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Evaluating Loss Functions in Differentiable Out-of-Domain Sound-Matching with Partial Parameter Distance

Amir Salimi, Daniel Penner, Kalvin Eng, Abram Hindle, Osmar R. Zaïane

Year: 2026Venue: arXiv preprintArea: cs.SDType: PreprintEmbeddings: 27

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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%

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Summary

This paper introduces Partial Parameter Distance (PPD), an automatic evaluation metric for out-of-domain (OOD) sound-matching that applies parameter loss only to shared critical parameters between mismatched synthesizers. The authors evaluate four differentiable loss functions (SIMSE_Spec, L1_Spec, JTFS, DTW_Envelope) across seven scenarios involving band-pass filtering, amplitude modulation, and pitch-bending. Results show that loss function effectiveness is tightly coupled to the synthesis method: SIMSE_Spec excels at filter-cutoff recovery, DTW_Envelope at amplitude-modulation recovery, and JTFS at smooth pitch trajectories. PPD aligns with blinded listening tests in five of seven scenarios, demonstrating its utility as a diagnostic tool.

Entities (9)

Partial Parameter Distance · metric · 98%DTW_Envelope · loss-function · 95%JTFS · loss-function · 95%L1_Spec · loss-function · 95%SIMSE_Spec · loss-function · 95%Out-of-Domain Sound-Matching · task · 90%Amplitude Modulation · synthesis-method · 85%Band-Pass Filtering · synthesis-method · 85%Pitch-Bending · synthesis-method · 85%

Relation Signals (5)

Partial Parameter Distance → usedfor → Out-of-Domain Sound-Matching

confidence 95% · We introduce Partial Parameter Distance (PPD)... enabling automatically evaluated OOD experiments

SIMSE_Spec → excelsat → Band-Pass Filtering

confidence 90% · SIMSE_Spec excels at filter-cutoff recovery

DTW_Envelope → excelsat → Amplitude Modulation

confidence 90% · DTW_Envelope at amplitude-modulation recovery

JTFS → excelsat → Pitch-Bending

confidence 90% · JTFS at smooth pitch trajectories

Partial Parameter Distance → agreeswith → Listening Tests

confidence 85% · Parameter-based evaluation agrees with listening tests on the top-ranked loss function in five of seven scenarios

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Abstract

Abstract:In out-of-domain (OOD) sound-matching, a synthesizer is optimized to mimic a sound it did not generate. OOD evaluation of loss functions is underexplored in part because the standard "parameter loss" metric requires a shared parameter space between target and imitator, which OOD settings lack. We introduce Partial Parameter Distance (PPD), which applies parameter loss only to the critical parameters that mismatched synthesizers share (e.g., filter cutoffs), enabling automatically evaluated OOD experiments; we verify its results with blinded listening tests. Across seven scenarios involving band-pass filtering, amplitude modulation, and pitch-bending, we evaluate four differentiable loss functions (SIMSE_Spec, L1_Spec, JTFS, DTW_Envelope). Loss-function effectiveness remains tightly coupled to the method of synthesis: SIMSE_Spec excels at filter-cutoff recovery, DTW_Envelope at amplitude-modulation recovery, and JTFS at smooth pitch trajectories. Parameter-based evaluation agrees with listening tests on the top-ranked loss function in five of seven scenarios, demonstrating its utility as a diagnostic tool.

