Андрей Иванов

Andrei Ivanov, Nikoli Dryden, Tal Ben-Nun et al.

As deep learning models grow, sparsity is becoming an increasingly critical component of deep neural networks, enabling improved performance and reduced storage. However, existing frameworks offer poor support for sparsity. Specialized sparsity engines focus exclusively on sparse inference, while general frameworks primarily focus on sparse tensors in classical formats and neglect the broader sparsification pipeline necessary for using sparse models, especially during training. Further, existing frameworks are not easily extensible: adding a new sparse tensor format or operator is challenging and time-consuming. To address this, we propose STen, a sparsity programming model and interface for PyTorch, which incorporates sparsity layouts, operators, and sparsifiers, in an efficient, customizable, and extensible framework that supports virtually all sparsification methods. We demonstrate this by developing a high-performance grouped n:m sparsity layout for CPU inference at moderate sparsity. STen brings high performance and ease of use to the ML community, making sparsity easily accessible.

Roberto L. Castro, Andrei Ivanov, Diego Andrade et al.

The increasing success and scaling of Deep Learning models demands higher computational efficiency and power. Sparsification can lead to both smaller models as well as higher compute efficiency, and accelerated hardware is becoming available. However, exploiting it efficiently requires kernel implementations, pruning algorithms, and storage formats, to utilize hardware support of specialized sparse vector units. An example of those are the NVIDIA's Sparse Tensor Cores (SPTCs), which promise a 2x speedup. However, SPTCs only support the 2:4 format, limiting achievable sparsity ratios to 50%. We present the V:N:M format, which enables the execution of arbitrary N:M ratios on SPTCs. To efficiently exploit the resulting format, we propose Spatha, a high-performance sparse-library for DL routines. We show that Spatha achieves up to 37x speedup over cuBLAS. We also demonstrate a second-order pruning technique that enables sparsification to high sparsity ratios with V:N:M and little to no loss in accuracy in modern transformers.

Andrei Ivanov, Stefan Maria Ailuro

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for constructing a high-order polynomial regression based on the Taylor map factorization. This method naturally implements multi-target regression and can capture internal relationships between targets. Additionally, we introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on UCI open access datasets, Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate that the proposed method performs comparable to the state-of-the-art regression methods and outperforms them on specific tasks.

Oliver Rausch, Tal Ben-Nun, Nikoli Dryden et al.

Rapid progress in deep learning is leading to a diverse set of quickly changing models, with a dramatically growing demand for compute. However, as frameworks specialize performance optimization to patterns in popular networks, they implicitly constrain novel and diverse models that drive progress in research. We empower deep learning researchers by defining a flexible and user-customizable pipeline for optimizing training of arbitrary deep neural networks, based on data movement minimization. The pipeline begins with standard networks in PyTorch or ONNX and transforms computation through progressive lowering. We define four levels of general-purpose transformations, from local intra-operator optimizations to global data movement reduction. These operate on a data-centric graph intermediate representation that expresses computation and data movement at all levels of abstraction, including expanding basic operators such as convolutions to their underlying computations. Central to the design is the interactive and introspectable nature of the pipeline. Every part is extensible through a Python API, and can be tuned interactively using a GUI. We demonstrate competitive performance or speedups on ten different networks, with interactive optimizations discovering new opportunities in EfficientNet.

Andrei Ivanov, Alena Sholokhova, Sergei Andrianov et al.

In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. The proposed architecture can be trained with small data sets, extrapolate predictions outside the training data, and provide a possibility for interpretation. We provide a theoretical explanation of the proposed architecture, as well as demonstrate it in several applications. We present the results of modeling and identification for both simple and well-known dynamical systems, and more complicated examples from price dynamics, chemistry, and accelerator physics. From a practical point of view, we describe the training of a Lie transform--based neural network with a small data set containing only 10 data points. We also demonstrate an interpretation of the fitted neural network by converting it to a system of differential equations.