Nir Ailon

Aakshita Chandiramani, Aaron Blakeman, Abdullahi Olaoye et al. · amazon-science, cmu

We describe the pre-training, post-training, and quantization of Nemotron 3 Super, a 120 billion (active 12 billion) parameter hybrid Mamba-Attention Mixture-of-Experts model. Nemotron 3 Super is the first model in the Nemotron 3 family to 1) be pre-trained in NVFP4, 2) leverage LatentMoE, a new Mixture-of-Experts architecture that optimizes for both accuracy per FLOP and accuracy per parameter, and 3) include MTP layers for inference acceleration through native speculative decoding. We pre-trained Nemotron 3 Super on 25 trillion tokens followed by post-training using supervised fine tuning (SFT) and reinforcement learning (RL). The final model supports up to 1M context length and achieves comparable accuracy on common benchmarks, while also achieving up to 2.2x and 7.5x higher inference throughput compared to GPT-OSS-120B and Qwen3.5-122B, respectively. Nemotron 3 Super datasets, along with the base, post-trained, and quantized checkpoints, are open-sourced on HuggingFace.

Aaron Blakeman, Aaron Grattafiori, Aarti Basant et al. · nvidia

We introduce the Nemotron 3 family of models - Nano, Super, and Ultra. These models deliver strong agentic, reasoning, and conversational capabilities. The Nemotron 3 family uses a Mixture-of-Experts hybrid Mamba-Transformer architecture to provide best-in-class throughput and context lengths of up to 1M tokens. Super and Ultra models are trained with NVFP4 and incorporate LatentMoE, a novel approach that improves model quality. The two larger models also include MTP layers for faster text generation. All Nemotron 3 models are post-trained using multi-environment reinforcement learning enabling reasoning, multi-step tool use, and support granular reasoning budget control. Nano, the smallest model, outperforms comparable models in accuracy while remaining extremely cost-efficient for inference. Super is optimized for collaborative agents and high-volume workloads such as IT ticket automation. Ultra, the largest model, provides state-of-the-art accuracy and reasoning performance. Nano is released together with its technical report and this white paper, while Super and Ultra will follow in the coming months. We will openly release the model weights, pre- and post-training software, recipes, and all data for which we hold redistribution rights.

Nir Ailon, Holger Rauhut

We study constructions of $k \times n$ matrices $A$ that both (1) satisfy the restricted isometry property (RIP) at sparsity $s$ with optimal parameters, and (2) are efficient in the sense that only $O(n\log n)$ operations are required to compute $Ax$ given a vector $x$. Our construction is based on repeated application of independent transformations of the form $DH$, where $H$ is a Hadamard or Fourier transform and $D$ is a diagonal matrix with random $\{+1,-1\}$ elements on the diagonal, followed by any $k \times n$ matrix of orthonormal rows (e.g.\ selection of $k$ coordinates). We provide guarantees (1) and (2) for a larger regime of parameters for which such constructions were previously unknown. Additionally, our construction does not suffer from the extra poly-logarithmic factor multiplying the number of observations $k$ as a function of the sparsity $s$, as present in the currently best known RIP estimates for partial random Fourier matrices and other classes of structured random matrices.

Akhiad Bercovich, Nir Ailon, Vladimir Anisimov et al.

Reasoning-focused LLMs improve answer quality by generating longer reasoning traces, but the additional tokens dramatically increase serving cost, motivating inference optimization. We extend and apply Puzzle, a post-training neural architecture search (NAS) framework, to gpt-oss-120B to produce gpt-oss-puzzle-88B, a deployment-optimized derivative. Our approach combines heterogeneous MoE expert pruning, selective replacement of full-context attention with window attention, FP8 KV-cache quantization with calibrated scales, and post-training reinforcement learning to recover accuracy, while maintaining low generation length. In terms of per-token speeds, on an 8XH100 node we achieve 1.63X and 1.22X throughput speedups in long-context and short-context settings, respectively. gpt-oss-puzzle-88B also delivers throughput speedups of 2.82X on a single NVIDIA H100 GPU. However, because token counts can change with reasoning effort and model variants, per-token throughput (tok/s) and latency (ms/token) do not necessarily lead to end-to-end speedups: a 2X throughput gain is erased if traces grow 2X. Conversely, throughput gains can be spent on more reasoning tokens to improve accuracy; we therefore advocate request-level efficiency metrics that normalize throughput by tokens generated and trace an accuracy--speed frontier across reasoning efforts. We show that gpt-oss-puzzle-88B improves over gpt-oss-120B along the entire frontier, delivering up to 1.29X higher request-level efficiency. Across various benchmarks, gpt-oss-puzzle-88B matches or slightly exceeds the parent on suite-average accuracy across reasoning efforts, with retention ranging from 100.8% (high) to 108.2% (low), showing that post-training architecture search can substantially reduce inference costs without sacrificing quality.

