{"id":"b0e36393-f0ed-4888-977b-e9c01fe8709b","arxiv_id":"2505.10500","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The authors demonstrate the first fully homomorphic encryption pipeline that computes STFT, Mel, MFCC, and gammatone features directly from raw audio, with approximate variants that improve accuracy in some private audio tasks.","lead":"This paper demonstrates that audio can be processed under fully homomorphic encryption, computing spectrograms and acoustic features without ever decrypting the raw sound. It introduces approximate spectrogram methods and finds some, like dilated transforms, reduce error in private audio analyses, though computation remains extremely slow.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed approximation improvements in Tables 2–3 cannot reach statistical significance; even the most favorable pairing yields McNemar p ≥ 0.25.","rationale":"The reader's weakest assumption concerned calibration-set representativeness; that is a valid reliability concern, but the more load-bearing issue is inferential: even taking the reported error counts at face value, the paper does not demonstrate that the approximations improve on the conventional STFT. The tables show small absolute differences on paired nominal outcomes with no significance test, and the 'best' method is picked post hoc across 12 variants. Since the paper's title and abstract center on quantized approximate signal processing and its claimed benefits, the unsupported improvement claim directly affects the central contribution. I do not reject the underlying pipeline: the end-to-end FHE computation of STFT, Mel, MFCC, and gammatone features and the classifiers is a real demonstration, and the poorman's transform has a valid theoretical error bound (Appendix A.2). However, the empirical evidence for approximation superiority should be subjected to paired significance testing before the headline claims are accepted. This reinforces the reader's CONDITIONAL verdict: the authors should narrow the performance claims and provide statistical support, not necessarily abandon the approach. Hence the verdict remains unchanged, but the conditions should explicitly include significance testing and pre-registered selection of the approximation (or a proper validation split for choosing among the 12 variants).","tokens_in":17717,"tokens_out":13732,"duration_ms":126897,"concrete_test":"For each claimed improvement in Tables 2 and 3, compute the two-sided McNemar exact p-value under the most favorable pairing (all discordant pairs in favor of the approximation). With the published error totals, the best-case p-values are 0.25 (for Δ=3) and 0.50 or larger (for Δ=1–2), all above 0.05. If the authors instead supply per-pair error status, run the exact McNemar test directly; either way, the claim of significant improvement fails unless a p-value below 0.05 is obtained.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline claim that approximate STFT formulations 'substantially reduce error rates' and yield 'significant performance improvements' over conventional STFT in FHE is not supported by the error counts in Section 5.2 / Tables 2 and 3. The reported gains are tiny: e.g., VocalSet Mean Gammatone stds drops from 15/144 to 12/144; OxVoc Std RMS from 3/27 to 1/27. The best approximation is chosen post hoc among 12 variants, and the winner changes by marker and dataset (Poorman L=8 gives 0.0 on OxVoc Mean Mel but 12.5% on VocalSet Mean Gammatone), making 'dilation factor 4 ... best across both datasets' an unstable conclusion. No significance test is reported. A McNemar test on paired class-pair outcomes is the appropriate analysis; even under the most favorable pairing of errors (all discordant pairs favoring the approximation), the largest reported difference (Δ=3, e.g., 15 vs 12 errors) yields a two-sided exact p-value of 0.25, and differences of Δ=1–2 yield p≥0.50. Since the minimum possible p-values exceed 0.05, the observed improvements are statistically indistinguishable from chance regardless of how the errors are paired. The central empirical contribution of the paper is therefore not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents Quantized Approximate Signal Processing (QASP), a framework for computing standard time-frequency representations (STFT, Mel filterbanks, MFCCs, gammatone filters) on encrypted raw audio under the TFHE scheme, using quantized neural network layers and several approximate STFT formulations (dilation, frequency-dependent windows, poorman's projection, l1 energy, cropping). The authors derive error bounds for the approximations and evaluate the pipeline on VocalSet and OxVoc through intrinsic spectrogram distances, statistical tests over audio descriptors, and CNN gender/vocal-exercise classification, comparing conventional STFT with the approximations. The paper claims that the approximations significantly improve error rates and classification performance relative to conventional FHE STFT.","tokens_in":17995,"tokens_out":12010,"duration_ms":111683,"significance":"If