Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models
| Authors | Arkaprabha Ganguli et al. |
| Year | 2026 |
| Field | Statistics / ML |
| arXiv | 2602.23518 |
| Download | |
| Categories | stat.ML, cs.LG |
Abstract
Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.
Engineering Breakdown
Plain English
This paper tackles the problem of disentangling physical factors in deep generative models trained on thermal Sunyaev-Zel'dovich maps of dark matter halos. The authors introduce an auxiliary-variable-guided framework that uses halo mass and concentration as explicit conditioning signals, combined with a lightweight alignment penalty, to force the latent space to meaningfully separate these physical quantities. They extend latent conditional flow matching (LCFM) into a new model called Disentangled Latent-CFM (DL-CFM) that generates sharp, realistic samples while maintaining interpretable latent dimensions. The approach successfully recovers the established mass-concentration scaling relation and identifies outlier structures in latent space that may represent unusual or previously uncharacterized halo configurations.
Core Technical Contribution
The core novelty is a practical framework for enforcing disentanglement in generative models through auxiliary variables without requiring major architectural changes or expensive supervision. Rather than relying on unsupervised disentanglement methods that often fail in high-dimensional physics simulations, the authors directly inject known physical quantities (mass, concentration) as guidance signals during training. They extend conditional flow matching—a modern generative approach—with an alignment penalty that encourages specific latent dimensions to correlate with these auxiliary variables. This is technically distinct from prior work because it combines explicit physical conditioning with a lightweight penalty mechanism, avoiding the computational overhead of fully supervised approaches while maintaining generative quality.
How It Works
The input is a set of thermal Sunyaev-Zel'dovich maps derived from dark matter halo simulations, along with labeled auxiliary variables (halo mass and concentration) for each sample. The model encodes these maps into a latent space using a learned encoder, where the representation is subject to two objectives: standard generative modeling loss (via conditional flow matching) and a disentanglement alignment penalty that pushes specific latent dimensions toward the auxiliary variables. The LCFM component uses conditional flows to model the latent distribution conditioned on the auxiliary variables, enabling generation of physically realistic samples by sampling from this learned latent distribution. A decoder then reconstructs sharp tSZ maps from the disentangled latent codes. The alignment penalty is lightweight—likely a simple regression or correlation loss—that ties latent dimensions to mass/concentration values without requiring adversarial training or complex information bottleneck mechanisms.
Production Impact
For teams working with scientific simulations or observational astronomy data, this approach provides a practical way to build interpretable generative models without sacrificing sample quality. Production pipelines could adopt DL-CFM to simultaneously generate realistic synthetic data (for augmentation or analysis) while extracting meaningful latent structure, reducing the need for separate unsupervised discovery methods. The auxiliary-variable guidance pattern is generalizable: any domain where you have labeled physical quantities (redshift, stellar mass, galaxy type) could benefit from this framework, making it a reusable recipe for scientific ML. Trade-offs include modest computational overhead from the alignment penalty and the requirement to have labeled auxiliary variables at training time—you cannot apply this retrospectively to unlabeled data. Integration is straightforward since the method extends existing flow-matching implementations; practitioners would primarily need to add the auxiliary variable data loader and penalty term.
Limitations and When Not to Use This
The method requires auxiliary variables to be available and accurately labeled during training, which may not be feasible for all domains or for studying truly novel phenomena where the governing physical quantities are unknown. The paper focuses on a specific dataset (tSZ maps) and it is unclear how robustly the disentanglement generalizes to very different data modalities or when auxiliary variables have non-linear relationships with the physical phenomena. The approach assumes that the auxiliary variables chosen (mass and concentration) are indeed the primary factors driving variation in the maps—if latent structure is driven by unmeasured confounders, the method may fail to capture them. Follow-up work is needed to quantify how much labeled auxiliary data is necessary, whether weak labels or noisy labels degrade performance, and how to handle cases where multiple physical quantities entangle in the latent space.
Research Context
This work sits at the intersection of disentangled representation learning and physics-informed machine learning, building directly on recent advances in conditional flow matching as a generative framework. It extends prior work on auxiliary-variable guided learning (common in semi-supervised settings) into the domain of scientific simulations, where physical ground truth is often available. The paper contributes to the broader research direction of making generative models interpretable and scientifically useful rather than purely generative, which has growing importance in cosmology and astrophysics. The mass-concentration scaling relation recovery serves as a validation against known physics, establishing a benchmark that future disentanglement methods in this domain should meet.
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