Synergistic Intra- and Cross-Layer Regularization Losses for MoE Expert Specialization

Sparse Mixture-of-Experts (MoE) models scale Transformers efficiently but suffer from expert overlap -- redundant representations across experts and routing ambiguity, resulting in severely underutilized model capacity. While architectural solutions like DeepSeekMoE promote specialization, they require substantial structural modifications and rely solely on intra-layer signals. In this paper, we propose two plug-and-play regularization losses that enhance MoE specialization and routing efficiency without modifying router or model architectures. First, an intra-layer specialization loss penalizes cosine similarity between experts' SwiGLU activations on identical tokens, encouraging experts to specialize in complementary knowledge. Second, a cross-layer coupling loss maximizes joint Top-$k$ routing probabilities across adjacent layers, establishing coherent expert pathways through network depth while reinforcing intra-layer expert specialization. Both losses are orthogonal to the standard load-balancing loss and compatible with both the shared-expert architecture in DeepSeekMoE and vanilla top-$k$ MoE architectures. We implement both losses as a drop-in Megatron-LM module. Extensive experiments across pre-training, fine-tuning, and zero-shot benchmarks demonstrate consistent task gains, higher expert specialization, and lower-entropy routing; together, these improvements translate into faster inference via more stable expert pathways.

SPARKLE: A Unified Single-Loop Primal-Dual Framework for Decentralized Bilevel Optimization

This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient tracking to mitigate the influence of data heterogeneity, without exploring other well-known heterogeneity-correction techniques such as EXTRA or Exact Diffusion. Additionally, these studies often employ identical decentralized strategies for both upper- and lower-level problems, neglecting to leverage distinct mechanisms across different levels. To address these limitations, this paper proposes SPARKLE, a unified Single-loop Primal-dual AlgoRithm frameworK for decentraLized bilEvel optimization. SPARKLE offers the flexibility to incorporate various heterogeneitycorrection strategies into the algorithm. Moreover, SPARKLE allows for different strategies to solve upper- and lower-level problems. We present a unified convergence analysis for SPARKLE, applicable to all its variants, with state-of-the-art convergence rates compared to existing decentralized bilevel algorithms. Our results further reveal that EXTRA and Exact Diffusion are more suitable for decentralized bilevel optimization, and using mixed strategies in bilevel algorithms brings more benefits than relying solely on gradient tracking.

Decentralized Bilevel Optimization over Graphs: Loopless Algorithmic Update and Transient Iteration Complexity

Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in which nodes communicate with immediate neighbors without a central server, thereby improving communication efficiency and enhancing algorithmic robustness. However, current decentralized SBO algorithms face challenges, including expensive inner-loop updates and unclear understanding of the influence of network topology, data heterogeneity, and the nested bilevel algorithmic structures. In this paper, we introduce a single-loop decentralized SBO (D-SOBA) algorithm and establish its transient iteration complexity, which, for the first time, clarifies the joint influence of network topology and data heterogeneity on decentralized bilevel algorithms. D-SOBA achieves the state-of-the-art asymptotic rate, asymptotic gradient/Hessian complexity, and transient iteration complexity under more relaxed assumptions compared to existing methods. Numerical experiments validate our theoretical findings.