the IEFE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2020.
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A PROOF OF PROPOSITION 3.1
Let us write ž = Fin (20). By linearity of the gradient, we may decompose V ( over paths:
Labe
(3).
(13)
Let us denote the Jacobian of Fe at w by JF. (w). For each E P, we apply the chain rule:
( o (u)) Jrz (w))
L0 (
(14)
Plugging the identity above into Equation 13 yields:
P-1
o Fe) = Σ
JFz (Fx(w) 1
(8)
p=0
= JFg (ws)
p Σ
(15)
where the latter equation holds by distributivity of matrix multiplication.
We now compute the expected value of V GoV
(Ø) for Up, i... uniform distribution over P:
E
Σ
(t).
(16)
We recognize the column vector on the right-hand side of Equation 13
Thus:
o Fz) = JFz (w)
Ez
Fz-
JFu (w)
(17)
where the latter equation holds by linearity of the expected value. Finally, we use the reverse form of the chain rule in Equation 14 to identify the expected SCRAPL gradient:
S (w) = Eg
(. m
F (w))
(18)
concluding the proof.
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B ADDITIONAL GRANULAR SYNTH EVALUATION RESULTS
Table 5: Loss function benchmark results for one optimization step (forward + backward, 32768 samples of audio, batch size 4, I thread, single precision, NVIDIA RTX A5000 GPU, CUDA 12.4, PyTorch 2.8.0). SCRAPI. paths are benchmarked individually and then aggregated across all paths using the median for time and interquartile range (IQR), and maximum for memory usage.
Method
Median Time (ms)
IQR (ms)
Max. Memory (MB) +
JTFS
1730
23.9
12967
SCRAPL
89.8
3.62
2503
MSS Linear
26.3
1.12
694
MSS Log Linear
19.1
0.696
702
MSS Revisited
17.0
0.210
663
MSS Random
24.7
5.81
706
MS-CLAP
75.6
1.69
2032
PANNs Wavegram-Logmel
29.3
5.92
1360
P-loss (dim(Osynth)
0.516
0.108
625
0.8
1.0
Supervised
JTFS
Relative Error
SCRAPL
1.2
PANNS
MS-CLAP
MSS Random
1.4-
MSS Log + Linear
1.6
Revisited
MSS Linear
1.8
1
2
16
32
Relative Computational Cost
Figure 3: Mean average JTFS perceptual audio distance (y-axis) versus computational cost (x-axis) of unsupervised sound matching models for the granular synthesis task. Both axes are rescaled by the performance of supervised model with the same number of parameters. Whiskers denote 95% CI, estimated over 20 random seeds. Due to computational limitations, JTFS-based sound matching evaluated only once.
Table Statistical significance and relative improvement of each additional SCRAPL optimization technique for the unsupervised granular synth sound matching task. Convergence is defined as Oyytth L1 < 100 %o. See Tarle absolute results and comparisons to JTFS and P-loss. Uncertainties are 95% CI for 20 training runs using different random seeds. Due to computational limitations, the JTFS method only evaluated once.
Opt.
Test
Validation
Technique
A synth lA %
A Total Var. $
A Conv. Steps J
+ Adam
-12.3 177 (p 1p=000 0.15)
1.68 + 0.35
(p 0.01) -2900 = 1800 < 0.01)
+ P-SAA
-13.6 + 5.6 (p < 0.01)
-3,52
+ 0.18 (p < 0.01) -710 450 < 0.01
+ 0-IS
18.13 (p 0.26)
+0.188
0.092 0.01) -1280= 410(p<0.01
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0.25
SCRAPL: no P-Adam, no PSSAA, no 0-15
SCRAPL: no P-SGA, no 0-IS
0.20
SCRAPL: no 6-Importance Sampling (0-15)
SCRAPL
JTFS
synth L1
0.15
0.10
0.05
0.00
0
2500
5000
7500
10000 12500 15000 17500 Steps
Figure 4: Validation convergence graphs of A.RAPia and the JTFS for the unsupervised granular synth sound matching task. Shaded areas are 95% CI for 20 training runs using different random seeds. Due computational limitations, the JTFS method is only evaluated once.
