Bolt: Optimized Mel Filterbank Matrix Multiplication

[ysdede]

What:
Precomputed the start and end indices (_fbStart, _fbEnd) for each row in the Mel filterbank matrix in the MelSpectrogram constructor. Updated computeRawMel to use these bounds in the inner loop instead of iterating over all frequency bins.

Why:
The Mel filterbank is a sparse, triangular matrix. Iterating over all 257 frequency bins (for 512 FFT) for every Mel bin involves many multiplications by zero. By skipping these zeros, we significantly reduce the number of floating-point operations.

Impact:

• Processing 60s audio: 834ms -> 232ms (~3.6x faster)
• Realtime factor: 71.9x -> 258.5x

Measurement:
Ran bench.js (created temporarily) which processes 60s of random noise 10 times. Verified correctness with existing tests, including ONNX numerical cross-validation.

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PR created automatically by Jules for task 16003308894749395639 started by @ysdede

Summary by CodeRabbit

• Documentation

• Added documentation on Mel filterbank sparsity optimization strategies and performance improvements in audio processing.

• Refactor

• Optimized Mel spectrogram computation by leveraging sparsity patterns in filterbank matrices, achieving approximately 3.6x performance improvement for audio processing without API changes.

[coderabbitai]

📝 Walkthrough

Walkthrough

Adds documentation and implements a sparsity optimization for Mel filterbank computation. The optimization precomputes the non-zero range boundaries for each Mel filter during initialization, then constrains the inner loop during computation to skip zero coefficients, achieving approximately 3.6x performance improvement for audio processing.

Changes

Cohort / File(s)	Summary
Documentation .jules/bolt.md	New Markdown document explaining the Mel filterbank sparsity optimization strategy and its performance benefits (~3.6x speedup).
Mel Filterbank Optimization src/mel.js	Introduced precomputed _fbStart and _fbEnd Int32Array fields to store non-zero coefficient ranges for each Mel bin; populated during initialization by scanning the filterbank; modified the dot-product loop in computeRawMel to use bounded iteration instead of scanning all frequency bins.

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~20 minutes

Poem

🐰 A sparse trick, so clever and clean,
Mel filters now faster than ever seen,
We skip what is zero with mathematical grace,
And race through the spectrum at triple the pace! ✨

🚥 Pre-merge checks | ✅ 4

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately describes the main change: optimizing Mel filterbank matrix multiplication through sparse matrix techniques (precomputing non-zero bounds).
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Merge Conflict Detection	✅ Passed	✅ No merge conflicts detected when merging into main

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✨ Finishing touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch bolt-mel-filterbank-optimization-16003308894749395639

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No actionable comments were generated in the recent review. 🎉

🧹 Recent nitpick comments

src/mel.js (1)

352-357: Hoist _fbStart / _fbEnd out of the hot loop for consistency.

Every other instance property used in the per-frame loop is destructured once on lines 344-345. this._fbStart and this._fbEnd are accessed inside the nFrames × nMels inner loop, adding repeated property lookups.

♻️ Suggested change

-    const { hannWindow: window, melFilterbank: fb, nMels, twiddles: tw, nFft, nFreqBins, hopLength, logZeroGuard } = this;
+    const { hannWindow: window, melFilterbank: fb, nMels, twiddles: tw, nFft, nFreqBins, hopLength, logZeroGuard, _fbStart: fbStart, _fbEnd: fbEnd } = this;
 
     for (let t = 0; t < nFrames; t++) {
       ...
       for (let m = 0; m < nMels; m++) {
         let melVal = 0;
         const fbOff = m * nFreqBins;
-        const start = this._fbStart[m];
-        const end = this._fbEnd[m];
+        const start = fbStart[m];
+        const end = fbEnd[m];
         for (let k = start; k < end; k++) melVal += powerBuf[k] * fb[fbOff + k];

.jules/bolt.md (1)

1-3: Documentation accurately captures the optimization rationale.

Minor nit: the date header says "2024-05-22" while this PR is from February 2026. Worth correcting if this serves as a changelog.

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