Training deep neural networks–and more recently, large models–demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https://github.com/tensorgi/TPA.

MOTIVATION: High-resolution Hi-C contact matrices reveal the detailed three-dimensional architecture of the genome, but high-coverage experimental Hi-C data are expensive to generate. Simultaneously, chromatin structure analyses struggle with extremely sparse contact matrices. To address this problem, computational methods to enhance low-coverage contact matrices have been developed, but existing methods are largely based on resolution enhancement methods for natural images and hence often employ models that do not distinguish between biologically meaningful contacts, such as loops and other stochastic contacts. RESULTS: We present Capricorn, a machine learning model for Hi-C resolution enhancement that incorporates small-scale chromatin features as additional views of the input Hi-C contact matrix and leverages a diffusion probability model backbone to generate a high-coverage matrix. We show that Capricorn outperforms the state of the art in a cross-cell-line setting, improving on existing methods by 17% in mean squared error and 26% in F1 score for chromatin loop identification from the generated high-coverage data. We also demonstrate that Capricorn performs well in the cross-chromosome setting and cross-chromosome, cross-cell-line setting, improving the downstream loop F1 score by 14% relative to existing methods. We further show that our multiview idea can also be used to improve several existing methods, HiCARN and HiCNN, indicating the wide applicability of this approach. Finally, we use DNA sequence to validate discovered loops and find that the fraction of CTCF-supported loops from Capricorn is similar to those identified from the high-coverage data. Capricorn is a powerful Hi-C resolution enhancement method that enables scientists to find chromatin features that cannot be identified in the low-coverage contact matrix. AVAILABILITY AND IMPLEMENTATION: Implementation of Capricorn and source code for reproducing all figures in this paper are available at https://github.com/CHNFTQ/Capricorn.