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Gavin Brown

Publications and source records attributed to Gavin Brown.

At least 55 records · Page 3Linked to original sources

Is Deep Learning Safe for Robot Vision? Adversarial Examples against the iCub Humanoid

Deep neural networks have been widely adopted in recent years, exhibiting impressive performances in several application domains. It has however been shown that they can be fooled by adversarial examples, i.e., images altered by a barely-perceivable adversarial noise, carefully crafted to mislead classification. In this work, we aim to evaluate the extent to which robot-vision systems embodying deep-learning algorithms are vulnerable to adversarial examples, and propose a computationally efficient countermeasure to mitigate this threat, based on rejecting classification of anomalous inputs. We then provide a clearer understanding of the safety properties of deep networks through an intuitive empirical analysis, showing that the mapping learned by such networks essentially violates the smoothness assumption of learning algorithms. We finally discuss the main limitations of this work, including the creation of real-world adversarial examples, and sketch promising research directions.

cs.LG↗

Fano 3-folds in $\mathbb {P^2} \times \mathbb {P^2}$ format, Tom and Jerry

We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2 x P^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state of classification in three different ways. Some families arise as unprojections of degenerations of complete intersections, where the generic unprojection is a known prime Fano 3-fold in codimension 3; these are new, and an analysis of their Gorenstein projections reveals yet other new families. Others represent the "second Tom" unprojection families already known in codimension 4, and we show that every such family contains one of our models. Yet others have no easy Gorenstein projection analysis at all, so prove the existence of Fano components on their Hilbert scheme.

math.AG↗

Ranking Biomarkers Through Mutual Information

We study information theoretic methods for ranking biomarkers. In clinical trials there are two, closely related, types of biomarkers: predictive and prognostic, and disentangling them is a key challenge. Our first step is to phrase biomarker ranking in terms of optimizing an information theoretic quantity. This formalization of the problem will enable us to derive rankings of predictive/prognostic biomarkers, by estimating different, high dimensional, conditional mutual information terms. To estimate these terms, we suggest efficient low dimensional approximations, and we derive an empirical Bayes estimator, which is suitable for small or sparse datasets. Finally, we introduce a new visualisation tool that captures the prognostic and the predictive strength of a set of biomarkers. We believe this representation will prove to be a powerful tool in biomarker discovery.

stat.ML↗

Modular Autoencoders for Ensemble Feature Extraction

We introduce the concept of a Modular Autoencoder (MAE), capable of learning a set of diverse but complementary representations from unlabelled data, that can later be used for supervised tasks. The learning of the representations is controlled by a trade off parameter, and we show on six benchmark datasets the optimum lies between two extremes: a set of smaller, independent autoencoders each with low capacity, versus a single monolithic encoding, outperforming an appropriate baseline. In the present paper we explore the special case of linear MAE, and derive an SVD-based algorithm which converges several orders of magnitude faster than gradient descent.

cs.LG↗

Boosting Java Performance using GPGPUs

Heterogeneous programming has started becoming the norm in order to achieve better performance by running portions of code on the most appropriate hardware resource. Currently, significant engineering efforts are undertaken in order to enable existing programming languages to perform heterogeneous execution mainly on GPUs. In this paper we describe Jacc, an experimental framework which allows developers to program GPGPUs directly from Java. By using the Jacc framework, developers have the ability to add GPGPU support into their applications with minimal code refactoring. To simplify the development of GPGPU applications we allow developers to model heterogeneous code using two key abstractions: \textit{tasks}, which encapsulate all the information needed to execute code on a GPGPU; and \textit{task graphs}, which capture the inter-task control-flow of the application. Using this information the Jacc runtime is able to automatically handle data movement and synchronization between the host and the GPGPU; eliminating the need for explicitly managing disparate memory spaces. In order to generate highly parallel GPGPU code, Jacc provides developers with the ability to decorate key aspects of their code using annotations. The compiler, in turn, exploits this information in order to automatically generate code without requiring additional code refactoring. Finally, we demonstrate the advantages of Jacc, both in terms of programmability and performance, by evaluating it against existing Java frameworks. Experimental results show an average performance speedup of 32x and a 4.4x code decrease across eight evaluated benchmarks on a NVIDIA Tesla K20m GPU.