the empirical claims were fully supported, this would be a valuable proof-of-concept: it would show that a server can compute standard audio features and simple classifiers over encrypted raw audio without seeing plaintext, with error bounds guiding parameter choice. The derivation of the poorman's transform error bound (Appendix A.2) and the decomposition of quantization bit widths (Section 3.3) are clear strengths, as are the use of public datasets and the explicit statement of limitations (lost harmonics above 4 kHz, very high FHE latency). However, the headline claims about approximation gains are not established by the reported numbers, and several statements go beyond what the tables show.","major_comments":[{"comment":"The claim that the approximations 'substantially reduce error rates' and yield 'significant performance improvements' is not supported by the reported error counts. The largest improvement over the conventional STFT in any cell is 3 errors (e.g., 15 vs 12 on VocalSet Mean Gammatone; 3 vs 1 on OxVoc Std RMS). For paired binary outcomes, a McNemar exact test with a total-error difference of 3 has a minimum two-sided p-value of 0.25, and differences of 1 or 2 have p-values of at least 0.5; therefore no cell in these tables can reach statistical significance no matter how the discordant pairs are arranged. The paper reports no significance test, no confidence intervals, and no raw confusion matrices. Moreover, the best variant is selected post hoc among 12 approximations, and the winner changes across markers and datasets (e.g., OxVoc Mean Mel has 0.0 errors for Poorman L=6, Poorman L=8, and Dilation d=2, while Dilation d=4 gives 3.7), so the inference that 'dilation factor 4 ... is the best approach across both datasets' is not established.","section":"Section 5.2, Tables 2 and 3; Abstract"},{"comment":"The quantization bit widths Bi, Bo, Bw, and Bm are selected by grid search on a 10% calibration set and then used to evaluate on the remaining 90%, but the manuscript provides no evidence that the selected widths generalize to the evaluation distribution. Because the calibration criterion is Pearson correlation with clear descriptors, the comparison of approximation methods on the evaluation set can be biased toward methods that happen to overfit the calibration split. Please report repeated calibration/evaluation splits (or a bootstrap) and the stability of the selected bit widths, or otherwise demonstrate that the ranking of approximations is robust to the calibration set choice.","section":"Sections 4.1.2 and 4.2"},{"comment":"The statement that the approximations 'helped to get closer to the clear computation' for CNN classification is inconsistent with the tables. For binary gender classification, Poorman is worse than the conventional FHE pipeline for every representation (e.g., 0.82 vs 0.89 for STFT) and Dilation is worse for Mel (0.82 vs 0.86) and Gammatone (0.82 vs 0.89). For 4-class vocal exercises, Dilation improves only STFT and Mel, and Poorman degrades STFT (0.50 vs 0.54) and MFCC (0.50 vs 0.53) relative to the conventional STFT. No significance test is reported across the 5 runs, and the standard deviations (0.01–0.04) are large relative to the differences, so the claimed classification improvements are not established.","section":"Section 5.3, Tables 4 and 5"},{"comment":"The 'first' claims (first system to perform FHE on raw audio; 'First complete end-to-end demonstration of FHE applied directly to raw audio signals') are not reconciled with the authors' own description of Zhang et al. [59] as avoiding filterbanks and 'using only smaller convolutions on audio'. If prior work already applied homomorphic computations directly to raw audio, the novelty should be stated more narrowly (e.g., first to compute these four time-frequency representations under TFHE, or first with this particular CNN pipeline). Please cite and compare explicitly so that the contribution is accurately scoped.","section":"Section 1 and Highlights"}],"minor_comments":[{"comment":"The dilation indicator function notation is ambiguous: '1_{n≡0[min(d,dk)]}' should be defined as n ≡ 0 mod min(d, d_k), and Appendix A.1 uses a different form '1_{n≡0[d]}'; please align the notation and define all symbols.","section":"Equation (7) and Appendix A.1"},{"comment":"The caption says the figure shows the FHE-friendly transformation 'corresponding to lowest Euclidean distance' but does not specify which approximation is used; please state the configuration explicitly.","section":"Figure 3"},{"comment":"The conclusion states that all four time-frequency representations were 'successfully demonstrated', but Section 5.1 reports MFCC mean normalized 2D Euclidean distances of 0.78–0.85 with maxima above 1.5, far above the other features (0.13–0.18); please qualify the MFCC claim and discuss the practical utility of the encrypted MFCCs.","section":"Section 5.1 and Section 6"},{"comment":"The limitation section reports an FHE latency of 12,970 seconds for a 64 ms audio clip; this practical constraint should be reflected in the abstract or conclusion to avoid a misleading impression about deployability.","section":"Section 5.5"},{"comment":"The paper does not include a data/code availability statement; given the many pipeline parameters, releasing code or a detailed configuration file would improve reproducibility.","section":"General"},{"comment":"There are minor typographical inconsistencies (e.g., 'Vocalset' vs 'VocalSet' in Figure 3, a stray period in the Table 3 caption); please proofread carefully.