Tensor parallelism (TP) in large-scale LLM inference and training introduces frequent collective operations that dominate inter-GPU communication. While in-switch computing, exemplified by NVLink SHARP (NVLS), accelerates collective operations by reducing redundant data transfer, its communication-centric design philosophy introduces the mismatch between its communication mode and the memory semantic requirement of LLM's computation kernel. Such a mismatch isolates the compute and communication phases, resulting in underutilized resources and limited overlap in multi-GPU systems. To address the limitation, we propose CAIS, the first ComputeAware In-Switch computing framework that aligns communication modes with computation's memory semantics requirement. CAIS consists of three integral techniques: (1) compute-aware ISA and microarchitecture extension to enable compute-aware in-switch computing. (2) merging-aware TB (Thread Block) coordination to improve the temporal alignment for efficient request merging. (3) graph-level dataflow optimizer to achieve a tight cross-kernel overlap. Evaluations on LLM workloads show that CAIS achieves$1.38 \times$average end-to-end training speedup over the SOTA NVLS-enabled solution, and$1.61 \times$over T3, the SOTA compute-communicate overlap solutions but do not leverage NVLS, demonstrating its effectiveness in accelerating TP on multi-GPU systems.

Mixture-of-Experts (MoE) has been adopted by many leading large models to reduce computational requirements. However, frequent inter-GPU communication in MoE expert parallelism (EP) becomes a performance challenge. We observe substantial redundant inter-GPU data transfers in MoE that can be potentially addressed by in-switch computing. Unfortunately, the existing solution, NVLink SHARP (NVLS), can only support static collectives with regular patterns, incapable of dynamic communication with irregular patterns in MoE. To bridge the functionality gap, we propose DySHARP, an integral dynamic in-switch computing solution to accelerate MoE, encompassing both communication primitives and communication-aware scheduling: 1) Dynamic multimem addressing co-designs ISA, architecture, and runtime, as a dynamic extension to NVLS, reducing redundant traffic. However, the resulting traffic reduction is inherently asymmetric between two directions, preventing it from directly translating into speedup. 2) Token-centric kernel fusion deeply fuses the dispatch-computation-combine pipeline, resolving this asymmetry to translate traffic reduction into actual speedup. Compared with the state-of-the-art solution, DySHARP achieves up to 1.79× speedup.

Online optimization has witnessed a massive surge of research attention in recent years. In this paper, we propose online gradient descent and online bandit algorithms over Riemannian manifolds in full information and bandit feedback settings respectively, for both geodesically convex and strongly geodesically convex functions. We establish a series of upper bounds on the regrets for the proposed algorithms over Hadamard manifolds. We also find a universal lower bound for achievable regret on Hadamard manifolds. Our analysis shows how time horizon, dimension, and sectional curvature bounds have impact on the regret bounds. When the manifold permits positive sectional curvature, we prove similar regret bound can be established by handling non-constrictive project maps. In addition, numerical studies on problems defined on symmetric positive definite matrix manifold, hyperbolic spaces, and Grassmann manifolds are provided to validate our theoretical findings, using synthetic and real-world data.

We consider a distributed online convex optimization problem when streaming data are distributed among computing agents over a connected communication network. Since the data are high-dimensional or the network is large-scale, communication load can be a bottleneck for the efficiency of distributed algorithms. To tackle this bottleneck, we apply the state-of-art data compression scheme to the fundamental GD-based distributed online algorithms. Three algorithms with difference-compressed communication are proposed for full information feedback (DC-DOGD), one-point bandit feedback (DC-DOBD), and two-point bandit feedback (DC-DO2BD), respectively. We obtain regret bounds explicitly in terms of time horizon, compression ratio, decision dimension, agent number, and network parameters. Our algorithms are proved to be no-regret and match the same regret bounds, w.r.t. time horizon, with their uncompressed versions for both convex and strongly convex losses. Numerical experiments are given to validate the theoretical findings and illustrate that the proposed algorithms can effectively reduce the total transmitted bits for distributed online training compared with the uncompressed baseline.

We consider online optimization over Riemannian manifolds, where a learner attempts to minimize a sequence of time-varying loss functions defined on Riemannian manifolds. Though many Euclidean online convex optimization algorithms have been proven useful in a wide range of areas, less attention has been paid to their Riemannian counterparts. In this paper, we study Riemannian online gradient descent (R-OGD) on Hadamard manifolds for both geodesically convex and strongly geodesically convex loss functions, and Riemannian bandit algorithm (R-BAN) on Hadamard homogeneous manifolds for geodesically convex functions. We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension. We also find a universal lower bound for the achievable regret by constructing an online convex optimization problem on Hadamard manifolds. All the obtained regret bounds match the corresponding results are provided in Euclidean spaces. Finally, some numerical experiments validate our theoretical results.