cs.DC↗

Polarized Calabi-Yau 3-folds in codimension 4

We construct Calabi-Yau 3-folds as orbifolds embedded in weighted projective space in codimension 4. For each Hilbert series that is realised, there are at least two different components of Calabi-Yau 3-folds.

math.AG↗

Diptych varieties. II: Polar varieties

Part I introduced diptych varieties $V_{ABLM}$ and gave a rigorous construction of them in the case $d,e\ge 2$ and $de>4$. Here we prove the existence of $V_{ABLM}$ in all the cases with $de\le4$. At the same time we construct some classes of interesting quasihomogeneous spaces for groups such as $\GL(2)\times\G_m^r$ based on the algebra of polars.

math.AG↗

Four-dimensional projective orbifold hypersurfaces

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi-Yau, and Fano fourfolds. We also consider other classes of hypersurfaces, including Fano hypersurfaces of index greater than 1 in dimensions 3 and 4.

math.AG↗

Gorenstein formats, canonical and Calabi-Yau threefolds

We extend the known classification of threefolds of general type that are complete intersections to various classes of non-complete intersections, and find other classes of polarised varieties, including Calabi-Yau threefolds with canonical singularities, that are not complete intersections. Our methods apply more generally to construct orbifolds described by equations in given Gorenstein formats.

math.AG↗

Maps of toric varieties in Cox coordinates

The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric arieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.

math.AG↗

ManTIME: Temporal expression identification and normalization in the TempEval-3 challenge

This paper describes a temporal expression identification and normalization system, ManTIME, developed for the TempEval-3 challenge. The identification phase combines the use of conditional random fields along with a post-processing identification pipeline, whereas the normalization phase is carried out using NorMA, an open-source rule-based temporal normalizer. We investigate the performance variation with respect to different feature types. Specifically, we show that the use of WordNet-based features in the identification task negatively affects the overall performance, and that there is no statistically significant difference in using gazetteers, shallow parsing and propositional noun phrases labels on top of the morphological features. On the test data, the best run achieved 0.95 (P), 0.85 (R) and 0.90 (F1) in the identification phase. Normalization accuracies are 0.84 (type attribute) and 0.77 (value attribute). Surprisingly, the use of the silver data (alone or in addition to the gold annotated ones) does not improve the performance.

cs.CL↗

Seven new champion linear codes

We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F_8, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the [0,5]x[0,5] lattice square.

math.CO↗

Diptych varieties. I

We present a new class of affine Gorenstein 6-folds obtained by smoothing the 1-dimensional singular locus of a reducible affine toric surface; their existence is established using explicit methods in toric geometry and serial use of Kustin-Miller Gorenstein unprojection. These varieties have applications as key varieties in constructing other varieties, including local models of Mori flips of Type A.

math.AG↗

Small polygons and toric codes

We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best known minimum distance. This includes a [36,19,12]-code over F_7 whose minimum distance 12 exceeds that of all previously known codes.

math.CO↗

Fano 3-folds in codimension 4, Tom and Jerry, Part I

This work is part of the Graded Ring Database project [GRDB], and is a sequel to [Altinok's 1998 PhD thesis] and [Altinok, Brown and Reid, Fano 3-folds, K3 surfaces and graded rings, in SISTAG (Singapore, 2001), Contemp. Math. 314, 2002, pp. 25-53]. We introduce a strategy based on Kustin-Miller unprojection that constructs many hundreds of Gorenstein codimension 4 ideals with 9x16 resolutions (that is, 9 equations and 16 first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology.

math.AG↗

Computational birational geometry of minimal rational surfaces

The classification of minimal rational surfaces and the birational links between them by Iskovskikh, Manin and others is a well-known subject in the theory of algebraic surfaces. We explain algorithms that realise links of type II between minimal del Pezzo surfaces, one of the major classes of birational links, and we describe briefly how this fits into a large project to implement the results of Iskovskikh's programme in Magma.

math.AG↗

Elliptic fibrations on cubic surfaces

We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an implementation of this analysis in computer algebra.

math.AG↗