Generator-Inquisitor Pair Architecture

Updated 2 October 2025

Generator-Inquisitor Pair is an architectural paradigm where a generator produces candidate objects and an inquisitor iteratively refines them.
This framework enables practical advancements in deep learning, coding theory, and simulation by leveraging cyclical feedback and bi-level optimization.
Its methodological precision supports enhanced model performance, error correction, and robust system validation across diverse applications.

A generator-inquisitor pair is an architectural or algorithmic paradigm in which two complementary components—a generator and an inquisitor—work in tandem to produce, refine, or probe structures such as hypotheses, codes, neural networks, or mathematical functions. The specific nature and interaction of these components depend on the research domain, but a unifying property is the cyclical or reciprocal information flow where the generator produces candidates or syntheses and the inquisitor evaluates, interrogates, or modifies them. This framework occurs in symbolic algebra, probabilistic inference, generative modeling, deep learning architecture search, coding theory, and Monte Carlo simulation.

1. Foundational Principles of Generator-Inquisitor Pairing

The generator-inquisitor architecture encapsulates two distinct modules:

The generator is responsible for synthesizing or producing candidate objects per some generative function or process—examples include deep neural architectures (Wong et al., 2018), codewords in error-correcting codes (Tang et al., 2022, Tang et al., 2022), or simulated events in collider generators [(Czyz et al., 2011); (Czyz et al., 2013); (Jadach et al., 2022); (Banerjee et al., 2021)].
The inquisitor probes, analyzes, or refines these objects—this could entail parameter updates via feedback (as in generative synthesis (Wong et al., 2018)), inversion processes for attribution (Albright et al., 2019, Lin et al., 2019), diagnostic ranking networks in question generation (Gao et al., 2022), or verification modules in invariant generation (Padhi et al., 2017).

The interaction is typically cyclical: the generator produces, the inquisitor evaluates, and the cycle iterates towards improved or more suitable designs. Mathematically, this is often formalized via a bi-level optimization, adversarial game, or constrained iterative process:

$\text{Generator:} \quad x \sim G(s); \quad \text{Inquisitor:} \quad \Delta \theta_G \sim I(G(s)).$

2. Implementations in Monte Carlo and Simulation Engines

The generator-inquisitor concept is instantiated in advanced simulation engines for particle physics and collider phenomenology:

In PHOKHARA [(Czyz et al., 2011); (Czyz et al., 2013)], Monte Carlo sampling (generator) is coupled with model-based configuration (inquisitor) that incorporates emergent resonance and interference effects. Event generation procedures split contributions (zero, one, two photons) and integrate radiative corrections through sophisticated tensor and phase-space factorization.
In KKMCee (Jadach et al., 2022), the event generator produces multi-photon lepton and quark pair events, while external libraries (DIZET for electroweak corrections, TAUOLA for tau decays, PHOTOS for photon emission) serve as physical inquisitors, scrutinizing and modifying characteristics such as decay channels and polarized states.
Modular frameworks, such as those described for Belle II energies (Banerjee et al., 2021), extend this pairwise abstraction to discrete subsystems, separating phase-space generators (for particle decays and radiation) from matrix element evaluators, each probing or sampling physical attributes.

These implementations are marked by strict modularity, efficient sampling in challenging regions (resonances), and integrated corrections (FSR/ISR, weak effects), showing how generator-inquisitor dynamics enforce physical fidelity.

3. Symbolic and Coding Theory Realizations

In coding theory, generator-inquisitor pairs appear as systematic methods for code construction and validation:

In MDS and AMDS symbol-pair codes from repeated-root cyclic codes (Tang et al., 2022, Tang et al., 2022), the generator constructs codewords via parametrized polynomials:

$g(x) = \prod_{j} (x - \alpha_j)^{r_j}$

where exponents and roots are chosen based on finite field properties. The inquisitor analyzes solutions to systems of equations (e.g., $c(1)=0$ , $c(\omega)=0$ , derivatives), ensuring minimum pair-distances and ruling out low-weight codeword solutions.

