Giuseppe Bruno, Shi Chen, Zhengjiang Lin, Yury Polyanskiy, Philippe Rigollet
We study the long-context limit of softmax self-attention with a fixed query and a random context of $n$ i.i.d. keys on the sphere with the intrinsic dimension of the key distribution held fixed, viewing the inverse temperature $β_n$ as the scaling parameter that decides whether attention degenerates into uniform averaging or collapses onto the single closest key. We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $β_n^\ast \asymp n^{2/(d-1)}$ for uniform keys on $\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across all regimes of $β_n$: a subcritical regime in which the output reduces to a local average around $q$ with explicit deterministic bias and Gaussian fluctuations; a critical regime in which a finite collection of nearest keys retains macroscopic mass without single-key collapse; and a supercritical regime in which all mass concentrates on the closest key. Of notable interest is the subcritical case with identity value matrix where the attention map approximately implements a backward heat equation.
We introduce Nemotron 3.5 Super and Nemotron 3.5 Lightning, open and efficient Mixture-of-Experts Hybrid Mamba-Transformer models designed for reasoning, long-context understanding, and agentic workloads. Super is a 120B-parameter, 12B-active multimodal model, while Lightning is a smaller 30B-parameter, 3B-active text model; both designed for efficient deployment. Both models combine large-scale distillation, long-context training, and native speculative decoding, while Super further incorporates Indic continued pretraining and agentic software-engineering mid-training. We develop a comprehensive post-training pipeline spanning supervised fine-tuning and reinforcement learning (RLVR and RLHF), complemented in Super by specialized teacher training and multi- teacher on-policy distillation (MOPD). This transforms Super from a text-only base model into a multimodal agent capable of reasoning over text, images, video, and interactive tool environments. We further explore test-time scaling through parallel agent execution and self-verification. Across training and deployment, we jointly optimize capability and efficiency. Indic continued pretraining improves Indian-language benchmarks by up to 9.82 percentage points, while agentic mid-training strengthens software-engineering capabilities and robustness across agent harnesses. The post-trained Super model achieves 51.78% on SWE-bench Pro, surpassing Nemotron 3 Ultra despite using approximately 4.6x fewer active parameters. Post-training MTP boosting improves speculative- decoding acceptance length by up to 21.8% under probabilistic draft sampling, while NVFP4 quantization achieves 99.62% median accuracy recovery relative to BF16. Inference optimizations enable up to 4,856 output tokens/s/GPU on GB200 while sustaining at least 50 tokens/s/user.