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The main stress-test concern lands: the approximation improvements in Tables 2–3 cannot be statistically significant under any reasonable paired test, and the abstract's wording must be softened or substantiated with proper testing. The calibration-generalization concern is also legitimate. I do not see circularity or a fundamental flaw in the FHE pipeline; this is a major revision rather than a reject because the core demonstration is new and useful if the claims are recalibrated and the missing analyses are added."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this is the first paper to compute STFT, Mel, MFCC, and gammatone features from raw audio entirely under FHE, using quantized neural network ops as the implementation layer. That result seems to hold up and is worth knowing about. The second thing: the paper's headline claim that the approximate STFT variants 'substantially reduce error rates' does not survive contact with the tables. The error counts are tiny (15 vs 12 out of 144), and a McNemar test on the most favorable pairing gives p≥0.25. The approximations may help in places, but 'significant' and 'substantially' are not earned.\n\nWhat's genuinely new: the end-to-end pipeline itself, and the error bounds for the poorman's transform and dilation in the FHE bit-budget context. The derivations in the appendix are fine. The experiments on VocalSet and OxVoc show that FHE spectrograms for STFT/Mel/Gammatone are close to clear computation (Euclidean distance ~0.13-0.18), and the classification drops are moderate (gender: 0.89 vs 0.94; vocal exercise: 0.59 vs 0.62). That is a credible proof of concept.\n\nThe soft spots, in order of importance. First, the approximation gains are not statistically established. The paper does not report any significance test, and the raw counts are too small to support the abstract's language. Second, the bit-width parameters are selected by grid search on a 10% calibration set; without code or detailed parameter files, it's hard to know if that selection generalizes. Third, the best approximation is picked post hoc among 12 variants, and the winner changes by dataset and marker; calling dilation factor 4 'best across both datasets' is not supported. Fourth, the related-work description of Thaine and Penn is inaccurate: they computed cepstral coefficients on encrypted signals, not merely encrypted precomputed MFCCs. Minor but should be fixed. Also, the 12,970 seconds for 64 ms of audio underlines that this is a feasibility demo, not a deployable system.\n\nWho should read it: anyone working on private speech analytics or FHE for audio. It deserves a serious referee and a revise in which the performance claims are narrowed and the statistical uncertainty is reported. I'd be fine citing the pipeline result, but I'd look elsewhere for evidence that approximations help.\n\nRecommendation: send it to peer review, with the expectation that the authors soften the approximation claims and release the code.","headline":"First FHE pipeline for raw-audio time-frequency features is real, but the abstract oversells the approximate STFT gains; the improvement tables are within statistical noise.","tokens_in":18533,"tokens_out":5982,"would_cite":true,"duration_ms":48527,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Fully homomorphic encryption can compute standard audio time-frequency representations on encrypted raw audio.","keywords":["fully homomorphic encryption","audio privacy","time-frequency representations","STFT","quantization","MFCC","gammatone filters","approximate signal processing"],"falsifier":"Take the exact grid-selected quantization parameters and bit widths reported for the best conventional and approximate models on VocalSet, and evaluate them on a held-out set of the same classes recorded in a different room, microphone, or signal-to-noise ratio; if the statistical-test error rate jumps well above the reported 1.9-6.5% range, or encrypted classification accuracy drops far below the clear baseline, then the calibration-to-evaluation generalization on which the results depend has failed. A sharper test of the approximation claim: measure the FHE-vs-clear distance for a signal whose energy lies mostly above 4 kHz, where the paper states quantization zeroes the spectrum; a large distance there is expected, and only matters if downstream tasks rely on that band.","tokens_in":17497,"feed_emoji":"🔐","tokens_out":6712,"duration_ms":62206,"temperature":0.7,"pith_summary":"This