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C ADDITIONAL CHIRPLET SYNTH EVALUATION RESULTS
Chirplet Synth: slow AM, moderate
Chirplet Synth: fast fast
0.30
0.30
0.25
0.25
0.20
0.20
Oyyoh L
O L
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
1000
2000
3000
4000
1000
2000
4000
Steps
Steps
Chirplet Synth: slow AM, slow FM
Chirplet Synth: fast AM, moderate FM
0.30
0.30
0.25
0.25
0.20
0.20
0.15
Orynnh
0.00
1000
2000
3000
4000
1000
2000
3000
4000
Steps
Steps
Figure 5: SCRAPL Syyth L1 validation values during training for four different AM FM chirplet synths with two continuous 0 synhh parameters: 9AM and 0PM (more details Section 4.3). Blue using the O-importance sampling initialization heuristic, and black is using uniform sampling. Shaded areas are 95% CI for 20 training runs using different random seeds.
Table 7: Convergence rate (CR) and steps for SCRAPL with and without the O 0-importance sampling initialization heuristic on unsupervised sound matching of four different AM FM chirplet synths with continuous synh parameters: AAM and θрm (more details in Section 4.3). Convergence is defined as L1 < 100 % for AAM or 6FM- Uncertainties are 95% CI for 20 training runs using different random seeds.
Sampling Method
Synth Configuration
0A
FFM
(πt
OAM (Hz)
FFm (oct/s)
CR
Conv. Steps |
CR
Conv. Steps
Uniform 0-1S
60%
3944 + 342
45%
4064 + 372
1
0.5 1.0
100 %
2002 + 324
100 %
3134 + 492
Uniform 0-IS
100% %
2203 + 135
100% %
1536 + 194
1.0 1.0-2.0 2.0
2.0 2.0-4.0 4.0
100% %
1099 + 173
100 %
768 + 118
Uniform 6-IS
95%
3254 + 250
0%
N/A 2966 = 210
2.8 8.4
2.0 100-4.0 4.0
100 %
1925 + 165
100% %
Uniform 0-1S
100 %
3096 + 334
95%
3208 + 235
2.8 8.4
4.0 12.0
95%
2253 + 218
95%
2178 + 173
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Chirplet Synth: slow AM, moderate FM
Chirplet Synth: fast AM, fast FM
16.0
16.0
4.0
8.0
4.0
Ratio
8.0
Unform Prebablitty Ratio
rate (nstaves/ 5
2.0
2.0
1.0
1.0
0.5
0.5
0.5
1.0
2.0
4.0
8.0
0.0
0.0
(Hz)
Chirplet Synth: slow slow
Chirplet Synth: fast maderate
16.0
Unfform Probabiity Ratto
1M rate lotaves:
2,00
4.0
Uniform Probabiity
4,0
2.0
2.0
2.0
1..0
1.0
1.0
1.0
0.5
0.5
0.0
1.0
2.0
4.0
8.0
1.0
2.0
4,0
8.0
AM rate (H2)
AM rate (H2)
Figure 6: SCRAPL path θ 9-importance sampling probabilities for four different AM / FM chirplet synths calculated from batch of 32 log-uniformly randomly sampled Symth values. Black dots individual path (wavelet) AM/ / FM center frequency locations and each dashed rectangle is the 0 4syath range for each synth configuration. uniform probability ratio of 1.0 means path is sampled with probability 1/P.
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D ADDITIONAL ROLAND TR-808 EVALUATION RESULTS
Table 8: Drum transient evaluation results for the unsupervised Roland TR-808 DDSP synth sound matching task with continuous Synuth parameters (more details in Section 4.4). Uncertainties are 95% CT for 40 training runs using different random seeds and dataset splits. Due to computational limitations, the JTFS method is only trained and evaluated for random seeds.
