Parametric Cataloging: Principles & Applications

• Parametric cataloging is a methodology that constructs catalogs as objects of inference or specification through defined parameter spaces, generative models, and formal schemas.
• In astronomy, it employs multi-band generative models and Bayesian inference to enhance detection depth and reduce false discovery rates.
• Beyond astronomy, it supports schema reconciliation in product catalogs, constraint-preserving CAD workflows, and formal verification, enabling scalability and interoperability.

Searching arXiv for recent and foundational papers on parametric cataloging across domains. Across the cited works, parametric cataloging denotes the construction, maintenance, or querying of catalogs through explicit parameter spaces, generative models, or formally specified schemas rather than through ad hoc records or purely heuristic pipelines. In astronomy, it is defined as building catalogs by fitting a generative, parameterized model of image data and inferring posterior distributions over catalog parameters, including the number of sources (Feder et al., 2019). In product, engineering, exoplanet, and AI-system settings, it denotes representing entries through structured fields, schema-aligned attributes, provenance, and interoperable metadata (Nguyen et al., 2011); (Schneider et al., 2011); (Golpayegani et al., 2024). In CAD and catalog image generation, it further refers to constraint-aware modeling sequences and parameter-driven workflows for geometry, placement, and occlusion handling (Dong et al., 8 Dec 2025); (Jain et al., 10 Apr 2026).

1. Scope and core idea

A unifying feature across these literatures is that the catalog is treated as an explicit object of inference or specification. In astronomical probabilistic cataloging, the catalog is the latent set of sources together with positions, fluxes, colors, morphologies, and sometimes source count itself (Feder et al., 2019); (Regier et al., 2018). In product synthesis and engineering document processing, the catalog is a schema-conformant collection of product specifications assembled from heterogeneous offers or PDF catalogs (Nguyen et al., 2011); (Bank et al., 2024). In exoplanet and AI-system registries, the catalog is a curated parameter space with explicit inclusion criteria, field definitions, update policies, and query semantics (Schneider et al., 2011); (Golpayegani et al., 2024).

Domain	Catalog unit	Parameterization mode
Astronomy	Source catalog	Generative image model, priors, posterior inference
Product search	Product record	Schema reconciliation, clustering, data fusion
Exoplanet databases	Planet/system entry	Fixed field schema, derived quantities, status flags
AI registries	AI system/model/dataset	RDF/DCAT-aligned metadata profile
CAD	Editable part	History-based sequence, parameters, geometric constraints
Catalog image generation	Composite layout	Anchor, scale policy, aspect-ratio tolerance, occlusion parameters

This diversity also shows that “parametric” is not restricted to numeric knobs. Depending on the domain, parameters may be latent source populations, schema correspondences, controlled-vocabulary fields, CAD constraints, or workflow settings such as anchor choice and occlusion thresholds. A plausible implication is that parametric cataloging is best understood as a design pattern: the catalog is generated or constrained by a formal parameterization that is explicit enough to support inference, validation, interoperability, or editability.

2. Generative and probabilistic cataloging in astronomy

The astronomical literature gives the most explicit formalization. Multiband probabilistic cataloging defines catalog construction as fitting a single generative model to all pixels across bands, with source positions shared across bands and fluxes linked by color priors (Feder et al., 2019). The per-band image model is

$$I_b(\mathbf{x}) = \sum_{n=1}^{N} f_{n,b}\, [\mathrm{PSF}_b \star \delta(\mathbf{x}-\mathbf{x}_n)] + B_b(\mathbf{x}),$$

with Gaussian or Poisson pixel likelihoods and a joint likelihood across bands. The framework places explicit priors on $N$, positions, reference-band fluxes, and colors, and samples the posterior over catalogs using transdimensional MCMC. In crowded and low-S/N regimes, this differs sharply from pipelines that detect peaks in a single band or coadd, fit PSF photometry per band, and output a single catalog with point estimates and limited covariances (Feder et al., 2019).

The multiband extension shows concrete performance gains. On SDSS observations of M2, a joint $r+i$ fit goes $\sim 0.4$ mag deeper than single-band probabilistic cataloging and has false discovery rate less than $20\%$ for F606W$\leq 20$; relative to DAOPHOT, the two-band fit goes nearly $1.5$ magnitudes deeper using the same data and maintains lower false discovery rate down to F606W$\sim 20.5$ (Feder et al., 2019). On mocks, adding bands improves completeness consistent with S/N scaling, with $\Delta m \approx 0.37$ for 2 bands and $0.60$ for 3 bands. The same work reports an approximately $N$0 speedup over the prior single-band implementation through PSF caching, matrix evaluation, and fast astrometric transforms.

