OmniPulse WST Core (omni-wst-core)

GPU-Accelerated Wavelet Scattering & Joint Time-Frequency Scattering (JTFS) Primitives

omni-wst-core is a production-grade, highly optimized C++/CUDA mathematical extension module for Python. It provides extreme-throughput primitives for calculating the Wavelet Scattering Transform (WST) and the Joint Time-Frequency Scattering (JTFS) transform.

Designed for formally grounded perceptual fingerprinting, robust signal representation, and transient anomaly detection, this module orchestrates dual-stream, double-buffered execution over pinned cudaMallocHost memory. The result is zero-copy NumPy ingestion that virtually eliminates PCIe bottleneck latency, achieving processing speeds unachievable by standard deep learning frameworks.

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📑 Table of Contents

1. Mathematical Formalism
2. Architectural Implementation
3. Cross-Domain Use Cases
4. Installation
5. Usage Guide
6. Testing & Validation
7. License

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🔬 Mathematical Formalism

The Wavelet Scattering Transform provides an incredibly rich, deformation-stable representation of high-frequency time-series data. It is constructed through a deep convolutional network architecture where learned, opaque filters are replaced by explicit, analytically defined wavelet filter banks.

1. The Scattering Cascade

Let $x(u)$ be an input signal. We construct a complex-valued analytic wavelet filter bank $\psi_\lambda(u)$ defined by dilations of a mother wavelet, alongside a low-pass scaling function $\phi_J(u)$ at scale $2^J$.

• Zero-order coefficients (the local average): $$S[0]x(u) = x * \phi_J(u)$$
• First-order coefficients are obtained by computing the wavelet transform and applying a complex modulus nonlinearity ($|\cdot|$) to discard rapidly varying phase: $$S[1]x(u, \lambda_1) = |x * \psi_{\lambda_1}| * \phi_J(u)$$
• Depth-$m$ coefficients are obtained by cascading this convolution and modulus operator $m$ times: $$S[p]x(u) = |,| \dots |x * \psi_{\lambda_1}| * \dots | * \psi_{\lambda_m}| * \phi_J(u)$$

2. Parseval Energy Conservation

To prevent the loss of informational energy across deep cascades (information collapse), the filter bank must satisfy a Parseval frame condition. By enforcing this during the initialization of the WSTEngine, we guarantee that the energy of the input signal is perfectly partitioned and conserved: $$\sum_{p} ||S[p]x||^2 = ||x||^2$$

3. Adversarial Robustness & Lipschitz Continuity

The fundamental advantage of WST over ad-hoc spectrograms or standard neural networks is formal deformation stability. The WST is strictly Lipschitz continuous, meaning minor signal deformations or background noise result in linearly bounded changes to the fingerprint.

The depth-$m$ propagator is mathematically bounded by: $$||S[p]x - S[p]y||_{L^2} \le (||\psi||1)^m \cdot ||x - y||{L^2}$$ Because our explicitly constructed Morlet wavelets satisfy $||\psi||_1 < 1$, the Lipschitz constant $L_m$ decays exponentially with depth, strictly bounding the impact of adversarial noise.

4. Joint Time-Frequency Scattering (JTFS)

The standard WST modulus operator ($|\cdot|$) destroys critical phase-coupling information between adjacent frequency bands. This limits discriminative power for signals with complex frequency-modulated structures (e.g., chirps, overlapping formants).

JTFS recovers this structure by executing a fully separable 2D convolution across both the temporal axis $t$ and the log-frequency axis $\lambda$: $$\Psi_{\mu,l,s}(t,\lambda) = \psi_\mu(t) \cdot \psi_{l,s}(\lambda)$$ omni-wst-core computes this massive multidimensional operation concurrently by dispatching parallel CUDA streams (stream0 for time, stream1 for frequency) to maximize ALU saturation.

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⚡ Architectural Implementation

This repository utilizes an aggressive host-to-device memory architecture to bypass standard PCIe bottlenecks:

• Template Metaprogramming: TilePolicy<ArchTag> eliminates dynamic runtime branching, specializing convolution tile sizes dynamically for Ampere (TILE_M=64) or Hopper (TILE_M=128) architectures at compile time.
• Zero-Copy FFI: Utilizing pybind11 buffer protocols, NumPy memory buffers are seamlessly mapped without host-side replication.
• UVA & Pinned Memory: MemoryStaging utilizes cudaMallocHost to lock RAM. By asynchronously swapping double buffers via cudaMemcpyAsync, memory is shuttled to VRAM in the background while the cuFFT logic saturates the compute cores.

