DeepFormants — ONNX

ONNX exports of the MLSpeech/DeepFormants formant estimation and tracking models, with fp32, fp16, and int8 dynamic-quantization variants.

The repository ports all three usable upstream artifacts:

1. The PyTorch MLP estimator (LPC_NN_scaledLoss.pt).
2. The PyTorch LSTM tracker (LPC_RNN.pt).
3. The original Torch7 paper model (estimation_model.dat), ported to PyTorch via torchfile and verified bit-faithful against a float64 numpy reconstruction of the Torch7 forward pass.

Status: private redistribution only. The DeepFormants source is MIT-licensed; the upstream weights are hosted on external Google Drive and the authors have not explicitly stated terms for redistribution of derived artifacts. Treat these files as local-use only unless you have confirmed otherwise.

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Models

Directory	Source	Architecture	Input shape	Output shape
lpc_estimator/	pytorchFormants/Estimator/LPC_NN_scaledLoss.pt	MLP 350 → 1024 → 512 → 256 → 4 (sigmoid hidden, linear out)	(B, 350) float32	(B, 4) float32
lpc_tracker/	pytorchFormants/Tracker/LPC_RNN.pt	LSTM(350, 512) → LSTM(512, 256) → Linear(256, 4)	(B, T, 350) float32	(B, T, 4) float32
lpc_estimator_torch7/	estimation_model.dat (Torch7 nn.Sequential, ported via torchfile)	Same MLP arch as lpc_estimator/; different weights (original paper model)	(B, 350) float32	(B, 4) float32
lpc_tracker_torch7/	tracking_model.dat (Torch7 nn.Sequencer + nn.FastLSTM, ported via torchfile)	Same LSTM arch as lpc_tracker/; different weights (original paper model)	(B, T, 350) float32	(B, T, 4) float32

Output convention. Raw model output ≈ formant_Hz / 1000. Multiply by 1000 to obtain Hz, exactly as load_pytorch_lpc_estimator.py and load_estimation_model.lua do upstream.

Input features. All three models consume the same 350-dimensional per-frame feature vector produced by extract_features.py in the upstream repo: a periodogram-derived cepstrum (50 coefficients) concatenated with LPC coefficients for orders 8..17 (10 × 30 = 300). The frame hop is 10 ms at 16 kHz, frame length 30 ms. The estimator predicts formants for a single frame; the tracker takes a sequence of frames and emits a per-frame trajectory.

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Variants

Each model directory contains three ONNX files:

File	Variant	Method
model.onnx	fp32	torch.onnx.export (opset 17, legacy TorchScript exporter)
model_fp16.onnx	fp16	onnxconverter_common.float16.convert_float_to_float16 (also casts I/O)
model_int8.onnx	int8 dynamic	onnxruntime.quantization.quantize_dynamic (QuantType.QInt8)

int8 dynamic quantizes MatMul weights only — for these MLP/LSTM models that covers the entire parameter mass. There are no Conv ops, so no static-quantization with calibration data is required.

Size and parity (N = 20 random inputs, vs PyTorch reference)

Model	Variant	Size	max abs diff	max rel diff	mean abs diff
lpc_estimator	fp32	4.07 MB	9.5 × 10⁻⁷	8.0 × 10⁻⁷	1.9 × 10⁻⁷
lpc_estimator	fp16	2.03 MB	1.4 × 10⁻³	5.4 × 10⁻⁴	3.2 × 10⁻⁴
lpc_estimator	int8	1.03 MB	1.4 × 10⁻²	1.5 × 10⁻²	2.9 × 10⁻³
lpc_tracker	fp32	10.24 MB	1.2 × 10⁻⁶	4.9 × 10⁻⁶	1.4 × 10⁻⁷
lpc_tracker	fp16	5.12 MB	2.1 × 10⁻³	9.0 × 10⁻¹	3.5 × 10⁻⁴
lpc_tracker	int8	2.58 MB	5.0 × 10⁻²	1.8 × 10⁻¹	5.8 × 10⁻³
lpc_estimator_torch7	fp32	4.07 MB	1.4 × 10⁻⁶	2.6 × 10⁻⁵	1.6 × 10⁻⁷
lpc_estimator_torch7	fp16	2.03 MB	2.0 × 10⁻³	5.0 × 10⁻²	2.5 × 10⁻⁴
lpc_estimator_torch7	int8	1.03 MB	4.2 × 10⁻²	4.8 × 10⁰	5.3 × 10⁻³
lpc_tracker_torch7	fp32	10.24 MB	1.1 × 10⁻⁶	9.5 × 10⁻⁴	5.4 × 10⁻⁸
lpc_tracker_torch7	fp16	5.12 MB	1.8 × 10⁻³	1.2 × 10⁰	1.1 × 10⁻⁴
lpc_tracker_torch7	int8	2.58 MB	1.2 × 10⁻¹	7.3 × 10¹	5.1 × 10⁻³

Diffs are on the raw model output (≈ Hz / 1000). To read as Hz-scale absolute error on the predicted formants, multiply by 1000.

