Quantizer Redundancy and Exact Index Recoding in a Frozen Neural Audio Codec

Youssef Hemimy

cs.SDOct 14, 2026

Quantizer Redundancy and Exact Index Recoding in a Frozen Neural Audio Codec

Authors: Youssef Hemimy

Organizations: St. Thomas University, Miami Gardens, Florida, USA

Abstract

Residual scalar quantization can produce highly dependent indices when successive stages reuse identical, unscaled grids. This case study examines that behavior in a frozen neural audio codec and develops an exact recoding procedure that reduces storage while preserving its decoder inputs. Analysis of the repeated-grid recurrence identifies predictable stage sequences; finite-precision checks motivate preserving every original index through explicit exception records. The model weights and reconstruction graph remain fixed. On the studied 62- and 512-file cohorts, a predictor, adaptive coding and explicit file selection reduce complete stored bytes. The final 512-file rate is 129.591 kbps including headers, 25.943% below an original-index XZ control. Original recorded CPU runs establish bitwise latent and waveform preservation; independent readers verify exact index and metadata recovery in subsequent saved-stream experiments. Later coding choices use previously studied cohorts, and fresh encoding requires generating three alternatives. The engineering result is implementation-specific storage reduction with exact index recovery; the underlying lossy reconstruction quality remains unchanged.

Figures & tables

Panel of Figure 1 — Figure 1: Frozen reconstruction system with the final three-mode storage path. Gray boxes change index storage; saved grids and neural parameters remain unchanged. Independent readers verify restored indices and metadata for the final formats. Bitwise latent and waveform comparisons belong to the original CPU runs. No source audio or dataset-derived imagery is shown.

$q$	$L$	$q^{L}$	$K$	$K_{\mathrm{n}}$
4	4	256	31	7
5	4	625	17	5
8	4	4096	105	15
5	6	15625	25	5
8	6	262144	211	15

Table 1: Exhaustive float32 code-decoder classes.

K

counts all tuple outputs;

K_{\mathrm{n}}

counts outputs of the current predictor’s normal family. The latter contains

q

tuples for odd

q

and

2q

for even

q

Preserved object	Evidence
Indices and decoder metadata	Original versus unpacked values; independent saved-stream readers, including later formats.
Latent bit patterns	Forward versus code-decoded, and original-code versus unpacked-code decoding, in the original CPU runs.
Waveform bit patterns	The same two comparisons in the original CPU runs.

Table 2: Preservation evidence and its execution scope. The original inference runs cover both cohorts (62 and 512 files).

Representation	62 files	512 files
	Rate (kbps)
Original	915.523	915.751
Predictive	245.587	245.666
Original + zlib	240.692	218.670
Predictive + zlib	154.057	139.923

Table 3: Measured rates, including all framing and compressor overhead. “Original” stores every stage index in fixed-width scalar fields.

Representation	62 files	512 files
	Rate (kbps)
Original + XZ	193.606	174.988
Predictive + zlib	154.057	139.923
First-order adaptive	148.610	137.184
Two-mode selector	146.642	132.557
Second-order adaptive	143.379	131.929

Table 4: Complete compressed-file rates. XZ is the original-index control selected in the predefined 14-candidate comparison. Subsequent selectors and the second-order context are descriptive follow-ups on these known cohorts.

Candidate	Encode (s)	Decode (s)
Predictive + zlib	7.949	6.524
First-order adaptive	10.348	10.333
Second-order adaptive	10.159	9.967

Table 5: Warm candidate totals over 512 files. The first two rows share the original comparison run; second-order was measured separately.

Metric (dB)	Mean	Q25	Median	Q75
SI-SDR	4.332	$-5.055$	6.553	14.278
HF-SI-SDR-6k	10.090	9.233	12.053	13.942

Table 6: Additional screened cohort: objective metrics (512 files). Quartiles use linear interpolation. All scores are finite; silent references remain included.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Offset	Bytes	Field and required value
0	8	ASCII magic EMCRCODE
8	1	Version: 1
9	1	Mode: 0 original, 1 predictive
10	2	Reserved flags: 0
12	4	Sample rate: 44100
16	4	LF stages, HF stages, groups, dimensions/group: 4, 6, 4, 32

Appendix

Table 1: Version-1 inner header, in transmission order. Integers are unsigned big-endian. Offsets count bytes from zero; the complete header occupies 120 bytes.

Configuration	SI-SDR (dB)	HF-SI-SDR-6k (dB)	Transient F1
MRHF@595k	8.47 [6.37, 10.68]; 7.60 [2.42, 13.92]	11.64 [10.52, 12.57]; 12.84 [11.06, 14.34]	0.869 [0.807, 0.923]; 1.000 [0.826, 1.000]
DAC	9.75 [7.37, 12.00]; 10.85 [5.11, 14.26]	$-30.44$ [ $-33.61$ , $-27.35$ ]; $-28.15$ [ $-38.06$ , $-21.72$ ]	0.863 [0.795, 0.919]; 1.000 [0.859, 1.000]
MRHF@140k	6.73 [4.56, 8.91]; 5.99 [1.81, 11.65]	8.11 [6.97, 9.17]; 9.31 [7.46, 10.67]	0.825 [0.757, 0.890]; 0.977 [0.756, 1.000]
SinglePath@100k	$-3.77$ [ $-8.17$ , 0.36]; 1.49 [ $-12.59$ , 6.21]	$-38.83$ [ $-41.70$ , $-35.81$ ]; $-37.81$ [ $-46.38$ , $-29.91$ ]	0.820 [0.752, 0.883]; 0.971 [0.701, 1.000]
RVQ@100k	$-4.21$ [ $-8.29$ , $-0.23$ ]; 1.13 [ $-10.35$ , 5.05]	$-35.48$ [ $-38.28$ , $-32.90$ ]; $-35.34$ [ $-41.32$ , $-27.66$ ]	0.803 [0.729, 0.870]; 0.969 [0.671, 1.000]
NoHFLoss@100k	3.26 [ $-0.04$ , 6.50]; 6.04 [ $-2.16$ , 10.73]	$-38.16$ [ $-41.10$ , $-35.27$ ]; $-37.55$ [ $-43.95$ , $-29.69$ ]	0.821 [0.748, 0.888]; 0.974 [0.761, 1.000]

