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REVIEW 4 major objections 5 minor 31 references

Aliasing Reduction in Neural Amp Modeling by Smoothing Activations

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Smoother, horizontally stretched tanh activations reduce aliasing in neural amplifier models while keeping modeling error modest.

desk verdict Solid empirical sweep showing smooth activations reduce aliasing in neural amp models; the ASR metric is promising but unvalidated, and missing test details make the 27% headline provisional. read the letter →

arxiv 2505.04082 v2 pith:GMNVI6VT submitted 2025-05-07 eess.AS cs.SDeess.SP

Ryota Sato , Julius O. Smith III This is my paper · ORCID
classification eess.AScs.SDeess.SP
keywords neuralampmodelingaliasingactivationfunctionsAliasing-to-SignalRatioCustomTanhWaveNeterror-to-signalaudioeffects
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the aliasing artifacts plaguing neural guitar-amplifier models are not an inevitable cost of nonlinearity: the choice of activation function can suppress them substantially. It introduces a metric, the Aliasing-to-Signal Ratio (ASR), built on a number-theoretic choice of DFT length, to measure aliasing energy separately from harmonic energy, and uses it to rank 124 activation configurations. The central finding is that smoother, ungated activations—above all the horizontally stretched tanh, $\mathrm{CustomTanh}(x)=\tanh(x/\alpha)$—produce markedly less aliasing, with $\alpha=1.8$ keeping aliasing components below $-60$ dB and cutting ASR by about 27 percent relative to the standard $\alpha=1$ baseline while raising ESR only modestly. If this holds, neural amp models can become cleaner without architectural changes or extra computation.

What carries the argument

The load-bearing piece is the newly defined Aliasing-to-Signal Ratio (ASR), computed on the output of a single-tone sine test. The trick is to choose the DFT length $N$ and the fundamental bin $k_0$ coprime (here $N=48{,}017$, a prime, and $f_0=1249$ Hz), so that the set $\{n\cdot k_0 \bmod N\}$ fills every bin exactly once before any bin receives a second component; harmonic energy $E_H$ is read off the known harmonic bins and total spectral energy $E_Y$ from all bins, and $\mathrm{ASR}=(E_Y-E_H)/E_H$ estimates the aliasing fraction. Because no windowing or zero padding is used, each bin samples a single frequency, making the energy subtraction exact for a periodic steady-state response. The second object is the stretched tanh, $\mathrm{CustomTanh}(x)=\tanh(x/\alpha)$, whose larger $\alpha$ flattens the nonlinearity and is shown to lower ASR monotonically while ESR passes through a minimum near $\alpha=0.8$.

What would settle it

Run a listening test comparing CustomTanh $\alpha=1$ and $\alpha=1.8$ on real guitar input; if listeners cannot reliably tell which model is less aliased, or if the ASR ranking reverses when the sine test is repeated at different input amplitudes, the paper's central claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that smoother activation functions consistently produce less aliasing in TCN-based neural amp models, and that this gain can be purchased with only a modest rise in waveform-matching error. In the paper's own measurements, non-gated CustomTanh with stretch factor $\alpha=1.8$ reaches aliasing components below $-60$ dB, an ASR of $0.001582$ versus $0.002173$ for $\alpha=1$, a 27 percent reduction, at ESR $0.016628$ versus $0.013467$. The authors also find a systematic trade-off: gated activations such as SELU achieve the lowest ESR ($0.010591$) but introduce roughly 6–9 times more aliasing than the best anti-aliasing configurations. The conclusion is that activation-function choice is a viable anti-aliasing lever that requires neither architectural change nor additional computation.

Load-bearing premise

The whole ranking of activations hangs on the assumption that ASR computed from one 1249 Hz sine tone, whose input level is not reported, captures the aliasing artifacts that listeners actually hear in musical signals; the paper itself notes that listening tests are still needed.

Editorial extensions

If this is right

  • Swapping the standard tanh for CustomTanh with $\alpha=1.8$ reduces aliasing components below $-60$ dB and cuts ASR by roughly 27 percent at the cost of a small ESR rise, with no change to architecture or compute.
  • Among 124 configurations, the ten lowest-ASR models are all ungated, while gated variants dominate the lowest-ESR list, so the ASR-ESR trade-off is systematic rather than specific to one function.
  • Increasing the stretch factor $\alpha$ reduces ASR continuously in the tanh family, giving practitioners a dial between aliasing and waveform error; the paper also suggests the possibility of adapting $\alpha$ in real time based on input pitch.
  • The same smoothing logic highlights Hardtanh as a near-Pareto option and motivates exploring spline-smoothed, rounded-corner variants, which the paper proposes as future work.
  • For the Snake family, ASR and ESR both have local minima near $\alpha=2.9$, so Snake offers a balanced operating point distinct from the stretched-tanh family.