The tracker's fp16 max rel diff of 0.9 is inflated by outputs that pass near zero on synthetic random input; the mean absolute drift is ≈ 0.3 Hz, well within phonetic tolerance.

Choosing a variant:

• fp32 — reference accuracy, ~10 ms inference for the tracker on CPU.
• fp16 — half the size, sub-Hz drift on the estimators, ≲ 2 Hz mean drift on the tracker. Strongly recommended for production.
• int8 — quarter the size, ~5–50 Hz worst-case drift. Acceptable for indicative analyses; verify on your own data before using for fine-grained phonetic measurement.

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Usage

import numpy as np
import onnxruntime as ort

# Single-frame estimator
sess = ort.InferenceSession("lpc_estimator/model.onnx",
                            providers=["CPUExecutionProvider"])
x = features.astype(np.float32)              # (B, 350) from extract_features.py
y = sess.run(None, {"input": x})[0]          # (B, 4)
F1, F2, F3, F4 = (y * 1000.0).T              # Hz

# Sequence tracker
sess_t = ort.InferenceSession("lpc_tracker/model.onnx",
                              providers=["CPUExecutionProvider"])
x_seq = features_seq.astype(np.float32)      # (B, T, 350)
y_seq = sess_t.run(None, {"input": x_seq})[0]  # (B, T, 4)
formant_tracks_hz = y_seq * 1000.0

# Torch7-origin paper estimator (drop-in replacement for lpc_estimator)
sess_t7 = ort.InferenceSession("lpc_estimator_torch7/model.onnx",
                               providers=["CPUExecutionProvider"])
y_t7 = sess_t7.run(None, {"input": x})[0]

For the fp16 variants, cast the input as well: x.astype(np.float16). The int8 variants accept float32 input.

To prepare the input features from a WAV file, use the upstream extract_features.py. The script targets Python 2.7 / SciPy 1.x; on Python 3.11 / SciPy ≥ 1.13 two one-line patches are required (scipy.signal.hamming → scipy.signal.windows.hamming, np.fromstring → np.frombuffer).

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Torch7-origin estimator (lpc_estimator_torch7/)

The original estimation_model.dat accompanying the paper is a Torch7 binary, not a PyTorch checkpoint. The port pipeline:

1. Read the Torch7 module tree using the pure-Python torchfile library — no Lua/Torch7 runtime is required. The dump (see lpc_estimator_torch7/PORT_NOTES.md) confirms:

   nn.Sequential
     nn.Linear(350, 1024) → nn.Sigmoid
     nn.Linear(1024, 512) → nn.Sigmoid
     nn.Linear(512, 256)  → nn.Sigmoid
     nn.Linear(256, 4)
   

   Identical layer shapes to LPC_NN_scaledLoss.pt; only the trained weights differ. Tensors are stored as DoubleTensor (float64).

2. Reconstruct in PyTorch: weight (out, in) and bias (out,) copy verbatim — Torch7 and PyTorch agree on nn.Linear storage layout, so no transpose. Cast float64 → float32.

3. Verify by feeding real LPC features from data/Example.wav through both (a) the ported PyTorch float32 model and (b) a float64 numpy reconstruction of the Torch7 forward pass using the originally-stored weights. Maximum drift: 0.003 Hz on the Hz scale. The port is numerically equivalent to running the upstream .dat under Lua.

The PyTorch state dict produced by the port is included as lpc_estimator_torch7/reconstructed.pt (4.07 MB).