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🌍 Cross-Domain Use Cases

While designed for perceptual hashing, the deterministic, energy-preserving nature of omni-wst-core makes it highly effective across multiple R&D fields:

1. Astrophysics (Gravitational Waves): The deformation stability of WST and the phase-coupling detection of JTFS are ideal for isolating the non-stationary "chirp" of compact binary coalescences (neutron star mergers) from massive broadband noise.
2. Neurology (EEG/ECG Analysis): Human physiological signals are notoriously noisy and non-stationary. WST filters out warping deformations, allowing researchers to maintain 90%+ accuracy in EEG emotion recognition without heavy pre-processing.
3. Bioinformatics (Genomics): Applied to ChIP-seq peak calling, WST provides a translation-invariant encoding of genomic read-depth signals, while JTFS captures co-modulated binding patterns between different histone modifications.
4. Audio Forensics & Copyright: Neutralizes adversarial phase-shifting attacks in media piracy by utilizing JTFS to recover the inter-band phase correlations that standard audio fingerprinting algorithms discard.

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🚀 Installation

Prerequisites:

• Python 3.10+
• CMake 3.18+
• NVIDIA CUDA Toolkit (v11.x or v12.x)
• C++17 compliant compiler (GCC/Clang/MSVC)

Build from Source (PEP 517):

git clone [https://github.com/samvardhan03/Module-I-omni-wst-core.git](https://github.com/samvardhan03/Module-I-omni-wst-core.git)
cd Module-I-omni-wst-core

# Install dependencies and build the C++/CUDA extension
pip install -e .

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💻 Usage Guide

1. Basic WST Fingerprinting

import numpy as np
import omni_wst_core as wst

# Initialize configuration
# J: Maximum wavelet scale (2^J samples)
# Q: Quality factor (wavelets per octave)
cfg = wst.WSTConfig(J=8, Q=16, depth=2, jtfs=False)

# Simulate 1 second of audio at 44.1kHz
signal = np.random.randn(44100).astype(np.float32)

# Generate formally grounded WST fingerprint
fingerprint = wst.fingerprint(signal, cfg)
print(f"WST Fingerprint Dimensions: {fingerprint.shape}")

2. Advanced: Joint Time-Frequency Scattering (JTFS)

To protect against phase-shifting attacks or to analyze highly modulated signals (like chirps), enable JTFS.

# Enable JTFS phase-recovery
jtfs_cfg = wst.WSTConfig(J=10, Q=16, depth=2, jtfs=True)

complex_signal = np.random.randn(44100).astype(np.float32)

# Executes parallel 2D separable wavelets on stream0 and stream1
jtfs_fingerprint = wst.fingerprint(complex_signal, jtfs_cfg)
print(f"JTFS Coefficient Shape: {jtfs_fingerprint.shape}")

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🧪 Testing & Validation

The module includes a rigorous suite of mathematical proofs implemented in pytest to validate the CUDA kernels against continuous mathematics constraints.

# Install test dependencies
pip install pytest numpy

# Run the test suite
pytest tests/

Key Validations Performed:

• test_lipschitz.py: Confirms that adversarial noise injections remain mathematically bounded by $L_{m}\le(||\psi||_{1})^{m}$.
• test_parseval.py: Validates that the generated frequency-domain Morlet filter banks strictly conserve signal energy.
• test_memory.py: Ensures CUdeviceptr handles do not leak memory during high-throughput batched ingestion.

(Note: For explicit memory safety checks on the GPU, run the test suite wrapped in compute-sanitizer --tool memcheck via make memcheck).

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⚖️ License

The mathematical primitives within omni-wst-core are licensed under the Apache License 2.0 for free open-source academic and research usage.

Commercial Deployment: Production deployment of OmniPulse modules for differential licensing or enterprise MLOps requires an Enterprise SaaS agreement. Academic and government institutions qualify for immediate enterprise waivers. Please refer to COMMERCIAL_LICENSE.md or contact the repository owner for details.

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Developed by Samvardhan Singh