paper claims that standard audio front-ends—short-time Fourier transform, Mel filterbanks, Mel-frequency cepstral coefficients, and gammatone filters—can be computed entirely inside fully homomorphic encryption (FHE), directly on encrypted raw audio, without ever decrypting the signal. The authors cast these time-frequency representations as quantized neural-network layers with fixed weights, then compile them into FHE circuits under a 16-bit integer budget. They introduce several approximate STFT variants—dilation, frequency-dependent windows, poorman's projection, $\\ell^1$ energy, and cropping—that reduce the bit cost of the computation and, for the best variants, lower the error of the encrypted outputs relative to conventional STFT. On VocalSet and OxVoc, the encrypted descriptors reproduce the statistical-test structure of clear computation with mean error rates between roughly 2% and 6%, and encrypted CNNs classify gender and vocal exercises with small accuracy drops. If correct, this means a server can run useful audio analytics on encrypted speech and return results to a client without ever seeing the plaintext audio.","feed_headline":"Encrypted audio now yields spectrograms, MFCCs, and gammatone features","feed_subtitle":"A quantized pipeline computes these features from encrypted raw audio, and approximations shrink the error.","key_machinery":"The load-bearing object is the quantized approximate STFT, treated as a fixed-weight convolutional layer whose input, kernel weights, outputs, and intermediate activations each have their own bit width, constrained so that no intermediate exceeds 16 bits. The argument runs through the bit-growth formula for a dot product, which shows that sparsifying the kernel (dilation, cropping), narrowing windows (frequency-dependent windows), or replacing complex exponentials by projections onto the $L$-th roots of unity (poorman's transform) reduces the bits needed for accumulation; the freed budget is then spent on higher input/output precision, which matters more for downstream statistical tests and classifiers. The poorman's transform comes with a provable error bound $\\|X-X_L\\|\\le 2|\\sin(\\pi/(2L))|\\sqrt{\\sum_i (x(i)w(i-mh))^2}$, and the dilation error is expressed as leakage from other frequency bins. These approximations are not free: they add their own approximation error, and the paper's heuristic is that the quantization-error reduction outweighs it.","core_discovery":"The central discovery is that the computational bottleneck of FHE audio processing is quantization error, not cryptographic noise, and that this error can be steered by choosing where bits are spent. By writing the STFT as a convolution, all four representations become quantized neural-network operations, and the accumulation width grows as $\\lceil \\log_2(L(2^N-1)(2^M-1))\\rceil$ for a length-$L$ dot product with $N$- and $M$-bit operands. The paper shows that inserting zeros into the STFT kernel (dilation, cropping), adapting windows to frequency, or projecting complex exponentials onto a finite set of roots of unity (poorman's transform, $L=4$) lowers the bit demand and lets more bits go to inputs and activations, yielding encrypted outputs that are closer to the clear computation than the conventional STFT is in FHE. Empirically, the best approximations cut mean statistical-test error rates from 5.9% to 4.7% on VocalSet and from 6.5% to 1.9% on OxVoc, and encrypted CNNs classify gender near clear accuracy while vocal-exercise classification stays within a few points of clear. The paper also acknowledges a cost: quantization zeroes much of the energy above 4 kHz in the spectrograms.","pith_inferences":["The same descriptor-based pipeline could be pointed at clinical or paralinguistic biomarkers (for example, vocal jitter or shimmer-like statistics) without architectural change, since the paper already computes mean and standard-deviation statistics over Mel and gammatone energies; a direct test is whether the low error rates survive on disordered speech.","Because the poorman and dilation error bounds are explicit functions of $L$ and $d$, one could replace the grid search for bit widths with a principled, bound-driven parameter selection, treating the allowed approximation error as a budget to be split between quantization and approximation.","The reported runtime of about 12,970 seconds for 64 ms of audio suggests that the practical bottleneck has shifted from accuracy to speed; the approximate kernels' sparsity may cut the number of encrypted multiplications and thus latency, an effect the paper does not quantify.","The large intrinsic distance for MFCCs hints that cepstral features need their own approximation strategy, for example handling the log and discrete cosine transform stages separately, before FHE-MFCCs are used in applications that depend on fine cepstral structure."],"forward_implications":["A server can compute STFT, Mel filterbanks, MFCCs, and gammatone features on encrypted raw audio and return them, or their statistics, to the