Reading between the lines

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

  • A natural extension the paper does not run: repeat the ASR measurement across input amplitudes and fundamental frequencies; the trade-off curve could flatten or invert, which would decide whether adaptive-$\alpha$ control should be level-aware.
  • The paper's gating results suggest an untested lever: because gated variants alias 6–9 times more than ungated ones, the sigmoid gate path itself is a likely aliasing source, and smoothing or removing that nonlinearity could combine low ESR with low ASR.
  • ASR is an unweighted spectral-energy ratio; before it is used to tune production models, a perceptually weighted or music-signal version would need validation against the listening tests the paper calls for.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper investigates whether smoother activation functions reduce aliasing artifacts in neural amplifier models built as temporal convolutional networks (TCNs). The authors introduce a new metric, the Aliasing-to-Signal Ratio (ASR), defined as the ratio of non-harmonic spectral energy to harmonic energy in the response to a periodic sine test. They train 12,400 models across 124 activation configurations (62 functions, gated and non-gated, with 100 seeds) and then 20,000 additional models to sweep the stretch/oscillation parameter for CustomTanh and Snake. They report that smoother activations, especially CustomTanh with larger stretch factors, reduce ASR while keeping the Error-to-Signal Ratio (ESR) modest, with a highlighted 27 percent ASR reduction for CustomTanh_1.8 relative to the baseline, accompanied by a modest ESR increase. The paper also includes spectrum and waveform analyses for three CustomTanh variants.

Significance. If the ASR metric is valid and the reported effect is robust, the paper provides a practically useful, architecture-free way to reduce aliasing in a widely used neural amp modeling framework: simply choose a smoother activation function. The experimental scale is a genuine strength: 100 deterministic seeds per configuration, 12,400 plus 20,000 trained models, and alpha-sweep experiments give the main trend empirical support rather than making it an artifact of a single run. The ASR definition is mathematically clean under the stated periodicity and coprimality assumptions, and no parameters are fitted to force the smoothness conclusion. However, the significance of the central quantitative claims currently rests on an unvalidated metric and a sine-test protocol whose key details are unreported; these issues must be addressed for the paper's headline numbers to be credible.

major comments (4)
  1. [Section 3.2 and Section 4.4] The ASR definition EA = EY - EH counts every DFT bin not at a low-order harmonic as aliasing, which is exact only for the periodic steady-state response to a single sine. The paper states in Section 3.2 that this requires 'any transient response is discarded,' but Section 4.4 reports no input amplitude, no transient-discard length, and no initial-state handling. The 18-layer TCN has a receptive field of 2045 samples (kernel 3 with the dilation pattern in Section 2.4), so a one-second test window that includes the onset will leak energy across all bins and misclassify that leakage as aliasing. Because the same ASR ranks all configurations, this missing detail directly affects the reported ranking and the 27 percent figure; the setup must be specified or the claim limited.
  2. [Section 3.2 and abstract] The abstract states that ASR 'quantitatively assesses the level of aliasing with high accuracy,' but no validation of the metric is provided. There is no comparison with a synthetic signal whose aliasing content is known exactly, no comparison with an established perceptual or objective aliasing measure, and no listening test (deferred in Section 5). Since the paper's central conclusion is an ASR-based ranking of 124 activation configurations, this is a load-bearing gap. A concrete validation, such as adding known aliasing components to a clean periodic signal and checking whether ASR tracks the added energy monotonically, or correlating ASR with listening-test ratings, would support the claim.
  3. [Section 4.4 and Table 2] The headline 27 percent reduction (ASR 0.001582 for False_CustomTanh_1.8 versus 0.002173 for False_CustomTanh_1) is measured with a single sine at 1249 Hz and no reported amplitude. Nonlinear aliasing depends strongly on drive level and input frequency; a single point does not establish that the improvement holds across the operating range of a guitar amplifier model. The authors should report an amplitude sweep and at least several fundamental frequencies, or explicitly restrict the claim to the tested condition.
  4. [Section 4.2.3] The exclusion of ReLUSquared and ReLUSquaredDip from the minimum-ASR analysis because they 'failed to train effectively (ESR about 1)' is a post-hoc criterion that is not stated in the methodology and is applied only to the minimum-ASR half of Table 1. The text acknowledges this, but the minimum-ASR ranking then depends on an unprincipled filter. Either state a rule (e.g., exclude all configurations with average ESR above a threshold) before presenting the table, or report the unfiltered results so readers can see the effect.
minor comments (5)
  1. [Sections 2.2 and 2.4] Training hyperparameters (optimizer, learning rate, batch size, and the epoch count at early stopping) are not stated; 'replicated from [15]' is insufficient for reproducibility of a study whose quantitative claims rest on 100-seed averages.
  2. [Section 4.4] The statement that aliasing 'remains below -60 dB' for alpha = 1.8 is based on visual inspection of the right column of Figure 6; the authors should define the quantitative criterion, such as the maximum magnitude of non-harmonic bins below 6 kHz.
  3. [Figures 3-5] In the submitted PDF, the figure labels and legend text contain garbled font-encoding sequences (e.g., '/uni00000014...'), making the plots unreadable; the final version must render these characters properly.
  4. [Section 4.1.1] The gated versus non-gated comparison confounds the choice of activation function with the additional sigmoid nonlinearity in the gate; the conclusion that 'gating introduces aliasing' should be qualified as applying to the gated architecture as a whole rather than to the activation alone.
  5. [Section 4.3] The 'balanced' points (alpha = 1.8 for Tanh, alpha = 2.9 for Snake) are chosen informally; the authors should state the selection rule, such as the lowest ASR subject to an ESR ceiling, to make the choices reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the ASR metric is defined from the output spectrum alone, alpha values are enumerated rather than fitted to ASR, and the central smoothness-aliasing claim does not reduce to its inputs.

