Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Search

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and enable fast approximate nearest-neighbor searches. We propose a probabilistic interpretation and utilize density estimation losses like Sliced Wasserstein to train TT decompositions, resulting in robust point cloud compression. We reveal an inherent hierarchical structure within TT point clouds, facilitating efficient approximate nearest-neighbor searches. In our paper, we provide detailed insights into the methodology and conduct comprehensive comparisons with existing methods. We demonstrate its effectiveness in various scenarios, including out-of-distribution (OOD) detection problems and approximate nearest-neighbor (ANN) search tasks.

Inverted Activations

The scaling of neural networks with increasing data and model sizes necessitates more efficient deep learning algorithms. This paper addresses the memory footprint challenge in neural network training by proposing a modification to the handling of activation tensors in pointwise nonlinearity layers. Traditionally, these layers save the entire input tensor for the backward pass, leading to substantial memory use. Our method involves saving the output tensor instead, reducing the memory required when the subsequent layer also saves its input tensor. This approach is particularly beneficial for transformer-based architectures like GPT, BERT, Mistral, and Llama. Application of our method involves taken an inverse function of nonlinearity. To the best of our knowledge, that can not be done analitically and instead we buid an accurate approximations using simpler functions. Experimental results confirm that our method significantly reduces memory usage without affecting training accuracy. The implementation is available at https://github.com/PgLoLo/optiacts.

Efficient GPT Model Pre-training using Tensor Train Matrix Representation

Large-scale transformer models have shown remarkable performance in language modelling tasks. However, such models feature billions of parameters, leading to difficulties in their deployment and prohibitive training costs from scratch. To reduce the number of the parameters in the GPT-2 architecture, we replace the matrices of fully-connected layers with the corresponding Tensor Train Matrix~(TTM) structure. Finally, we customize forward and backward operations through the TTM-based layer for simplicity and the stableness of further training. % The resulting GPT-2-based model stores up to 40% fewer parameters, showing the perplexity comparable to the original model. On the downstream tasks, including language understanding and text summarization, the model performs similarly to the original GPT-2 model. The proposed tensorized layers could be used to efficiently pre-training other Transformer models.

Few-Bit Backward: Quantized Gradients of Activation Functions for Memory Footprint Reduction

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.