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EVALUATING LOSS FUNCTIONS IN DIFFERENTIABLE OUT-OF-DOMAIN SOUND-MATCHING WITH PARTIAL PARAMETER DISTANCE Amir Salimi, Daniel Penner, Kalvin Eng, Abram Hindle, Osmar R. Zaïane University of Alberta ABSTRACT In out-of-domain (OOD) sound-matching, a synthesizer is optimized to mimic a sound it did not generate. OOD eval- uation of loss functions is underexplored in part because the standard “parameter loss” metric requires a shared parameter space between target and imitator, which OOD settings lack. We introduce Partial Parameter Distance (PPD), which applies parameter loss only to the critical parameters that mismatched synthesizers share (e.g., filter cutoffs), enabling automatically evaluated OOD experiments; we verify its results with blinded listening tests. Across seven scenarios involving band-pass filtering, amplitude modulation, and pitch-bending, we eval- uate four differentiable loss functions (SIMSE_Spec,L1_ Spec,JTFS,DTW_Envelope). Loss-function effectiveness remains tightly coupled to the method of synthesis:SIMSE_ Spec excels at filter-cutoff recovery,DTW_Envelopeat amplitude-modulation recovery, andJTFSat smooth pitch trajectories. Parameter-based evaluation agrees with listening tests on the top-ranked loss function in five of seven scenarios, demonstrating its utility as a diagnostic tool. 1. INTRODUCTION In sound design, artists iteratively manipulate the parameters of their digital synthesizers to produce a desired sound [1]. This manual process can be a rewarding creative outlet, but often requires expertise and patience. Sound-matching refers to the automation of this workflow: given a target sound and a synthesizer, the objective is to identify parameters that pro- duce a perceptually similar output [2, 3]. Sound-matching experiments are either in-domain or out-of-domain (OOD). For in-domain experiments, the target sound and the mimick- ing outputs are generated by the same synthesizer. In OOD settings, the target sound originates from a different synthe- sis process or recording. While OOD sound-matching more closely resembles practical sound design, prior work over- whelmingly focuses on in-domain evaluations, with the goal of replicating the entire sound [2, 4, 5, 6, 7]. Since manual audio evaluations are impractical at scale, the lack of reli- able automatic evaluation methods is a major hurdle in OOD sound-matching. We propose an approach to OOD experiments that can be automatically evaluated, and use this methodology to re- examine the results from recent in-domain experiments. In particular, recent work by Salimi et al. [7] tested audio loss functions (differentiable measures of similarity between two sounds) in different in-domain sound-matching tasks and ob- served that there is no best universal loss function; that is, the performance of loss functions depends on the method of synthesis. Here, we test whether the reported observations also occur in OOD scenarios, and verify the results with listening tests. Each scenario pairs a target synthesizer with an imitator whose parameters are optimized to mimic the target’s output. The synthesizers are designed to mismatch while retain- ing a partial, critical overlap in parameters. In addition, the synthesizers are minimal representations of common signal processing functions used by sound designers (e.g., filtering, amplitude/pitch modulation) [7]. This also simplifies the se- lection of a critical parameter for each synthesizer pair. For example, if two synthesizers apply amplitude modulation to different source signals, the modulation rate is the partially overlapping parameter and a reasonable starting point for mea- suring success. Matching a target sound’s critical characteris- tics, rather than replicating it outright, mirrors the practice of sound design; success on critical parameters is thus a mean- ingful unit of progress for OOD sound-matching. We call the application of parameter loss to mismatched synthesizers partial parameter distance (PPD). Our central hypothesis is that the performance rankings of loss functions vary with the synthesizers used in OOD sce- narios. We address three research questions: (RQ1) does the synthesis-dependent loss behavior observed in-domain also occur in OOD settings? (RQ2) do the reported advantages and limitations of common loss functions persist under partial syn- thesizer mismatch? (RQ3) can PPD serve as an automatic eval- uation procedure for OOD sound-matching, and how well does it align with human perception? To answer these questions, we contribute a methodology for controlled differentiable OOD sound-matching experiments based on synthesizer pairs with partially overlapping functionality, with PPD as its automated evaluation procedure, validated against blinded listening tests; the framework can serve as a screening tool for certifying loss functions before they are deployed in more complex settings. Replication code will be released upon publication. arXiv:2608.27698v1 [cs.SD] 27 Aug 2026 2. BACKGROUND Sound-matching