With the accumulation of resources in the era of big data and the rise of pre-trained models in deep learning, optimizing neural networks for various tasks often involves different strategies for fine-tuning pre-trained models versus training from scratch. However, existing optimizers primarily focus on reducing the loss function by updating model parameters, without fully addressing the unique demands of these two major paradigms. In this paper, we propose DualOpt, a novel approach that decouples optimization techniques specifically tailored for these distinct training scenarios. For training from scratch, we introduce real-time layer-wise weight decay, designed to enhance both convergence and generalization by aligning with the characteristics of weight updates and network architecture. For more importantly fine-tuning, we integrate weight rollback with the optimizer, incorporating a rollback term into each weight update step. This ensures consistency in the weight distribution between upstream and downstream models, effectively mitigating knowledge forgetting and improving fine-tuning performance. Additionally, we extend the layer-wise weight decay to dynamically adjust the rollback levels across layers, adapting to the varying demands of different downstream tasks. Extensive experiments across diverse tasks, including image classification, object detection, semantic segmentation, and instance segmentation, demonstrate the broad applicability and state-of-the-art performance of DualOpt. Code is available at https://github.com/qklee-lz/OLOR-AAAI-2024.
Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object. Yet every weight matrix carries two distinct quantities -- a \emph{magnitude} and a \emph{direction} -- and all optimizers stepping in the matrix as a whole couple their dynamics: the directional change from an update depends on the current magnitude, while the magnitude drifts as a byproduct of learning the direction, so neither is governed directly by the learning rate. Typical training therefore leans on surrounding recipes such as weight decay and warmup to keep learning stable at scale, though these regulate the coupling only indirectly; other recent methods instead constrain the weight to a fixed-norm sphere, but add no learnable magnitude, leaving scale control to normalization layers alone. We propose \emph{Magnitude--Direction (MD) Decoupling}, an optimizer modification that factorizes each weight into a fixed-norm direction on a hypersphere and learnable per-row and per-column magnitude gains, updated at separate learning rates, all while the model still sees a single fused weight tensor. The method is agnostic to the base optimizer and removes the need for weight decay and warmup. Across both Adam and Muon, MD Decoupling improves on well-tuned baselines, transfers the optimal LR across model width without retuning, and continues to help at scale on large Mixture-of-Experts (MoE) models. Treating magnitude and direction as separately controlled quantities thus yields more predictable training dynamics and a simple, broadly applicable improvement to modern optimizers.
Alexander Hägele, Alejandro Hernández-Cano, Atli Kosson +1
We introduce SODA, a generalization of Optimistic Dual Averaging, which provides a common perspective on state-of-the-art optimizers like Muon, Lion, AdEMAMix and NAdam, showing that they can all be viewed as optimistic instances of this framework. Based on this framing, we propose a practical SODA wrapper for any base optimizer that eliminates weight decay tuning through a theoretically-grounded 1/k decay schedule. Empirical results across various scales and training horizons show that SODA consistently improves performance without any additional hyperparameter tuning.
Learning rate scheduling has evolved from the single global fixed rate of early SGD to sophisticated layer-wise adaptive strategies. We systematize this evolution into five generations: (Gen1) global fixed learning rates, (Gen2) global scheduling, (Gen3) parameter-level adaptation, (Gen4) layer-level differentiation, and (Gen5) joint layer-time scheduling. We trace the fundamental motivation behind each transition, showing how the shift from one-size-fits-all to tailoring by layer and time addresses the impossible trinity of transfer learning: lower layers require small updates to preserve general knowledge while higher layers need large updates to adapt to new tasks. Building on this taxonomy, we propose Discriminative Adaptive Layer Scaling (DALS), a unified framework that integrates phase-adaptive cosine scheduling, depth-aware Grokfast gradient filtering, and LARS-style trust ratios into a single coherent optimizer. We benchmark 18 strategies including three DALS variants across all five generations on five datasets: synthetic, CIFAR-10 (from scratch), RTE, TREC-6, and IMDb (fine-tuning). On synthetic, DALS achieves the best accuracy at 98.0%, while DALS-Fast reaches 90% in just 3 epochs. The cross-dataset analysis reveals striking regime-dependent patterns -- no single strategy wins across all regimes. Critically, STLR+Discriminative, the ULMFiT champion, catastrophically fails on from-scratch tasks (43.6% on TREC-6 from scratch vs. 96.8% with RAdam), confirming that directional decay biases are harmful without pretrained features. DALS avoids either extreme, achieving the best synthetic result while maintaining competitive fine-tuning performance.