An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing

Jozef Coldenhoff; Kiril Ratmanski; Milos Cernak; Riccardo Rota

REVIEW 5 major objections 5 minor 44 references

An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing

T0 review · 5 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read A 1M-parameter neural controller that sets 35 biquad filters frame by frame matches a 2.3M-parameter black-box denoiser on perceptual scores.

desk verdict The abstract and the body describe different models — the headline 24k-parameter, 10.7ms, HASPI/HASQI result is absent from the full text — but the causal neural biquad-cascade idea is new, and the body's results, though selective, support a more modest proof-of-concept claim. read the letter →

arxiv 2603.02794 v3 pith:IFOENRYH submitted 2026-03-03 cs.SD cs.AIcs.LGeess.AS

Riccardo Rota , Kiril Ratmanski , Jozef Coldenhoff , Milos Cernak This is my paper · ORCID

classification cs.SDcs.AIcs.LGeess.AS

keywords speechenhancementtime-varyingIIRfiltersbiquadcascadeinterpretableDSPon-deviceinferencedifferentiablefilteringnoisesuppressionlowlatency

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 a compact neural network can control a cascade of 35 second-order IIR filters (biquads) in real time, predicting gain, center frequency, and Q per frame from the magnitude spectrum. This time-varying filtering chain tracks non-stationary noise while keeping every spectral modification explicit as an adjustable equalizer curve. Trained from scratch on a standard noisy-speech corpus, the 1.01M-parameter model matches a state-of-the-art deep denoiser with 2.31M parameters on PESQ, POLQA, and overall MOS, while using a strictly linear, causal signal path. The authors present this as a proof of concept for interpretable, on-device assistive hearing.

What carries the argument

The key object is the differentiable cascade of 35 biquad IIR filters, parameterized by gain, quality factor, and center frequency and updated every frame. A gated recurrent unit generates smooth coefficient trajectories to avoid audible discontinuities, and a systolic-style vectorized tensor formulation accelerates training; at inference the cascade runs serially with 21ms algorithmic latency.

What would settle it

Measure end-to-end inference time and energy on a low-power DSP or hearing-aid chip using the released model; if the 1.01M-parameter GRU cannot run within a few milliseconds and a few milliwatts, the on-device claim fails. Alternatively, retrain the 24k-parameter version and check whether it still stays within 0.02 of the deep baseline on HASPI/HASQI.

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Extended reading notes

Core claim

The central claim is that a GRU-based controller with about 1M parameters can map a 513-bin magnitude spectrum to 105 biquad coefficients (35 filters × 3 parameters) per 21ms frame, and that the resulting time-varying linear filter both adapts to changing noise and remains fully interpretable. In head-to-head training on the same corpus, TVF outperforms a static 35-band equalizer and roughly ties or beats a deep STFT-mask baseline on perceptual metrics, though it trails on waveform-reconstruction metrics like SI-SDR and log-spectral distance. The abstract asserts a much smaller 24k-parameter variant at 10.7ms latency, but the full text and experiments use the 1.01M-parameter model.

Load-bearing premise

The real-time on-device claim rests on an untested hardware assumption: the paper states 1.01M parameters and 21ms latency in the body but the abstract promises 24k parameters and 10.7ms, with no power or runtime measurement on a hearing-aid-class processor.

Editorial extensions

If this is right

A denoiser whose entire signal path is a linear equalizer can be examined and audited: every gain change corresponds to a visible filter curve.
The suppression-versus-preservation tradeoff can be rebalanced at inference without retraining by mixing noisy and denoised audio, enabling user-controlled hearing-aid behavior.
Because the model is structurally causal and low-latency, it can run inside a hearing aid's pipeline rather than on a server.
On small training corpora, the inductive bias of linear IIR filtering yields competitive perceptual quality with far fewer parameters than black-box masks.

Reading between the lines

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

If the claimed latency and parameter counts hold on real hardware, the same controller-plus-biquad architecture could be retargeted to other audio effects (EQ, compression, feedback suppression) with minimal changes.
The paper's abstract claims a 24k-parameter model at 10.7ms latency, while the body describes 1.01M parameters and 21ms; reconciling this on actual silicon would be the decisive next test.
The linear, causal constraint suggests a natural ceiling: in very low SNR or with transient interference, a phase-reconstructing nonlinear mask may still be unavoidable.
One could test the interpretability claim directly by asking hearing-impaired listeners to adjust the exposed filter curves to their preference.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. The abstract and the body describe different systems. The abstract's headline — 24k parameters, 10.7 ms latency, HASPI/HASQI within 0.02 of DFNet3, 29x fewer MACs, and inference-time controllability — does not appear in the experimental section. The body reports a 1.01M-parameter model (§3.1), 21 ms algorithmic latency (§3.3), and evaluation with PESQ, POLQA, eSTOI, SI-SDR, LSD, and SIGMOS (§4.3). No HASPI/HASQI, no MAC counts, no 24k row in Table 1, and the inference-time input mixing claimed in the abstract is not described in the methodology. That is a load-bearing inconsistency, not a cosmetic slip.