The process iterates between construction and algebraic validation, leading to codes that attain or nearly attain Singleton-type bounds on pair-error correction. This approach is characterized by careful generator polynomial design, exhaustive finite field analysis, and explicit error bound certifications.

4. Generative Synthesis and Machine Learning

In generative modeling and neural network architecture search, the generator-inquisitor pair underpins algorithms for automated design and model efficiency:

In generative synthesis (Wong et al., 2018), a learnable generator produces neural architectures $N_s = \{V_s, E_s\}$ from seed $s$ , maximizing a performance metric (NetScore, information density) subject to operational requirements. The inquisitor exposes network components to test stimuli $X$ , measures responses $Y$ , and computes feedback $\Delta \theta_G$ , leading to improved generator parameterization.
In cooperative learning frameworks such as CoopHash (Doan et al., 2022), the contrastive pair generator creates synthetic image pairs, while the multipurpose descriptor assigns energies, hash codes, latent codes, and categories, with both components trained through MCMC-based sampling and likelihood objectives.

This iterative scheme allows systematic exploration of the architectural space, adapts representations for efficiency objectives, and empirically attains superior model compression, computational cost, and energy efficiency at state-of-the-art levels.

5. Attribution, Inference, and Security

The generator-inquisitor abstraction is also central in inverse design and forensic analysis:

In source generator attribution (Albright et al., 2019), the generator is a known neural network (GAN, decoder); the inquisitor inverts the input image to estimate the latent vector $z$ that minimizes reconstructive loss:

$\hat{z} = \arg \min_{z} \| I - G(z) \|^2$

Comparison of reconstruction errors across candidate generators enables source attribution and latent recovery. The process is computationally demanding but yields interpretable forensic evidence.

InvGAN (Lin et al., 2019) formalizes encoder-based inversion of generator models for secure inference and adversarial defense. The inverter is trained to recover $z$ from $G(z)$ , with theoretical guarantees based on Lipschitz properties and concentration bounds. The generator-inverter pair enables projection-based defenses and exposes gradient reparameterization attacks.

These frameworks are notable for their explicit inversion loss, empirical validation on standard datasets, and dual application in both security and attribution.

6. Formal Generator Pairs in Aggregation Functions

Mathematical generalizations of generator-inquisitor pairs manifest in aggregation, overlap, and grouping functions (Liang et al., 2 Jan 2025):

An overlap function additively generated by $(\theta, \vartheta)$ is defined as:

$O_{(\theta, \vartheta)}(x, y) = \vartheta(\theta(x) + \theta(y))$

The existence of dual relationships (e.g., $\vartheta(\theta(x) + \theta(1)) = x$ ) is essential for the overlap function to be associative—a t-norm.

The inquisitor aspect appears when validating boundary/associativity properties, ensuring functions meet required norm conditions, and in deriving automorphism-based distortion representations:

$O_{(\theta, \vartheta)}(x, y) = F(T(x,y))$

where $T$ is a t-norm constructed from $\theta$ , and $F$ is a (pseudo) automorphism related to $\vartheta$ .

Dual results extend the scheme to grouping functions $(t, s)$ via similar constructs with increasing generators and conorm conditions. This unifies many aggregation functions under the generator-inquisitor paradigm.

7. Broader Implications and Applications

The generator-inquisitor model is broadly applicable:

In formal verification (LoopInvGen (Padhi et al., 2017)), it alternates between synthesizing candidate invariants and interrogating loop transition relations.
In question-answering (Abdallah et al., 2023, Takahashi et al., 2023, Gao et al., 2022), generators produce candidate questions or answers, while ranking classifiers or retrieval mechanisms select, validate, or refine outputs.

These principles drive progress in symbolic computation, programming language verification, deep learning, coding theory, natural language systems, and simulation-based inference, supporting scalable, adaptive, and domain-agnostic construction of complex systems. The paradigm is characterized by reciprocal transfer, cyclical validation, and domain-specific optimization.

This comprehensive treatment underscores the technical depth, formal structure, and cross-domain versatility of generator-inquisitor pairs as a central methodological construct in contemporary computational science.