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.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves $2$-$3\times$ end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.