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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta http-equiv="X-UA-Compatible" content="ie=edge">
<title>Toward a Sparse Interpretable Audio Codec</title>
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<div class="page-wrapper">
<h1>Toward a Sparse Interpretable Audio Codec</h1>
<details>
<summary>
<caption>Table of Contents</caption>
</summary>
<ul>
<li><a href="#Introduction">Introduction</h1></a></li>
<li><a href="#Previous Work">Previous Work</h1></a></li>
<li><a href="#Model">Model</h1></a><ul>
<li><a href="#Encoder">Encoder</h2></a></li>
<li><a href="#Decoder">Decoder</h2></a></li>
</ul>
</li>
<li><a href="#Training Procedure">Training Procedure</h1></a></li>
<li><a href="#Streaming Algorithm">Streaming Algorithm</h1></a></li>
<li><a href="#Future Work">Future Work</h1></a><ul>
<li><a href="#Better Perceptual Audio Losses">Better Perceptual Audio Losses</h2></a></li>
<li><a href="#Model Size, Training Time and Dataset">Model Size, Training Time and Dataset</h2></a></li>
<li><a href="#Different Event Generator Variants">Different Event Generator Variants</h2></a></li>
</ul>
</li>
<li><a href="#Cite this Article">Cite this Article</h1></a></li>
<li><a href="#Streaming Algorithm for Arbitrary-Length Audio Segments">Streaming Algorithm for Arbitrary-Length Audio Segments</h1></a><ul>
<li><a href="#Original (Streaming)">Original (Streaming)</h2></a></li>
<li><a href="#Reconstruction (Streaming)">Reconstruction (Streaming)</h2></a></li>
</ul>
</li>
<li><a href="#Audio Examples">Audio Examples</h1></a><ul>
<li><a href="#Example 1">Example 1</h2></a></li>
<li><a href="#Example 2">Example 2</h2></a></li>
<li><a href="#Example 3">Example 3</h2></a></li>
<li><a href="#Example 4">Example 4</h2></a></li>
<li><a href="#Example 5">Example 5</h2></a></li>
</ul>
</li>
<li><a href="#Notes">Notes</h1></a></li>
</ul>
</details>
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duration="5.944308390022676"
width="600"
height="300"
></audio-timeline>
<a id="Introduction"></a>
<h1>Introduction</h1>
<p>Most widely-used modern audio codecs, such as Ogg Vorbis and MP3, as well as more recent "neural" codecs like
<a href="https://arxiv.org/abs/2210.13438">Meta's Encodec</a> or <a href="https://arxiv.org/abs/2306.06546">Descript's</a> are based on
block-coding; audio is divided into overlapping, fixed-size "frames" which are then compressed. While they produce
excellent reproduction quality and can be used for downstream tasks such as text-to-audio, they do not produce an
intuitive, directly-interpretable representation.</p>
<p>In this work, we introduce a proof-of-concept audio encoder that seeks to encode audio as a sparse set of events and
their times-of-occurrence. Rudimentary physics-based assumptions are used to model attack and the physical resonance
of both the instrument being played and the room in which a performance occurs, hopefully encouraging a sparse,
parsimonious, and easy-to-interpret representation.</p>
<p>Early speech results from the LJ-Speech dataset can be found <a href="https://blog.cochlea.xyz/sparse-interpretable-audio-codec-paper-speech.html">here</a>.</p>
<a id="Previous Work"></a>
<h1>Previous Work</h1>
<p>This work takes inspiration from symbolic approaches, such as MIDI, iterative decomposition methods like matching pursuit
and granular synthesis, which represents audio as a sparse set of "grains" or simple audio atoms.</p>
<a id="Model"></a>
<h1>Model</h1>
<a id="Encoder"></a>
<h2>Encoder</h2>
<p>The encoder iteratively removes energy from the input spectrogram, producing an event vector and one-hot/dirac impulse
representing the time of occurrence.</p>
<p><img alt="Encoder Diagram" src="https://zounds-blog-media.s3.us-east-1.amazonaws.com/audio-codec.drawio.svg" /></p>
<a id="Decoder"></a>
<h2>Decoder</h2>
<p>The decoder uses the 32-dimensional event vector to choose an attack envelope, evolving resonance, and room impulse
response to model the acoustic event, and then "schedules" it by convolving the event with the one-hot/direc impulse. Audio
is not produced using typical upsampling convolutions, avoiding artifacts and producing more natural-sounding events.</p>
<a id="Training Procedure"></a>
<h1>Training Procedure</h1>
