Layer Normalization (LayerNorm) is one of the fundamental components in transformers that stabilizes training and improves optimization. In recent times, PreLayerNorm transformers have become the preferred choice over Post-LayerNorm transformers due to their stable gradient flow. However, the impact of LayerNorm on learning and memorization across these architectures remains unclear. In this work, we investigate how LayerNorm influences memorization and learning for Preand Post-LayerNorm transformers. We identify that LayerNorm serves as a key factor for stable learning in Pre-LayerNorm transformers, while in Post-LayerNorm transformers, it impacts memorization. Our analysis reveals that eliminating LayerNorm parameters in Pre-LayerNorm models exacerbates memorization and destabilizes learning, while in Post-LayerNorm models, it effectively mitigates memorization by restoring genuine labels. We further precisely identify that early layers LayerNorm are the most critical over middle/later layers and their influence varies across Pre and Post LayerNorm models. We have validated it through 13 models across 6 Vision and Language datasets. These insights shed new light on the role of LayerNorm in shaping memorization and learning in transformers2.

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the

Recent studies [42,56]have visualized the mean attention distance of ViTs, offering deeper insights into weight redundancy among attention heads across different layers.

With this data structure, DMoE can use beam search toselect the best experts. Manypopular architectures, including Transformers, can train entirely in that precision mode [7]. In addition, the deep learning architectures discussed in this work rely on backpropagation for training.

We study in-context learning for nonparametric regression with $α$-Hölder smooth regression functions, for some $α>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained transformer with $Θ(\log n)$ parameters and $Ω\bigl(n^{2α/(2α+d)}\log^3 n\bigr)$ pretraining sequences can achieve the minimax-optimal rate of convergence $O\bigl(n^{-2α/(2α+d)}\bigr)$ in mean squared error. Our result requires substantially fewer transformer parameters and pretraining sequences than previous results in the literature. This is achieved by showing that transformers are able to approximate local polynomial estimators efficiently by implementing a kernel-weighted polynomial basis and then running gradient descent.

Feedforward networks (FFN) are ubiquitous structures in neural systems and have been studied to understand mechanisms of reliable signal and information transmission. In many FFNs, neurons in one layer have intrinsic properties that are distinct from those in their pre-/postsynaptic layers, but how this affects network-level information processing remains unexplored. Here we show that layer-to-layer heterogeneity arising from lamina-specific cellular properties facilitates signal and information transmission in FFNs. Specifically, we found that signal transformations, made by each layer of neurons on an input-driven spike signal, demodulate signal distortions introduced by preceding layers. This mechanism boosts information transfer carried by a propagating spike signal, and thereby supports reliable spike signal and information transmission in a deep FFN. Our study suggests that distinct cell types in neural circuits, performing different computational functions, facilitate information processing on the whole.

We explore Multi-Head FFN (MH-FFN) as a replacement of FFN in the Transformer architecture, motivated by the structural similarity between single-head attention and FFN. While multi-head mechanisms enhance expressivity in attention, naively applying them to FFNs faces two challenges: memory consumption scaling with the head count, and an imbalanced ratio between the growing intermediate size and the fixed head dimension as models scale, which degrades scalability and expressive power. To address these challenges, we propose Flash Multi-Head FFN (FlashMHF), with two key innovations: an I/O-aware fused kernel computing outputs online in SRAM akin to FlashAttention, and a design using dynamically weighted parallel sub-networks to maintain a balanced ratio between intermediate and head dimensions. Validated on models from 128M to 1.3B parameters, FlashMHF consistently improves perplexity and downstream task accuracy over SwiGLU FFNs, while reducing peak memory usage by 3-5x and accelerating inference by up to 1.08x. Our work establishes the multi-head design as a superior architectural principle for FFNs, presenting FlashMHF as a powerful, efficient, and scalable alternative to FFNs in Transformers.