AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights (2006.08217v3)

Abstract: Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to LLMling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

• The paper identifies that normalization-induced scale invariance causes premature decay of effective step sizes in momentum optimizers.
• The paper introduces a projection-based method (AdamP and SGDP) to counter rapid learning rate decline while preserving convergence.
• Experimental results across 13 datasets, including ImageNet, demonstrate consistent performance improvements with the proposed approach.

Analysis of "AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-Invariant Weights"

The paper entitled "AdamP: slowing down the slowdown for momentum optimizers on scale-invariant weights" presents a detailed examination of the interaction between momentum-based gradient descent (GD) optimizers and scale-invariant weights in deep neural networks. This paper specifically identifies a problematic rapid reduction in the effective step sizes caused by the momentum in gradient descent, which the authors argue has previously been overlooked. The profound implication here is the potential sub-optimality introduced to the prevalent deep learning frameworks that leverage both momentum-based optimizers and normalization techniques.

Core Contributions

1. Scale Invariance and Momentum Interaction: The paper highlights that normalization techniques such as Batch Normalization (BN) introduce scale invariance which, in conjunction with momentum-based optimizers, leads to an undesirably rapid reduction in effective step sizes. This is attributed to increased weight norms that decelerate the optimization process in the effective space.
2. Theoretical Insights: Leveraging existing theories, the authors provide a rigorous exploration of step size dynamics. They argue that the combination of momentum and scale invariance spur the premature decay of effective step sizes, substantiating this with both theoretical formulations and empirical evidence.
3. Proposed Solution – AdamP and SGDP: The paper introduces an adaptation strategy to mitigate the identified rapid norm growth problem by projecting out the radial component from the update directions in momentum optimizers. This novel projection mechanism ensures increased stability without altering the effective update directions, thereby maintaining the convergence properties inherent in GD optimizers.
4. Experimental Validation: Through an exhaustive series of benchmarks, the paper verifies the proposed solutions, SGDP and AdamP, against traditional baselines. These benchmarks include diverse tasks such as image classification, object detection, LLMing, and more, across 13 datasets demonstrating consistent performance improvements.

Experimental Significance

The experiments spread across a range of applications prove the robustness and general applicability of the proposed optimization techniques. Notable improvements are observed in tasks ranging from large-scale image classification on ImageNet to audio tagging and LLMing. The application of AdamP resulted in performance enhancements across multiple architectures and datasets, reinforcing the practical efficacy of ameliorating the scale invariance-induced slowdown.

Practical and Theoretical Implications

From a practical standpoint, the research suggests a revision in how deep learning practitioners pair optimization techniques with network architectures incorporating normalization layers. This research challenges the status quo of momentum usage in optimization strategies within scale-invariant contexts, proposing a more refined framework to ensure optimal learning rates.

Theoretically, this work invites further exploration into the mechanics of optimization in deep learning, particularly in understanding the intricate relationship between various forms of normalization and optimizer configurations. The projection-based method devised in this paper raises broader questions about the adaptability of GD principles in non-standard parameter spaces, prompting discussion on future potential adjustments to optimizer design paradigms.

Future Directions

The insights and methodologies detailed in this paper could spearhead future research aimed at expounding the potential refinements in GD algorithms when interacting with advanced network designs. Exploring further generalizations of the AdamP principles to different forms of scale-invariance and normalization could expose new techniques for fast and stable convergence in deep learning and artificial intelligence frameworks.

In summary, this paper offers a comprehensive examination of a nuanced problem within the context of deep learning optimization, presenting a methodologically sound solution with tangible improvements seen across various benchmarks. The fusion of rigorous theoretical backing and practical success positions AdamP and SGDP as significant contributions to the ongoing evolution of optimization strategies in AI research.