<p>We train on the <a href="https://zenodo.org/records/5120004#.Yhxr0-jMJBA">MusicNet dataset</a> dataset) for ~76 hours, selecting
random ~6 second audio segments sampled at 22050hz (mono) with a batch-size of 2. The model takes the following steps
for 32 iterations on each training sample:</p>
<ol>
<li>The encoder analyzes the STFT spectrogram of the signal, producing a single 32-dimensional event vector and a one-hot vector representing time-of-occurrence</li>
<li>The decoder produces "raw" audio samples of the acoustic event</li>
<li>an STFT spectrogram of the acoustic event is produced and subtracted from the input spectrogram</li>
<li>The encoder analyzes the residual and the process is repeated</li>
</ol>
<p>The model is trained to maximize the amount of energy removed from the original signal at each step, and to minimize
an adversarial loss, produced by a small, convolutional down-sampling discriminator which is trained in parallel,
analyzing both the real and reproduced signals in the STFT spectrogram domain. Half of the generated events are
masked/removed when analyzed by the discriminator, encouraging each event vector to stand on its own as a realistic
event.</p>
<p>All training and model code can be
<a href="https://github.com/JohnVinyard/matching-pursuit/blob/main/iterativedecomposition.py">found here</a>.</p>
<a id="Streaming Algorithm"></a>
<h1>Streaming Algorithm</h1>
<p>When encoding, the entire ~6-second spectrogram is analyzed, but its second-half is masked when choosing the next event.
In this way, the model can slide along overlapping sections of audio and encode segments of arbitrary durations.</p>
<a id="Future Work"></a>
<h1>Future Work</h1>
<a id="Better Perceptual Audio Losses"></a>
<h2>Better Perceptual Audio Losses</h2>
<p>Recent experiments use a greedy, per-event loss which maximizes the energy removed from the signal at each step, as well
as a learned, adversarial loss. Reconstruction quality will likely benefit from a more perceptually-aligned loss and a
larger, more diverse dataset.</p>
<a id="Model Size, Training Time and Dataset"></a>
<h2>Model Size, Training Time and Dataset</h2>
<p>Firstly, this model is relatively small, weighing in at ~14M parameters (~80 MB on disk) and has only been trained for
around 76 hours, so it seems there is a lot of space to increase the model size, dataset size and training time to
further improve. The reconstruction quality of the examples on this page is not amazing, certainly not good enough
even for a lossy audio codec, but the structure the model extracts seems like it could be used for many interesting
applications, and future work will improve perceptual audio quality.</p>
<a id="Different Event Generator Variants"></a>
<h2>Different Event Generator Variants</h2>
<p>The decoder side of the model is very interesting, and all sorts of physical modelling-like approaches could yield
better, more realistic, and sparser renderings of the audio.</p>
<p>For example, <a href="https://blog.cochlea.xyz/rnn.html">simple RNNs</a> might serve as a natural alternative to the encoder used
for the sound reproductions in this article.</p>
<a id="Cite this Article"></a>
<h1>Cite this Article</h1>
<p>If you'd like to cite this article, you can use the following <a href="https://bibtex.org/">BibTeX block</a>.</p>
<citation-block
tag="johnvinyarditerativedecompositionv3"
author="Vinyard, John"
url="https://blog.cochlea.xyz/sparse-interpretable-audio-codec-paper.html"
header="Toward a Sparse Interpretable Audio Codec"
year="2025">
</citation-block>
<a id="Streaming Algorithm for Arbitrary-Length Audio Segments"></a>
<h1>Streaming Algorithm for Arbitrary-Length Audio Segments</h1>
<p>In this latest iteration of the work, we introduce a "streaming" algorithm so that we can decompose audio segments of
arbitrary lengths.</p>
<a id="Original (Streaming)"></a>
<h2>Original (Streaming)</h2>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/streamingorig_96172a177be89410fd57f6fbe4df6d824358957c"
height="100"
samples="256"
scale="4"
color="rgba(133, 174, 172, 0.5)"
controls
></audio-view>
<a id="Reconstruction (Streaming)"></a>
<h2>Reconstruction (Streaming)</h2>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/streamingrecon_745ea9ae9d9359473beb0befff0c3c46f02a28ab"