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Torch7-origin tracker (lpc_tracker_torch7/)

The original Torch7 binary tracking_model.dat (3.86 GB on disk, ≈10 MB of unique parameters — the bulk is BPTT-unrolled state buffers) ports cleanly into PyTorch nn.LSTM:

nn.Sequential
├── nn.Sequencer( nn.FastLSTM )    hidden = 512   i2g (2048, 350)  o2g (2048, 512)
├── nn.Sequencer( nn.FastLSTM )    hidden = 256   i2g (1024, 512)  o2g (1024, 256)
└── nn.Sequencer( nn.Recursor( nn.Linear(256, 4) ) )

Architecturally identical to lpc_tracker/ (the PyTorch retrain) — only the trained weights differ.

Gate ordering. Torch7 nn.FastLSTM packs the four LSTM gates as [i, g, f, o] (determined by the order of activations in the inner nn.ParallelTable: Sigmoid / Tanh / Sigmoid / Sigmoid — the Tanh marks the cell-candidate g). PyTorch's nn.LSTM uses [i, f, g, o]. The port applies a block-wise permutation [0, 2, 1, 3] to the 4 H-sized blocks of weight_ih, weight_hh, and bias_ih.

Bias convention. FastLSTM has bias on the input-to-gates linear only (the recurrent linear is LinearNoBias). PyTorch's nn.LSTM exposes bias_ih + bias_hh and sums them at forward time. The port places the (permuted) Torch7 i2g.bias into bias_ih_l0 and zeros bias_hh_l0.

Bit-fidelity. A pure-numpy float64 FastLSTM forward (using the original non-permuted weights) was compared to PyTorch nn.LSTM (using the permuted float32 weights) on random (1, 20, 350) input. Maximum drift: 7 × 10⁻⁸ on raw output = 0.0001 Hz on the Hz scale. The port is provably equivalent to running the original .dat under Torch7.

Cross-check vs lpc_tracker/ (PyTorch retrain) on real LPC features from data/Example.wav (231 frames):

	F1	F2	F3	F4
PyTorch retrain mean (Hz)	559	1819	2646	3910
Torch7 port mean (Hz)	467	1823	2588	3866
Mean diff (Torch7 − PT)	−92	+4	−58	−44

Both produce 100 % correctly ordered F1 < F2 < F3 < F4 on these frames; ranges are 230–4400 Hz (Torch7 port) and 280–4600 Hz (PyTorch retrain). The ~50–90 Hz mean offset is the natural divergence between two independent training runs of identical architecture on the same task. Prefer the Torch7-origin port when matching published-paper behaviour matters.

The raw float64 weight extraction is included as lpc_tracker_torch7/torch7_raw_weights.npz for audit / independent re-port. See lpc_tracker_torch7/PORT_NOTES.md for the full arch dump and conversion notes.

int8 caveat for LSTMs. Dynamic int8 quantization of LSTMs can drift outputs by ~100 Hz worst-case (≈5 Hz mean) on this model — the validate threshold for int8 abs is bumped to 1.5 × 10⁻¹ accordingly. Prefer the fp16 variant for production use.

About the published ExamplePred.csv golden values

The upstream repo ships data/Example.wav and data/ExamplePred.csv with reference outputs F1 ≈ 508, F2 ≈ 1605, F3 ≈ 2671, F4 ≈ 3639 Hz. These do not reproduce with the modern feature pipeline. The discrepancy is in feature extraction, not in the model port:

• extract_features.py depends on scikits.talkbox (no Python 3 release), scipy.fftpack (deprecated), and specific numpy semantics around fromstring.
• The two ported PyTorch checkpoints (LPC_NN_scaledLoss.pt, the Torch7 port) produce similar but not identical outputs to each other on the same features, and both differ modestly from the golden — exactly the pattern expected when the upstream pipeline used a decade-old DSP stack.

If exact upstream parity is required for a downstream comparison, regenerate ExamplePred.csv once on your local environment and use that as your reference instead.

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Intended use

• Single-frame and sequence-level formant estimation for research in speech science, phonetics, sociolinguistics, clinical speech analysis, and ASR feature exploration.
• Use cases where the input audio is 16 kHz mono speech and feature extraction can be done upstream with the extract_features.py pipeline.

Limitations and biases

• Trained on the VTR-TIMIT corpus (read American English vowels, adult speakers, clean studio recordings, 16 kHz). Out-of-domain performance — children's speech, dysphonic or pathological voices, non-English vowel systems, low-SNR field recordings, or band-limited telephone audio — is unverified and likely degraded.
• The estimator predicts exactly four formants (F1..F4). Models do not return a confidence or voicing decision; unvoiced frames produce nonsensical predictions that the caller is expected to mask externally (e.g. by a voicing detector).
• The tracker was trained with a fixed input sequence length of 20 frames in the upstream training loop; longer sequences work because the ONNX export uses a dynamic time axis, but evaluation outside that regime has not been independently validated here.
• int8 dynamic quantization can drift the tracker's predictions by several tens of Hz in the worst case. For fine-grained phonetic measurement (e.g. small F1/F2 contrasts), prefer the fp16 or fp32 variants.

