Architecture-Specific Randomized Training

• Architecture-specific randomized training algorithms are methods that inject targeted stochasticity into neural network architectures to enhance robustness and efficiency.
• They employ techniques such as randomized block selection, parameter generation, and domain randomization to align with hardware constraints and optimize learning dynamics.
• These methods improve computational performance and generalization in large-scale neural architecture search and hardware-aware deep learning applications.

An architecture-specific randomized training algorithm is a method that strategically injects stochasticity—such as randomized parameter generation, probabilistic update selection, domain randomization, or data-driven sampling—targeted to the neural network’s architectural constraints or hardware characteristics. These approaches may address computational efficiency, regularization, robustness, hardware mappability, or generalization, and are typically evaluated in the context of large-scale learning, neural architecture search, hardware-aware training, or neural operator networks.

1. Foundational Principles of Architecture-Specific Randomization

Architecture-specific randomization refers to the targeted integration of stochastic mechanisms within neural network training that exploit, adapt to, or are conditioned on specific aspects of the network architecture or deployment constraints. Exemplary principles include:

• Randomized Block or Layer Selection: Algorithms such as RAPSA (Mokhtari et al., 2016) and Randomized Progressive Training (RPT) (Szlendak et al., 2023) update randomly chosen blocks or layers in each iteration, matching parallel hardware or promoting progressive learning.
• Random Parameter Generation: Data-driven randomized feedforward network construction (Dudek, 2019) generates hidden node weights and biases based on local training data properties, rather than uniform sampling.
• Domain Randomization for Hardware Adaptation: HW-NAS approaches (e.g., Sim-is-More (Capuano et al., 1 Apr 2025)) train controllers over a stochastic ensemble of synthetic device profiles to ensure robustness when adapting to unknown hardware.
• Randomized Learning Rates: Stochastic gradient descent (SGD) schemes with randomized learning rates (Musso, 2020) regularize optimization dynamics, promoting generalization across architectural depths.
• Random Sampling of Training Points: Neural operator networks (e.g., DeepONet) utilize stochastic sampling of input points for trunk networks (Karumuri et al., 20 Sep 2024), mitigating poor generalization and high memory load.

These mechanisms are devised to either maximize algorithmic efficiency, optimize hardware resource allocation, enhance model robustness, or reduce model and deployment risk.

2. Algorithmic Formulations and Stochastic Update Rules

Architecture-specific randomized training algorithms formalize stochasticity in update selection, gradient computation, or architecture evaluation, often with architectural awareness. Key formulations across representative works include:

Algorithm/Class	Randomization Mechanism	Mathematical Expression
RAPSA	Random block selection + random samples	$x^{t+1}_b = x^t_b - y_t V_{x_b} f(x^t,\theta^t)$
RPT	Randomized coordinate block descent	$x_{t+1} = x_t - \gamma C_t \nabla f(x_t)$
Random Learning Rate SGD	Random learning rate per step	$x_{k+1} = x_k + l \alpha v_{k+1}$
RF-DARTS	Train BN params; freeze conv weights	$ō(x, w_{conv}, w_{bn}, \alpha)$ with $w_{conv}$ fixed
BDWP Sparse Training	Randomized bidirectional pruning	$\tilde{w}_i = w_i$ if $|w_i|$ among top $N$ of $\{|w_j|\}_{j=1}^M$, else $0$

These schemes may be combined with additional randomness for algorithmic control (e.g., Bernoulli sampling for SAM selection (Zhao et al., 2022)) or proxy-based architectures for deployment renormalization (Capuano et al., 1 Apr 2025).

3. Convergence Analysis, Complexity, and Theoretical Guarantees

The convergence and complexity of randomized training algorithms depend on the interaction between stochastic update selection and architectural partitioning:

• Block Sampling Probability: Analysis (e.g., RPT (Szlendak et al., 2023)) utilizes the quantity $$L_p = \lambda_{\max}\left(P^{-1/2} L P^{-1/2}\right)$$, reflecting block smoothness and sampling probability, to derive linear or sublinear convergence rates in both convex and nonconvex regimes.
• Effective Learning Rate and Temperature: In random learning rate SGD (Musso, 2020), a Fokker–Planck formalism yields an effective temperature $T = \frac{l D}{2C(1-\mu)}$ unifying batch size, learning rate, and momentum.
• Sharpness-Aware Regularization: Randomized SAM (RST) (Zhao et al., 2022) achieves convergence bounds akin to standard SAM, with computation costs reduced by a factor $1 + p(t)$ (where $p(t)$ is the probability of SAM selection).
• Routing-Aware Memory Constraints: Proxy-based approximations (e.g., sparsity profile in routing-aware training (Weber et al., 2 Dec 2024)) allow differentiable constraint integration and efficient traversal of non-differentiable hardware mapping functions.