height="100"
samples="256"
scale="4"
color="rgba(133, 174, 172, 0.5)"
controls
></audio-view>
<a id="Audio Examples"></a>
<h1>Audio Examples</h1>
<a id="Example 1"></a>
<h2>Example 1</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_b9f72d7de4fa5ee8951f4994ef520e2640c18e73"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<p>We mask the second half of the input audio to enable the streaming algorithm, so only the first half of the input audio is reproduced.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_3102ecbc769c403051d09a216906d48e172d6b5c"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Decomposition"></a>
<h3>Decomposition</h3>
<p>We can see that while energy is removed at each step, removed segments do not map cleanly onto audio "events" as a human listener would typically conceive of them. Future work will move toward fewer and more meaningul events via induced sparsity and/or clustering of events.</p>
<img class="full-width" src="https://iterative-decomposition-v3.s3.amazonaws.com/decomposition_0f5f9adbcce0c2f0e5cc7d9a90d218051634b5c3" height="200"></img>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_397fd7882e58847ec97858c46879477ddea8ed67"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_3e2a864f4fce26617600306efdf74ef066c627c5"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Random Perturbations"></a>
<h3>Random Perturbations</h3>
<p>Each event vector is "perturbed" or moved in the same direction in event space by adding a random event vector with
small magnitude</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/perturbed_dd7a54e133125e4ca9b1d46694e2c794c2966dc7"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<p>Different stopping conditions might be chosen during inference (e.g. norm of the residual) but during training, we remove energy for 32 steps. Each event vector is of dimension 32. The decoder generates an event from this vector, which is then scheduled. </p>
<img class="" src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_e6c3fa8783602f822a41fa050a9e2cf7553a8e65" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Time is along the x-axis, and a 32D -> 1D projection of event vectors using t-SNE constitutes the distribution along the y-axis. Colors are produced via a random projection from 32D -> 3D (RGB). Here it becomes clear that there are many redundant/overlapping events. Future work will stress more sparsity and less event overlap, hopefully increasing interpretability further.</p>
<audio-timeline
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duration="5.944308390022676"
width="600"
height="300"
></audio-timeline>
<a id="Example 2"></a>
<h2>Example 2</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_95e5be0eee6348db7c390a2fabda3a86ca6975ba"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<p>We mask the second half of the input audio to enable the streaming algorithm, so only the first half of the input audio is reproduced.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_cf1b9491e9c6dfaa7ba4ecdbe5d59eddeb819959"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Decomposition"></a>
<h3>Decomposition</h3>
<p>We can see that while energy is removed at each step, removed segments do not map cleanly onto audio "events" as a human listener would typically conceive of them. Future work will move toward fewer and more meaningul events via induced sparsity and/or clustering of events.</p>
<img class="full-width" src="https://iterative-decomposition-v3.s3.amazonaws.com/decomposition_af432951b140b2043666fd174a8acf45997e5ab4" height="200"></img>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_ed4f5947ecb8bb913e2a0483d4c5c8a8b8722e75"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_13f523f331d18ec264ff9cb0791ea5b696802f21"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Random Perturbations"></a>
<h3>Random Perturbations</h3>
<p>Each event vector is "perturbed" or moved in the same direction in event space by adding a random event vector with
small magnitude</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/perturbed_96f12b37ecd8d9d9f2d3a931acf6ca35d7ac6239"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<p>Different stopping conditions might be chosen during inference (e.g. norm of the residual) but during training, we remove energy for 32 steps. Each event vector is of dimension 32. The decoder generates an event from this vector, which is then scheduled. </p>
