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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>Audio Splatting With Physics-Inspired Event Generators</title>
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<body>
<h1>Audio Splatting With Physics-Inspired Event Generators</h1>
<details>
<summary>
<caption>Table of Contents</caption>
</summary>
<ul>
<li><a href="#Audio Splatting">Audio Splatting</h1></a><ul>
<li><a href="#Gaussian Splatting">Gaussian Splatting</h2></a></li>
<li><a href="#Application to Audio">Application to Audio</h2></a></li>
<li><a href="#Training Process">Training Process</h2></a></li>
<li><a href="#A Sparse, Interpretable Representation">A Sparse, Interpretable Representation</h2></a></li>
<li><a href="#Future Work">Future Work</h2></a></li>
<li><a href="#Cite this Work">Cite this Work</h2></a></li>
<li><a href="#Example 1">Example 1</h2></a></li>
<li><a href="#Example 2">Example 2</h2></a></li>
</ul>
</li>
</ul>
</details>
<a id="Audio Splatting"></a>
<h1>Audio Splatting</h1>
<a id="Gaussian Splatting"></a>
<h2>Gaussian Splatting</h2>
<p>In <a href="https://en.wikipedia.org/wiki/Gaussian_splatting">Gaussian Splatting</a>, a large number of three-dimensional
gaussians are randomly initialized and then fit via backpropagation to several two-dimensional views of a
three-dimensional scene/environment.</p>
<a id="Application to Audio"></a>
<h2>Application to Audio</h2>
<p>We draw inspiration from this field of research and apply a similar process to audio "atoms" used to compose a
reconstruction of acoustic instruments in a physical space.</p>
<p>In this work, we use a (roughly) physics-inspired event generator, similar to the one used in
<a href="https://blog.cochlea.xyz/sparse-interpretable-audio-codec-paper.html">Toward a Sparse Interpretable Audio Codec</a> to
<em>overfit</em> to a single audio segment, drawn from the <a href="https://zenodo.org/records/5120004#.Yhxr0-jMJBA">MusicNet dataset</a>.</p>
<a id="Training Process"></a>
<h2>Training Process</h2>
<p>We randomly initialize 64 event vectors and then iteratively minimize a differentiable, perceptually-inspired loss
function for 3,000 iterations.</p>
<p>Finally, we randomly perturb the learned/overfit event vectors to begin to get a sense for some of the ways we might
manipulate and edit the sparse representation.</p>
<a id="A Sparse, Interpretable Representation"></a>
<h2>A Sparse, Interpretable Representation</h2>
<p>The sparse, event-based representation shows promise for interpretability and manipulability, event without a <a href="https://blog.cochlea.xyz/sparse-interpretable-audio-codec-paper.html#Encoder">trained
encoder network</a>.</p>
<a id="Future Work"></a>
<h2>Future Work</h2>
<p>The current work deals only with mono audio at 22050hz, but it's possible to imagine extending to stereo, or even
multi-microphone situations where a three-dimensional sound "field" needs to be approximated.</p>
<p>A previous version of this article can be found <a href="https://blog.cochlea.xyz/gamma-audio-splat.html">here</a>.</p>
<p>All code for this experiment can be found
<a href="https://github.com/JohnVinyard/matching-pursuit/blob/main/hierarchical.py">here</a>.</p>
<a id="Cite this Work"></a>
<h2>Cite this Work</h2>
<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="johnvinyardaudiosplatting"
author="Vinyard, John"
url="https://blog.cochlea.xyz/audio-splatting.html"
header="Audio Splatting With Physics-Inspired Event Generators"
year="2025">
</citation-block>
<a id="Example 1"></a>
<h2>Example 1</h2>
<p>Original Audio</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/orig_e0800daf0eb43b6e1c720402255500a18279da06"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Reconstruction</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/recon_a7d036d4d3595f226b2ebe2c006ecb37abed93c1"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Perturbed Audio</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/perturbed_846e383d79450a6e0c145f5ec3996ccad87d423a"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Timeline</p>