Appendix

Table 2: Aggregate objective results for the preserved 62-file cohort. Format: mean [95% conditional file-bootstrap interval]; median [IQR].

Configuration	SI-SDR (dB)	HF-SI-SDR-6k (dB)	Transient F1
MRHF@595k	4.01 [3.46, 4.54]; 4.64 [ $-3.27$ , 12.49]	12.12 [11.92, 12.30]; 13.27 [11.17, 14.37]	0.940 [0.935, 0.945]; 0.988 [0.938, 1.000]
SinglePath@100k	$-11.23$ [ $-12.10$ , $-10.26$ ]; $-3.31$ [ $-26.15$ , 5.22]	$-44.71$ [ $-45.18$ , $-44.23$ ]; $-43.74$ [ $-51.37$ , $-36.94$ ]	0.901 [0.894, 0.908]; 0.968 [0.878, 1.000]
RVQ@100k	$-10.79$ [ $-11.64$ , $-9.93$ ]; $-3.12$ [ $-25.33$ , 4.96]	$-38.38$ [ $-38.79$ , $-37.98$ ]; $-37.15$ [ $-43.35$ , $-32.26$ ]	0.901 [0.894, 0.907]; 0.967 [0.875, 1.000]
NoHFLoss@100k	$-3.52$ [ $-4.30$ , $-2.73$ ]; 2.01 [ $-14.94$ , 9.82]	$-39.00$ [ $-39.45$ , $-38.53$ ]; $-38.03$ [ $-45.30$ , $-31.88$ ]	0.920 [0.914, 0.926]; 0.976 [0.906, 1.000]

Appendix

Table 3: Aggregate objective results for the preserved 2,144-file cohort. Format follows Table 2 .

Metric	Mean	Median	Top-1% sum share
Spectral convergence	68,139	0.147	99.9998%
HF spectral convergence	6,627	0.146	99.9974%
HF energy preservation	93,180	1.013	99.9989%

Appendix

Table 4: OOD denominator pathology for MRHF@595k; aggregate metric values only.

$q$	$L$	Ideal unrestricted sums	Float32 classes	Original bits	Class bits
4	4	13	31	8	5
5	4	17	17	12	5
8	4	29	105	12	7
5	6	25	25	18	5
8	6	43	211	18	8

Appendix

Table 5: Finite arithmetic counts and standalone field widths. The ideal sum column permits arbitrary tuples; it is different from the smaller alphabet of the bounded exact-real recurrence.

Candidate	Bytes	Rate (kbps)
Adaptive predictive	5344543	148.610
Predictive + XZ	5404552	150.278
Predictive + zlib	5540433	154.057
Separated sparse list + XZ	5594104	155.549
Separated bitmap + XZ	5601264	155.748
Predictive + Zstandard	5643730	156.929

Appendix

Table 6: Complete development results (62 files, 287.709 s). Every candidate recovers all indices and metadata exactly. Rates include all transmitted bytes.

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Oct 3, 2026J/K move · Enter open · S save

GS-Codec: A Gaussian-Splatting Bottleneck for Neural Audio Coding

Ron Aluf, Alon Canfi, Eliya Nachmani

School of Electrical and Computer Engineering Ben-Gurion University of the Negev

Neural Audio Codecs

Open paper AskPDF arXiv

Neural audio codecs compress waveforms into compact discrete tokens that underpin speech language models, real-time communication, and large-scale audio storage. Almost every dominant design, including residual vector quantization, finite scalar quantization, and single-codebook variants, follows the VQ-VAE template by partitioning the encoder latent through a learned codebook or a fixed scalar grid. We ask whether this partition is necessary. We introduce GS-Codec, a neural speech codec whose bottleneck is a parametric signal decomposition rather than a quantizer. We adapt Gaussian splatting from 3D scene reconstruction to one-dimensional latents. An inner optimization loop fits each encoder segment as a weighted sum of 1D Gaussian primitives. The decoder then reconstructs the waveform from the rendered sum. To avoid the cost of this iterative inner loop at inference time, we additionally train a lightweight GS Predictor Net that regresses the primitive parameters in a single forward pass. The encoder and decoder are trained end-to-end through the inner loop, with no quantizer anywhere in the training pipeline: the bottleneck is the decomposition itself, and scalar quantization is applied only post-training to the fitted parameters. Rather than relying on discrete codebook stages for bitrate control, our representation exposes a fine-grained rate-quality tradeoff: a single trained checkpoint supports post-training bitrate control by varying the number of primitives and the per-parameter bit depth, with no retraining required. GS-Codec matches or exceeds well-established open-source codecs such as EnCodec and DAC on speaker similarity (SIM), intelligibility (STOI), and perceptual quality (UTMOS) at comparable bitrates, while achieving comparable semantic performance (WER). Code and audio samples are available at https://ronaluf.github.io/gs-codec/

Abstract

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