Nir Ailon, Supratim Shit

Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur high costs in time and energy in both training and deployment. Using a matrix factorization technique, we show how to obtain similar guarantees to those obtained by a prior analysis while reducing training and inference resource costs. The importance of our result further increases when the input points' data dimension is in the same order as the number of input points. More generally, our work suggests how to analyze large width networks in which dense linear layers are replaced with a low complexity factorization, thus reducing the heavy dependence on the large width.

Akhiad Bercovich, Tomer Ronen, Talor Abramovich et al. · nvidia

Large language models (LLMs) offer remarkable capabilities, yet their high inference costs restrict wider adoption. While increasing parameter counts improves accuracy, it also broadens the gap between state-of-the-art capabilities and practical deployability. We present Puzzle, a hardware-aware framework that accelerates the inference of LLMs while preserving their capabilities. Using neural architecture search (NAS) at a large-scale, Puzzle optimizes models with tens of billions of parameters. Our approach utilizes blockwise local knowledge distillation (BLD) for parallel architecture exploration and employs mixed-integer programming for precise constraint optimization. We showcase our framework's impact via Llama-3.1-Nemotron-51B-Instruct (Nemotron-51B) and Llama-3.3-Nemotron-49B, two publicly available models derived from Llama-70B-Instruct. Both models achieve a 2.17x inference throughput speedup, fitting on a single NVIDIA H100 GPU while retaining 98.4% of the original model's benchmark accuracies. These are the most accurate models supporting single H100 GPU inference with large batch sizes, despite training on 45B tokens at most, far fewer than the 15T used to train Llama-70B. Lastly, we show that lightweight alignment on these derived models allows them to surpass the parent model in specific capabilities. Our work establishes that powerful LLM models can be optimized for efficient deployment with only negligible loss in quality, underscoring that inference performance, not parameter count alone, should guide model selection.

Nir Ailon, Akhiad Bercovich, Yahel Uffenheimer et al.

Modern AI relies on huge matrix multiplications (MatMuls), whose computation poses a scalability problem for inference and training. We propose an alternative, GPU native bilinear operator to MatMuls in neural networks, which offers a three-way tradeoff between: speed, accuracy and parameter count. In particular, this operator requires substantially fewer FLOPs to evaluate ($\ll n^3$), yet increases the parameter count compared to MatMul ($\gg n^2$). We call this operator Strassen-Tile (STL). The key idea behind STL is a local learnable change-of-basis, applied on tiles of the weight and activation matrices, followed by an element-wise product between the tiles, implemented simultaneously via MatMul. The key technical question we study is how to optimize the change-of-basis of a given layer, which is a highly non-convex problem. We show that theory-backed initializations (inspired by fast matrix and polynomial multiplication) lead to substantially better accuracy than random SGD initialization. This phenomenon motivates further algorithmic study of STL optimization in DNNs. Our experiments demonstrate that STL can approximate 4x4 MatMul of tiles while reducing FLOPs by a factor of 2.66, and can improve Imagenet-1K accuracy of SoTA T2T-ViT-7 (4.3M parameters) while lowering FLOPs. Even with non-CUDA optimized PyTorch code, STL achieves wall-clock speedups in the compute-bound regime. These results, together with its theoretical grounds, suggest STL as a promising building block for scalable and cost-efficient AI.

