Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the Canonical Polyadic tensor Decomposition is one of the most suited models. However, fitting the convolutional tensors by numerical optimization algorithms often encounters diverging components, i.e., extremely large rank-one tensors but canceling each other. Such degeneracy often causes the non-interpretable result and numerical instability for the neural network fine-tuning. This paper is the first study on degeneracy in the tensor decomposition of convolutional kernels. We present a novel method, which can stabilize the low-rank approximation of convolutional kernels and ensure efficient compression while preserving the high-quality performance of the neural networks. We evaluate our approach on popular CNN architectures for image classification and show that our method results in much lower accuracy degradation and provides consistent performance.
This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes descent direction in every iteration to guarantee equal relative decrease of objective functions. This descent direction is based on the normalized gradients of the individual losses. Therefore, it is appropriate to solve multi-objective optimization problems with multi-scale losses. We test the proposed method on the imbalanced classification problem and multi-task learning problem, where standard datasets are used. EDM is compared with other methods to solve these problems.
State-of-the-art deep learning models are untrustworthy due to their vulnerability to adversarial examples. Intriguingly, besides simple adversarial perturbations, there exist Universal Adversarial Perturbations (UAPs), which are input-agnostic perturbations that lead to misclassification of majority inputs. The main target of existing adversarial examples (including UAPs) is to change primarily the correct Top-1 predicted class by the incorrect one, which does not guarantee changing the Top-k prediction. However, in many real-world scenarios, dealing with digital data, Top-k predictions are more important. We propose an effective geometry-inspired method of computing Top-k adversarial examples for any k. We evaluate its effectiveness and efficiency by comparing it with other adversarial example crafting techniques. Based on this method, we propose Top-k Universal Adversarial Perturbations, image-agnostic tiny perturbations that cause true class to be absent among the Top-k pre-diction. We experimentally show that our approach outperforms baseline methods and even improves existing techniques of generating UAPs.
Low-dimensional representations, or embeddings, of a graph's nodes facilitate data mining tasks. Known embedding methods explicitly or implicitly rely on a similarity measure among nodes. As the similarity matrix is quadratic, a tradeoff between space complexity and embedding quality arises; past research initially opted for heuristics and linear-transform factorizations, which allow for linear space but compromise on quality; recent research has proposed a quadratic-space solution as a viable option too. In this paper we observe that embedding methods effectively aim to preserve the covariance among the rows of a similarity matrix, and raise the question: is there a method that combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees? We answer this question in the affirmative, with FREDE(FREquent Directions Embedding), a sketching-based method that iteratively improves on quality while processing rows of the similarity matrix individually; thereby, it provides, at any iteration, column-covariance approximation guarantees that are, in due course, almost indistinguishable from those of the optimal row-covariance approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs as well as SVD and competitively against current state-of-the-art methods in diverse data mining tasks, even when it derives an embedding based on only 10% of node similarities.
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so probabilistic approaches could give a more general picture of the process. At the same time, high-dimensional probabilities modeling is a challenging and data-intensive task. In this paper, we establish a parallel between the dynamical systems modeling and language modeling tasks. We propose a transformer-based model that incorporates geometrical properties of the data and provide an iterative training algorithm allowing the fine-grid approximation of the conditional probabilities of high-dimensional dynamical systems.
Normalization is an important and vastly investigated technique in deep learning. However, its role for Ordinary Differential Equation based networks (neural ODEs) is still poorly understood. This paper investigates how different normalization techniques affect the performance of neural ODEs. Particularly, we show that it is possible to achieve 93% accuracy in the CIFAR-10 classification task, and to the best of our knowledge, this is the highest reported accuracy among neural ODEs tested on this problem.
We present a different view on stochastic optimization, which goes back to the splitting schemes for approximate solutions of ODE. In this work, we provide a connection between stochastic gradient descent approach and first-order splitting scheme for ODE. We consider the special case of splitting, which is inspired by machine learning applications and derive a new upper bound on the global splitting error for it. We present, that the Kaczmarz method is the limit case of the splitting scheme for the unit batch SGD for linear least squares problem. We support our findings with systematic empirical studies, which demonstrates, that a more accurate solution of local problems leads to the stepsize robustness and provides better convergence in time and iterations on the softmax regression problem.
Machine learning (ML) methods and neural networks (NN) are widely implemented for crop types recognition and classification based on satellite images. However, most of these studies use several multi-temporal images which could be inapplicable for cloudy regions. We present a comparison between the classical ML approaches and U-Net NN for classifying crops with a single satellite image. The results show the advantages of using field-wise classification over pixel-wise approach. We first used a Bayesian aggregation for field-wise classification and improved on 1.5% results between majority voting aggregation. The best result for single satellite image crop classification is achieved for gradient boosting with an overall accuracy of 77.4% and macro F1-score 0.66.
In this paper, we propose a method, which allows us to alleviate or completely avoid the notorious problem of numerical instability and stiffness of the adjoint method for training neural ODE. On the backward pass, we propose to use the machinery of smooth function interpolation to restore the trajectory obtained during the forward integration. We show the viability of our approach, both in theory and practice.