That said, the underlying idea is genuinely new. A causal, neural-controlled biquad cascade for real-time speech denoising is a legitimate application — related dynamic EQ [11] is non-causal, time-varying biquads [9] target offline processing, and [10] uses FIR in a feedback loop. The systolic vectorization for training is a useful trick. The body also does some things right: all models are trained from scratch on the same data, DFNet3's lower-than-original numbers are acknowledged, and the conclusion explicitly calls it a proof of concept. TVF does beat the static PEQ baseline on essentially all metrics, which supports the value of time-varying control. On the DFNet3 comparison, it wins on PESQ, POLQA, MOS-Noise, and MOS-Overall, but loses on SI-SDR and LSD, with eSTOI about tied. That is "comparable" in a loose sense, but there are no significance tests, and SIGMOS is a learned proxy, not a listening test. For a hearing-aid claim, the absence of any hardware measurement — power, on-device latency, actual HA processing — is a real gap. The 1M-parameter GRU isn't obviously "ultra-lightweight" for a hearing aid.

The soft spots are in proportion: the central idea holds up as a proof of concept, but the submitted paper oversells it. The mismatch alone means the headline result cannot be checked against the reported data. Still, the body is worth reading for anyone working on interpretable DSP/ML denoisers.

Who is this for: people in hybrid DSP/ML speech enhancement; it would get a fair hearing at a workshop or INTERSPEECH-style venue after the authors fix the abstract, add MAC/latency numbers, and ideally a listening test or hardware profile. My recommendation: don't accept as is, but don't dismiss the work. If I were the editor, I'd ask the authors to reconcile the abstract and body and supply the missing evidence, then send it to a serious referee. It deserves a round of review, not a silent desk rejection.

Referee Report

5 major / 5 minor

Summary. The paper presents TVF (Time-Varying Filtering), a speech denoising system in which a neural network predicts, per frame, the coefficients of a cascade of 35 differentiable biquad IIR filters. The model is trained on Valentini-Botinhao and compared against a static differentiable-PEQ baseline and a from-scratch DeepFilterNet3 baseline. The body reports a 1.01M-parameter model with 21 ms algorithmic latency, evaluated with PESQ, POLQA, eSTOI, LSD, SI-SDR, and SIGMOS. The abstract, however, advertises a 24k-parameter model with 10.7 ms latency, HASPI/HASQI hearing-aid metrics, and 29x fewer MACs than DFNet3, none of which appear in the full text.

Significance. The core idea—using a compact neural controller to drive an interpretable, time-varying IIR filter cascade—is timely and potentially useful for on-device speech enhancement. The systolic vectorization for training (§3.3) is a practical contribution, and the decision to retrain DFNet3 from scratch on the same data is methodologically fair. If the abstract's claims were supported, this would be a notable result: an interpretable and controllable model competitive with a much larger black-box model on perceptual metrics. As it stands, the evidence in the body supports only a much weaker statement: a 1.01M-parameter TVF is competitive on some metrics and worse on others, with no significance testing and no hardware validation.

major comments (5)