Celeste extends the same paradigm to survey scale by treating the catalog as the set of unknown parameters in a Bayesian generative model of wide-field images (Regier et al., 2018). Pixels are modeled as Poisson random variables with means determined by PSF-convolved stars and galaxies plus background, with PSFs and galaxy profiles represented as mixtures of Gaussians to obtain analytic convolutions. Instead of RJMCMC, Celeste uses variational inference with block coordinate ascent and second-order trust-region updates. The implementation jointly optimized parameters for $N$1 stars and galaxies, loaded and processed $N$2 TB across $N$3 nodes in $N$4 minutes, and achieved a peak rate of $N$5 double-precision PFLOP/s on Cori Phase II (Regier et al., 2018). Validation on SDSS Stripe 82 showed improved astrometry, photometry, colors, and morphology relative to the SDSS Photo pipeline, although star–galaxy separation remained ambiguous in some cases.

Two later lines of work modify the inference engine while preserving the parametric premise. Neural posterior estimation with spatially varying backgrounds and PSFs trains a YOLOv5-inspired fully convolutional network to output amortized posteriors over variable-length catalogs conditioned on an image, a background representation, and PSF parameters (Patel et al., 28 Feb 2025). The underlying generative model still specifies Poisson or Gaussian-approximated pixel counts from stars and galaxies convolved with a spatially varying PSF, but inference is amortized rather than performed separately per field. On SDSS, detection precision exceeds $N$6 for $N$7-band magnitudes brighter than $N$8, recall exceeds $N$9 for $r+i$0, overall star/galaxy accuracy surpasses $r+i$1 for $r+i$2, and for faint sources $r+i$3 credible intervals achieve $r+i$4 empirical coverage (Patel et al., 28 Feb 2025).

A different reformulation replaces transdimensional inference with a fixed-dimensional spike-and-slab parameterization of source fluxes (Collin, 31 Jul 2025). There, the prior over counts is taken as a binomial prior with maximum source count $r+i$5, and each flux is reparameterized from an auxiliary $r+i$6 so that zero-flux and nonzero-flux cases are handled in a fixed-dimensional space:

$r+i$7

This makes gradient-based samplers usable at scales of tens of thousands of latent sources. In the demonstrated setup, $r+i$8 fits on a $r+i$9 GB RTX 4090, chains contain $\sim 0.4$0 samples with $\sim 0.4$1 warm-up, runtime is about $\sim 0.4$2 GPU-hours per chain, and posterior estimates recover $\sim 0.4$3 in one scenario and $\sim 0.4$4 in an approximate Poisson regime (Collin, 31 Jul 2025). This does not eliminate classical failure modes—prior regularity near zero flux, multimodality, PSF mismatch, and memory pressure remain material—but it removes the need for bespoke reversible-jump proposal design.

3. Structured parameter spaces in product, scientific, and AI-system catalogs

Outside astronomy, parametric cataloging often means that catalog entries are represented as schema-aligned parameter vectors with explicit provenance and operational policies. In large-scale product synthesis, offers from merchants are reconciled into category-specific catalog schemas $\sim 0.4$5 by learning merchant/category-specific mappings $\sim 0.4$6 (Nguyen et al., 2011). Candidate correspondences are scored by logistic regression on six features—JS-MC, JS-C, JS-M, Jaccard-MC, Jaccard-C, and Jaccard-M—computed from value distributions restricted by historical offer-to-product associations. Reconciled offers are then clustered by keys such as UPC/EAN/GTIN or MPN and fused into consolidated product specifications using a centroid-based choice over textual values. On Bing Shopping data, this system processed $\sim 0.4$7 offers from $\sim 0.4$8 merchants across $\sim 0.4$9 categories, produced $20\%$0 synthesized products and $20\%$1 attribute–value pairs, and achieved attribute precision $20\%$2 with product precision $20\%$3 (Nguyen et al., 2011). The crucial point is that the catalog is not merely extracted text; it is a typed, reconciled, fused parameterization of products relative to a taxonomy.