<audio-timeline
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duration="2.972154195011338"
width="1000"
height="500"
></audio-timeline>
<a id="Example 2"></a>
<h2>Example 2</h2>
<p>Original Audio</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/orig_8ecfea32af20052bf8af102c7bebe31fc895c5b4"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Reconstruction</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/recon_5872b6538bd5358c1ef4401d8497fccc43b6496d"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Perturbed Audio</p>
<audio-view
src="https://audio-splatting.s3.amazonaws.com/perturbed_ec0fa7c50f724101dfacadd2d61ea75cd43b5572"
height="100"
samples="256"
scale="1"
controls
></audio-view>
<p>Timeline</p>
<audio-timeline
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duration="2.972154195011338"
width="1000"
height="500"
></audio-timeline>
<code-block language="python">import argparse
from itertools import count
from typing import Tuple, Dict, List
import numpy as np
import torch
from torch import nn
from torch.optim import Adam
from conjure import LmdbCollection, loggers, serve_conjure, SupportedContentType, NumpySerializer, NumpyDeserializer, \
conjure_article, CompositeComponent, S3Collection, AudioComponent, AudioTimelineComponent, CitationComponent
from conjure.logger import encode_audio, Logger
from data import get_one_audio_segment
from modules import unit_norm, flattened_multiband_spectrogram, sparse_softmax, max_norm, amplitude_envelope, \
iterative_loss
from modules.eventgenerators.splat import SplattingEventGenerator
from modules.infoloss import CorrelationLoss
from modules.multiheadtransform import MultiHeadTransform
from util import device, make_initializer
from sklearn.manifold import TSNE
initializer = make_initializer(0.05)
article_title = 'Audio Splatting With Physics-Inspired Event Generators'
class OverfitHierarchicalEvents(nn.Module):
def __init__(
self,
n_samples: int,
samplerate: int,
n_events: int,
context_dim: int):
super().__init__()
self.n_samples = n_samples
self.samplerate = samplerate
self.n_events = n_events
self.context_dim = context_dim
self.n_frames = n_samples // 256
event_levels = int(np.log2(n_events))
total_levels = int(np.log2(n_samples))
self.event_levels = event_levels
self.event_generator = SplattingEventGenerator(
n_samples=n_samples,
samplerate=samplerate,
n_resonance_octaves=64,
n_frames=n_samples // 256,
hard_reverb_choice=False,
hierarchical_scheduler=True,
wavetable_resonance=True,
)
self.transform = MultiHeadTransform(
self.context_dim, hidden_channels=128, shapes=self.event_generator.shape_spec, n_layers=1)
self.event_time_dim = int(np.log2(self.n_samples))
rng = 0.1
self.event_vectors = nn.Parameter(torch.zeros(1, 2, self.context_dim).uniform_(-rng, rng))
self.hierarchical_event_vectors = nn.ParameterDict(
{str(i): torch.zeros(1, 2, self.context_dim).uniform_(-rng, rng) for i in range(event_levels - 1)})
self.times = nn.Parameter(
torch.zeros(1, 2, total_levels, 2).uniform_(-rng, rng))
self.hierarchical_time_vectors = nn.ParameterDict(
{str(i): torch.zeros(1, (2 ** (i + 2)), total_levels, 2).uniform_(-rng, rng) for i in
range(event_levels - 1)})
self.apply(initializer)
@property
def normalized_atoms(self):
return unit_norm(self.atoms, dim=-1)
def _forward(
self,
events: torch.Tensor,
times: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
for i in range(self.event_levels - 1):
# scale = 1 / (i + 1)
scale = 1
# TODO: consider bringing back scaling as we approach the leaves of the tree
events = \
events.view(1, -1, 1, self.context_dim) \
+ (self.hierarchical_event_vectors[str(i)].view(1, 1, 2, self.context_dim) * scale)
events = events.view(1, -1, self.context_dim)
