Architecture-Driven Parameterization

• Architecture-driven parameterization is a framework that explicitly aligns model structure with parameter design to improve optimization, interpretability, and deployment across varied domains.
• It conditions parameter spaces and search strategies using architectural cues, resulting in efficient and robust designs with minimal computational overhead.
• Applications span re-parameterized CNNs, mechanism synthesis, and 3D procedural modeling, achieving notable gains in speed, accuracy, and system performance.

Architecture-driven parameterization refers to frameworks and methodologies in which parameter spaces, optimization constraints, or mappings are explicitly constructed, conditioned, or guided by the architectural structure of a model, system, or mechanism. This paradigm is central to multiple fields—machine learning, mechanism design, computational geometry, software performance modeling, and system identification—enabling interpretability, flexibility, superior optimization, and, critically, deployment efficiency. “Architecture” here encodes the high-level composition (such as neural cell topologies, kinematic linkage types, split grammars, or code/control-flow structure) and “parameterization” refers to the associated set of learnable or tunable variables, often designed to exploit architectural symmetries, constraints, or operational regimes.

1. Parameter Spaces Conditioned by Network or System Architecture

Architecture-driven parameterization typically arises when variable spaces and search procedures are constructed as direct functionals of network topology, block composition, or system model architecture.

In convolutional networks, this is seen in re-parameterization techniques where the set of learnable parameters for a convolutional block is dynamically defined by the union of operation branches that can be algebraically fused into a fixed kernel at inference. For example, the improved re-parameterization search space in "Efficient Re-parameterization Operations Search for Easy-to-Deploy Network Based on Directional Evolutionary Strategy" expands the candidate operations to include 1×1, 1×3, 3×1, multiple dilated convolutions, and others, each branch being parametrically embedded to the backbone and ultimately fused without runtime cost (Yu et al., 2022).

In mechanism synthesis, the architecture-driven parameterization for planar linkages constructs a mapping:

$$f: \{(\theta_i^{\text{in}}, \theta_i^{\text{out}})\}_{i=1}^n \times \{k\} \rightarrow (r_1, r_2, r_3, r_4)$$

where $k$ indexes the linkage architecture (type plus inversion). The parameterization layer ensures only dimensions geometrically compatible with type $k$ are generated (Kim et al., 11 Jul 2025).

In procedural modeling of 3D architectures, the grammar extraction pipeline parameterizes the grammar search directly by adjustable segmentation/grouping thresholds, such that the discovered rule set (non-terminals, terminals, rule repetitions) matches user-demanded architectural statistics (Demir et al., 2018).

System identification leverages architectural structure by expressing the feasible system-parameter set as a quadratic matrix inequality whose structure is dictated by the data’s regressor (row span of $X$) and architectural splitting; this underpins exact data-driven estimator synthesis (Brändle et al., 2024).

2. Optimization and Search Methods Conditioned on Structure

Architecture-driven parameterization is fundamentally coupled to search or learning procedures that either optimize within, adapt, or auto-tune the parameter space given the architectural structure.

• The directional evolutionary strategy in (Yu et al., 2022) navigates the binary mask space of operation branches within each block, guided by branch strengths ($\alpha$) and block importances ($\beta$), to select architectures maximizing validation accuracy under constrained branch budgets.
• In architecture-conditioned HyperNetwork frameworks such as ADWPNAS, the weight-generating MLP is conditioned on the architecture encoding (per-cell $\phi(a)$), enabling predictive forward passes for arbitrary candidates without per-model training (XuZhang et al., 2020).
• Tiered (hierarchical) search strategies, as in auto-re-parameterized image enhancement, perform width-level, depth-level, and cell-level optimization, successively refining the multi-branch training architecture before collapsing to a single branch for deployment (An et al., 27 Feb 2025).
• For function-generation mechanisms, a Mixture-of-Experts approach is employed, where each LSTM-based expert is specialized for a distinct architecture, ensuring that only type-compatible parameterizations and mappings are ever considered by a specific expert (Kim et al., 11 Jul 2025).

3. Deployment, Fusion, and Efficiency Implications

A major motivation for architecture-driven parameterization is to enable efficient inference or simulation by exploiting architectural properties:

• In re-parameterized CNNs, once the optimal branch composition is discovered, all branch weights and accompanying batch norms are merged into a single $3\times3$ kernel per block, yielding a pure convolutional backbone with no runtime branching and preserving parameter and FLOPs count relative to the original model (Yu et al., 2022).
• In image enhancement via auto-re-parameterization, all dynamically learned branch weights are algebraically summed at export time, yielding a single $3\times3$ convolution layer. This enables real-time inference across hardware targets with significantly reduced latency and memory footprint (An et al., 27 Feb 2025).
• In mechanism design, by embedding architectural constraints into the mapping layer, only defect-free and physically feasible designs are ever generated, obviating post-checking for kinematic singularities or invalid linkages (Kim et al., 11 Jul 2025).
• Grammar-based parameterization for 3D models enables reconstructions and editing at multiple levels of granularity, as the procedural rules extracted by the pipeline are not only compact but also directly manipulable to generate variants or completions with high expressiveness and fidelity (Demir et al., 2018).

