Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the updates depending on how the two LoRA factors are scaled or rotated. This deficiency leads to inefficient learning and sub-optimal solutions in practice. This paper introduces LoRA-RITE, a novel adaptive matrix preconditioning method for LoRA optimization, which can achieve transformation invariance and remain computationally efficient. We provide theoretical analysis to demonstrate the benefit of our method and conduct experiments on various LLM tasks with different models including Gemma 2B, 7B, and mT5-XXL. The results demonstrate consistent improvements against existing optimizers. For example, replacing Adam with LoRA-RITE during LoRA fine-tuning of Gemma-2B yielded 4.6% accuracy gain on Super-Natural Instructions and 3.5% accuracy gain across other four LLM benchmarks (HellaSwag, ArcChallenge, GSM8K, OpenBookQA).

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's performance. We analyze the gradients backpropagated through the softmax operation in the attention mechanism and observe that these gradients can often be small. This poor gradient signal backpropagation can lead to inefficient learning of parameters preceeding the attention operations. To this end, we introduce a new attention mechanism called LASER, which we analytically show to admit a larger gradient signal. We show that LASER attention can be implemented by making small modifications to existing attention implementations. We conduct experiments on autoregressive large language models (LLMs) with upto 7.7 billion parameters with an average improvement of upto 1.44% over standard attention on downstream evaluations and 1.65% finetuning improvements. Additionally, LASER demonstrates generalization performance improvement across a variety of tasks (vision, text and speech):Vision Transformer (ViT) on Imagenet, Conformer on the Librispeech speech-to-text and BERT with 2.2 billion parameters.

Adaptive regularization based optimization methods such as full-matrix Adagrad which use gradient second-moment information hold significant potential for fast convergence in deep neural network (DNN) training, but are memory intensive and computationally demanding for large neural nets. We develop a technique called Combining AxeS PReconditioners (CASPR), which optimizes matrix-shaped DNN parameters by finding different preconditioners for each mode/axis of the parameter and combining them using a Kronecker-sum based approximation. We show tighter convergence guarantees in stochastic optimization compared to a Kronecker product based preconditioner, Shampoo, which arises as a special case of CASPR. Furthermore, our experiments demonstrates that CASPR approximates the gradient second-moment matrix in full-matrix Adagrad more accurately, and shows significant improvement in training and generalization performance compared to existing practical adaptive regularization based methods such as Shampoo and Adam in a variety of tasks including graph neural network on OGBG-molpcba, Transformer on a universal dependencies dataset and auto-regressive large language modeling on C4 dataset.

Second-order methods hold significant promise for enhancing the convergence of deep neural network training; however, their large memory and computational demands have limited their practicality. Thus there is a need for scalable second-order methods that can efficiently train large models. In this paper, we introduce the Sparsified Online Newton~(SONew) method, a memory-efficient second-order algorithm that yields a sparsified yet effective preconditioner. The algorithm emerges from a novel use of the LogDet matrix divergence measure; we combine it with sparsity constraints to minimize regret in the online convex optimization framework. Empirically, we test our method on large scale benchmarks of up to 1B parameters. We achieve up to $30\\%$ faster convergence, $3.4\\%$ relative improvement in validation performance, and $80\\%$ relative improvement in training loss, in comparison to memory efficient optimizers including first order methods. Powering the method is a surprising fact -- imposing structured sparsity patterns, like tridiagonal and banded structure, requires little to no overhead, making it as efficient and parallelizable as first-order methods. In wall-clock time, tridiagonal SONew is only about $3\\%$ slower per step than first-order methods but gives overall gains due to much faster convergence. In contrast, one of the state-of-the-art (SOTA) memory-intensive second-order methods, Shampoo, is unable to scale to large benchmarks. Additionally, while Shampoo necessitates significant engineering efforts to scale to large benchmarks, SONew offers a more straightforward implementation, increasing its practical appeal. SONew code is available at: https://github.com/devvrit/SONew

Adaptive methods with non-diagonal preconditioning have shown state-of-the-art results on various tasks. However, their computational complexity and memory requirement makes it challenging to scale these methods to modern neural network architectures. To address this challenge, some previous works have adopted block-diagonal preconditioners. However, the memory cost of storing the block-diagonal matrix remains substantial, leading to the use of smaller block sizes and ultimately resulting in suboptimal performance. To reduce the time and memory complexity without sacrificing performance, we propose approximating each diagonal block of the second moment matrix by low-rank matrices and enforcing the same basis for the blocks within each layer. We provide theoretical justification for such sharing and design an algorithm to efficiently maintain this shared-basis block low-rank approximation during training. Our results on a deep autoencoder and a transformer benchmark demonstrate that the proposed method outperforms first-order methods with slightly more time and memory usage, while also achieving competitive or superior performance compared to other second-order methods with less time and memory usage.

We present a vision of data-informed network simulation to address significant shortcomings in the state of the art. We substantiate our position with proof points based on iBox, which leverages networking domain knowledge and machine learning (ML) models, coupled with plentiful data, to provide a pathway to perpetual renewal of network simulators.