# TODO: Consider masking lower bits as we approach the leaves of the tree, so that
# new levels can only _refine_, and not completely move entire branches
batch, n_events, n_bits, _ = times.shape
times = times.view(batch, n_events, 1, n_bits, 2).repeat(1, 1, 2, 1, 1).view(batch, n_events * 2, n_bits, 2)
times = times + (self.hierarchical_time_vectors[str(i)] * scale)
event_vectors = events
params = self.transform.forward(events)
print('TIMES', times.shape)
events = self.event_generator.forward(**params, times=times)
return events, event_vectors, times
def perturbed(self):
events = self.event_vectors.clone()
times = self.times.clone()
perturbation = torch.zeros_like(events).uniform_(-0.5, 0.5)
return self._forward(events + perturbation, times)
def forward(self) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
events = self.event_vectors.clone()
times = self.times.clone()
return self._forward(events, times)
def loss_transform(x: torch.Tensor) -> torch.Tensor:
return flattened_multiband_spectrogram(
x,
stft_spec={
'long': (128, 64),
'short': (64, 32),
'xs': (16, 8),
},
smallest_band_size=512)
def reconstruction_loss(target: torch.Tensor, recon: torch.Tensor) -> torch.Tensor:
target_spec = loss_transform(target)
recon_spec = loss_transform(recon)
loss = torch.abs(target_spec - recon_spec).sum()
return loss
def to_numpy(x: torch.Tensor):
return x.data.cpu().numpy()
def overfit():
n_samples = 2 ** 16
samplerate = 22050
n_events = 64
event_dim = 16
# Begin: this would be a nice little helper to wrap up
collection = LmdbCollection(path='hierarchical')
collection.destroy()
collection = LmdbCollection(path='hierarchical')
recon_audio, orig_audio, perturbed_audio = loggers(
['recon', 'orig', 'perturbed'],
'audio/wav',
encode_audio,
collection)
eventvectors, eventtimes = loggers(
['eventvectors', 'eventtimes'],
SupportedContentType.Spectrogram.value,
to_numpy,
collection,
serializer=NumpySerializer(),
deserializer=NumpyDeserializer()
)
audio = get_one_audio_segment(n_samples, samplerate, device='cpu')
target = audio.view(1, 1, n_samples).to(device)
orig_audio(target)
serve_conjure([
orig_audio,
recon_audio,
perturbed_audio,
eventvectors,
eventtimes,
], port=9999, n_workers=1)
# end proposed helper function
model = OverfitHierarchicalEvents(
n_samples, samplerate, n_events, context_dim=event_dim).to(device)
optim = Adam(model.parameters(), lr=1e-3)
loss_model = CorrelationLoss(n_elements=512).to(device)
for i in count():
optim.zero_grad()
recon, vectors, times = model.forward()
times = sparse_softmax(times, dim=-1)
weights = torch.from_numpy(np.array([0, 1])).to(device).float()
eventvectors(max_norm(vectors[0]))
t = times[0] @ weights
eventtimes((t > 0).float())
recon_summed = torch.sum(recon, dim=1, keepdim=True)
recon_audio(max_norm(recon_summed))
perturbed, _, _ = model.perturbed()
perturbed_summed = torch.sum(perturbed, dim=1, keepdim=True)
perturbed_summed = max_norm(perturbed_summed)
perturbed_audio(perturbed_summed)
loss = loss_model.multiband_noise_loss(target, recon_summed, 128, 32)
loss.backward()
optim.step()
print(i, loss.item())
def process_events2(
logger: Logger,
events: torch.Tensor,
vectors: torch.Tensor,
times: torch.Tensor,
total_seconds: float,
n_events:int,
context_dim: int) -> Tuple[List[Dict], Dict]:
# compute amplitude envelopes
envelopes = amplitude_envelope(events, 128).data.cpu().numpy().reshape((n_events, -1))
norms = torch.norm(events, dim=-1).reshape((-1))
max_norm = torch.max(norms)
opacities = norms / (max_norm + 1e-12)
# compute event positions/times, in seconds
times = [float(x) for x in times.reshape((-1,))]
# 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)
# 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]}, {opacities[i]})' for i, c in enumerate(colors)]
evts = {f'event{i}': events[:, i: i + 1, :] for i in range(events.shape[1])}
#
#
event_components = {}