optimizes parametersθof a synthesizerg(θ) so thatx θ = g(θ)matches a targetx t = g t (θ t )under a similar- ity measureL(x θ ,x t ); in a differentiable pipeline,θis updated via gradients ofL[4, 8]. Most similarity measures fall into two families: audio-based and parameter-based. Audio-based losses compute distances between acoustic representations such as STFT spectrograms (e.g., L1, L2, or scale-invariant MSE) or amplitude envelopes; extensions such as Joint Time- Frequency Scattering (JTFS) apply wavelet transformations to a time-frequency representation and have been proposed for capturing mesostructures [9, 6, 10]. Parameter Loss (P-Loss) compares the target and imitator parameter vectors directly (e.g.,∥θ− θ t ∥ 2 ) and requires that both synthesizers share the same parameter space. While P-Loss can serve as a training ob- jective when ground-truth parameters are available [4, 8], it is undefined in OOD settings, where there is no 1-to-1 parameter mapping between the target and imitator synthesizers. Systematic comparison of loss functions under controlled OOD conditions is largely absent from the literature; most works evaluate exclusively in-domain [2, 3, 4, 5, 6, 11]. Re- cent OOD work has focused on training-time adaptation: fine- tuning parameter estimators on OOD targets [12, 13, 14] or using reinforcement learning for cross-domain matching [15], rather than comparing loss functions in controlled OOD condi- tions. We address this gap by comparing loss functions across OOD scenarios built from minimal synthesizer pairs, each representing a fundamental approach to sound design [7]. 3. METHODOLOGY 3.1. Problem Setup We evaluate four differentiable loss functions across seven sce- narios (six OOD, one in-domain). A scenario is an imitator– target synthesizer pair(g,g t ); for each scenario we run one experiment per loss function, and each experiment consists of at least 300 independent trials in which the target parameters θ t and the imitator parameters ˆ θare initialized by uniform sampling over predefined ranges; 200 steps of gradient-based optimization then update ˆ θto minimize the loss betweeng( ˆ θ) andg t (θ t ). This yields at least 300 PPD scores per loss per sce- nario for statistical comparison; listening tests provide verifica- tion. All synthesizers produce 1-second signals at 48,000 Hz. 3.2. Loss Functions The four loss functions are as follows.L1_Specis the pointwise L1 distance between log-magnitude STFT spec- trograms.SIMSE_Specreplaces the L1 term with Scale- Invariant Mean Squared Error (SIMSE) [16], which is invariant to constant offsets in log-magnitude and therefore less sensitive to global level differences.JTFSapplies the L2 distance to the 1-D Joint Time-Frequency Scattering transform [9] (J=10, Q=2), which captures wavelet-based time-frequency struc- ture.DTW_Envelopecomputes the soft-DTW distance [17] (γ=1) between amplitude envelopes, where the envelope at each time step is obtained by summing all frequency bins of an STFT. For all STFT-based computations (L1_Spec,SIMSE_ Spec, and theDTW_Envelopeenvelope), we use a 512- point FFT (257 frequency bins), a Hann window, and a hop length of 100 samples. 3.3. Evaluation Methods Partial Parameter Distance. In OOD settings, full parameter comparison is undefined because the target and imitator syn- thesizers have different architectures or parameter ranges. For example, if the target is a sine-wave AM synthesizer (carrier 200 Hz, modulation 10 Hz) and the imitator is a saw-wave AM synthesizer (carrier 30–5000 Hz, modulation 1–15 Hz), the only reasonable point of comparison is the modulation rate. Partial Parameter Distance (PPD) applies P-Loss only to the subset of parameters with critical perceptual correspondence between the two synthesizers, computed after optimization: PPD =∥θ t crit − ˆ θ crit ∥ 2 ,(1) whereθ crit denotes normalized[0, 1]parameters common tog andg t . Selecting critical parameters requires domain knowl- edge and carries some subjectivity; our scenarios (Section 4) are designed with a single dominant synthesis task per pair to keep this selection unambiguous. PPD is thus a per-scenario evaluation procedure rather than a universal metric, consistent with the premise that no single similarity measure serves all synthesis tasks [7]. Listening tests. Listening tests serve as the primary ground truth. Following Salimi et al. [7], in each scenario we randomly sample 40 (target, imitator) audio pairs per loss function; four authors independently rate each pair on a 5-point Likert scale (“are the two sounds similar?”), yielding 160 scores per loss per scenario. Raters are blinded to the generating loss function, and three of the four raters were not involved in synthesizer implementation, limiting familiarity-driven bias. 3.4. Optimization Loop The four loss functions are implemented as differentiable JAX functions, and the synthesizers are written in Faust and tran- spiled into JAX via DawDreamer [18]; this pipeline is faster than real-time and parallelizable. Parameters are updated using RMSProp with a fixed learning rate of 0.045 for 200 iterations, following [7]. Gradients are clipped to an L2 norm of 1 to mitigate exploding gradients [7]. 