The exoplanet.eu database shows a related but curator-driven version of the same idea (Schneider et al., 2011). Its main tables define a fixed field schema for planets and host stars, including PLANET, M[.sin i], RADIUS, PERIOD, SEM-MAJ. AXIS, ECC., INCL., STATUS, DISCOV., and UPDATE, with additional parameters on Notes pages. Derived quantities such as $20\%$4 may be computed from Kepler’s third law when absent from discovery papers. The database is updated daily, records per-datum provenance through “ref” links, and exposes VO services including ConeSearch and TAP. A central controversy is explicit in the source: there is a conflict between the sharpness required for catalog membership and the fuzziness of confidence levels for planet candidates (Schneider et al., 2011). The catalog therefore separates ontological inclusion criteria from qualitative status flags R, S, C, and W rather than pretending that a universal probabilistic threshold exists.

AICat applies the same parametric logic to AI-system registries mandated by the EU AI Act (Golpayegani et al., 2024). It extends DCAT v3 with aicat:Catalog and reuses AIRO, DPV/TECH, and AIUP/ODRL to represent AI systems, models, and datasets as machine-readable metadata. For AI systems, the profile includes fields such as dct:identifier, dct:title, dct:description, airo:isProvidedBy, airo:isDeployedBy, odrl:hasPolicy, tech:hasMarketAvailabilityStatus, dpv:hasCountry, airo:hasModel, airo:hasInput, and dcat:contactPoint. The design is intentionally minimal and aligned with Annex VIII and XII of the AI Act, while SHACL examples show how to constrain identifier cardinality, provider presence, market status, country values, and model release dates (Golpayegani et al., 2024). This is parametric cataloging in a strongly semantic-web sense: the catalog is a typed graph whose parameters are interoperable IRIs and literals rather than latent random variables.

A recurring misconception is that structured cataloging is equivalent to mere metadata accumulation. The cited systems reject that view. Product synthesis couples schema reconciliation with clustering and fusion (Nguyen et al., 2011); exoplanet.eu couples field definitions with inclusion rules, uncertainty policy, and derived-quantity conventions (Schneider et al., 2011); AICat couples an application profile with validation, federation, and SPARQL retrieval (Golpayegani et al., 2024). This suggests that in non-astronomical settings, “parametric” principally names a governance and representation regime rather than an inference algorithm.

4. Constraint-aware design, engineering documents, and catalog image generation

In CAD, parametric cataloging is explicitly tied to editability under geometric constraints. HistCAD organizes parts as history-based parametric programs comprising sketch planes, primitives, feature operations, parameters, and 10 explicit geometric constraint types: coincident, parallel, perpendicular, horizontal, vertical, tangent, equal, concentric, fix, and normal (Dong et al., 8 Dec 2025). Each sample aligns five modalities: constraint-aware modeling sequences, textual annotations, STEP-format B-reps, native parametric files, and multi-view renderings. The dataset contains $20\%$5 total sequences, with $20\%$6 in HistCAD-Academic and $20\%$7 in HistCAD-Industrial; the industrial subset contains substantially longer, more complex Siemens NX histories (Dong et al., 8 Dec 2025). Constraint coverage is quantified, with coincident at $20\%$8, horizontal at $20\%$9, perpendicular at $\leq 20$0, parallel at $\leq 20$1, and rarer types such as normal at $\leq 20$2.

The representation is flat rather than hierarchically face-declared: sketch planes are given by translations and Euler angles, primitives are lines/circles/arcs, loops are inferred automatically, and operations include standard extrude, rotated extrusion, and Boolean new/join/subtract/intersect (Dong et al., 8 Dec 2025). Explicit constraints materially change behavior under edits. The paper states that removing constraints breaks semantic relations during edits, while preserving them maintains design intent. Quantitatively, HistCAD with constraints has average token length $\leq 20$3 under the Qwen3-0.6B tokenizer, remains more compact than Text2CAD at $\leq 20$4, and improves Chamfer Distance on the shared subset to $\leq 20$5 versus $\leq 20$6 for Text2CAD (Dong et al., 8 Dec 2025). In text-driven CAD generation, the invalidity ratio falls from $\leq 20$7 for Text2CAD_T to $\leq 20$8 for HistCAD_T with constraint prediction.