Method
Loudness L1 4
Spectral Centroid L1 +
Spectral Flatness L1 +
Micro
Meso
Micro
Meso
Micro
Meso
JTFS
137 10 158
20
859 + 68
819 + 96
1200
87
1090 110
SCRAPL
(no 0-IS)
389 4111
460
60
1020 + 100
992 110
1800
170
1990 180
SCRAPI.
374 39
377
+ 32
1000 120
1080 120
1750 + 270
1820 220
MSS Lin.
381 -
2510
4880
902 + 27
2350 #310
962 = 43
3620 680
MSS L+L
492 44
1080 = 91
928 + 65
1380 + 76
916 = 50
1320 = 150
MSS Rev.
330 21
808
40
1070 + 49
1540 + 53
1390 = 62
2640 96
MSS Rand.
584 75
1030 = 89
1200 100
1350 + 99
1690 = 120
1950 + 140
Table 9: Drum decay evaluation results the unsupervised Roland TR-808 DDSP synth sound matching task with 14 continuous Synthh parameters (more details in Section 4.4 Uncertainties are 95% CI for 40 training runs using different random seeds and dataset splits. Due to computational limitations, the JTFS method is only trained and evaluated for 4 random seeds.
Method
Loudness L1
Spectral Centroid L1 |
Spectral Flatness L1 |
Micro
Meso
Micro
Meso
Micro
Meso
JTFS
315 + 22
355 + 110
614 + 51 617 + 71
527 = 31
718 + 190
SCRAPL
(no 0-IS)
1810
= 190
2210 220
1530 + 170
1860 + 170
2620 3110
3300 +370
SCRAPL
1810
= 160
1740 170
1490 + 120
1470 + 140
2540 290
2480 290
MSS Lin.
357
= 12
1120
#260
654 + 18
1110 = 160
472
17
1500 +350
MSS L+I.
389
+ 42
466 45
563 + 22
597 + 24
565 = 29
644 51
MSS Rev.
279
12
494 + 22
589 + 21
801 + 29
552
22
846 + 29
MSS Rand.
453 + 21
485 + 24
660 + 27
640 + 35
594 = 30
658 + 33
19

---

p Published as a conference paper at ICLR 2026
E
EXPERIMENT TRAINING DETAILS AND HYPERPARAMETERS
Table 10: Unsupervised granular synth sound matching task hyperparameters.
Category
Hyperparameter Name
Value
Data
N (# of examples)
5120
train / val test split
60% / 20% 20%
Encoder
# of parameters
604
CQT # of octaves
5
CQT bins / octave
12
CQT hop length
256
CQT postprocessing
loglp 5
CNN # of conv. blocks
CNN kernel size
(3, 3)
CNN stride
(1, 1)
CNN pooling
(2
CNN conv. block channels
128
CNN activation function
PReLU
CNN embedding dim.
64
CNN dense layer dropout prob.
0.5
Decoder (Synth)
dim ( syath) sampling rate
2
8192 Hz
T (# of samples)
32768
max. # of grains
64
grain # of samples min. grain pitch
4096
256 Hz
max. grain pitch
2048 Hz
SCRAPL JTFS
12
Q
8
Qz
Jr
3
Qt
T
4096
F
8
identity function
P (# of paths)
315
0 I-pportance Sampling
Nis (# of examples)
320
max. # of deflated power iterations
20
Training
# of random seed training runs epochs batch size
20
200
32
starting learning rate
10-5
learning rate scheduler
none
Adam B]
0.9
Adam B2
0.999
weight decay
0.01
20

---

Published as a conference paper at ICLR 2026
Table 11: Unsupervised AM / FM chirplet synth sound matching task hyperparameters.
