In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.
Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special structure of learned parameter space, we question if it is possible to mimic it with an alternative and more lightweight approach. We develop a new tensor factorization-based model that ingrains the structural knowledge about sequential data within the learning process. We demonstrate how certain properties of a self-attention network can be reproduced with our approach based on special Hankel matrix representation. The resulting model has a shallow linear architecture and compares competitively to its neural counterpart.
Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In this paper we propose a novel, robust and accelerated stochastic optimizer that relies on two key elements: (1) an accelerated Nesterov-like Stochastic Differential Equation (SDE) and (2) its semi-implicit Gauss-Seidel type discretization. The convergence and stability of the obtained method, referred to as NAG-GS, are first studied extensively in the case of the minimization of a quadratic function. This analysis allows us to come up with an optimal step size (or learning rate) in terms of rate of convergence while ensuring the stability of NAG-GS. This is achieved by the careful analysis of the spectral radius of the iteration matrix and the covariance matrix at stationarity with respect to all hyperparameters of our method. We show that NAG-GS is competitive with state-of-the-art methods such as momentum SGD with weight decay and AdamW for the training of machine learning models such as the logistic regression model, the residual networks models on standard computer vision datasets, and Transformers in the frame of the GLUE benchmark.
The majority of real-world processes are spatiotemporal, and the data generated by them exhibits both spatial and temporal evolution. Weather is one of the most important processes that fall under this domain, and forecasting it has become a crucial part of our daily routine. Weather data analysis is considered the most complex and challenging task. Although numerical weather prediction models are currently state-of-the-art, they are resource intensive and time-consuming. Numerous studies have proposed time-series-based models as a viable alternative to numerical forecasts. Recent research has primarily focused on forecasting weather at a specific location. Therefore, models can only capture temporal correlations. This self-contained paper explores various methods for regional data-driven weather forecasting, i.e., forecasting over multiple latitude-longitude points to capture spatiotemporal correlations. The results showed that spatiotemporal prediction models reduced computational cost while improving accuracy; in particular, the proposed tensor train dynamic mode decomposition-based forecasting model has comparable accuracy to ConvLSTM without the need for training. We use the NASA POWER meteorological dataset to evaluate the models and compare them with the current state of the art.
The size and complexity of deep neural networks continue to grow exponentially, significantly increasing energy consumption for training and inference by these models. We introduce an open-source package eco2AI to help data scientists and researchers to track energy consumption and equivalent CO2 emissions of their models in a straightforward way. In eco2AI we put emphasis on accuracy of energy consumption tracking and correct regional CO2 emissions accounting. We encourage research community to search for new optimal Artificial Intelligence (AI) architectures with a lower computational cost. The motivation also comes from the concept of AI-based green house gases sequestrating cycle with both Sustainable AI and Green AI pathways.
Unlike 2D raster images, there is no single dominant representation for 3D visual data processing. Different formats like point clouds, meshes, or implicit functions each have their strengths and weaknesses. Still, grid representations such as signed distance functions have attractive properties also in 3D. In particular, they offer constant-time random access and are eminently suitable for modern machine learning. Unfortunately, the storage size of a grid grows exponentially with its dimension. Hence they often exceed memory limits even at moderate resolution. This work explores various low-rank tensor formats, including the Tucker, tensor train, and quantics tensor train decompositions, to compress time-varying 3D data. Our method iteratively computes, voxelizes, and compresses each frame's truncated signed distance function and applies tensor rank truncation to condense all frames into a single, compressed tensor that represents the entire 4D scene. We show that low-rank tensor compression is extremely compact to store and query time-varying signed distance functions. It significantly reduces the memory footprint of 4D scenes while surprisingly preserving their geometric quality. Unlike existing iterative learning-based approaches like DeepSDF and NeRF, our method uses a closed-form algorithm with theoretical guarantees.
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear maps. This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact. The collection of associated techniques are called, tensor network methods: the subject developed independently in several distinct fields of study, which have more recently become interrelated through the language of tensor networks. The tantamount questions in the field relate to expressability of tensor networks and the reduction of computational overheads. A merger of tensor networks with machine learning is natural. On the one hand, machine learning can aid in determining a factorization of a tensor network approximating a data set. On the other hand, a given tensor network structure can be viewed as a machine learning model. Herein the tensor network parameters are adjusted to learn or classify a data-set. In this survey we recover the basics of tensor networks and explain the ongoing effort to develop the theory of tensor networks in machine learning.
Collaborative filtering models generally perform better than content-based filtering models and do not require careful feature engineering. However, in the cold-start scenario collaborative information may be scarce or even unavailable, whereas the content information may be abundant, but also noisy and expensive to acquire. Thus, selection of particular features that improve cold-start recommendations becomes an important and non-trivial task. In the recent approach by Nembrini et al., the feature selection is driven by the correlational compatibility between collaborative and content-based models. The problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) which, due to its NP-hard complexity, is solved using Quantum Annealing on a quantum computer provided by D-Wave. Inspired by the reported results, we contend the idea that current quantum annealers are superior for this problem and instead focus on classical algorithms. In particular, we tackle QUBO via TTOpt, a recently proposed black-box optimizer based on tensor networks and multilinear algebra. We show the computational feasibility of this method for large problems with thousands of features, and empirically demonstrate that the solutions found are comparable to the ones obtained with D-Wave across all examined datasets.
Conventional collaborative filtering techniques don't take into consideration the effect of discrepancy in users' rating perception. Some users may rarely give 5 stars to items while others almost always assign 5 stars to the chosen item. Even if they had experience with the same items this systematic discrepancy in their evaluation style will lead to the systematic errors in the ability of recommender system to effectively extract right patterns from data. To mitigate this problem we introduce the ratings' similarity matrix which represents the dependency between different values of ratings on the population level. Hence, if on average the correlations between ratings exist, it is possible to improve the quality of proposed recommendations by off-setting the effect of either shifted down or shifted up users' rates.
We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer (TTOpt) method for various tasks, ranging from minimization of multidimensional functions to reinforcement learning. Our algorithm compares favorably to popular evolutionary-based methods and outperforms them by the number of function evaluations or execution time, often by a significant margin.