Normalization is a critical component for stabilizing Transformer training, yet the choice between static strategies such as Layer Normalization (LN) and adaptive alternatives remains largely task-dependent. In this paper, we investigate a key optimization challenge in differentiable normalization gating. Our experiments show that, on relatively stationary vision tasks, the high gradient variance introduced by Gumbel-Softmax gating can hinder convergence of the routing mechanism, causing learned gates to underperform simple random selection. In contrast, on non-stationary language modeling and classification tasks, sustained gating diversity enables the model to learn more effective layer-wise normalization policies. Motivated by these observations, we propose AutoNorm-S (Stabilized), a training strategy that mitigates optimization instability through a gate-freezing schedule. AutoNorm-S achieves competitive or improved performance across multiple benchmarks, outperforming adaptive normalization baselines on NLP datasets, including PTB and SST-2, while remaining competitive on standard vision benchmarks. These results suggest that decoupling normalization selection from optimization noise provides a practical and principled approach for adaptive normalization in Transformer architectures.
The Normalized Transformer, or nGPT (arXiv:2410.01131) achieves impressive training speedups and does not require weight decay or learning rate warmup. However, despite having hyperparameters that explicitly scale with model size, we observe that nGPT does not exhibit learning rate transfer across model dimension and token horizon. To rectify this, we combine numerical experiments with a principled use of alignment exponents (arXiv:2407.05872) to revisit and modify the μP approach to hyperparameter transfer (arXiv:2011.14522). The result is a novel nGPT parameterization we call νGPT. Through extensive empirical validation, we find νGPT exhibits learning rate transfer across width, depth, and token horizon.
Low-rank adaptation (LoRA) is commonly viewed as an update-space approximation to full fine-tuning, yet this view is incomplete for self-gated Transformer feed-forward networks. In gated FFNs, a low-rank residual can change not only projected features but also the nonlinear selection weights that determine which channels contribute to the output. We formalize this effect as selection misalignment and connect it to the local effective homogeneity of self-gated activations. This motivates a nonlinearity-aware principle for parameter-efficient fine-tuning: low-rank updates should allocate capacity to gate channels whose nonlinear states remain responsive and should shape the temporal evolution of selection. We propose NA-LoRA, a training-only method with two lightweight mechanisms: a derivative-based temporal-importance mask for gate-related LoRA updates and an activation-specific step-scaling rule when a meaningful coarse effective-homogeneity partition is available. NA-LoRA adds no auxiliary loss and incurs no inference-time overhead. Experiments on language-model fine-tuning and vision-language transfer benchmarks show that NA-LoRA consistently improves over vanilla LoRA and is competitive with or better than strong PEFT variants.
We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical risk minimization (ERM) with a primal-dual training scheme. This approach yields models whose intermediate representations decrease the loss monotonically in expectation across layers. We apply our method to both unrolled transformer architectures and conventional pretrained transformers on tasks of video denoising and text classification. Across these settings, we observe constrained transformers achieve stronger robustness to perturbations and maintain higher out-of-distribution generalization, while preserving in-distribution performance.
Javier Porras-Valenzuela, Samar Hadou, Alejandro Ribeiro