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Alexander Cloninger

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JMLR Journal 2021 Journal Article

LDLE: Low Distortion Local Eigenmaps

Dhruv Kohli
Alexander Cloninger
Gal Mishne

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a data set in lower dimension and registers them to obtain a global embedding. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE can embed closed and non-orientable manifolds into their intrinsic dimension by tearing them apart. It also provides gluing instruction on the boundary of the torn embedding to help identify the topology of the original manifold. Our experimental results will show that LDLE largely preserved distances up to a constant scale while other techniques produced higher distortion. We also demonstrate that LDLE produces high quality embeddings even when the data is noisy or sparse. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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UAI Conference 2020 Conference Paper

Coresets for Estimating Means and Mean Square Error with Limited Greedy Samples

Saeed Vahidian
Baharan Mirzasoleiman
Alexander Cloninger

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction steps (in contrast to Frank–Wolfe and its variants), a variant of gradient ascent for coreset selection in graphs, that greedily selects a weighted subset of vertices that are deemed most important to sample. Our algorithm estimates the mean of the function by taking a weighted sum only at these vertices, and we provably bound the estimation error in terms of the location and weights of the selected vertices in the graph. In addition, we consider the case where nodes have different selection costs and provide bounds on the quality of the low-cost selected coresets. We demonstrate the benefits of our algorithm on the semi-supervised node classification of graph convolutional neural network, point clouds and structured graphs, as well as sensor placement where the cost of placing sensors depends on the location of the placement. We also elucidate that the empirical convergence of our proposed method is faster than random selection and various clustering methods while still respecting sensor placement cost. The paper concludes with validation of the developed algorithm on both synthetic and real datasets, demonstrating that it outperforms the current state of the art.

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ICML Conference 2020 Conference Paper

Divide and Conquer: Leveraging Intermediate Feature Representations for Quantized Training of Neural Networks

Ahmed Taha Elthakeb
Prannoy Pilligundla
Niloofar Mireshghallah
Alexander Cloninger
Hadi Esmaeilzadeh

The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network, this paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al. , 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher accuracy quantization. As such, our algorithm logically divides a pretrained full-precision DNN to multiple sections, each of which exposes intermediate features to train a team of students independently in the quantized domain and simply stitching them afterwards. This divide and conquer strategy, makes the training of each student section possible in isolation, speeding up training by enabling parallelization. Experiments on various DNNs (AlexNet, LeNet, MobileNet, ResNet-18, ResNet-20, SVHN and VGG-11) show that, this approach{—}called DCQ (Divide and Conquer Quantization){—}on average, improves the performance of a state-of-the-art quantized training technique, DoReFa-Net (Zhou et al. , 2016) by 21. 6% and 9. 3% for binary and ternary quantization, respectively. Additionally, we show that incorporating DCQ to existing quantized training methods leads to improved accuracies as compared to previously reported by multiple state-of-the-art quantized training methods.

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