As Large Language Models (LLMs) become increasingly computationally complex, developing efficient deployment strategies, such as quantization, becomes crucial. State-of-the-art Post-training Quantization (PTQ) techniques often rely on calibration processes to maintain the accuracy of these models. However, while these calibration techniques can enhance performance in certain domains, they may not be as effective in others. This paper aims to draw attention to robust statistical approaches that can mitigate such issues. We propose a weight-adaptive PTQ method that can be considered a precursor to calibration-based PTQ methods, guiding the quantization process to preserve the distribution of weights by minimizing the Kullback-Leibler divergence between the quantized weights and the originally trained weights. This minimization ensures that the quantized model retains the Shannon information content of the original model to a great extent, guaranteeing robust and efficient deployment across many tasks. As such, our proposed approach can perform on par with most common calibration-based PTQ methods, establishing a new pre-calibration step for further adjusting the quantized weights with calibration. We show that our pre-calibration results achieve the same accuracy as some existing calibration-based PTQ methods on various LLMs.

Deployment of Large Language Models (LLMs) has major computational costs, due to their rapidly expanding size. Compression of LLMs reduces the memory footprint, latency, and energy required for their inference. Post-training Quantization (PTQ) techniques have been developed to compress LLMs while avoiding expensive re-training. Most PTQ approaches formulate the quantization error based on a layer-wise $\ell_2$ loss, ignoring the model output. Then, each layer is calibrated using its layer-wise Hessian to update the weights towards minimizing the $\ell_2$ quantization error. The Hessian is also used for detecting the most salient weights to quantization. Such PTQ approaches are prone to accuracy drop in low-precision quantization. We propose Output-adaptive Calibration (OAC) to incorporate the model output in the calibration process. We formulate the quantization error based on the distortion of the output cross-entropy loss. OAC approximates the output-adaptive Hessian for each layer under reasonable assumptions to reduce the computational complexity. The output-adaptive Hessians are used to update the weight matrices and detect the salient weights towards maintaining the model output. Our proposed method outperforms the state-of-the-art baselines such as SpQR and BiLLM, especially, at extreme low-precision (2-bit and binary) quantization.

The ever-growing computational complexity of Large Language Models (LLMs) necessitates efficient deployment strategies. The current state-of-the-art approaches for Post-training Quantization (PTQ) often require calibration to achieve the desired accuracy. This paper presents AdpQ, a novel zero-shot adaptive PTQ method for LLMs that achieves the state-of-the-art performance in low-precision quantization (e.g. 3-bit) without requiring any calibration data. Inspired by Adaptive LASSO regression model, our proposed approach tackles the challenge of outlier activations by separating salient weights using an adaptive soft-thresholding method. Guided by Adaptive LASSO, this method ensures that the quantized weights distribution closely follows the originally trained weights and eliminates the need for calibration data entirely, setting our method apart from popular approaches such as SpQR and AWQ. Furthermore, our method offers an additional benefit in terms of privacy preservation by eliminating any calibration or training data. We also delve deeper into the information-theoretic underpinnings of the proposed method. We demonstrate that it leverages the Adaptive LASSO to minimize the Kullback-Leibler divergence between the quantized weights and the originally trained weights. This minimization ensures the quantized model retains the Shannon information content of the original model to a great extent, guaranteeing efficient deployment without sacrificing accuracy or information. Our results achieve the same accuracy as the existing methods on various LLM benchmarks while the quantization time is reduced by at least 10x, solidifying our contribution to efficient and privacy-preserving LLM deployment.

In neural network binarization, BinaryConnect (BC) and its variants are considered the standard. These methods apply the sign function in their forward pass and their respective gradients are backpropagated to update the weights. However, the derivative of the sign function is zero whenever defined, which consequently freezes training. Therefore, implementations of BC (e.g., BNN) usually replace the derivative of sign in the backward computation with identity or other approximate gradient alternatives. Although such practice works well empirically, it is largely a heuristic or ''training trick.'' We aim at shedding some light on these training tricks from the optimization perspective. Building from existing theory on ProxConnect (PC, a generalization of BC), we (1) equip PC with different forward-backward quantizers and obtain ProxConnect++ (PC++) that includes existing binarization techniques as special cases; (2) derive a principled way to synthesize forward-backward quantizers with automatic theoretical guarantees; (3) illustrate our theory by proposing an enhanced binarization algorithm BNN++; (4) conduct image classification experiments on CNNs and vision transformers, and empirically verify that BNN++ generally achieves competitive results on binarizing these models.