<img class="" src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_b70f9e65979bd33a9c8f4102ac15e8c963a0f79a" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Time is along the x-axis, and a 32D -> 1D projection of event vectors using t-SNE constitutes the distribution along the y-axis. Colors are produced via a random projection from 32D -> 3D (RGB). Here it becomes clear that there are many redundant/overlapping events. Future work will stress more sparsity and less event overlap, hopefully increasing interpretability further.</p>
<audio-timeline
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<a id="Example 3"></a>
<h2>Example 3</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_716659050a30c93a93f58de7437c2e5979d64965"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<p>We mask the second half of the input audio to enable the streaming algorithm, so only the first half of the input audio is reproduced.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_6fb24e5fee9599a5d8936265d564affdc6f663de"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Decomposition"></a>
<h3>Decomposition</h3>
<p>We can see that while energy is removed at each step, removed segments do not map cleanly onto audio "events" as a human listener would typically conceive of them. Future work will move toward fewer and more meaningul events via induced sparsity and/or clustering of events.</p>
<img class="full-width" src="https://iterative-decomposition-v3.s3.amazonaws.com/decomposition_274e7d819b18bfae2736204a0c37c042c709826a" height="200"></img>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_61d4daa7ef83e087718d38bbe8cb5813341b73a1"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_d7b5542865288d95d0213e40c1bcdc07cd8dfd19"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Random Perturbations"></a>
<h3>Random Perturbations</h3>
<p>Each event vector is "perturbed" or moved in the same direction in event space by adding a random event vector with
small magnitude</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/perturbed_a036dee169f7e8cd4b102a44a830a2c50ff68d99"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<p>Different stopping conditions might be chosen during inference (e.g. norm of the residual) but during training, we remove energy for 32 steps. Each event vector is of dimension 32. The decoder generates an event from this vector, which is then scheduled. </p>
<img class="" src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_88209ba87c3ca22f0e495fb2a6d5910a1d1be44e" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Time is along the x-axis, and a 32D -> 1D projection of event vectors using t-SNE constitutes the distribution along the y-axis. Colors are produced via a random projection from 32D -> 3D (RGB). Here it becomes clear that there are many redundant/overlapping events. Future work will stress more sparsity and less event overlap, hopefully increasing interpretability further.</p>
<audio-timeline
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duration="5.944308390022676"
width="600"
height="300"
></audio-timeline>
<a id="Example 4"></a>
<h2>Example 4</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_f8e34229015d28753643613e19265135e1f437ab"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<p>We mask the second half of the input audio to enable the streaming algorithm, so only the first half of the input audio is reproduced.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_40f5eb8d4068cb36f7362bd8797aa124bdedb832"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Decomposition"></a>
<h3>Decomposition</h3>
<p>We can see that while energy is removed at each step, removed segments do not map cleanly onto audio "events" as a human listener would typically conceive of them. Future work will move toward fewer and more meaningul events via induced sparsity and/or clustering of events.</p>