Nir Ailon, Omer Leibovich, Vineet Nair

A butterfly network consists of logarithmically many layers, each with a linear number of non-zero weights (pre-specified). The fast Johnson-Lindenstrauss transform (FJLT) can be represented as a butterfly network followed by a projection onto a random subset of the coordinates. Moreover, a random matrix based on FJLT with high probability approximates the action of any matrix on a vector. Motivated by these facts, we propose to replace a dense linear layer in any neural network by an architecture based on the butterfly network. The proposed architecture significantly improves upon the quadratic number of weights required in a standard dense layer to nearly linear with little compromise in expressibility of the resulting operator. In a collection of wide variety of experiments, including supervised prediction on both the NLP and vision data, we show that this not only produces results that match and at times outperform existing well-known architectures, but it also offers faster training and prediction in deployment. To understand the optimization problems posed by neural networks with a butterfly network, we also study the optimization landscape of the encoder-decoder network, where the encoder is replaced by a butterfly network followed by a dense linear layer in smaller dimension. Theoretical result presented in the paper explains why the training speed and outcome are not compromised by our proposed approach.

Elad Hoffer, Itay Hubara, Nir Ailon

Convolutional networks have marked their place over the last few years as the best performing model for various visual tasks. They are, however, most suited for supervised learning from large amounts of labeled data. Previous attempts have been made to use unlabeled data to improve model performance by applying unsupervised techniques. These attempts require different architectures and training methods. In this work we present a novel approach for unsupervised training of Convolutional networks that is based on contrasting between spatial regions within images. This criterion can be employed within conventional neural networks and trained using standard techniques such as SGD and back-propagation, thus complementing supervised methods.

Elad Hoffer, Nir Ailon

Deep networks are successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are usually much less suited for semi-supervised problems because of their tendency to overfit easily when trained on small amounts of data. In this work we will explore a new training objective that is targeting a semi-supervised regime with only a small subset of labeled data. This criterion is based on a deep metric embedding over distance relations within the set of labeled samples, together with constraints over the embeddings of the unlabeled set. The final learned representations are discriminative in euclidean space, and hence can be used with subsequent nearest-neighbor classification using the labeled samples.

Elad Hoffer, Itay Hubara, Nir Ailon

Convolutional networks have marked their place over the last few years as the best performing model for various visual tasks. They are, however, most suited for supervised learning from large amounts of labeled data. Previous attempts have been made to use unlabeled data to improve model performance by applying unsupervised techniques. These attempts require different architectures and training methods. In this work we present a novel approach for unsupervised training of Convolutional networks that is based on contrasting between spatial regions within images. This criterion can be employed within conventional neural networks and trained using standard techniques such as SGD and back-propagation, thus complementing supervised methods.

Elad Hoffer, Nir Ailon

Deep learning has proven itself as a successful set of models for learning useful semantic representations of data. These, however, are mostly implicitly learned as part of a classification task. In this paper we propose the triplet network model, which aims to learn useful representations by distance comparisons. A similar model was defined by Wang et al. (2014), tailor made for learning a ranking for image information retrieval. Here we demonstrate using various datasets that our model learns a better representation than that of its immediate competitor, the Siamese network. We also discuss future possible usage as a framework for unsupervised learning.

Nir Ailon, Thorsten Joachims, Zohar Karnin

We present algorithms for reducing the Dueling Bandits problem to the conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits problem is an online model of learning with ordinal feedback of the form "A is preferred to B" (as opposed to cardinal feedback like "A has value 2.5"), giving it wide applicability in learning from implicit user feedback and revealed and stated preferences. In contrast to existing algorithms for the Dueling Bandits problem, our reductions -- named $\Doubler$, $\MultiSbm$ and $\DoubleSbm$ -- provide a generic schema for translating the extensive body of known results about conventional Multi-Armed Bandit algorithms to the Dueling Bandits setting. For $\Doubler$ and $\MultiSbm$ we prove regret upper bounds in both finite and infinite settings, and conjecture about the performance of $\DoubleSbm$ which empirically outperforms the other two as well as previous algorithms in our experiments. In addition, we provide the first almost optimal regret bound in terms of second order terms, such as the differences between the values of the arms.

