The Quantization Benefits of Residual-Free Transformers

Large-scale transformer training and deployment are increasingly constrained by the transfer of activations, gradients, and optimizer states across accelerators. Low-bit quantization offers a natural remedy, but transformer activations are often heavy-tailed and outlier-dominated, making simple quantization highly lossy. We show that this difficulty is not only a property of the quantizer, but also of the architecture. Specifically, residual connections can drive transformer activations away from Gaussianity during training. Using controlled comparisons between residual and residual-free transformers, we demonstrate that this effect leads to substantially higher quantization error and accuracy degradation at low precision in residual models. We explain the phenomenon through an excess kurtosis analysis, showing that residual mixing can amplify non-Gaussianity, whereas dense mixing in residual-free contracts non-Gaussianity. We then show that residual-free transformers can be made trainable using orthogonal initialization, spectral or second-order optimization, and depth-aware scaling of attention temperature. In language tasks, while there is a small drop in full precision performance, these models retain near-Gaussian activations and exhibit significantly improved robustness to low-bit quantization. Our results identify an accuracy--compressibility trade-off in transformer design and motivate architecture-level approaches to quantization-friendly foundation models.

Compressing Sine-Activated Low-Rank Adapters through Post-Training Quantization

Low-Rank Adaptation (LoRA) has become a standard approach for parameter-efficient fine-tuning, offering substantial reductions in trainable parameters by modeling updates as the product of two low-rank matrices. While effective, the low-rank constraint inherently limits representational capacity, often resulting in reduced performance compared to full-rank fine-tuning. Recent work by Ji et al. (2025) has addressed this limitation by applying a fixed-frequency sinusoidal transformation to low-rank adapters, increasing their stable rank without introducing additional parameters. This raises a crucial question: can the same sine-activated technique be successfully applied within the context of Post-Training Quantization to retain benefits even after model compression? In this paper, we investigate this question by extending the sinusoidal transformation framework to quantized LoRA adapters. We develop a theoretical analysis showing that the stable rank of a quantized adapter is tightly linked to that of its full-precision counterpart, motivating the use of such rank-enhancing functions even under quantization. Our results demonstrate that the expressivity gains from a sinusoidal non-linearity persist after quantization, yielding highly compressed adapters with negligible loss in performance. We validate our approach across a range of fine-tuning tasks for language, vision and text-to-image generation achieving significant memory savings while maintaining competitive accuracy.

Always Skip Attention

We highlight a curious empirical result within modern Vision Transformers (ViTs). Specifically, self-attention catastrophically fails to train unless it is used in conjunction with a skip connection. This is in contrast to other elements of a ViT that continue to exhibit good performance (albeit suboptimal) when skip connections are removed. Further, we show that this critical dependence on skip connections is a relatively new phenomenon, with previous deep architectures (\eg, CNNs) exhibiting good performance in their absence. In this paper, we theoretically characterize that the self-attention mechanism is fundamentally ill-conditioned and is, therefore, uniquely dependent on skip connections for regularization. Additionally, we propose Token Graying -- a simple yet effective complement (to skip connections) that further improves the condition of input tokens. We validate our approach in both supervised and self-supervised training methods.

Rethinking Softmax: Self-Attention with Polynomial Activations

This paper challenges the conventional belief that softmax attention in transformers is effective primarily because it generates a probability distribution for attention allocation. Instead, we theoretically show that its success lies in its ability to implicitly regularize the Frobenius norm of the attention matrix during training. We then explore alternative activations that regularize the Frobenius norm of the attention matrix, demonstrating that certain polynomial activations can achieve this effect, making them suitable for attention-based architectures. Empirical results indicate these activations perform comparably or better than softmax across various computer vision and language tasks, suggesting new possibilities for attention mechanisms beyond softmax.

Sine Activated Low-Rank Matrices for Parameter Efficient Learning

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of parameters, striking a balance between compactness and performance. However, a common challenge has been the compromise between parameter efficiency and the accuracy of the model, where reduced parameters often lead to diminished accuracy compared to their full-rank counterparts. In this work, we propose a novel theoretical framework that integrates a sinusoidal function within the low-rank decomposition process. This approach not only preserves the benefits of the parameter efficiency characteristic of low-rank methods but also increases the decomposition's rank, thereby enhancing model accuracy. Our method proves to be an adaptable enhancement for existing low-rank models, as evidenced by its successful application in Vision Transformers (ViT), Large Language Models (LLMs), Neural Radiance Fields (NeRF), and 3D shape modeling. This demonstrates the wide-ranging potential and efficiency of our proposed technique.