<img class="full-width" src="https://iterative-decomposition-v3.s3.amazonaws.com/decomposition_73c08452fa3fc2b55ea804650b8dce75df05c736" height="200"></img>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_2680049e533ccb4a0f4f3726b364d26b5017b8df"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_c059e2eb3e17a920449a4204b92e482b1c8d07bc"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Random Perturbations"></a>
<h3>Random Perturbations</h3>
<p>Each event vector is "perturbed" or moved in the same direction in event space by adding a random event vector with
small magnitude</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/perturbed_1a5f6dd3283aae37a9b053fbe93d8e03c27f28ae"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<p>Different stopping conditions might be chosen during inference (e.g. norm of the residual) but during training, we remove energy for 32 steps. Each event vector is of dimension 32. The decoder generates an event from this vector, which is then scheduled. </p>
<img class="" src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_cdd9f8fbc4bf52073388ce13aee0d035d20508cb" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Time is along the x-axis, and a 32D -> 1D projection of event vectors using t-SNE constitutes the distribution along the y-axis. Colors are produced via a random projection from 32D -> 3D (RGB). Here it becomes clear that there are many redundant/overlapping events. Future work will stress more sparsity and less event overlap, hopefully increasing interpretability further.</p>
<audio-timeline
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duration="5.944308390022676"
width="600"
height="300"
></audio-timeline>
<a id="Example 5"></a>
<h2>Example 5</h2>
<a id="Original Audio"></a>
<h3>Original Audio</h3>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/original_4edccb1c778164a374b4dea9b6b019bc8b0233c3"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Reconstruction"></a>
<h3>Reconstruction</h3>
<p>We mask the second half of the input audio to enable the streaming algorithm, so only the first half of the input audio is reproduced.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/reconstruction_ae42601b222884fc672662a640f45aa42d693baa"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Decomposition"></a>
<h3>Decomposition</h3>
<p>We can see that while energy is removed at each step, removed segments do not map cleanly onto audio "events" as a human listener would typically conceive of them. Future work will move toward fewer and more meaningul events via induced sparsity and/or clustering of events.</p>
<img class="full-width" src="https://iterative-decomposition-v3.s3.amazonaws.com/decomposition_08307c7f05c00282fdfb394955414395305ab7f5" height="200"></img>
<a id="Randomized"></a>
<h3>Randomized</h3>
<p>Here, we generate random event vectors with the original event times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedevents_b1aebbfa0ac030dd564443a019788b19d1f1d84b"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<p>Here we use the original event vectors, but generate random times.</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/randomizedtimes_a3b4be5c7b133f17a6d68d208ce60d32ab9dbccf"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Random Perturbations"></a>
<h3>Random Perturbations</h3>
<p>Each event vector is "perturbed" or moved in the same direction in event space by adding a random event vector with
small magnitude</p>
<audio-view
src="https://iterative-decomposition-v3.s3.amazonaws.com/perturbed_9d997c3c6766a07f95607b5260df745020dd0eb8"
height="100"
samples="256"
scale="1"
color="rgba(100, 200, 150, 0.5)"
controls
></audio-view>
<a id="Event Vectors"></a>
<h3>Event Vectors</h3>
<p>Different stopping conditions might be chosen during inference (e.g. norm of the residual) but during training, we remove energy for 32 steps. Each event vector is of dimension 32. The decoder generates an event from this vector, which is then scheduled. </p>
<img class="" src="https://iterative-decomposition-v3.s3.amazonaws.com/latents_9ff423034b997db2705e11021eaa72afd7cd5610" height="200"></img>
<a id="Event Scatterplot"></a>
<h3>Event Scatterplot</h3>
<p>Time is along the x-axis, and a 32D -> 1D projection of event vectors using t-SNE constitutes the distribution along the y-axis. Colors are produced via a random projection from 32D -> 3D (RGB). Here it becomes clear that there are many redundant/overlapping events. Future work will stress more sparsity and less event overlap, hopefully increasing interpretability further.</p>