Category
Hyperparameter Name
Value
Data
N (# of examples)
5120
train val test split
60% / 20% / 20%
Encoder
# of parameters
604 K
CQT # of octaves
5
CQT bims / octave
12
CQT hop length
256
CQT postprocessing
loglp
CNN of conv. blocks
CNN kernel size
5 x (3, 3)
CNN stride
x (1, 1)
CNN pooling
5 (2
CNN conv. block channels
128
CNN activation function
PReLU
CNN embedding dim.
64
CNN dense layer dropout prob.
0.5
Decoder (Synth)
dim sampling rate
8192 Hz
T' of samples) chirplet center frequency chirplet bandwidth min. time shift
32768
512 Hz
octaves
-2048 samples
max. time shift
+2048 samples
SCRAPL & JTFS
J
12
Qi
8
Q:
2
Jir
Qir
2
T
4096
F
8
p
identity function
P (# of paths)
315
O-Importance Sampling
Nis (# of examples)
32
max. # of deflated power iterations
20
Training
# of random seed training runs epochs
20
50
batch size
32
starting learning rate
1 x 10 44
learning rate scheduler
none
Adam Bi
0.9
Adam Bz
0.999
weight decay
0.01
21

---

Published as a conference paper at ICLR 2026
Table 12: Unsupervised Roland TR-808 synth sound matching task hyperparametens.
Category
Hyperparameter Name
Value
Data
N (# of examples)
681
Noass drum
215
Nanare
240
Num
189
Nni hat
37
Nirain
425
Nvul
128
Nest
128
Encoder
# of parameters
724 K
CQT # of octaves
CQT bins / octave
12
CQT hop length
256
CQT postprocessing
loglp
CNN of conv. blocks
CNN kernel size
5 (3, 3)
CNN stride
x (1, 1)
CNN pooling
(2, 2), (2, (2, 2), (2. 3), (3. 3), (3.
CNN conv. block channels
128
CNN activation function
PReLU
CNN embedding dim.
128
CNN dense layer dropout prob.
0.25
Decoder (Synth)
dim sampling rate
14
44100 Hz
T (# of samples) min. time shift
44100
-2048 samples
max. time shift
+2048 samples
SCRAPL & JTFS
J
12
Qi
Qz
Jn
Qn
2
T
2048
F
P
loglp 483
P (# of paths)
f I-portancce Sampling
Nis of examples)
16
max. # of deflated power iterations
20
Training
# of random seed training runs epochs batch size
40
50
starting learning rate
1 1x 10
learning rate scheduler
linearly decreasing until
x 10
Adam Bi
0.9
Adam Bz
0.999
weight decay
0.01
22


Reviews:
[{"review_id": "VPoVroGZXr", "reviewer": "Reviewer_HNRU", "summary": "The paper introduces a stochastic optimization scheme to make the computationally expensive wavelet scattering transform (ST) viable for large-scale machine learning, particularly in Differentiable Digital Signal Processing (DDSP). The core problem addressed is that the full scattering transform, the Joint Time-Frequency Scattering Transform (JTFS), may be used as a perceptually relevant loss function for tasks like sound matching, but its complexity makes it too slow and memory-intensive for use in stochastic gradient descent. The proposed solution, SCRAPL (Scattering transform with Random Paths for machine Learning), uses a stochastic approach to efficiently approximate the gradient of the full ST loss.\nThe study reports the results for using SCRAPL in the context unsupervised sound matching—a nonlinear inverse problem where an autoencoder learns the control parameters of an audio synthesizer (DDSP)—for which SCRAPL demonstrates a superior tradeoff between accuracy and computational efficiency compared to other losses.", "questions": "I think this paper would win a lot if one had a better idea about the performance of the underlying JTFS algorithm in the context of sound matching. Listening to the examples, I had the feeling that the results are particularly bad for HH (higher frequencies) and noise. Some sounds are perceptually very close, and others have hardly anything in common. I had a HH, which was transformed into a chirp.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 1, "presentation": 3, "contribution": 3, "strengths": "•\tSCRAPL makes the Joint Time-Frequency Scattering (JTFS) transform feasible for use in the loss function of large-scale deep learning by overcoming its prohibitively high computational and memory costs.\n•\tThe paper proposes an innovative stochastic approximation scheme—sampling just a single path—which guarantees an unbiased estimate of the true loss gradient in expectation, together with a novel Path-Wise Optimization (P-Adam) to manage the high variance of the single-path sampling, stabilizing convergence by maintaining individual moment statistics for every scattering path.