Random projections constitute a simple, yet effective technique for dimensionality reduction with applications in learning and search problems. In the present paper, we consider the problem of estimating cosine similarities when the projected data undergo scalar quantization to $b$ bits. We here argue that the maximum likelihood estimator (MLE) is a principled approach to deal with the non-linearity resulting from quantization, and subsequently study its computational and statistical properties. A specific focus is on the on the trade-off between bit depth and the number of projections given a fixed budget of bits for storage or transmission. Along the way, we also touch upon the existence of a qualitative counterpart to the Johnson-Lindenstrauss lemma in the presence of quantization.

The large communication overhead has imposed a bottleneck on the performance of distributed Stochastic Gradient Descent (SGD) for training deep neural networks. Previous works have demonstrated the potential of using gradient sparsification and quantization to reduce the communication cost. However, there is still a lack of understanding about how sparse and quantized communication affects the convergence rate of the training algorithm. In this paper, we study the convergence rate of distributed SGD for non-convex optimization with two communication reducing strategies: sparse parameter averaging and gradient quantization. We show that $O(1/\sqrt{MK})$ convergence rate can be achieved if the sparsification and quantization hyperparameters are configured properly. We also propose a strategy called periodic quantized averaging (PQASGD) that further reduces the communication cost while preserving the $O(1/\sqrt{MK})$ convergence rate. Our evaluation validates our theoretical results and shows that our PQASGD can converge as fast as full-communication SGD with only $3\%-5\%$ communication data size.

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that quantization impacts effective model and data capacities or acts as an additive error, the theoretical mechanisms governing these effects remain largely unexplored. In this work, we initiate a theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework. By analyzing multiplicative (signal-dependent) and additive (signal-independent) quantization, we identify a critical dichotomy in their scaling behaviors. Our analysis reveals that while both schemes introduce an additive error and degrade the effective data size, they exhibit distinct effects on effective model size: multiplicative quantization maintains the full-precision model size, whereas additive quantization reduces the effective model size. Numerical experiments validate our theoretical findings. By rigorously characterizing the complex interplay among model scale, dataset size, and quantization error, our work provides a principled theoretical basis for optimizing training protocols under practical hardware constraints.

Diffusion models (DMs) have been significantly developed and widely used in various applications due to their excellent generative qualities.

Training large neural networks requires substantial hardware and energy resources.

In this paper, we propose a post-training quantization framework of large vision-language models (L VLMs) for efficient multi-modal inference. Conventional quantization methods sequentially search the layer-wise rounding functions by minimizing activation discretization errors, which fails to acquire optimal quantization strategy without considering cross-layer dependency.

We leverage this unique capability to propose NoMAD-Attention, an efficient attention algorithm that replaces MAD operations with in-register lookups.