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Register a new userDeep Learning Meets Projective Clustering
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A common approach for compressing NLP networks is to encode the embedding layer as a matrix $Ainmathbb{R}^{ntimes d}$, compute its rank-$j$ approximation $A_j$ via SVD, and then factor $A_j$ into a pair of matrices that correspond to smaller fully-connected layers to replace the original embedding layer. Geometrically, the rows of $A$ represent points in $mathbb{R}^d$, and the rows of $A_j$ represent their projections onto the $j$-dimensional subspace that minimizes the sum of squared distances (errors) to the points. In practice, these rows of $A$ may be spread around $k>1$ subspaces, so factoring $A$ based on a single subspace may lead to large errors that turn into large drops in accuracy. Inspired by emph{projective clustering} from computational geometry, we suggest replacing this subspace by a set of $k$ subspaces, each of dimension $j$, that minimizes the sum of squared distances over every point (row in $A$) to its emph{closest} subspace. Based on this approach, we provide a novel architecture that replaces the original embedding layer by a set of $k$ small layers that operate in parallel and are then recombined with a single fully-connected layer. Extensive experimental results on the GLUE benchmark yield networks that are both more accurate and smaller compared to the standard matrix factorization (SVD). For example, we further compress DistilBERT by reducing the size of the embedding layer by $40%$ while incurring only a $0.5%$ average drop in accuracy over all nine GLUE tasks, compared to a $2.8%$ drop using the existing SVD approach. On RoBERTa we achieve $43%$ compression of the embedding layer with less than a $0.8%$ average drop in accuracy as compared to a $3%$ drop previously. Open code for reproducing and extending our results is provided.
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We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be optimized via gradient adaptations on the Stiefel manifold, leading to significant acceleration over spectral methods relying on eigendecompositions. Finally, our trained embedding can be directly applied to out-of-sample data. We show experimentally that our approach outperforms several state-of-the-art deep clustering methods, as well as traditional approaches such as $k$-means and spectral clustering over a broad array of real-life and synthetic datasets.
Clustering is a fundamental task in data analysis. Recently, deep clustering, which derives inspiration primarily from deep learning approaches, achieves state-of-the-art performance and has attracted considerable attention. Current deep clustering methods usually boost the clustering results by means of the powerful representation ability of deep learning, e.g., autoencoder, suggesting that learning an effective representation for clustering is a crucial requirement. The strength of deep clustering methods is to extract the useful representations from the data itself, rather than the structure of data, which receives scarce attention in representation learning. Motivated by the great success of Graph Convolutional Network (GCN) in encoding the graph structure, we propose a Structural Deep Clustering Network (SDCN) to integrate the structural information into deep clustering. Specifically, we design a delivery operator to transfer the representations learned by autoencoder to the corresponding GCN layer, and a dual self-supervised mechanism to unify these two different deep neural architectures and guide the update of the whole model. In this way, the multiple structures of data, from low-order to high-order, are naturally combined with the multiple representations learned by autoencoder. Furthermore, we theoretically analyze the delivery operator, i.e., with the delivery operator, GCN improves the autoencoder-specific representation as a high-order graph regularization constraint and autoencoder helps alleviate the over-smoothing problem in GCN. Through comprehensive experiments, we demonstrate that our propose model can consistently perform better over the state-of-the-art techniques.
Federated learning has emerged as a promising, massively distributed way to train a joint deep model over large amounts of edge devices while keeping private user data strictly on device. In this work, motivated from ensuring fairness among users and robustness against malicious adversaries, we formulate federated learning as multi-objective optimization and propose a new algorithm FedMGDA+ that is guaranteed to converge to Pareto stationary solutions. FedMGDA+ is simple to implement, has fewer hyperparameters to tune, and refrains from sacrificing the performance of any participating user. We establish the convergence properties of FedMGDA+ and point out its connections to existing approaches. Extensive experiments on a variety of datasets confirm that FedMGDA+ compares favorably against state-of-the-art.
A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions (e.g., linear classifiers, neural networks etc.). A failure of the learning algorithm can occur due to two possible reasons: wrong choice of hypothesis class (hardness of approximation), or failure to find the best function within the hypothesis class (hardness of learning). Although both approximation and learnability are important for the success of the algorithm, they are typically studied separately. In this work, we show a single hardness property that implies both hardness of approximation using linear classes and shallow networks, and hardness of learning using correlation queries and gradient-descent. This allows us to obtain new results on hardness of approximation and learnability of parity functions, DNF formulas and $AC^0$ circuits.
We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential of deep k-means to outperform traditional two-step feature extraction and shallow-clustering strategies. We achieve this by developing a gradient-estimator for the non-differentiable k-means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concrete k-means model can be optimised with respect to the canonical k-means objective and is easily trained end-to-end without resorting to alternating optimisation. We demonstrate the efficacy of our method on standard clustering benchmarks.
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