\n•\tThe experimental evaluation is performed in the context of unsupervised sound matching with DDSP. It demonstrates that despite the stochastic approximation, the proposed algorithm offers sound matching results that are close to the full JTFS, while achieving a significantly smaller memory footprint, proving its practical efficiency.", "weaknesses": "•\tLimited Experimental Scope and Generalizability: The evaluation is performed on a relatively limited number of sound matching examples, which does not permit concluding on the general applicability of the method across different audio domains or tasks.\n•\tWhen listening to the audio examples, one should note that while the sound matching algorithm converges, the perceptual similarity of the original and generated sounds is not generally satisfying. In quite a few of the examples, the output sound is perceptually very far from the target. This calls the usefulness of the JTFS, and with it the SCRAPL algorithm, into question.\n•\tIncreased Implementation and Hyperparameter Complexity: The solution requires specialized algorithms (P-Adam, ϕ-SAGA) and a novel sampling heuristic (θ-IS), which significantly increases the implementation burden and the number of hyperparameters that need careful tuning.", "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": "aho0YHZ3TS", "reviewer": "Reviewer_7Spt", "summary": "This paper introduces SCRAPL (Scattering transform with Random Paths for machine Learning), a stochastic optimization framework that accelerates the use of multivariable scattering transforms as differentiable loss functions in deep learning. Scattering transforms (ST) are wavelet-based operators offering invariance and stability properties useful for perceptual modeling, but their computational cost has hindered large-scale training. SCRAPL addresses this by sampling a subset of ST “paths” at each iteration, yielding unbiased stochastic gradient estimates. To reduce variance and improve convergence, the authors introduce P-Adam (path-wise adaptive moment estimation) and P-SAGA (path-wise stochastic average gradient) algorithms, as well as a θ-importance sampling heuristic that biases path sampling toward perceptually informative regions. The method is implemented for the joint time–frequency scattering transform (JTFS) and evaluated on three differentiable digital signal processing (DDSP) tasks: granular synth, chirplet synth, and Roland TR-808 sound matching. Results show SCRAPL achieves accuracy close to JTFS at a fraction of its computational cost, outperforming existing perceptual losses such as multiscale spectral loss (MSS) and audio embedding distances.", "questions": "Have you tested or considered SCRAPL in vision tasks using 2D scattering transforms (e.g., roto-translation ST)? If not, do you anticipate any challenges extending it to images?\n\nCould you clarify how often this importance distribution must be recomputed during training, and how its computational cost compares to one full scattering transform?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "SCRAPL is a novel and technically well-motivated approach that makes scattering transforms practical for end-to-end differentiable learning. The paper is clearly written and grounded in both theory and application. The proposed stochastic approximation is theoretically justified (unbiased gradient under uniform sampling) and supported by well-designed optimization variants (P-Adam, P-SAGA) that address variance and non-i.i.d. gradient issues. The θ-importance sampling heuristic is a creative contribution that connects the optimization strategy to perceptual signal characteristics. Experimental validation is thorough, spanning synthetic and real-world DDSP tasks, with convincing quantitative and qualitative results. The work provides clear computational benchmarks, reproducibility details, and a public implementation, all of which increase its credibility and impact. Overall, the paper bridges an important gap between scattering theory and modern deep learning practice.", "weaknesses": "While the proposed framework is promising, certain limitations remain. The experiments are largely confined to audio applications, and it is unclear how well SCRAPL generalizes to image or other modalities that use scattering transforms. Although θ-importance sampling improves convergence, its computation involves complex gradient–Hessian interactions that may limit scalability in higher-dimensional settings. The empirical comparisons, while comprehensive, rely on relatively small neural networks and do not explore how