client, enabling private speech analytics without exposing the signal.","Approximation is not merely a lossy shortcut: in FHE, approximate STFT variants such as dilation and poorman can be more faithful to the clear computation than the conventional STFT, because they reduce quantization error.","End-to-end encrypted classification from raw audio is feasible for at least simple CNNs: gender classification stays within about 0.05 of clear accuracy, and 4-class vocal exercise classification remains well above chance.","A practical heuristic for FHE parameter selection follows from the bit-budget analysis: spend more bits on activations and outputs, fewer on convolution weights, which the post-hoc bit distributions support."],"supporting_citations":[{"why":"supplies the fast torus-based FHE scheme that the compiled circuits are built on.","marker":"[8]"},{"why":"provides the quantized neural network layer implementation used to cast audio features as quantized convolutions.","marker":"[34]"},{"why":"defines the range-based affine uniform quantization used throughout the pipeline.","marker":"[25]"},{"why":"introduces the poorman's DFT projection onto {1,-1,j,-j} that becomes the L=4 approximation.","marker":"[26]"},{"why":"shows how to formulate STFT computation as 1D convolutional neural network operations.","marker":"[7]"},{"why":"introduces dilated convolutions, the basis of the dilation approximation.","marker":"[57]"},{"why":"motivates frequency-dependent window widths via the constant-Q transform.","marker":"[5]"},{"why":"supplies the FHE compiler that enforces the 16-bit intermediate-value limit.","marker":"[58]"}],"fun_headline_variants":["Encrypted audio gets quantized STFT, MFCCs, and gammatone","Private audio features: FHE-computed spectrograms and more","Approximating STFT cuts error in homomorphically encrypted audio","FHE audio: quantization error tamed by approximate STFT","Encrypted spectrograms, MFCCs, and gammatone via FHE"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The pipeline rests on the assumption that quantization parameters (bit widths, and min/max calibration ranges) chosen on a stratified 10% calibration set remain good for the other 90% of the data; if the calibration audio is not representative of the evaluation distribution, the reported FHE-vs-clear errors are optimistic.","fun_headline_variants_meta":{"raw":{"variants":["Encrypted audio gets quantized STFT, MFCCs, and gammatone","Private audio features: FHE-computed spectrograms and more","Approximating STFT cuts error in homomorphically encrypted audio","FHE audio: quantization error tamed by approximate STFT","Encrypted spectrograms, MFCCs, and gammatone via FHE"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001223,"raw_usage":{"total_tokens":5111,"prompt_tokens":1109,"completion_tokens":4002,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":725,"completion_tokens_details":{"reasoning_tokens":3902}},"tokens_in":725,"tokens_out":4002,"duration_ms":26970,"temperature":1.0,"reasoning_tokens":3902,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:07:45.630515+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the exact grid-selected quantization parameters and bit widths reported for the best conventional and approximate models on VocalSet, and evaluate them on a held-out set of the same classes recorded in a different room, microphone, or signal-to-noise ratio; if the statistical-test error rate jumps well above the reported 1.9-6.5% range, or encrypted classification accuracy drops far below the clear baseline, then the calibration-to-evaluation generalization on which the results depend has failed. A sharper test of the approximation claim: measure the FHE-vs-clear distance for a signal whose energy lies mostly above 4 kHz, where the paper states quantization zeroes the spectrum; a large distance there is expected, and only matters if downstream tasks rely on that band.","supporting_citations":[{"cited_title":"Tfhe: Fast fully homomorphic encryption over the torus","cited_arxiv_id":null,"evidence_quote":"supplies the fast torus-based FHE scheme that the compiled circuits are built on."},{"cited_title":"Lamoureux","cited_arxiv_id":null,"evidence_quote":"introduces the poorman's DFT projection onto {1,-1,j,-j} that becomes the L=4 approximation."},{"cited_title":"nnaudio: An on-the-fly gpu audio to spectrogram conversion toolbox using 1d convolutional neural networks.IEEE Access, 8:161981–162003,","cited_arxiv_id":null,"evidence_quote":"shows how to formulate STFT computation as 1D convolutional neural network operations."},{"cited_title":"an efficient algorithm for the cal- culation of a constant q transform","cited_arxiv_id":null,"evidence_quote":"motivates frequency-dependent window widths via the constant-Q transform."},{"cited_title":"Concrete: TFHE Compiler that converts python programs into FHE equivalent, 2022.https://github.com/zama-ai/concrete","cited_arxiv_id":null,"evidence_quote":"supplies the FHE compiler that enforces the 16-bit intermediate-value limit."}],"review_version":1}