arXiv subjects

Benjamin Graham

Publications and source records attributed to Benjamin Graham.

30 records · Page 2Linked to original sources

arXiv2018

Unsupervised learning with sparse space-and-time autoencoders

We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their usefulness for downstream tasks. Applications are to handwriting recognition in 2D, segmentation for parts in 3D objects, segmentation for objects in 3D scenes, and body-part segmentation for 4D wire-frame models generated from motion capture data.

cs.CV↗

arXiv2018

The iisignature library: efficient calculation of iterated-integral signatures and log signatures

Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine learning. We present algorithms for efficiently calculating these signatures, and benchmark their performance. We release the methods as a Python package.

cs.DS↗

arXiv2017

3D Semantic Segmentation with Submanifold Sparse Convolutional Networks

Convolutional networks are the de-facto standard for analyzing spatio-temporal data such as images, videos, and 3D shapes. Whilst some of this data is naturally dense (e.g., photos), many other data sources are inherently sparse. Examples include 3D point clouds that were obtained using a LiDAR scanner or RGB-D camera. Standard "dense" implementations of convolutional networks are very inefficient when applied on such sparse data. We introduce new sparse convolutional operations that are designed to process spatially-sparse data more efficiently, and use them to develop spatially-sparse convolutional networks. We demonstrate the strong performance of the resulting models, called submanifold sparse convolutional networks (SSCNs), on two tasks involving semantic segmentation of 3D point clouds. In particular, our models outperform all prior state-of-the-art on the test set of a recent semantic segmentation competition.

cs.CV↗

arXiv2017

Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55

We introduce a large-scale 3D shape understanding benchmark using data and annotation from ShapeNet 3D object database. The benchmark consists of two tasks: part-level segmentation of 3D shapes and 3D reconstruction from single view images. Ten teams have participated in the challenge and the best performing teams have outperformed state-of-the-art approaches on both tasks. A few novel deep learning architectures have been proposed on various 3D representations on both tasks. We report the techniques used by each team and the corresponding performances. In addition, we summarize the major discoveries from the reported results and possible trends for the future work in the field.

cs.CV↗

arXiv2017

Submanifold Sparse Convolutional Networks

Convolutional network are the de-facto standard for analysing spatio-temporal data such as images, videos, 3D shapes, etc. Whilst some of this data is naturally dense (for instance, photos), many other data sources are inherently sparse. Examples include pen-strokes forming on a piece of paper, or (colored) 3D point clouds that were obtained using a LiDAR scanner or RGB-D camera. Standard "dense" implementations of convolutional networks are very inefficient when applied on such sparse data. We introduce a sparse convolutional operation tailored to processing sparse data that differs from prior work on sparse convolutional networks in that it operates strictly on submanifolds, rather than "dilating" the observation with every layer in the network. Our empirical analysis of the resulting submanifold sparse convolutional networks shows that they perform on par with state-of-the-art methods whilst requiring substantially less computation.

cs.NE↗

arXiv2017

Low-Precision Batch-Normalized Activations

Artificial neural networks can be trained with relatively low-precision floating-point and fixed-point arithmetic, using between one and 16 bits. Previous works have focused on relatively wide-but-shallow, feed-forward networks. We introduce a quantization scheme that is compatible with training very deep neural networks. Quantizing the network activations in the middle of each batch-normalization module can greatly reduce the amount of memory and computational power needed, with little loss in accuracy.

cs.NE↗

arXiv2015

Confusing Deep Convolution Networks by Relabelling

Deep convolutional neural networks have become the gold standard for image recognition tasks, demonstrating many current state-of-the-art results and even achieving near-human level performance on some tasks. Despite this fact it has been shown that their strong generalisation qualities can be fooled to misclassify previously correctly classified natural images and give erroneous high confidence classifications to nonsense synthetic images. In this paper we extend that work, by presenting a straightforward way to perturb an image in such a way as to cause it to acquire any other label from within the dataset while leaving this perturbed image visually indistinguishable from the original.

cs.CV↗

arXiv2015

Fractional Max-Pooling

Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor alpha. The amazing by-product of discarding 75% of your data is that you build into the network a degree of invariance with respect to translations and elastic distortions. However, if you simply alternate convolutional layers with max-pooling layers, performance is limited due to the rapid reduction in spatial size, and the disjoint nature of the pooling regions. We have formulated a fractional version of max-pooling where alpha is allowed to take non-integer values. Our version of max-pooling is stochastic as there are lots of different ways of constructing suitable pooling regions. We find that our form of fractional max-pooling reduces overfitting on a variety of datasets: for instance, we improve on the state-of-the art for CIFAR-100 without even using dropout.

cs.CV↗

arXiv2014

Spatially-sparse convolutional neural networks

Convolutional neural networks (CNNs) perform well on problems such as handwriting recognition and image classification. However, the performance of the networks is often limited by budget and time constraints, particularly when trying to train deep networks. Motivated by the problem of online handwriting recognition, we developed a CNN for processing spatially-sparse inputs; a character drawn with a one-pixel wide pen on a high resolution grid looks like a sparse matrix. Taking advantage of the sparsity allowed us more efficiently to train and test large, deep CNNs. On the CASIA-OLHWDB1.1 dataset containing 3755 character classes we get a test error of 3.82%. Although pictures are not sparse, they can be thought of as sparse by adding padding. Applying a deep convolutional network using sparsity has resulted in a substantial reduction in test error on the CIFAR small picture datasets: 6.28% on CIFAR-10 and 24.30% for CIFAR-100.

cs.CV↗

arXiv2013

Sparse arrays of signatures for online character recognition

In mathematics the signature of a path is a collection of iterated integrals, commonly used for solving differential equations. We show that the path signature, used as a set of features for consumption by a convolutional neural network (CNN), improves the accuracy of online character recognition---that is the task of reading characters represented as a collection of paths. Using datasets of letters, numbers, Assamese and Chinese characters, we show that the first, second, and even the third iterated integrals contain useful information for consumption by a CNN. On the CASIA-OLHWDB1.1 3755 Chinese character dataset, our approach gave a test error of 3.58%, compared with 5.61% for a traditional CNN [Ciresan et al.]. A CNN trained on the CASIA-OLHWDB1.0-1.2 datasets won the ICDAR2013 Online Isolated Chinese Character recognition competition. Computationally, we have developed a sparse CNN implementation that make it practical to train CNNs with many layers of max-pooling. Extending the MNIST dataset by translations, our sparse CNN gets a test error of 0.31%.

cs.CV↗

arXiv2013

A binary deletion channel with a fixed number of deletions

Suppose a binary string x = x_1...x_n is being broadcast repeatedly over a faulty communication channel. Each time, the channel delivers a fixed number m of the digits (m<n) with the lost digits chosen uniformly at random, and the order of the surviving digits preserved. How large does m have to be to reconstruct the message?

math.PR↗

arXiv2011

Sharp thresholds for the random-cluster and Ising models

A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.

math.PR↗