Quantized training of Large Language Models (LLMs) remains an open challenge, as maintaining accuracy while performing all matrix multiplications in low precision has proven difficult. This is particularly the case when fine-tuning pre-trained models, which can have large weight, activation, and error (output gradient) outlier values that make lower-precision optimization difficult. To address this, we present HALO, a new quantization-aware training approach for Transformers that enables accurate and efficient low-precision training by combining 1) strategic placement of Hadamard rotations in both forward and backward passes, which mitigate outliers, 2) high-performance kernel support, and 3) FSDP integration for low-precision communication. Our approach ensures that all large matrix multiplications during the forward and backward passes are executed in lower precision.

We consider the problem of preprocessing an n n matrix M, and supporting queries that, for any vector v, returns the matrix-vector product Mv. This problem has been extensively studied in both theory and practice: on one side, practitioners have developed algorithms that are highly efficient in practice, whereas on the other side, theoreticians have proven that the problem cannot be solved faster than naive multiplication in the worst-case. This lower bound holds even in the average-case, implying that existing average-case analyses cannot explain this gap between theory and practice. Hence, we study the problem for structured matrices. We show that for n n Boolean matrices of VC-dimension d, the matrix-vector multiplication problem can be solved with eO(n2)preprocessing and eO(n2 1/d) query time.

Quantized training of Large Language Models (LLMs) remains an open challenge, as maintaining accuracy while performing all matrix multiplications in low precision has proven difficult. This is particularly the case when fine-tuning pre-trained models, which can have large weight, activation, and error (output gradient) outlier values that make lower-precision optimization difficult. To address this, we present HALO, a new quantization-aware training approach for Transformers that enables accurate and efficient low-precision training by combining 1) strategic placement of Hadamard rotations in both forward and backward passes, which mitigate outliers, 2) high-performance kernel support, and 3) FSDP integration for low-precision communication. Our approach ensures that all large matrix multiplications during the forward and backward passes are executed in lower precision.

Large language models (LLMs) are highly capable but also computationally expensive. Characterizing the fundamental tradeoff between inference efficiency and model capabilities is thus important, but requires an efficiency metric that is comparable across models from different providers. Unfortunately, raw runtimes measured through black-box APIs do not satisfy this property: model providers can implement software and hardware optimizations orthogonal to the model, and shared infrastructure introduces performance contention. We propose a new metric for inference efficiency called idealized runtime, that puts models on equal footing as though they were served on uniform hardware and software without performance contention, and a cost model to efficiently estimate this metric for autoregressive Transformer models. We also propose variants of the idealized runtime that incorporate the number and type of accelerators needed to serve the model. Using these metrics, we compare ten LLMs developed in 2022 to provide the first analysis of inference efficiency-capability tradeoffs; we make several observations from this analysis, including the fact that the superior inference runtime performance of certain APIs is often a byproduct of optimizations within the API rather than the underlying model.

Quantizing the activation, weight, and gradient to 4-bit is promising to accelerate neural network training. However, existing 4-bit training methods require custom numerical formats which are not supported by contemporary hardware. In this work, we propose a training method for transformers with all matrix multiplications implemented with the INT4 arithmetic. Training with an ultra-low INT4 precision is challenging. To achieve this, we carefully analyze the specific structures of activation and gradients in transformers to propose dedicated quantizers for them. For forward propagation, we identify the challenge of outliers and propose a Hadamard quantizer to suppress the outliers.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to post-training pruning for generating efficient models. In principle, DST allows for a much more memory efficient training process,as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, mostimplementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classificationwith large output spaces, where memory-efficiency is paramount. With a label space of possibly millions of candidates,the classification layer alone will consume several gigabytes of memory. Switching from a dense to a fixed fan-in sparse layer updated with sparse evolutionary training (SET); however, severely hampers training convergence, especiallyat the largest label spaces. We find that the gradients fed back from the classifier into the text encoder make itmuch more difficult to learn good input representations, despite using a dense encoder.By employing an intermediate layer or adding an auxiliary training objective, we recover most of the generalisation performance of the dense model. Overall, we demonstrate the applicability of DST in a challenging domain, characterized by a highly skewed label distribution, that lies outside of DST's typical benchmark datasets, and enable end-to-end training with millions of labels on commodity hardware.

Transformer models have gained significant attention due to their power in machine learning tasks. Their extensive deployment has raised concerns about the potential leakage of sensitive information during inference. However, when being applied to Transformers, existing approaches based on secure two-party computation (2PC) bring about efficiency limitations in two folds: (1) resource-intensive matrix multiplications in linear layers, and (2) complex non-linear activation functions like $\mathsf{GELU}$ and $\mathsf{Softmax}$. This work presents a new two-party inference framework $\mathsf{Nimbus}$ for Transformer models. Specifically, we propose a new 2PC paradigm to securely compute matrix multiplications based on an outer-product insight, which achieves $2.9\times \sim 12.5\times$ performance improvements compared to the state-of-the-art (SOTA) protocol. Furthermore, through a new observation of utilizing the input distribution, we propose an approach of low-degree polynomial approximation for $\mathsf{GELU}$ and $\mathsf{Softmax}$, which improves the performance of the SOTA polynomial approximation by $2.9\times \sim 4.0\times$, where the average accuracy loss of our approach is 0.08\% compared to the non-2PC inference without privacy. Compared with the SOTA two-party inference, $\mathsf{Nimbus}$ improves the end-to-end performance of $BERT_{base}$ inference by $2.7\times \sim 4.7\times$ across different network settings.