The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous.

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Quantization of neural networks provides benefits of inference in less compute and memory requirements. Previous work in quantization lack two important aspects which this work provides. First almost all previous work in quantization used a non-differentiable approach and for learning; the derivative is usually set manually in backpropogation which make the learning ability of algorithm questionable, our approach is not just differentiable, we also provide proof of convergence of our approach to the optimal neural network. Second previous work in shift/logrithmic quantization either have avoided activation quantization along with weight quantization or achieved less accuracy. Learning logrithmic quantize values of form $2^n$ requires the quantization function can scale to more than 1 bit quantization which is another benifit of our quantization that it provides $n$ bits quantization as well. Our approach when tested with image classification task using imagenet dataset, resnet18 and weight quantization only achieves less than 1 percent accuracy compared to full precision accuracy while taking only 15 epochs to train using shift bit quantization and achieves comparable to SOTA approaches accuracy in both weight and activation quantization using shift bit quantization in 15 training epochs with slightly higher(only higher cpu instructions) inference cost compared to 1 bit quantization(without logrithmic quantization) and not requiring any higher precision multiplication.

The continuous improvements on image compression with variational autoencoders have lead to learned codecs competitive with conventional approaches in terms of rate-distortion efficiency. Nonetheless, taking the quantization into account during the training process remains a problem, since it produces zero derivatives almost everywhere and needs to be replaced with a differentiable approximation which allows end-to-end optimization. Though there are different methods for approximating the quantization, none of them model the quantization noise correctly and thus, result in suboptimal networks. Hence, we propose an additional finetuning training step: After conventional end-to-end training, parts of the network are retrained on quantized latents obtained at the inference stage. For entropy-constraint quantizers like Trellis-Coded Quantization, the impact of the quantizer is particularly difficult to approximate by rounding or adding noise as the quantized latents are interdependently chosen through a trellis search based on both the entropy model and a distortion measure. We show that retraining on correctly quantized data consistently yields additional coding gain for both uniform scalar and especially for entropy-constraint quantization, without increasing inference complexity. For the Kodak test set, we obtain average savings between 1% and 2%, and for the TecNick test set up to 2.2% in terms of Bjøntegaard-Delta bitrate.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

The growing computational demands of training large language models (LLMs) necessitate more efficient methods. Quantized training presents a promising solution by enabling low-bit arithmetic operations to reduce these costs. While FP8 precision has demonstrated feasibility, leveraging FP4 remains a challenge due to significant quantization errors and limited representational capacity. This work introduces the first FP4 training framework for LLMs, addressing these challenges with two key innovations: a differentiable quantization estimator for precise weight updates and an outlier clamping and compensation strategy to prevent activation collapse. To ensure stability, the framework integrates a mixed-precision training scheme and vector-wise quantization. Experimental results demonstrate that our FP4 framework achieves accuracy comparable to BF16 and FP8, with minimal degradation, scaling effectively to 13B-parameter LLMs trained on up to 100B tokens. With the emergence of next-generation hardware supporting FP4, our framework sets a foundation for efficient ultra-low precision training.

Efficient inference of Deep Neural Networks (DNNs) on resource-constrained edge devices is essential. Quantization and sparsity are key algorithmic techniques that translate to repetition and sparsity within tensors at the hardware-software interface. This paper introduces the concept of repetition-sparsity trade-off that helps explain computational efficiency during inference. We propose Signed Binarization, a unified co-design framework that synergistically integrates hardware-software systems, quantization functions, and representation learning techniques to address this trade-off. Our results demonstrate that Signed Binarization is more accurate than binarization with the same number of non-zero weights. Detailed analysis indicates that signed binarization generates a smaller distribution of effectual (non-zero) parameters nested within a larger distribution of total parameters, both of the same type, for a DNN block. Finally, our approach achieves a 26% speedup on real hardware, doubles energy efficiency, and reduces density by 2.8x compared to binary methods for ResNet 18, presenting an alternative solution for deploying efficient models in resource-limited environments.

Distributed adaptive stochastic gradient methods have been widely used for large-scale nonconvex optimization, such as training deep learning models. However, their communication complexity on finding $\varepsilon$-stationary points has rarely been analyzed in the nonconvex setting. In this work, we present a novel communication-efficient distributed Adam in the parameter-server model for stochastic nonconvex optimization, dubbed {\em Efficient-Adam}. Specifically, we incorporate a two-way quantization scheme into Efficient-Adam to reduce the communication cost between the workers and server. Simultaneously, we adopt a two-way error feedback strategy to reduce the biases caused by the two-way quantization on both the server and workers, respectively. In addition, we establish the iteration complexity for the proposed Efficient-Adam with a class of quantization operators, and further characterize its communication complexity between the server and workers when an $\varepsilon$-stationary point is achieved. Finally, we apply Efficient-Adam to solve a toy stochastic convex optimization problem and train deep learning models on real-world vision and language tasks. Extensive experiments together with a theoretical guarantee justify the merits of Efficient Adam.