CatalogBank addresses a different bottleneck: converting PDF product catalogs into structured engineering records (Bank et al., 2024). The dataset spans $\leq 20$9 pages from Misumi, Newark, Thorlabs, McMaster-Carr, 8020, and Grainger, and DocumentLabeler provides semi-automatic annotation of Tables, TableTitle, Title, SubTitle, SubsubTitle, Categories, SubCategories, SubsubCategories, Description, List, Image, and PageNumber. The paper reports that UI improvements reduce manual annotation from roughly $1.5$0 minutes to a few minutes per page, and that model-assisted labeling further reduces effort because users correct rather than draw most boxes (Bank et al., 2024). On CatalogBank, PICK achieves overall mEP, mER, mEF, and mEA of $1.5$1, with especially strong per-element scores for Table and Description. The paper does not prescribe a normative product schema, but it explicitly frames parametric cataloging as transforming vendor catalogs into structured records with attribute name, value, unit, tolerances or conditions, identifiers, and source-region evidence.

CatalogStitch extends the notion again, this time to catalog image generation (Jain et al., 10 Apr 2026). It treats placement and occlusion handling as parameters rather than manual edits. The dimension-aware mask computation uses target and product aspect ratios, anchor choice, scale policy, and tolerance $1.5$2 to adapt target masks; the occlusion-aware hybrid restoration uses EntitySeg, an IoU threshold $1.5$3, inpainting, and exact pixel pasteback to preserve foreground occluders. Evaluated on the 58-example CatalogStitch-Eval benchmark, the wrappers consistently improve ObjectStitch, OmniPaint, and InsertAnything. For example, ObjectStitch plus the wrappers reduces AR Error from $1.5$4 to $1.5$5, improves FID from $1.5$6 to $1.5$7, and raises occluder PSNR from $1.5$8 to $1.5$9 dB; InsertAnything plus the wrappers reduces AR Error from $\sim 20.5$0 to $\sim 20.5$1 and increases occluder PSNR from $\sim 20.5$2 to $\sim 20.5$3 dB (Jain et al., 10 Apr 2026). The authors explicitly describe this as turning generative compositing into a parameter-driven, production-ready catalog workflow.

Across these engineering cases, parametric cataloging is less about posterior uncertainty than about editability, normalization, and repeatable control. The relevant parameters are geometric constraints, history operations, document regions, unit-bearing fields, aspect-ratio tolerances, and anchor semantics. That is a materially different emphasis from astronomy, but it retains the same architectural principle: catalog artifacts are generated or maintained through explicit, manipulable parameterizations.

5. Catalogs as formal interfaces in verification and process-data systems

A further extension appears in formal methods, where a catalog is a persistent structure that parameterizes behavior or verification artifacts. Catalog-nets, or CLog-nets, extend colored Petri nets with guards that query a read-only, persistent database and with output inscriptions that can inject data from the database or generate fresh values (Ghilardi et al., 2020). Formally, a CLog-net is a tuple

$\sim 20.5$4

where guards lie in a typed FO fragment based on unions of conjunctive queries with inequalities and atomic negation. The operational semantics permits transitions to inspect tokens and catalog facts simultaneously, enabling multiple cases to co-evolve while remaining parameterized by an external catalog instance. For verification, the model is encoded into MCMT using arrays for places and functional encodings of read-only relations. The paper distinguishes conservative CLog-nets, which avoid fresh-value generation and admit sound and complete backward reachability, from the general case, where local freshness requires universal quantification over indices and may induce spurious UNSAFE results (Ghilardi et al., 2020).

The UPPAAL property specification pattern catalog uses “catalog” in a different but related sense: a parameterized library of requirement patterns and scopes that generates observer automata and TCTL queries (Vogel et al., 2022). Patterns include Absence, Universality, Existence, Bounded Existence, Recurrence, Minimum/Maximum Duration, Precedence, Response, Constrained Response/Precedence, Response Invariance, and Until; scopes include Globally, Before $\sim 20.5$5, After $\sim 20.5$6, Between $\sim 20.5$7 and $\sim 20.5$8, and After $\sim 20.5$9 until $\Delta m \approx 0.37$0. Parameters such as propositions $\Delta m \approx 0.37$1, time bounds $\Delta m \approx 0.37$2, and counters $\Delta m \approx 0.37$3 determine the generated artifact. For example, Bounded Response Globally is formalized as

$\Delta m \approx 0.37$4

and is realized by an observer with locations such as idle, wait, satisfied, and violation plus a local clock $\Delta m \approx 0.37$5 (Vogel et al., 2022). The work is motivated by UPPAAL’s restricted TCTL fragment, which lacks the nesting and past-time expressiveness required by many qualitative and real-time requirements. The catalog therefore acts as a parametric frontend whose outputs are formula templates, model instrumentation, and observer templates.