3.5. Bootstrapping and Ranking Procedures We follow the methodology of Salimi et al. [7] for ranking the loss functions. For each loss function and scenario, we 0.75 1.00 1.25 1 / PPD 1 4 3 2 BP: saw →noise — ICC3k 0.66 SIMSEL1JTFSDTW 1.2 1.8 2.4 Likert 1 2 4 3 1.0 1.5 2.0 2 3 4 1 AM: non-overlap — ICC3k 0.81 SIMSEL1JTFSDTW 1.5 2.0 2.5 3 2 4 1 1.2 1.6 2.0 3 4 2 1 AM: sine →saw — ICC3k 0.75 SIMSEL1JTFSDTW 1.2 1.8 2.4 1 4 3 2 1.2 1.5 1.8 2 3 4 1 AM: saw →sine — ICC3k 0.79 SIMSEL1JTFSDTW 1.6 2.0 2.4 2 1 3 4 1.2 1.6 1 / PPD 3 4 1 2 Chirp: delayed — ICC3k 0.86 SIMSEL1JTFSDTW 2.4 3.2 4.0 Likert 3 4 1 2 0.8 1.0 1.2 3 2 1 4 Chirp: no delay — ICC3k 0.89 SIMSEL1JTFSDTW 2.4 3.2 4.0 3 2 1 4 0.7 0.8 0.9 2 3 2 1 Chirp: pulsating — ICC3k 0.89 SIMSEL1JTFSDTW 1.6 2.0 2.4 2 3 2 1 NPSK rank (1 = best): 1234 Top of each cell: bootstrapped 1/PPD (P-Loss for “no delay”). Bottom: bootstrapped mean Likert score. Fig. 1. Bootstrapped1/PPD(top panel of each cell; P-Loss for the in-domain “no delay” scenario) and mean Likert rating (bottom panel) distributions for each scenario, with violins colored and numbered by NPSK rank (1 = best). Higher is better on both axes. Scenario labels read target→ imitator; each title gives the ICC3k inter-rater reliability of the four-rater average. bootstrap 1,000 resampled means from the PPD scores (or 160 Likert scores) to obtain nonparametric performance dis- tributions [19]; since PPD is a distance, we use the reciprocal of each resampled mean (1/PPD, as plotted in Fig. 1) so that higher values indicate better performance for both measures. These distributions are then ranked using the nonparametric Scott-Knott procedure (NPSK), which recursively partitions distributions into statistically distinct groups without assuming normality [20]. Rank 1 indicates the best-performing loss; ties indicate distributions that NPSK cannot distinguish. The scenario rankings are summarized in Figure 1; we discuss each scenario and its rankings in the following section. 4. SCENARIOS AND RESULTS The scenarios tested here use simple synthesis methods com- mon in prior work [21, 6] and sound design [22]; this sim- plicity isolates the interaction between loss function and syn- thesizer [7]. Searchable parameters are likewise restricted to those that dominate each sound’s perceptual identity (e.g., fil- ter cutoffs rather than resonance), keeping critical-parameter selection unambiguous; the pulsating chirp is deliberately uncommon, composing a pitch trajectory with an LFO to probeJTFS’s reported strength on mesostructures [6]. Fig- ure 1 shows the per-scenario bootstrapped distributions, NPSK ranks, and inter-rater reliability. 4.1. Band-Pass Matching Two synthesizers apply band-pass filtering to different source signals: BP-Saw (target: band-passed saw oscillator) and BP-Noise (imitator: band-passed white noise). Both share cutoffslp_cut∈[100,5000] Hz andhp_cut∈[1,400] Hz; the differing source signals (broadband stochastic vs. deter- ministic harmonic series) make exact replication impossible. PPD is the L2 distance between the normalized cutoffs. Both PPD and listeners rankSIMSE_Specfirst (Fig. 1), consis- tent with in-domain findings that spectrogram-based losses are best for filter-cutoff recovery [7]; the remaining ranks disagree between the two measures. 4.2. AM-Synthesizer Matching Three OOD scenarios are built from two AM synthesizers: SineSaw-AM (saw carrier modulated by a sine LFO) and SineSine-AM (sine carrier modulated by a sine LFO). Each has a modulation-rate parameteramp∈[1,15] Hz and a carrier frequencycarrier. Because the modulator sits in the sub- audio range, the effect is a slow tremolo rather than the side- bands of true ring modulation. PPD is the L2 distance onamp; carrieris excluded because the carrier ranges or wave- forms differ by design and, given logarithmic pitch perception, no single “correct” frequency match exists [23]. The three variants are: (i) non-overlapping frequencies: two SineSine- AM instances with disjoint carrier ranges (50–1500 Hz target, 2000–8000 Hz imitator); (i) sine→saw and (i) saw→sine: mirrored scenarios between SineSine-AM and SineSaw-AM on overlapping carrier ranges (30–5000 Hz), where numerical carrier values can coincide but harmonic content still differs. DTW_Enveloperanks first on PPD in all three, confirming accurate recovery of the modulation rate. Listeners agree in the non-overlapping case, but in the overlapping-carrier scenarios they prefer a spectrogram-based loss, whose outputs achieve better timbral similarity at the cost of envelope accuracy. This highlights the divergence between PPD and holistic perceptual judgments when multiple perceptual factors compete. 