<audio-timeline
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duration="5.944308390022676"
width="600"
height="300"
></audio-timeline>
<code-block language="python">n_samples = 2 ** 17
samples_per_event = 2048
# this is cut in half since we'll mask out the second half of encoder activations
n_events = (n_samples // samples_per_event) // 2
context_dim = 32
# the samplerate, in hz, of the audio signal
samplerate = 22050
# derived, the total number of seconds of audio
n_seconds = n_samples / samplerate
transform_window_size = 2048
transform_step_size = 256
n_frames = n_samples // transform_step_size
from argparse import ArgumentParser
from typing import Dict, Tuple, List
import numpy as np
import torch
from sklearn.manifold import TSNE
from torch import nn
from conjure import S3Collection, \
conjure_article, CitationComponent, AudioComponent, ImageComponent, \
CompositeComponent, Logger, ScatterPlotComponent, AudioTimelineComponent
from data import get_one_audio_segment, AudioIterator
from iterativedecomposition import Model as IterativeDecompositionModel
from modules.eventgenerators.overfitresonance import OverfitResonanceModel
from modules import max_norm, sparse_softmax, amplitude_envelope
remote_collection_name = 'iterative-decomposition-v3'
def to_numpy(x: torch.Tensor):
return x.data.cpu().numpy()
# thanks to https://discuss.pytorch.org/t/how-do-i-check-the-number-of-parameters-of-a-model/4325/9
def count_parameters(model):
return sum(p.numel() for p in model.parameters() if p.requires_grad)
def process_events2(
logger: Logger,
events: torch.Tensor,
vectors: torch.Tensor,
times: torch.Tensor,
total_seconds: float) -> Tuple[List[Dict], Dict]:
# compute amplitude envelopes
envelopes = amplitude_envelope(events, 128).data.cpu().numpy().reshape((n_events, -1))
# compute event positions/times, in seconds
positions = torch.argmax(times, dim=-1, keepdim=True) / times.shape[-1]
times = [float(x) for x in (positions * total_seconds).view(-1).data.cpu().numpy()]
# normalize event vectors and map onto the y dimension
normalized = vectors.data.cpu().numpy().reshape((-1, context_dim))
normalized = normalized - normalized.min(axis=0, keepdims=True)
normalized = normalized / (normalized.max(axis=0, keepdims=True) + 1e-8)
tsne = TSNE(n_components=1)
points = tsne.fit_transform(normalized)
points = points - points.min()
points = points / (points.max() + 1e-8)
print(points)
# create a random projection to map colors
proj = np.random.uniform(0, 1, (context_dim, 3))
colors = normalized @ proj
colors -= colors.min()
colors /= (colors.max() + 1e-8)
colors *= 255
colors = colors.astype(np.uint8)
colors = [f'rgba({c[0]}, {c[1]}, {c[2]}, 0.5)' for c in colors]
evts = {f'event{i}': events[:, i: i + 1, :] for i in range(events.shape[1])}
event_components = {}
scatterplot_srcs = []
for k, v in evts.items():
_, e = logger.log_sound(k, v)
scatterplot_srcs.append(e.public_uri)
event_components[k] = AudioComponent(e.public_uri, height=15, controls=False)
return [{
'eventTime': times[i],
'offset': times[i],
'y': float(points[i]),
'color': colors[i],
'audioUrl': scatterplot_srcs[i].geturl(),
'eventEnvelope': envelopes[i].tolist(),
'eventDuration': total_seconds,
} for i in range(n_events)], event_components
def load_model(wavetable_device: str = 'cpu') -> nn.Module:
hidden_channels = 512
model = IterativeDecompositionModel(
in_channels=1024,
hidden_channels=hidden_channels,
resonance_model=OverfitResonanceModel(
n_noise_filters=64,
noise_expressivity=4,
noise_filter_samples=128,
noise_deformations=32,
instr_expressivity=4,
n_events=1,
n_resonances=4096,
n_envelopes=64,
n_decays=64,
n_deformations=64,
n_samples=n_samples,
n_frames=n_frames,
samplerate=samplerate,
hidden_channels=hidden_channels,
wavetable_device=wavetable_device,
fine_positioning=True,
fft_resonance=True
))
with open('iterativedecomposition11.dat', 'rb') as f:
model.load_state_dict(torch.load(f, map_location=lambda storage, loc: storage))
print('Total parameters', count_parameters(model))
print('Encoder parameters', count_parameters(model.encoder))
print('Decoder parameters', count_parameters(model.resonance))