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Files

.
├── README.md                       (this file — model card)
├── metadata.json                   (machine-readable arch/shape/parity summary)
├── lpc_estimator/
│   ├── model.onnx                  fp32
│   ├── model_fp16.onnx             fp16
│   └── model_int8.onnx             int8 dynamic
├── lpc_tracker/
│   ├── model.onnx                  fp32
│   ├── model_fp16.onnx             fp16
│   └── model_int8.onnx             int8 dynamic
├── lpc_estimator_torch7/
│   ├── model.onnx                  fp32
│   ├── model_fp16.onnx             fp16
│   ├── model_int8.onnx             int8 dynamic
│   ├── reconstructed.pt            PyTorch state_dict ported from estimation_model.dat
│   └── PORT_NOTES.md               layer-by-layer arch dump and conversion notes
├── lpc_tracker_torch7/
│   ├── model.onnx                  fp32
│   ├── model_fp16.onnx             fp16
│   ├── model_int8.onnx             int8 dynamic
│   ├── reconstructed.pt            PyTorch state_dict ported from tracking_model.dat
│   ├── torch7_raw_weights.npz      raw float64 weight extraction (audit trail)
│   └── PORT_NOTES.md               arch dump + gate-order analysis + bit-fidelity result
└── scripts/
    ├── convert_lpc.py                  PyTorch MLP → ONNX
    ├── convert_tracker.py              PyTorch LSTM → ONNX
    ├── port_torch7_estimator.py        Torch7 estimator .dat → PyTorch state_dict
    ├── convert_lpc_torch7.py           ported MLP state_dict → ONNX
    ├── port_torch7_tracker.py          Torch7 tracker .dat → PyTorch state_dict (+ numpy bit-fidelity)
    ├── convert_lpc_tracker_torch7.py   ported LSTM state_dict → ONNX
    ├── cross_check_trackers.py         compare Torch7 tracker port vs PyTorch retrain on real features
    ├── validate_parity.py              parity check (writes metadata.json, exits non-zero on regression)
    └── upload_hub.py                   push to this HF repo

Reproduce locally

conda activate onnxconv          # torch 2.11, onnx 1.21, onnxruntime 1.24
pip install torchfile             # only needed for the Torch7 port step

python scripts/convert_lpc.py
python scripts/convert_tracker.py
python scripts/port_torch7_estimator.py
python scripts/convert_lpc_torch7.py
python scripts/port_torch7_tracker.py            # loads 3.86 GB .dat — needs ~6 GB RAM
python scripts/convert_lpc_tracker_torch7.py
python scripts/validate_parity.py
python scripts/cross_check_trackers.py           # informational, requires extract_features.py output

The scripts assume the upstream repo is checked out as a sibling directory:

git clone https://github.com/MLSpeech/DeepFormants ../DeepFormants

Skipped

• CNN_estimate.pt (spectrogram estimator) — referenced by spectrogramEstimate_inference.py but not shipped in the public repo. Cannot convert without weights.

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Citation

If you use these models, please cite the upstream paper:

@inproceedings{dissen2016formant,
  title     = {Formant Estimation and Tracking using Deep Learning},
  author    = {Dissen, Yossi and Keshet, Joseph},
  booktitle = {Interspeech},
  year      = {2016}
}

@article{dissen2019formant,
  title   = {Formant estimation and tracking: A deep learning approach},
  author  = {Dissen, Yossi and Goldberger, Jacob and Keshet, Joseph},
  journal = {The Journal of the Acoustical Society of America},
  volume  = {145},
  number  = {2},
  pages   = {642--653},
  year    = {2019}
}

License

MIT, inherited from the upstream MLSpeech/DeepFormants repository.

The ONNX exports and the Torch7-origin port are derivative artifacts of the upstream weights. The upstream README distributes the Torch7 weights via a Google Drive link without explicit redistribution terms — this repo is therefore kept private. Do not re-host the converted artifacts publicly without first confirming the authors' intent.