Knowledge Distillation (KD) is extensively used to compress and deploy large pre-trained language models on edge devices for real-world applications. However, one neglected area of research is the impact of noisy (corrupted) labels on KD. We present, to the best of our knowledge, the first study on KD with noisy labels in Natural Language Understanding (NLU). We document the scope of the problem and present two methods to mitigate the impact of label noise. Experiments on the GLUE benchmark show that our methods are effective even under high noise levels. Nevertheless, our results indicate that more research is necessary to cope with label noise under the KD.
Knowledge Distillation (KD) is a model compression algorithm that helps transfer the knowledge of a large neural network into a smaller one. Even though KD has shown promise on a wide range of Natural Language Processing (NLP) applications, little is understood about how one KD algorithm compares to another and whether these approaches can be complimentary to each other. In this work, we evaluate various KD algorithms on in-domain, out-of-domain and adversarial testing. We propose a framework to assess the adversarial robustness of multiple KD algorithms. Moreover, we introduce a new KD algorithm, Combined-KD, which takes advantage of two promising approaches (better training scheme and more efficient data augmentation). Our extensive experimental results show that Combined-KD achieves state-of-the-art results on the GLUE benchmark, out-of-domain generalization, and adversarial robustness compared to competitive methods.
The development of over-parameterized pre-trained language models has made a significant contribution toward the success of natural language processing. While over-parameterization of these models is the key to their generalization power, it makes them unsuitable for deployment on low-capacity devices. We push the limits of state-of-the-art Transformer-based pre-trained language model compression using Kronecker decomposition. We use this decomposition for compression of the embedding layer, all linear mappings in the multi-head attention, and the feed-forward network modules in the Transformer layer. We perform intermediate-layer knowledge distillation using the uncompressed model as the teacher to improve the performance of the compressed model. We present our KroneckerBERT, a compressed version of the BERT_BASE model obtained using this framework. We evaluate the performance of KroneckerBERT on well-known NLP benchmarks and show that for a high compression factor of 19 (5% of the size of the BERT_BASE model), our KroneckerBERT outperforms state-of-the-art compression methods on the GLUE. Our experiments indicate that the proposed model has promising out-of-distribution robustness and is superior to the state-of-the-art compression methods on SQuAD.
Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semi-supervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare it with t-SNE and LargeVis algorithms. We discuss negative sampling and repulsive forces in UMAP's cost function. DensMAP is then explained for density-preserving embedding. We then introduce parametric UMAP for embedding by deep learning and progressive UMAP for streaming and out-of-sample data embedding.
This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random projections with $\ell_1$ norm and interpolation norm are introduced. Two main applications of random projection, which are low-rank matrix approximation and approximate nearest neighbor search by random projection onto hypercube, are explained. Random Fourier Features (RFF) and Random Kitchen Sinks (RKS) are explained as methods for nonlinear random projection. Some other methods for nonlinear random projection, including extreme learning machine, randomly weighted neural networks, and ensemble of random projections, are also introduced.
This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics.
This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data.
Various phenomena in biology, physics, and engineering are modeled by differential equations. These differential equations including partial differential equations and ordinary differential equations can be converted and represented as integral equations. In particular, Volterra Fredholm Hammerstein integral equations are the main type of these integral equations and researchers are interested in investigating and solving these equations. In this paper, we propose Legendre Deep Neural Network (LDNN) for solving nonlinear Volterra Fredholm Hammerstein integral equations (VFHIEs). LDNN utilizes Legendre orthogonal polynomials as activation functions of the Deep structure. We present how LDNN can be used to solve nonlinear VFHIEs. We show using the Gaussian quadrature collocation method in combination with LDNN results in a novel numerical solution for nonlinear VFHIEs. Several examples are given to verify the performance and accuracy of LDNN.
Symbolic regression is the task of identifying a mathematical expression that best fits a provided dataset of input and output values. Due to the richness of the space of mathematical expressions, symbolic regression is generally a challenging problem. While conventional approaches based on genetic evolution algorithms have been used for decades, deep learning-based methods are relatively new and an active research area. In this work, we present SymbolicGPT, a novel transformer-based language model for symbolic regression. This model exploits the advantages of probabilistic language models like GPT, including strength in performance and flexibility. Through comprehensive experiments, we show that our model performs strongly compared to competing models with respect to the accuracy, running time, and data efficiency.
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing Kernel Hilbert Space (RKHS), Mercer's theorem and its proof, frequently used kernels, kernel construction from distance metric, important classes of kernels (including bounded, integrally positive definite, universal, stationary, and characteristic kernels), kernel centering and normalization, and eigenfunctions are explained in detail. Then, we introduce types of use of kernels in machine learning including kernel methods (such as kernel support vector machines), kernel learning by semi-definite programming, Hilbert-Schmidt independence criterion, maximum mean discrepancy, kernel mean embedding, and kernel dimensionality reduction. We also cover rank and factorization of kernel matrix as well as the approximation of eigenfunctions and kernels using the Nystr{\"o}m method. This paper can be useful for various fields of science including machine learning, dimensionality reduction, functional analysis in mathematics, and mathematical physics in quantum mechanics.