Data-Aware Training Quality Monitoring and Certification for Reliable Deep Learning

TL;DR

The YES training bounds, a novel framework for real-time, data-aware certification and monitoring of neural network training, are introduced, offering a powerful tool for real-time evaluation and setting a new standard for training quality assurance in deep learning.

Abstract

Deep learning models excel at capturing complex representations through sequential layers of linear and non-linear transformations, yet their inherent black-box nature and multi-modal training landscape raise critical concerns about reliability, robustness, and safety, particularly in high-stakes applications. To address these challenges, we introduce YES training bounds, a novel framework for real-time, data-aware certification and monitoring of neural network training. The YES bounds evaluate the efficiency of data utilization and optimization dynamics, providing an effective tool for assessing progress and detecting suboptimal behavior during training. Our experiments show that the YES bounds offer insights beyond conventional local optimization perspectives, such as identifying when training losses plateau in suboptimal regions. Validated on both synthetic and real data, including image denoising tasks, the bounds prove effective in certifying training quality and guiding adjustments to enhance model performance. By integrating these bounds into a color-coded cloud-based monitoring system, we offer a powerful tool for real-time evaluation, setting a new standard for training quality assurance in deep learning.

Figures (13)

• Figure 1: Schematic of the iterative mapping from $\mathbf{X}$ to $\mathbf{Y}$ through intermediate steps $\mathbf{Y}_2, \mathbf{Y}_3, \ldots, \mathbf{Y}_K$.
• Figure 2: The illustration of a non-monotonic per-layer error (in dB) observed across both training and test stages for a DUN.
• Figure 3: YES training cloud-system for quality monitoring: A training loss that remains above the YES training cloud (red area) indicates ineffective training. When the loss penetrates the cloud (yellow area), it suggests that meaningful training has occurred or is in progress—network weights have been significantly influenced by the data. However, caution is advised, as the training is certainly not optimal. Dropping below the cloud (green area) signals effective training in in progress and suggests potential for optimality. It may also indicate diminishing returns in the training process, where further gains could be incremental.
• Figure 4: YES training clouds for the phase retrieval model. The clouds are shown for a fully connected network with $5$ layers, each corresponding to different training parameter settings. Figs (a)-(c) illustrate the performance of the YES bounds for different batch sizes: $20$, $100$, and $500$, respectively, with a learning rate of $1e-3$. Figs. (d)-(f) compare the YES bounds to the training process with different learning rates: $1e-3$, $1e-2$, and $1e-4$. As seen in Figs. (b) and (c), increasing the batch size slows the convergence rate, with the training loss entering the green region after more than $100$ epochs. Interestingly, when adjusting the learning rate to $1e-2$ and $1e-4$, as shown in Figs. (e) and (f), the training struggles to reach the green region, suggesting that a learning rate of $1e-3$ is the proper parameter for this task. This observation is further supported by comparing the loss functions across Figs. (d)-(f). Another notable observation in Fig. (f) is that both the YES bound and the training loss converge relatively closely until the final convergence, indicating that the training solution behaves similarly to a linear projection.
• Figure 5: YES training clouds are utilized for the signal denoising task, displayed for a fully connected network comprising five layers, each representing a unique training parameter configuration. Figs. (a)-(c) demonstrate the YES bounds' performance across different batch sizes: $20$, $100$, and $500$ with a learning rate of $1e-3$. Lastly, Figs. (d)-(f) compare the YES bounds against the training process employing varying learning rates: $1e-3$, $5e-3$, and $1e-4$. As shown in Fig. (b), training with a batch size of $100$ significantly delays reaching the green region, indicating that convergence is faster with a batch size of $20$ than $100$. As shown in Fig. (c), the training plateaus in the yellow region, indicating that the solution obtained by the network is far from the optimal. In Fig. (e), increasing the learning rate to $1e-2$ accelerates convergence compared to $1e-3$, while in Fig. (f), the training loss plateaus in the yellow region for the learning rate of $1e-4$.

Theorems & Definitions (2)

• Theorem 1
• proof