SCRAPL performs in large-scale or supervised training contexts. The ablation studies, though informative, could include statistical significance tests to strengthen claims. Finally, the paper’s reliance on many heuristic design choices (e.g., importance weighting, hyperparameter schedules) makes it difficult to assess robustness across diverse architectures and datasets.", "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": "2hcmkTAhBx", "reviewer": "Reviewer_iLNX", "summary": "This paper presents a computationally efficient stochastic approximation to the full scattering transform to enable use of scattering based similarity as a loss function, one that relates to perceptual quality, in generative modeling.  The proposed approach consists of four steps: a) A sampling of scattering “paths”, b) a path-wise adaptive momentum estimation and using that in an extension of the Adam optimization algorithm, c) path-wise stochastic average gradient with acceleration using previous gradient values, and d) an importance sampling approach to bring stochastic approximation of spectral loss closer to P-loss.  Empirical results are presented on unsupervised sound matching experiments with granular synth, chirplet synth, and Roland TR-808 synth.", "questions": "n/a", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "* A stochastic approach that makes optimization under scattering transforms computationally efficient\n* Empirical results demonstrating that proposed approach achieves accuracies within a factor of two relative to the extensive joint time-frequency scattering transforms, while being within 3x of the much more efficient multi-scale spectral loss approach.\n* Clear, well written paper", "weaknesses": "* The empirical results on a sound matching setup which is of relatively limited interest to the broader NeurIPS and ML community.  Results on more audio generation tasks utilizing perceptual qualities of scattering transforms will strengthen the paper significantly.", "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": "JhElijyke6", "reviewer": "Reviewer_3oJ4", "summary": "This article introduces an efficient way to compute  the wavelet scattering transform based on random sampling. This allows to learn auto-encoder at scale To measure dissimilarity between isolated sounds, under a perceptual distance defined by this transform. To avoid the variance of the random sampling, various methods from the literature of stochastic gradient descent (SGD) are considered.  The proposed scheme is applied to unsupervised sound matching, showing comparable performance compared to joint-time frequency scattering transform and other baseline methods.", "questions": "- Is it possible to add some reference to the convergence analysis of P-Adam and P-SAGA methods? Why don’t you just use the standard SAGA method?\n- In Section 3.4, is theta belong R^U according to eq. 11? Is theta = the output of encoder?\n- how pi_p in eq. 10 is used next?\n- Is C_{u,p} in eq. 12 always positive? If yes, can you explain clearly? If not , how to ensure that pi_p is a probability in eq. 10?\n- To understand the numerical convergence of SCRARL, an analysis on the final training loss (eq. 4) is needed to compare with JTFS. \n- Could you give a definition on the theta_syn, theta_density etc to explain Table 1?  \n- How the supervised version P-loss method works? Why do you choose this to compare with the other methods?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "-\tThe problem on how to compute the scattering transform efficiently is well motivated. \n-\tThe obtained results are very promising. \n-\tThe article is mostly well written.", "weaknesses": "- The modified SGD in P-Adam (eq 8) and P-SAGA (eq 9) seem to be quite heuristic as there is no convergence analysis in the literature. For example, in P-SAGA, which rely on the gradients from P-ADAM is not a standard SAGA method given in the citation (Defazio et al 2014). \n- The section 3.4 is not so clear and might contain some technical flaw.\n- It is not clear whether the proposed scheme has any numerical convergence. \n- The evaluation metric is not so clear in Table 1 to non-expert. In Table 4, the evaluation scores seem to be biased towards the loss function that you are optimizing. Any human-based or more objective evaluation would be needed to compare different methods.", "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)