These analyses facilitate optimization of update frequencies, regularization strength, and resource trade-offs, tailored to the architecture and deployment target.

4. Hardware and Architecture Adaptation

Randomization is often dictated by the deployment environment:

• Hardware Co-Design: Bidirectional pruning (BDWP) and sparse tensor acceleration (Fang et al., 2023) implement fine-grained sparsity (e.g., N:M pattern) directly aligned with hardware systolic array architecture, with corresponding on-the-fly dataflow optimizations (e.g., SORE engine for sparse group indexing).
• Routing-Aware Training: DeepR extensions and dynamic pruning (Weber et al., 2 Dec 2024) shape network connectivity to minimize routing memory usage, ensuring compliance with hardware mappability proxies and enabling full chip utilization.
• Synthetic Device Randomization for HW-NAS: HW-NAS frameworks (e.g., Sim-is-More (Capuano et al., 1 Apr 2025)) create stochastic device profiles via Gaussian sampling for device-conditioned policy learning, circumventing risk of latency model overfitting and promoting robust adaptation.

These algorithms leverage stochasticity to efficiently match architectural constraints—from parallel processor block selection to neuromorphic routing layouts.

5. Neural Architecture Search with Randomization

Randomization plays a critical role in NAS:

• Random Label NAS: RLNAS (Zhang et al., 2021) dispenses with ground-truth labels, relying on the “ease of convergence” hypothesis. By measuring weight change (via angle metrics), architectures are ranked by their learning speed under random labeling, a proxy for subsequent real-task generalization.
• Random Feature Search in DARTS: RF-DARTS (Zhang et al., 2022) freezes convolution weights and trains only BN parameters, breaking skip-connection dominance (performance collapse) by ensuring unbiased gradient propagation and expressive feature selection.
• Training-Free Accuracy Proxies: HW-NAS methods (Capuano et al., 1 Apr 2025) use metrics like NASWOT, LogSynflow, and SkipScore for efficient, training-free reward estimation during architecture selection — facilitating fast controller adaptation over randomized device distributions.

Such approaches decouple architecture quality evaluation from exhaustive training, leveraging stochastic descriptors and randomized parameter selection.

6. Generalization, Robustness, and Practical Benefits

Architecture-specific randomized training algorithms confer distinct advantages:

• Enhanced Generalization: Random sampling of data points or domain coordinates (Karumuri et al., 20 Sep 2024) reduces overfitting, especially in operator learning for PDEs.
• Robust Feature Representation: Deep randomized neural networks (Gallicchio et al., 2020) and deep operator networks benefit from rich, diverse mappings where only the final readout layer is trained—leading to state-of-the-art results in domains such as time-series prediction, audio processing, and structured data learning.
• Computational Efficiency: Randomized update selection, block partitioning, and sparsity induction yield substantial speedups (e.g., up to 1.75× average, and up to 25× throughput over prior FPGA systems (Fang et al., 2023)) across various benchmarks.
• Deployment Scalability: Routing-aware memory minimization (Weber et al., 2 Dec 2024) achieves iso-accuracy at 10× less memory, directly impacting resource-constrained (e.g., neuromorphic or embedded) environments.
• Risk Mitigation: Domain randomization (Capuano et al., 1 Apr 2025) ensures HW-NAS controllers are robust to device model estimation errors, critical for risk-sensitive applications.

The combination of architectural awareness and stochastic training yields algorithms that are not only theoretically sound and computationally efficient but also tailored for large-scale, hardware-adaptive, and resource-constrained neural network deployment contexts.

7. Outlook and Future Directions

Recent trends indicate that architecture-specific randomized training algorithms will continue evolving alongside hardware accelerators, large-scale neural operator paradigms, and efficient NAS systems. Open challenges include:

• Dynamic Partitioning: Developing adaptive block partitioning and sampling strategies for nonhomogeneous architectures.
• Generalization Theory: Extending theoretical guarantees to cover collective phenomena in nonconvex, multi-objective, or hardware-constrained learning.
• Integrated Hardware-Algorithm Design: Further co-optimization of algorithmic randomization with programmable hardware and dataflow abstractions.
• Automated Proxy Design: Learning or optimizing function proxies for complex hardware constraints (e.g., mappability, latency, routing).
• Underexplored Domains: Applying architecture-specific randomization strategies to neural operators, graph neural networks, transformers, and neuromorphic computing.

The trajectory of research demonstrates the utility and adaptability of randomized algorithms in architecture-specific training, positioning this class of methods as essential to the future landscape of efficient, scalable, and robust deep learning.