Xiaofeng Ye | Searcharxiv

arXiv2025

MixNet: A Runtime Reconfigurable Optical-Electrical Fabric for Distributed Mixture-of-Experts Training

Mixture-of-Expert (MoE) models outperform conventional models by selectively activating different subnets, named experts, on a per-token basis. This gated computation generates dynamic communications that cannot be determined beforehand, challenging the existing GPU interconnects that remain static during the distributed training process. In this paper, we advocate for a first-of-its-kind system, called MixNet, that unlocks topology reconfiguration during distributed MoE training. Towards this vision, we first perform a production measurement study and show that the MoE dynamic communication pattern has strong locality, alleviating the requirement of global reconfiguration. Based on this, we design and implement a regionally reconfigurable high-bandwidth domain on top of existing electrical interconnects using optical circuit switching (OCS), achieving scalability while maintaining rapid adaptability. We have built a fully functional MixNet prototype with commodity hardware and a customized collective communication runtime that trains state-of-the-art MoE models with in-training topology reconfiguration across 32 A100 GPUs. Large-scale packet-level simulations show that MixNet delivers comparable performance as the non-blocking fat-tree fabric while boosting the training cost efficiency (e.g., performance per dollar) of four representative MoE models by 1.2x-1.5x and 1.9x-2.3x at 100 Gbps and 400 Gbps link bandwidths, respectively.

cs.NI↗

arXiv2024

Fourier integral operators on Hardy spaces with Hormander class

In this note, we consider a Fourier integral operator defined by \begin{align*} T_{ϕ,a}f(x) = \int_{\mathbb{R}^{n}}e^{iϕ(x,ξ)}a(x,ξ)\widehat{f} ξ)dξ, \end{align*}here $a$ is the amplitude, and $ϕ$ is the phase. Let $0\leqρ\leq 1,n\geq 2$ or $0\leqρ<1,n=1$ and $$m_p=\frac{ρ-n}{p}+(n-1)\min\{\frac 12,ρ\}.$$ If $a$ belongs to the forbidden Hörmander class $S^{m_p}_{ρ,1}$ and $ϕ\in Φ^{2}$ satisfies the strong non-degeneracy condition, then for any $\frac {n}{n+1}<p\leq 1$, we can show that the Fourier integral operator $T_{ϕ,a}$ is bounded from the local Hardy space $h^p$ to $L^p$. Furthermore, if $a$ has compact support in variable $x$, then we can extend this result to $0<p\leq 1$. As $S^{m_p}_{ρ,δ}\subset S^{m_p}_{ρ,1}$ for any $0\leq δ\leq 1$, our result supplements and improves upon recent theorems proved by Staubach and his collaborators for $a\in S^{m}_{ρ,δ}$ when $δ$ is close to 1. As an important special case, when $n\geq 2$, we show that $T_{ϕ,a}$ is bounded from $H^1$ to $L^1$ if $a\in S^{(1-n)/2}_{1,1}$ which is a generalization of the well-known Seeger-Sogge-Stein theorem for $a\in S^{(1-n)/2}_{1,0}$. This result is false when $n=1$ and $a\in S^{0}_{1,1}$.

math.DG↗