These papers show that parametric cataloging can be operational rather than archival. In CLog-nets, the catalog constrains transition enablement and data injection (Ghilardi et al., 2020). In the UPPAAL setting, the catalog is a typed repertoire of parameterized requirements whose instances are executable verification objects (Vogel et al., 2022). A plausible implication is that once a domain adopts explicit parameter spaces and validity rules, the distinction between “catalog” and “program” becomes thinner.

6. Recurring principles, limitations, and points of contention

Several design principles recur across the literature. First, explicit model or schema specification is central. Astronomical works write down image formation, priors, and posteriors (Feder et al., 2019); (Regier et al., 2018); (Collin, 31 Jul 2025). Product and AI-system works define schemas, mappings, cardinalities, and controlled vocabularies (Nguyen et al., 2011); (Golpayegani et al., 2024). CAD and document systems define constraints, history operators, and labeled region types (Dong et al., 8 Dec 2025); (Bank et al., 2024). Second, parameterization is used to preserve information that conventional pipelines often discard: posterior covariances and model uncertainty in astronomy, source references and evidence regions in engineering catalogs, provenance and status flags in exoplanet databases, and formal validation constraints in AI registries.

Third, scalability is a persistent driver of architectural choice. Multiband PCAT relies on RJMCMC but adds PSF caching, matrix evaluation, and fast astrometric transforms to cut runtime by approximately $\Delta m \approx 0.37$6 (Feder et al., 2019). Celeste moves to variational inference and petascale scheduling (Regier et al., 2018). NPE amortizes inference into a single forward pass (Patel et al., 28 Feb 2025). Fixed-dimensional Parametric Cataloging uses spike-and-slab reparameterization so that off-the-shelf gradient-based samplers can scale to tens of thousands of sources (Collin, 31 Jul 2025). Product synthesis blocks by merchant and category and uses automatically created training sets (Nguyen et al., 2011). DocumentLabeler reduces annotation effort through semi-automatic workflows (Bank et al., 2024). CatalogStitch keeps overhead negligible relative to the compositor and inpainting model (Jain et al., 10 Apr 2026).

The limitations are equally consistent. Model misspecification remains difficult: poor PSFs, spatially varying backgrounds, and astrometric errors degrade astronomical fits (Feder et al., 2019); (Patel et al., 28 Feb 2025). Fixed PSFs and absence of galaxy models limit some PCAT deployments (Feder et al., 2019). Variational or amortized approximations impose tile independence or restricted posterior families (Patel et al., 28 Feb 2025). In CAD, constraint coverage is finite and parameter quantization induces slight geometric approximation (Dong et al., 8 Dec 2025). CatalogBank’s reported baseline focuses on layout analysis rather than complete cross-page table parsing (Bank et al., 2024). AICat is intentionally minimal and leaves mandatory/recommended/optional classification and richer evaluative metadata to future profiles (Golpayegani et al., 2024). In formal verification, fresh-value injection complicates soundness, and UPPAAL’s native logic remains too weak for many real-time patterns without observer synthesis (Ghilardi et al., 2020); (Vogel et al., 2022).

A common misconception is that parameterization automatically settles ambiguity. The sources do not support that claim. Exoplanet.eu explicitly foregrounds the conflict between crisp catalog membership and fuzzy confidence (Schneider et al., 2011). Product synthesis still depends on thresholding and may suffer from sparse merchant/category blocks (Nguyen et al., 2011). Astronomical posterior inference still faces multimodality and prior sensitivity (Collin, 31 Jul 2025). Constraint-aware CAD datasets still depend on LLM-generated annotations whose noise is acknowledged (Dong et al., 8 Dec 2025). Parametric cataloging therefore does not remove epistemic or operational uncertainty; it makes that uncertainty, and the assumptions behind it, structurally explicit.

Taken together, these works show that parametric cataloging is not a single algorithm but a cross-domain methodology for representing catalogs as explicit parameterized objects. In one regime it is Bayesian inference over latent source populations; in another it is schema reconciliation and metadata interoperability; in another it is constraint-preserving procedural geometry; and in another it is a formal catalog of parameterized verification artifacts. What remains invariant is the replacement of opaque or purely heuristic catalog construction with a representation in which the relevant variables, constraints, priors, and update rules are made first-class.