Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization (1906.02107v2)

Abstract: Optimization of Binarized Neural Networks (BNNs) currently relies on real-valued latent weights to accumulate small update steps. In this paper, we argue that these latent weights cannot be treated analogously to weights in real-valued networks. Instead their main role is to provide inertia during training. We interpret current methods in terms of inertia and provide novel insights into the optimization of BNNs. We subsequently introduce the first optimizer specifically designed for BNNs, Binary Optimizer (Bop), and demonstrate its performance on CIFAR-10 and ImageNet. Together, the redefinition of latent weights as inertia and the introduction of Bop enable a better understanding of BNN optimization and open up the way for further improvements in training methodologies for BNNs. Code is available at: https://github.com/plumerai/rethinking-bnn-optimization

• The paper critically re-interprets Binarized Neural Network (BNN) training, challenging the traditional view of latent weights and proposing an inertia-focused perspective.
• Based on this view, the authors introduce Bop, the first BNN optimizer designed without latent weights, using exponential moving averages of gradients and thresholds for weight flips.
• Empirical evaluation shows Bop achieves competitive accuracy on CIFAR-10 and ImageNet across various BNN architectures, validating its effectiveness and conceptual clarity.

Overview of "Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization"

This paper presents a critical examination and re-interpretation of the optimization methodologies employed in Binarized Neural Networks (BNNs). It challenges the traditional paradigm of using real-valued "latent weights" during the training of BNNs, suggesting a shift in perspective that prioritizes the role of inertia over the common approximation view. BNNs, where both weights and activations are limited to {-1, +1}, offer substantial reductions in computation and memory usage, making them appealing for edge applications. However, training these networks efficiently remains a key challenge.

The authors claim that the latent weights conventionally utilized in BNN training do not function analogously to their counterparts in real-valued networks. Rather, they serve as inertia during training, maintaining stability by providing resistance against changes to the binary weights. This inertia-oriented perspective deviates from previous interpretations that viewed binary weights as approximations to latent weights.

Introduction of the Binary Optimizer (Bop)

Using insights from this novel interpretation, the authors introduce "Bop," the first optimizer designed specifically for BNNs. Unlike traditional methods that rely heavily on gradient information encoded in latent weights, Bop operates without them, utilizing a direct mechanism to determine weight flips. The optimizer focuses on the consistency and strength of gradient signals to manipulate the inertia, thus reducing the noise typically associated with BNN training.

Bop is built around three central ideas: simplifying the optimization to focus solely on weight flips, relying on exponential moving averages of gradients to assess the consistency of updates, and employing a threshold to filter out weak signals. By doing so, Bop reduces the complexity seen in traditional training methods and instead offers parameters that have a clear connection to weight flipping—namely the adaptivity rate $\gamma$ and the threshold $\tau$.

Empirical Evaluation

The paper includes an extensive empirical evaluation of Bop. The authors validate their approach using CIFAR-10 and ImageNet datasets, achieving competitive results that either match or exceed the state-of-the-art accuracy for various BNN architectures such as BinaryNet, XNOR-Net, and BiReal-Net. For CIFAR-10, the combination of a decaying adaptivity rate and consistent threshold levels proves effective in maintaining stable optimization trajectories, evidenced by lower weight flip rates and improved accuracy. On ImageNet, Bop demonstrates its adaptability and robustness across diverse BNN models, further supporting the authors' claims about its efficacy and conceptual clarity.

Implications and Future Directions

The implications of stripping away latent weights suggest a wider array of strategies to improve BNN optimization beyond the goal of better approximating real-valued networks. This paradigm shift not only simplifies methodological complexity—reducing memory usage and hyperparameter tuning—but also paves the way for future research into optimization mechanics uniquely suited to BNNs. Potential avenues include the development of novel regularization techniques designed explicitly for binary domains or adaptive mechanisms that dynamically adjust parameters such as $\gamma$ and $\tau$.

The paper invites reconsideration of numerous BNN optimization practices, suggesting that improving performance may be less about mimicking real-valued paradigms and more about embracing binary-specific characteristics. Future research could explore adaptive schedules for Bop parameters to further refine binary optimization artefacts, potentially leading to improved generalization and efficiency in diverse applications.

Overall, this paper offers a thoughtful re-evaluation of BNN training strategies and provides a robust basis for continued advancement in this burgeoning field.