[Abstract vs. §3.1, §3.3, §4.3, Table 1] The abstract's headline numbers are absent from the full text. The abstract claims 24k parameters, 10.7 ms latency, HASPI/HASQI results within 0.02 of DFNet3, and 29x fewer MACs, but §3.1 reports a 1.01M-parameter model, §3.3 gives 21 ms algorithmic latency, §4.3 lists no HASPI/HASQI among the metrics, and Table 1 reports no 24k row, no MAC counts, and no hearing-aid metrics. Additionally, the abstract calls DFNet3 "almost two orders of magnitude larger" than TVF, while the actual parameter ratio is 2.31M/1.01M ≈ 2.3x. The reader cannot verify the paper's central advertised result because the evaluated system appears to be different from the one described in the abstract.
[§5.1, Table 1] The claim that TVF is "comparable" to DFNet3 is selectively supported. On eSTOI (0.79 vs. 0.80), LSD (1.97 vs. 1.40), SI-SDR (13.71 vs. 14.58), and MOS-Signal (2.95 vs. 3.02), DFNet3 is numerically better; only on PESQ, POLQA, MOS-Noise, and MOS-Overall is TVF better. The standard deviations overlap substantially on all metrics, so without paired significance tests the observed differences are not established. The text's wording in §5.1, "performs even better than DFNet3 on PESQ and POLQA," overstates the case given the lack of statistical testing and the mixed pattern across metrics.
[Abstract vs. §5.2] The abstract promises an inference-time controllability mechanism: "it can be set during training through the loss weighting, and adjusted at inference, with no retraining, by mixing the noisy input with the denoised output." The full text, however, only describes adjusting the time-domain loss weight during training (§5.2). The inference-time mixing operation is never defined in the methodology and no experiment demonstrates it. This is a missing component of the claimed contribution, not merely a presentation issue.
[§3.3, Abstract] The on-device, hearing-aid-ready premise is unsupported. The paper provides an algorithmic latency of 21 ms (§3.3) but no actual runtime, power, or memory measurements on any device. The abstract's 10.7 ms and 29x MAC figures do not appear in the body. The claim that the model is "within hearing-aid budgets" is therefore an assertion without evidence, and the title's "On-Device Assistive Hearing" is not validated by any hardware experiment.
[§5.3, §6] The assertions of "artifact-free linear processing" (§6) and that the GRU smoothly changes coefficients "avoid[ing] artifacts" (§5.3) are presented as conclusions without any artifact-specific evaluation or listening test. Figure 2 is a single qualitative example; it cannot substantiate a general artifact-free claim. This is a strong claim that requires either a perceptual listening test, an artifact metric, or a clearly hedged statement.

minor comments (5)

[§2, References] Reference [4] contains a typo: "V ocoder" for "Vocoder"; reference [5] has "V ocoder" as well. Please proofread the reference list.
[Author block] The author names include "ID" strings and a double asterisk that is not explained in the footnote. These appear to be artifacts of the submission template and should be cleaned.
[Figure 2] The spectrograms in Figure 2 would benefit from time/frequency axis labels and display ranges; without them it is hard to assess the claimed -40 dB attenuation and 0 dB passband behavior.
[§4.2] The DFNet3 retraining uses "default hyperparameters" from the official repository, but the paper does not specify whether the optimizer schedule, loss weights, or data sampling were tuned for the much smaller Valentini-Botinhao dataset. A sentence acknowledging this limitation would strengthen the fairness discussion.
[§5.2] The MOS-Noise/MOS-Signal trade-off is described as "tunable" based on the loss weight, but no experiment varies this weight. Consider adding an ablation or explicitly labeling this as future work.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: TVF is empirically trained and evaluated on held-out metrics; the abstract/full-text mismatch is an evidentiary inconsistency, not a circularity.

full rationale

The paper's derivation chain is empirical rather than deductive: a neural controller is trained on Valentini-Botinhao and compared against held-out test metrics (PESQ, POLQA, eSTOI, SI-SDR, LSD, SIGMOS). No target metric is used as a training objective and then reported as a prediction; the enhancement metrics are external, reference-based or non-intrusive estimators applied to model outputs. The biquad coefficient mapping uses standard formulae cited from prior work [2], and the systolic/vectorized implementation is an engineering optimization, not a result that assumes its conclusion. There are no self-citations by the present authors used as load-bearing evidence, no invoked uniqueness theorem, and no ansatz presented as independently derived. The abstract does make claims (24k parameters, 10.7 ms latency, HASPI/HASQI, inference-time mixing) that do not appear in the full text; however, that is an internal consistency/support problem, not circularity, because it does not reduce any derived result to its own inputs. Consequently, no circular step can be exhibited with the required specificity, and the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No code or weights are released, so the central claim rests on learned weights and hand-set design choices. The abstract's 24k-parameter claim is absent from the body, making the actual contributed system ambiguous.

free parameters (4)

Neural controller weights = ~1.01M learned weights (24k claimed in abstract)
The denoising behavior is learned from Valentini-Botinhao; no weights are published.
Time-domain MSE loss scale = 5×10^4
Hand-set in §4.2; controls the suppression-vs-preservation trade-off and is not swept.
35-band spacing and frequency ranges = 20–60 Hz low shelf, 33 resonant bands, 12–22 kHz high shelf; hybrid spacing
Hand-designed band layout in §3.2; affects what noise shapes can be represented.
Parameter ranges = gain ±20 dB, Q 0.1–2.0
Clipped ranges chosen by hand in §3.1; bound achievable frequency responses.

assumptions (4)

domain assumption Direct Form I biquad recursion with state passing is numerically stable for predicted coefficient ranges
§3.3 applies Equations 2–3; no stability check is reported for all predicted (g, q, f0) combinations.
domain assumption SIGMOS/DNSMOS scores track perceived hearing-aid quality
§4.3 uses reference-free SIGMOS to support MOS claims; no human listening test is reported.
domain assumption Valentini-Botinhao is representative of on-device assistive hearing conditions
§4.1 uses one small benchmark; the abstract's hearing-aid metrics (HASPI/HASQI) are absent from evaluation.
domain assumption Difference of clean/noisy pairs yields valid pure noise for augmentation
§4.1 assumes additive noise and no nonlinearity in dataset generation.