full rationale

Walking the paper's derivation chain—ASR definition (Sec. 3.2), model training on ESR (Sec. 2.2), alpha enumeration (Secs. 4.1–4.3), and the waveform/spectrum analysis (Sec. 4.4)—I find no step that reduces to its own inputs by construction. ASR is defined purely from the DFT of the model output: EA = EY − EH, so every bin not at a low-order harmonic of the 1249 Hz test tone counts as aliasing energy. This definition contains no reference to activation-function smoothness, stretch factor, gating, or the ESR training objective, so the smoother-means-less-aliasing conclusion is not built into the metric. The alpha sweep is genuinely empirical: alpha values are enumerated (log-spaced 10^-2 to 10^2), 100 seeds per configuration, and no parameter is fitted to ASR; the headline 27% figure is a ratio of two measured averages (0.002173/0.001582) from Table 2, not a fitted prediction. The metric even surfaces an unanticipated result—non-smooth, piecewise-linear False_Hardtanh sits near the Pareto frontier with ASR 0.002246 and ESR 0.012443—which is evidence that ASR does not tautologically reward smoothness. Self-citations by the second author (refs [1], [4]) are background survey and wave-digital-filter material and are not load-bearing for the central claim. The paper's own limitation, that listening tests are needed to perceptually validate the results (Sec. 5), plus the unreported sine-test amplitude and transient-discard details, is a validation and reproducibility gap in ASR, not a circularity: an unvalidated or even biased metric can be wrong without the argument being circular. No fitted-parameter-renamed-as-prediction, no definitional equivalence, and no self-citation chain exist here, so the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central claim rests mainly on the domain assumption that the ASR sine-test procedure captures audible aliasing, and on the representativeness of the single NAM training data. No parameters are fitted to force the ASR trend; the headline alpha values are post hoc operating points, and the unreported test amplitude is an omitted control.