Nir Ailon, Kohei Hatano, Eiji Takimoto

The permutahedron is the convex polytope with vertex set consisting of the vectors $(π(1),\dots, π(n))$ for all permutations (bijections) $π$ over $\{1,\dots, n\}$. We study a bandit game in which, at each step $t$, an adversary chooses a hidden weight weight vector $s_t$, a player chooses a vertex $π_t$ of the permutahedron and suffers an observed loss of $\sum_{i=1}^n π(i) s_t(i)$. A previous algorithm CombBand of Cesa-Bianchi et al (2009) guarantees a regret of $O(n\sqrt{T \log n})$ for a time horizon of $T$. Unfortunately, CombBand requires at each step an $n$-by-$n$ matrix permanent approximation to within improved accuracy as $T$ grows, resulting in a total running time that is super linear in $T$, making it impractical for large time horizons. We provide an algorithm of regret $O(n^{3/2}\sqrt{T})$ with total time complexity $O(n^3T)$. The ideas are a combination of CombBand and a recent algorithm by Ailon (2013) for online optimization over the permutahedron in the full information setting. The technical core is a bound on the variance of the Plackett-Luce noisy sorting process's "pseudo loss". The bound is obtained by establishing positive semi-definiteness of a family of 3-by-3 matrices generated from rational functions of exponentials of 3 parameters.

Nir Ailon

Given a set $V$ of $n$ objects, an online ranking system outputs at each time step a full ranking of the set, observes a feedback of some form and suffers a loss. We study the setting in which the (adversarial) feedback is an element in $V$, and the loss is the position (0th, 1st, 2nd...) of the item in the outputted ranking. More generally, we study a setting in which the feedback is a subset $U$ of at most $k$ elements in $V$, and the loss is the sum of the positions of those elements. We present an algorithm of expected regret $O(n^{3/2}\sqrt{Tk})$ over a time horizon of $T$ steps with respect to the best single ranking in hindsight. This improves previous algorithms and analyses either by a factor of either $Ω(\sqrt{k})$, a factor of $Ω(\sqrt{\log n})$ or by improving running time from quadratic to $O(n\log n)$ per round. We also prove a matching lower bound. Our techniques also imply an improved regret bound for online rank aggregation over the Spearman correlation measure, and to other more complex ranking loss functions.

Nir Ailon, Yudong Chen, Xu Huan

This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be sufficiently large (in particular, $\tildeΩ(\sqrt{n})$ where $n$ is the number of nodes of the graph). We show that this is not really a restriction: by a more refined analysis of the trace-norm based recovery approach proposed in Jalali et al. (2011) and Chen et al. (2012), we prove that small clusters, under certain mild assumptions, do not hinder recovery of large ones. Based on this result, we further devise an iterative algorithm to recover {\em almost all clusters} via a "peeling strategy", i.e., recover large clusters first, leading to a reduced problem, and repeat this procedure. These results are extended to the {\em partial observation} setting, in which only a (chosen) part of the graph is observed.The peeling strategy gives rise to an active learning algorithm, in which edges adjacent to smaller clusters are queried more often as large clusters are learned (and removed). From a high level, this paper sheds novel insights on high-dimensional statistics and learning structured data, by presenting a structured matrix learning problem for which a one shot convex relaxation approach necessarily fails, but a carefully constructed sequence of convex relaxationsdoes the job.

Nir Ailon, Ron Begleiter

Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many versions of this problem have been defined, most notably $k$-means and $k$-median. An underlying problem with the unsupervised nature of clustering it that of determining a similarity function. One approach for alleviating this difficulty is known as clustering with side information, alternatively, semi-supervised clustering. Here, the practitioner incorporates side information in the form of "must be clustered" or "must be separated" labels for data point pairs. Each such piece of information comes at a "query cost" (often involving human response solicitation). The collection of labels is then incorporated in the usual clustering algorithm as either strict or as soft constraints, possibly adding a pairwise constraint penalty function to the chosen clustering objective. Our work is mostly related to clustering with side information. We ask how to choose the pairs of data points. Our analysis gives rise to a method provably better than simply choosing them uniformly at random. Roughly speaking, we show that the distribution must be biased so as more weight is placed on pairs incident to elements in smaller clusters in some optimal solution. Of course we do not know the optimal solution, hence we don't know the bias. Using the recently introduced method of $\eps$-smooth relative regret approximations of Ailon, Begleiter and Ezra, we can show an iterative process that improves both the clustering and the bias in tandem. The process provably converges to the optimal solution faster (in terms of query cost) than an algorithm selecting pairs uniformly.