Low-precision fine-tuning of language models has gained prominence as a cost-effective and energy-efficient approach to deploying large-scale models in various applications. However, this approach is susceptible to the existence of outlier values in activation. The outlier values in the activation can negatively affect the performance of fine-tuning language models in the low-precision regime since they affect the scaling factor and thus make representing smaller values harder. This paper investigates techniques for mitigating outlier activation in low-precision integer fine-tuning of the language models. Our proposed novel approach enables us to represent the outlier activation values in 8-bit integers instead of floating-point (FP16) values. The benefit of using integers for outlier values is that it enables us to use operator tiling to avoid performing 16-bit integer matrix multiplication to address this problem effectively. We provide theoretical analysis and supporting experiments to demonstrate the effectiveness of our approach in improving the robustness and performance of low-precision fine-tuned language models.

Efficiently deploying deep neural networks on low-resource edge devices is challenging due to their ever-increasing resource requirements. To address this issue, researchers have proposed multiplication-free neural networks, such as Power-of-Two quantization, or also known as Shift networks, which aim to reduce memory usage and simplify computation. However, existing low-bit Shift networks are not as accurate as their full-precision counterparts, typically suffering from limited weight range encoding schemes and quantization loss. In this paper, we propose the DenseShift network, which significantly improves the accuracy of Shift networks, achieving competitive performance to full-precision networks for vision and speech applications. In addition, we introduce a method to deploy an efficient DenseShift network using non-quantized floating-point activations, while obtaining 1.6X speed-up over existing methods. To achieve this, we demonstrate that zero-weight values in low-bit Shift networks do not contribute to model capacity and negatively impact inference computation. To address this issue, we propose a zero-free shifting mechanism that simplifies inference and increases model capacity. We further propose a sign-scale decomposition design to enhance training efficiency and a low-variance random initialization strategy to improve the model's transfer learning performance. Our extensive experiments on various computer vision and speech tasks demonstrate that DenseShift outperforms existing low-bit multiplication-free networks and achieves competitive performance compared to full-precision networks. Furthermore, our proposed approach exhibits strong transfer learning performance without a drop in accuracy. Our code was released on GitHub.

Deep models are dominating the artificial intelligence (AI) industry since the ImageNet challenge in 2012. The size of deep models is increasing ever since, which brings new challenges to this field with applications in cell phones, personal computers, autonomous cars, and wireless base stations. Here we list a set of problems, ranging from training, inference, generalization bound, and optimization with some formalism to communicate these challenges with mathematicians, statisticians, and theoretical computer scientists. This is a subjective view of the research questions in deep learning that benefits the tech industry in long run.

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

Deep neural networks are getting larger. Their implementation on edge and IoT devices becomes more challenging and moved the community to design lighter versions with similar performance. Standard automatic design tools such as \emph{reinforcement learning} and \emph{evolutionary computing} fundamentally rely on cheap evaluations of an objective function. In the neural network design context, this objective is the accuracy after training, which is expensive and time-consuming to evaluate. We automate the design of a light deep neural network for image classification using the \emph{Mesh Adaptive Direct Search}(MADS) algorithm, a mature derivative-free optimization method that effectively accounts for the expensive blackbox nature of the objective function to explore the design space, even in the presence of constraints.Our tests show competitive compression rates with reduced numbers of trials.

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually performed in single-precision floating-point number format. The convergence of single-precision SGD is normally aligned with the theoretical results of real numbers since they exhibit negligible error. However, the numerical error increases when the computations are performed in low-precision number formats. This provides compelling reasons to study the SGD convergence adapted for low-precision computations. We present both deterministic and stochastic analysis of the SGD algorithm, obtaining bounds that show the effect of number format. Such bounds can provide guidelines as to how SGD convergence is affected when constraints render the possibility of performing high-precision computations remote.