free parameters (4)
  • CustomTanh stretch factor alpha (balanced point) = 1.8
    Chosen post hoc in Section 4.3 to represent 'increased aliasing reduction with good modeling accuracy'; the reported 27 percent aliasing reduction refers to this hand-picked value.
  • Snake oscillation frequency alpha (balanced point) = 2.9
    Selected post hoc as the ASR local minimum within the low-ESR region (Section 4.3).
  • Sine-test fundamental frequency f0 = 1249 Hz (k0=1249 at fs=48017)
    All ASR comparisons use this single test tone; the conclusion is not shown to hold across a frequency range (Section 3.2, Section 4.4).
  • Sine-test input amplitude = not reported
    The drive level of the sine is never specified, though it strongly affects the nonlinearity's operating region and hence the measured ASR (Section 4.4).
assumptions (5)
  • domain assumption The trained network output to a periodic sine is periodic after discarding the transient, so the DFT bin energies are discrete Fourier series samples.
    Invoked in Section 3.2 before ASR is defined; if the network has significant time-varying behavior or long memory, the metric could mix transient and steady-state energy.
  • domain assumption Aliasing originating from harmonics above the Nth harmonic (~60 MHz) is negligible.
    Section 3.2 assumes harmonic amplitudes roll off rapidly for smooth activations; if a trained model retains significant high-order harmonics, the ASR could undercount aliasing.
  • domain assumption The training setup of [15] and the single NAM sample are representative enough to support general conclusions about activation function choice.
    Section 2 states the authors replicated [15] and used one heavy-distortion boutique tube amp dataset; all ESR and ASR results come from this single amp.
  • standard math For prime DFT length N and coprime k0, the set {n k0 mod N} for n=0..N-1 covers every residue exactly once.
    This number-theoretic fact underlies the ASR bin-collision argument in Section 3.2; it is correct for the chosen N=48017 and k0=1249.
  • domain assumption ESR, taken from [13], is a valid measure of modeling accuracy for the purpose of characterizing the aliasing/accuracy trade-off.
    The paper bases all accuracy judgments on ESR; its perceptual validity is not examined, and the trade-off argument inherits any limits of ESR.
invented entities (1)
  • Aliasing-to-Signal Ratio (ASR)
    purpose: A metric to estimate the fraction of output spectral energy attributable to aliasing, defined as (EY - EH) / EH for a sine test.
    ASR is introduced by the authors and is the primary evidence for the central claim. No listening test, ground-truth annotation, or comparison with existing alias metrics is provided to validate that lower ASR corresponds to reduced audible aliasing; the conclusion explicitly defers this to future work.

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Pith. "Pith review of Aliasing Reduction in Neural Amp Modeling by Smoothing Activations." pith.science (2026). https://pith.science/paper/GMNVI6VT

@misc{pith2026250504082,
  author       = {Pith},
  title        = {Pith review of: Aliasing Reduction in Neural Amp Modeling by Smoothing Activations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMNVI6VT}},
  note         = {Machine review of arXiv:2505.04082}
}
read the original abstract

The increasing demand for high-quality digital emulations of analog audio hardware, such as vintage tube guitar amplifiers, led to numerous works on neural network-based black-box modeling, with deep learning architectures like WaveNet showing promising results. However, a key limitation in all of these models was the aliasing artifacts stemming from nonlinear activation functions in neural networks. In this paper, we investigated novel and modified activation functions aimed at mitigating aliasing within neural amplifier models. Supporting this, we introduced a novel metric, the Aliasing-to-Signal Ratio (ASR), which quantitatively assesses the level of aliasing with high accuracy. Measuring also the conventional Error-to-Signal Ratio (ESR), we conducted studies on a range of preexisting and modern activation functions with varying stretch factors. Our findings confirmed that activation functions with smoother curves tend to achieve lower ASR values, indicating a noticeable reduction in aliasing. Notably, this improvement in aliasing reduction was achievable without a substantial increase in ESR, demonstrating the potential for high modeling accuracy with reduced aliasing in neural amp models.

Figures

Figures reproduced from arXiv: 2505.04082 by the authors.

Figure 1
Figure 1. Current neural amp modeling architecture [15] x[n] are fed to a series of dilated convolution layers with chan￾nel dimension of C. The outputs from each layer (CONV box) are computed as learned FIR filters feeding nonlinear activation func￾tions. The outputs from one layer to the next are called “residual outputs,” with channel dimension C, while the outputs zk[n] are called “skip outputs” with the number of “skip c… view at source ↗
Figure 2
Figure 2. Example activation functions mentioned in Section 4.1. Lightning to prevent overfitting. After excluding activation func￾tions from the default PyTorch library that were incompatible with our framework, we evaluated a total of 62 unique activation func￾tions. This set includes standard PyTorch activation functions as well as parameterized versions of CustomTanh, ReluSquared, Re￾luSquaredDip, and Snake, each tested w… view at source ↗
Figure 3
Figure 3. Scatter plot of average ASR and ESR performance, excluding points for which ESR > 0.2. Bold points represent notable models from Section 4.3 tion was tested with 100 unique deterministic seeds. Our comprehensive evaluation involved 20,000 models (2 ac￾tivation functions × 100 α values × 100 seeds), revealing distinct patterns for each activation function. Notable models are listed in [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Detailed graph of α value vs ESR/ASR for Snake. ASR shows a similar convex zone over the α range corresponding to ESR below 10%, or roughly α ∈ [0.1, 40]. The very-low ASR regions at the extremes coincide with ESR values approaching 1, indicating severely compromised m…
Figure 6
Figure 6. Figure 6: Comparing prediction and target output waveform (left column), prediction and target spectra, with a black dashed at 6kHz indicating a typical guitar-cabinet bandwidth (center column), and sine-wave spectrum with harmonics circled (right column). 128) as demonstrated i…

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