4. Architectural Parameterization in Data-Driven and Hybrid Modeling

The architecture-driven paradigm is critical for guaranteeing interpretability, transferability, and robustness in data-driven estimation, system identification, and performance prediction.

• In direct data-driven estimator synthesis, parameterizations exploit known architectural features (such as the row space of design matrices) to exactly characterize system uncertainty and enable tractable robust synthesis via convex QMI constraints. This approach generalizes to arbitrary model structures provided the regressor matrix and feature map are explicitly constructed from the architecture (Brändle et al., 2024).
• For performance modeling, the Continuous Integration of Performance Models (CIPM) pipeline continually updates parametric mappings for performance model parameters, with regression and decision-tree fits reflecting structural changes in the underlying software (such as addition of branches or loops). Instrumentation and calibration routines adaptively focus only on changed architectural elements (Mazkatli et al., 2020).

5. Analysis, Visualization, and Interpretability

Architecture-driven parameterization frameworks provide intrinsic interpretability and facilitate analysis:

• Plots of operation- and block-level parameters ($\alpha$, $\beta$) reveal architectural preferences at different network depths, corresponding to theoretical intuitions about feature extraction and channel mixing (Yu et al., 2022).
• Difference heatmaps across alternative parameterizations reveal structural regularities, such as asymmetric convolutions being consistently favored over their dilated analogues, for the same representational cost.
• Type-specific mapping layers (via sign masks and orthogonal transforms) in mechanism synthesis clarify the explicit connection between generated link dimensions and architectural feasibility (Kim et al., 11 Jul 2025).
• In procedural grammar extraction, the explicit mapping from shape-processing parameters to grammar statistics and subsequent grammar structure enables user-guided architectural editing and direct evaluation of compactness versus fidelity (Demir et al., 2018).

6. Quantitative Results and Empirical Benchmarks

Architecture-driven parameterization consistently unlocks empirical improvements in accuracy, efficiency, and interpretability. On large-scale benchmarks:

Domain	Architecture-Driven Variant	Key Result/Benchmark
CNNs (ImageNet, ResNet-50)	IRepResNet-50 (Yu et al., 2022)	+1.82% top-1 accuracy, same FLOPs/params, 20% faster
Four-bar mechanism synthesis	MoE-LSTM, type-layered (Kim et al., 11 Jul 2025)	$R_{\text{sim}}$ < $10^{-3}$, defect-free, 4 designs/sec
3D Grammar Extraction	Multi-parameter pipeline (Demir et al., 2018)	$>$ 95% compression, matched/varied grammars
Low-light image enhancement	Single-layer auto-reparam (An et al., 27 Feb 2025)	PSNR 24.02 dB (MIT), $0.0003$M params, sub-msec inference
System identification	Primal QMI (Brändle et al., 2024)	Recovers true estimator when data are fully informative
Performance model calibration	CIPM (Mazkatli et al., 2020)	KS distance $\approx 0.13$ (CoCoME), $<$18s/commit

These empirical results confirm that architecture-driven parameterization enables both highly optimized inference and design, as well as generalization and robustness across a range of domains.

7. Generalization, Extensions, and Prospects

The architecture-driven parameterization paradigm generalizes across fields wherever architectural structure and parameter space are intrinsically coupled. In future work, extensions include:

• Incorporation of richer, topology-aware encoding (e.g., via graph neural networks in NAS (XuZhang et al., 2020), type-conditional outputs in mechanism design (Kim et al., 11 Jul 2025)).
• Multi-objective architecture-conditioning, e.g., incorporating deployment, safety, or hardware cost directly into the parameterization/search loop.
• Analytical extension of exact parameterization techniques to LPV, Hammerstein/Wiener, and other nonlinear system architectures (Brändle et al., 2024).
• Broader application to data-driven discovery in physical systems, dynamical modeling, and interactive design interfaces, leveraging interpretable, architecture-tied representations.

By embedding or aligning parameter spaces and learning procedures with architectural constraints and objectives, architecture-driven parameterization provides a principled, efficient, and robust foundation for scalable modeling, optimization, and design across computational disciplines.