# for k, v in events.items():
# _, e = logger.log_sound(k, v)
# scatterplot_srcs.append(e.public_uri)
# event_components[k] = AudioComponent(e.public_uri, height=15, controls=False)
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
# t = np.array(times) / total_seconds
# points = np.concatenate([points.reshape((-1, 1)), t.reshape((-1, 1))], axis=-1)
#
# return points, times, colors
def reconstruction_section(logger: Logger, samplerate: int, context_dim: int, n_iterations: int = 1000) -> CompositeComponent:
n_samples = 2 ** 16
samplerate = 22050
n_events = 64
event_dim = 16
total_seconds = n_samples / samplerate
audio = get_one_audio_segment(n_samples, samplerate, device='cpu')
target = audio.view(1, 1, n_samples).to(device)
model = OverfitHierarchicalEvents(
n_samples, samplerate, n_events, context_dim=event_dim).to(device)
optim = Adam(model.parameters(), lr=1e-3)
loss_model = CorrelationLoss(n_elements=512).to(device)
for i in range(n_iterations):
optim.zero_grad()
recon, vectors, times = model.forward()
recon_summed = torch.sum(recon, dim=1, keepdim=True)
# loss = loss_model.multiband_noise_loss(target, recon_summed, 128, 32)
# loss = iterative_loss(target, recon, loss_transform)
t = loss_transform(target)
r = loss_transform(recon_summed)
loss = torch.abs(t - r).sum()
loss.backward()
optim.step()
print(i, loss.item())
recon, vectors, times = model.forward()
perturbed, _, _ = model.perturbed()
perturbed = torch.sum(perturbed, dim=1, keepdim=True)
recon_summed = torch.sum(recon, dim=1, keepdim=True)
recon_summed = max_norm(recon_summed)
# first, ensure only one element is activated
times = sparse_softmax(times, dim=-1)
# project to [0, 1] space
weights = torch.from_numpy(np.array([0, 1])).to(device).float()
t = times[0] @ weights
t = t.data.cpu().numpy()
time_levels = int(np.log2(n_samples))
# create coefficients for each entry in the binary vector
time_coeffs = np.zeros((time_levels, 1))
time_coeffs[:] = 2
exponents = np.linspace(0, time_levels - 1, time_levels)
print('EXPONENTS', exponents, exponents.shape)
time_coeffs = time_coeffs ** exponents
print(time_coeffs)
sample_times = t @ time_coeffs[..., None]
print('TIME IN SAMPLES', sample_times.min(), sample_times.max())
times_in_seconds = sample_times / samplerate
print('TIMES IN SECONDS', times_in_seconds.min(), times_in_seconds.max())
_, orig_audio = logger.log_sound('orig', target)
orig_component = AudioComponent(orig_audio.public_uri, height=100)
_, recon_audio = logger.log_sound('recon', recon_summed)
recon_component = AudioComponent(recon_audio.public_uri, height=100)
_, p_audio = logger.log_sound('perturbed', perturbed)
p_component = AudioComponent(p_audio.public_uri, height=100)
events, event_components = process_events2(logger, recon, vectors, times_in_seconds, total_seconds, n_events, context_dim)
timeline = AudioTimelineComponent(duration=total_seconds, width=1000, height=500, events=events)
return CompositeComponent(
orig='Original Audio',
orig_audio=orig_component,
recon='Reconstruction',
recon_audio=recon_component,
perturbed='Perturbed Audio',
perturbed_audio=p_component,
timeline='Timeline',
timeline_component=timeline
)
def demo_page_dict() -> Dict[str, any]:
remote = S3Collection('audio-splatting', is_public=True, cors_enabled=True)
logger = Logger(remote)
n_iterations = 2000
samplerate = 22050
context_dim = 16
example_1 = reconstruction_section(logger, samplerate, context_dim, n_iterations)
example_2 = reconstruction_section(logger, samplerate, context_dim, n_iterations)
# example_3 = reconstruction_section(logger, samplerate, context_dim, n_iterations)
# example_4 = reconstruction_section(logger, samplerate, context_dim, n_iterations)
citation = CitationComponent(
tag='johnvinyardaudiosplatting',
author='Vinyard, John',
url='https://blog.cochlea.xyz/audio-splatting.html',
header=article_title,
year='2025',
)
return dict(
example_1=example_1,
example_2=example_2,
# example_3=example_3,