4.3. Pitch-Bending Three “chirplet” [24, 10] scenarios use a base synthesizer that emits a sine tone at a starting pitch (30–100 Hz) that, afterδsamples of steady tone, undergoes an exponential up- ward pitch bend at rateincrease_speed∈[1,20]. (i) De- layed (OOD):δis drawn uniformly from 5000–30000 sam- ples and is not searched, so the imitator cannot replicate the onset time; PPD is the L2 distance onstarting_pitch andincrease_speed. (i) No-delay (in-domain,δ = 0): a close replication of the chirplet experiments in Vahidi et al. [6]. (i) Pulsating (OOD): a saw-wave LFO with fre- quencypulse_rate∈[1,10] Hz oscillates the pitch around the increasing trajectory (increase_speedrestricted to [2, 7]for this variant); the pulse depth is an unsearched con- stant sampled per synthesizer (50–1000 Hz), so target and imitator generally cannot coincide. PPD is the L2 distance onincrease_speedandpulse_rate.JTFSranks first in the delayed and no-delay scenarios under both parameter- based and listening-test rankings, consistent with its reported agnosticism to small time and frequency shifts [6]. In the pulsating scenario,DTW_EnvelopedisplacesJTFSto a tie for second place with SIMSE_Spec. 5. DISCUSSION We find that synthesis-dependent loss behavior, as reported in previous in-domain work [7], generalizes to OOD settings (RQ1): SIMSE_Spec is best for band-pass matching, DTW_ Envelope for amplitude modulation and pulsating pitch, and JTFSfor smooth pitch trajectories.L1_Specranks first in only one case (Likert on AM: saw→sine) and is assigned NPSK rank 4 in five of the fourteen rankings of Fig. 1, while SIMSE_Specis never ranked last, suggesting that scale in- variance makes spectrogram losses more robust across syn- thesis tasks (RQ2). PPD agrees with listening tests on the top-ranked loss in five of seven scenarios (RQ3); the two disagreements occur in AM with overlapping carriers (Sec- tion 4.2), whereDTW_Enveloperanks first on PPD (accu- rate modulation rate) but listeners favor spectrogram losses (better timbral similarity). This emphasizes that PPD mea- sures a targeted parameter set and should be paired with listen- ing tests when multiple perceptual factors compete. Notably, JTFSexcels on smooth pitch bends but is displaced byDTW_ Envelopeon the pulsating variant (RQ2), indicating that its “mesostructure” domain is more narrowly scoped than previ- ously suggested [7, 6]. Inter-rater reliability of the four-rater average used in our analysis, measured by the intraclass corre- lation coefficient for the mean ofk=4raters (ICC3k) [25], is good (pooled ICC3k = 0.86,p < 0.001); per-scenario ICC3k values appear in the panel titles of Fig. 1. The listening-derived rankings are also robust to panel composition: the top-ranked loss is unchanged under every leave-one-rater-out ablation (mean rank correlationρ = 0.98). The noisiness of individual similarity judgments in OOD settings is itself an argument for complementing listening panels with automatic measures such as PPD. Practical implications. Loss selection should follow the synthesis task: spectrogram-based losses for filtering (with SIMSE_Specpreferred toL1_Spec),DTW_Envelopefor amplitude modulation, andJTFSfor smooth pitch trajecto- ries. For OOD evaluation, PPD with overlapping synthesizers is a viable strategy provided the critical parameters are per- ceptually dominant; pairing with a small listening panel is recommended. PPD is not intended for arbitrary synthesizer pairs, where critical parameters may be ill-defined; rather, it serves as a screening tool: loss functions certified in controlled scenarios can then be deployed in complex settings where parameter correspondence no longer exists. PPD may also complement P-Loss in in-domain settings where the goal is imitation of specific sound characteristics rather than direct parameter replication. Limitations and future work. Whether PPD scales to higher- dimensional parameter spaces or generalizes to real recorded targets is an open question; the selection of critical parame- ters also carries subjectivity that our simple synthesizer pairs sidestep. Our listening panel is small and composed of au- thors; blinding and high inter-rater reliability mitigate but do not remove this limitation, and validation against a larger external panel remains future work. All losses also share a single optimizer configuration, so rankings may partly re- flect interactions between loss scaling and the learning rate rather than intrinsic loss behavior. Our results are also condi- tioned on gradient-based optimization: differentiable pipelines are known to struggle with non-convex loss surfaces induced by oscillatory parameters [26, 27, 7], so loss rankings may shift under other search strategies (e.g., evolutionary methods). Promising directions include OOD matching with pre-recorded targets, real-time sound-matching [28], and composite match- ing algorithms that deploy task-specific losses validated in isolation (e.g.,DTW_Envelopefor envelope recovery and JTFS for pitch trajectories) within a single system. 6. REFERENCES [1] G. Krekovic, “Insights in habits and attitudes regarding programming sound synthesizers: A quantitative study,” in Proc. Sound and Music Computing Conf., 2019. [2]A. Horner, J. Beauchamp, and L. 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