Global Structure in Learned Latent Representations of Confusion-Limited LISA Data

Technical Summary: Global Structure in Learned Latent Representations of Confusion-Limited LISA Data

Problem Statement
The Laser Interferometer Space Antenna (LISA) mission will operate in a frequency band crowded with unresolved galactic compact binaries, creating a "confusion-limited" foreground. While individual bright sources may be resolvable, the superposition of thousands of weak sources forms a complex background that can obscure or distort weaker signals. Traditional gravitational-wave searches rely on matched filtering for modeled sources or coherent burst methods for transients, but these approaches struggle with the dense, unresolved foreground. The paper addresses the challenge of distinguishing resolvable sources from this confusion foreground using machine learning. Specifically, it investigates whether the information required to separate resolvable sources is best captured by the local geometry of a learned latent space (manifold proximity) or by the global density distribution of that latent space.

Methodology
The study employs a controlled synthetic benchmark using data generation and preprocessing protocols established in prior work [18].

• Data Generation: Synthetic LISA segments (3600 seconds duration, 1 Hz sampling) are generated containing instrumental noise and a superposition of 1000 weak galactic binary waveforms (confusion foreground). Positive test cases add a single resolvable source (Massive Black Hole Binaries, Extreme Mass Ratio Inspirals, or bright galactic binaries) with a Signal-to-Noise Ratio (SNR) between 10 and 50.
• Representation Learning: A continuous wavelet transform (CWT) is applied to the time-series data to generate Morlet scalograms (100 scales $\times$ 3600 time steps). A lightweight convolutional autoencoder (32-dimensional bottleneck) is trained exclusively on the confusion foreground to learn a low-dimensional latent representation ($Z \in \mathbb{R}^{32}$).
• Scoring Strategies: The authors compare one-class anomaly scoring rules applied to the fixed latent representation:
  1. Geometry-Based (Local): Uses reconstruction error combined with an off-manifold distance metric ($d_M$) calculated via $k$-nearest neighbors in the latent space. This measures local deviation from the learned foreground manifold.
  2. Morphology-Augmented: Combines the geometric score with hand-crafted time-frequency morphology descriptors (e.g., track continuity, anisotropy) using a weighted fusion.
  3. Likelihood-Based (Global): Models the probability density of the foreground latent vectors explicitly using Gaussian Mixture Models (GMM) and Kernel Density Estimation (KDE). Anomalies are scored by negative log-likelihood ($-\log p(z)$).
• Experimental Protocol: To ensure fair comparison, all methods utilize the exact same latent space representation and test data. Performance is evaluated across three independent training seeds using threshold-independent metrics (ROC-AUC and PR-AUC).

Key Results
The study finds that likelihood-based scoring consistently outperforms geometry-based methods across all seeds:

• Performance Metrics: The latent likelihood model (GMM with 48 components) achieved a mean ROC-AUC of 0.8555 ± 0.0181 and PR-AUC of 0.9219 ± 0.0118. In contrast, the geometry baseline (AE + Manifold) achieved a ROC-AUC of 0.7663 ± 0.0450 and PR-AUC of 0.8667 ± 0.0255.
• Robustness: The likelihood-based approach demonstrated lower seed-to-seed variability than the geometry baseline, suggesting greater stability.
• Ablation Studies:
  • Increasing the complexity of the GMM (number of mixture components) improved performance up to 48 components, indicating the latent distribution is multi-modal and not well-described by a single Gaussian.
  • Morphology augmentation provided only marginal gains over the geometry baseline, and combining morphology with likelihood did not outperform latent likelihood alone. This suggests the autoencoder's latent space already encodes the discriminative information present in hand-crafted morphology features.
  • The morphology-only $k$-NN baseline performed the worst, confirming that learned latent representations capture structure beyond simple time-frequency descriptors.

Key Contributions

1. Comparative Analysis: The paper provides a direct, controlled comparison between local manifold-distance scoring and global latent density modeling for gravitational-wave source separation, isolating the scoring rule as the sole variable.
2. Empirical Evidence for Global Structure: The results demonstrate that resolvability information in learned latent representations is not fully captured by local geometric proximity but is instead reflected in the global properties of the latent distribution.
3. Reproducible Benchmark: The authors provide a reproducible framework with fixed seeds, data generation, and preprocessing artifacts to support future methodological work in LISA data analysis.

Significance and Claims
The paper claims that for confusion-limited LISA data, global latent density modeling is a more robust and effective strategy for anomaly detection than local geometric deviation.

The authors explicitly state that the goal is not to replace matched filtering but to construct low-dimensional latent vectors that preserve the intrinsic geometry of the waveform manifold. The findings suggest that "source-resolvability information in learned latent representations is organized globally." Consequently, exploiting the global latent distribution yields stronger discrimination than relying solely on local geometric deviation.

The work contributes to the development of "representation-aware methods" for LISA foreground characterization. The authors modestly frame this as a step toward integrating representation learning, latent geometry, and information-theoretic structure into future gravitational-wave analysis, noting that future work must test these findings under distribution shifts (e.g., varying confusion levels) and investigate coordinate invariance to determine if the observed density structure is intrinsic to the data or an artifact of parameterization.