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Cite this review

Pith. "Pith review of An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing." pith.science (2026). https://pith.science/paper/IFOENRYH

@misc{pith2026260302794,
  author       = {Pith},
  title        = {Pith review of: An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IFOENRYH}},
  note         = {Machine review of arXiv:2603.02794}
}

read the original abstract

We present TVF (Time-Varying Filtering), an interpretable, low-latency speech enhancement model for real-time, on-device assistive hearing. A lightweight neural controller predicts, in real time, the coefficients of a differentiable cascade of 35 second-order IIR filters (biquads), so the model tracks non-stationary noise while keeping a fully interpretable processing chain: every spectral modification is an explicit, adjustable equalizer curve rather than an opaque `black-box' transform. Because the biquad cascade carries the signal processing, the controller can be made very small, driving the cascade with only 24k parameters at a 10.7ms algorithmic latency, within hearing-aid budgets, and running entirely on-device so that audio never leaves the device. We also expose the suppression-versus-preservation trade-off as an explicit control: it can be set during training through the loss weighting, and adjusted at inference, with no retraining, by mixing the noisy input with the denoised output. On hearing-aid metrics (HASPI/HASQI) the 24k model stays within about 0.02 of DFNet3 (2.3M parameters, almost two orders of magnitude larger) while using about 29X fewer multiply-accumulates, although larger black-box models still lead on reference metrics such as PESQ. We present TVF as a proof of concept for a compact, interpretable, and controllable denoiser for on-device assistive hearing.

Figures

Figures reproduced from arXiv: 2603.02794 by the authors.

**Figure 1.** Model architecture: Here T is the total number of samples, N is the number of frames, L = 1024 is the frame length, F = 513 is the number of frequency bins, C = 129 is the number of features per channel after the two convolutions, D = 256 is the hidden and output dimension of the GRU. 3.5. The Static PEQ Baseline To isolate the benefit of time-varying control, we compare against the PEQ implementation by [2]1 , exte… view at source ↗

**Figure 2.** Analysis of the filtering on a track with non-stationary background noise. From top to bottom: noisy input spectrogram, adaptive frequency response of TVF, denoised output. weights to reconstruct phase and periodicity. This unconstrained, ”black box” approach excels on waveform-matching metrics like SI-SDR and LSD. In contrast, TVF applies linear time-domain filtering by mapping neural outputs to physically constr… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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However, classic DSP struggles to handle dynamic, non-stationary noise without manual tuning

Introduction While deep learning has transformed audio processing, tradi- tional Digital Signal Processing (DSP) remains vital for low- power applications due to its computational efficiency and inter- pretability. However, classic DSP struggles to handle dynamic, non-stationary noise without manual tuning. While Differen- tiable DSP (DDSP), introduced by...

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In the domain of audio effects, [2] represents a key contribu- tion, introducing differentiable implementations of Parametric Equalizer (PEQ) and Dynamic Range Compressor

Related Work The Differentiable Digital Signal Processing (DDSP) frame- work was originally introduced by [1], utilizing a spectral syn- thesizer to reconstruct and transfer musical instrument timbre. In the domain of audio effects, [2] represents a key contribu- tion, introducing differentiable implementations of Parametric Equalizer (PEQ) and Dynamic Ra...

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The input audio is segmented into non-overlapping frames of 1024 sam- ples, corresponding to a window of approximately 21 ms at 48 kHz

Methodology Our proposed system comprises a machine learning pipeline that controls a chain of 35 cascaded biquad filters. The input audio is segmented into non-overlapping frames of 1024 sam- ples, corresponding to a window of approximately 21 ms at 48 kHz. These frames are processed by two branches, as shown in Figure 1. The machine learning backbone an...

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Experiments We evaluate our TVF model on a speech denoising task, com- paring it against the static PEQ [2] described in the previous section and the DeepFilterNet3 (DFNet3) model [3]. 4.1. Dataset We train all three models using the 56-speaker Valentini- Botinhao noisy speech dataset [26]. While relatively small compared to modern large-scale corpora, it...

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Table 1 presents the mean values and standard deviations obtained across the 824 files in the test set

Results We evaluate the performance of the three models using the met- rics defined in the previous section. Table 1 presents the mean values and standard deviations obtained across the 824 files in the test set. The first column reports the metrics computed on the unprocessed input signal for reference. It is important to contextualize the performance of...