We study post-training for dynamically routed mixture-of-experts (MoE) models, focusing on integrating independently optimized specialists while keeping consolidation efficient. Our approach combines calibrated multi-teacher on-policy distillation (C-MOPD), which matches each selected teacher on a local Top-$K$ support with teacher-wise loss normalization and clipping, with an execution path that uses post-capacity bounded-width dispatch, final-route replay, and asynchronous rollout--training overlap. On Turing-20B-A2B, the selected model achieves a four-domain normalized integration score of 0.9988 and retains at least 90.16\% of the measured specialist gain in every domain. At matched $K=32$, the full calibration objective scores 0.9962, compared with 0.9724 without calibration and 0.9834 without clipping. At a matched 8K response cap, the model exceeds both shared SFT and Qwen3-8B on all four reasoning-enabled mathematics and code benchmarks (unweighted mean: 85.92, versus 80.33 for Qwen3-8B and 74.21 for SFT), and improves over SFT on ten of twelve broader evaluation metrics. In a PPU-based profile, the combined execution configuration reduces consolidation step time from 398.7 to 139.3 seconds, an observed 2.86$\times$ speedup over serial execution. These results demonstrate strong specialist integration alongside more efficient consolidation, while reflecting the complete training and execution framework rather than any single component.
Federated hypergraph learning with latent cross-client hyperedge correspondence poses fundamental identifiability and computational challenges, as the same local release can correspond to multiple global hypergraph structures. We characterize the tractability of recovering these latent correspondences, showing tractable pairwise assignment but generally intractable multi-client hyperedge matching. Building on this characterization, we derive a cross-entropy decomposition that reveals when local prediction can outperform predictors fitted with additional cross-client information. Motivated by this principle, we introduce Federated Adaptive Spectral Training with Representation Alignment (FedASTRA), which learns correspondence-invariant diffusion representations through adaptive heat diffusion and masked latent prediction while communicating model parameters only. We establish its asymptotic optimality with respect to the permitted local information and prove global population-risk convergence under explicit conditions on recovery, representation, and update alignment. Experiments on eight real-world datasets demonstrate the effectiveness of FedASTRA against identifier-free federated graph and hypergraph methods. On ogbn-papers100M, FedASTRA reaches the performance-communication Pareto frontier, achieving 50.07 Accuracy and 29.73 Macro-F1 while communicating only 59.60 MiB per round.
Most ATP benchmarks embed the final answer within the formal statement — a convention we call “Easy Mode” — a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model capability.We call the stricter, more realistic setting “Hard Mode”: the system must independently discover the answer before constructing a formal proof.To enable Hard Mode research, we make two contributions.First, we release MiniF2F-Hard and FIMO-Hard, expert-reannotated Hard Mode variants of two widely-used ATP benchmarks.Second, we introduce Discover And Prove (DAP), an agentic framework that uses LLM natural-language reasoning with explicit self-reflection to discover answers, then rewrites Hard Mode statements into Easy Mode ones for existing ATP provers.DAP sets the state of the art: on CombiBench it raises solved problems from 7 (previous SOTA, Pass@16) to 10; on PutnamBench it is the first system to formally prove 36 theorems in Hard Mode — while simultaneously revealing that state-of-the-art LLMs exceed 80% answer accuracy on the same problems where formal provers manage under 10%, exposing a substantial gap that Hard Mode benchmarks are uniquely suited to measure.
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cs.CL · cs.AI
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表