We introduce the problem of zero-data learning, where a model must generalize to classes or tasks for which no training data are available and only a description of the classes or tasks are provided. Zero-data learning is useful for problems where the set of classes to distinguish or tasks to solve is very large and is not entirely covered by the training data. The main contributions of this wo...

With the recent renaissance of deep convolution neural networks, encouraging breakthroughs have been achieved on the supervised recognition tasks, where each class has sufficient training data and fully annotated training data. However, to scale the recognition to a large number of classes with few or now training samples for each class remains an unsolved problem. One approach to scaling up th...

Stofan, A.G. Hayes, R.L. Kirk, J.I. Lunine. J. Radebaugh; and M. Malaska. Planetary Science Institute, Tucson, AZ 85721 & Wheeling Jesuit University, Wheeling, WV; [email protected]; Proxemy Research, Gaithersburg, MD 20882; Cornell Univ., Ithaca, NY 14853; Astrogeology Science Center, USGS, Flagstaff AZ 86001; Brigham Young University, Provo, UT 84602; JPL, California Institute of Technology, ...

Let E be a real Banach space, let C be a closed convex subset of E, let T be a nonexpansive mapping of C into itself, that is, ‖Tx−Ty‖ ≤ ‖x− y‖ for each x, y ∈ C, and let A⊂ E×E be an accretive operator. For r > 0, we denote by Jr the resolvent of A, that is, Jr = (I + rA)−1. The problem of finding a solution u∈ E such that 0∈ Au has been investigated by many authors; for example, see [3, 4, 7,...

A fairly long-standing conjecture is that the Davenport constant of a group G = Zn1 ⊕ · · · ⊕ Znk with n1| . . . |nk is 1 + ∑k i=1(ni − 1). This conjecture is false in general, but it remains to know for which groups it is true. By using inductive methods we prove that for two fixed integers k and ! it is possible to decide whether the conjecture is satisfied for all groups of the form Zk ⊕ Zn ...

Let G be a finite Abelian group and D(G) its Davenport constant, which is defined as the maximal length of a minimal zero-sum sequence in G. We show that various problems on zero-sum sequences in G may be interpreted as certain covering problems. Using this approach we study the Davenport constant of groups of the form (Z/nZ)r , with n ≥ 2 and r ∈ N. For elementary p-groups G, we derive a resul...

Consider multisets A in the group G = (Z/nZ) such that no non-empty subset has sum zero. It is known for long that the maximal cardinality of such a set is 2n − 2, and there is a conjecture of Gao and Geroldinger describing the structure of such sets of maximal cardinality (called “property B”). Recently, Gao, Geroldinger and Grynkiewicz showed that it is enough to prove the conjecture for n pr...

WITH EXTENT OF CHONDRULE MELTING. L.R. Varley, L.A. Leshin, Y. Guan, B. Zanda, and M. Bourot-Denise, Dept. of Geological Sciences, Arizona State University, PO Box 871404, Tempe, AZ , 85287-1404 ([email protected]), Center for Meteorite Studies, ASU,. Geological Sciences, Rutgers University, Piscataway, NJ, 08855-1179, Laboratoire de Minéralogie, Muséum d’Histoire Naturelle, 75005 Paris, France.

We are interested in large-scale image classification and especially in the setting where images corresponding to new or existing classes are continuously added to the training set. Our goal is to devise classifiers which can incorporate such images and classes on-the-fly at (near) zero cost. We cast this problem into one of learning a metric which is shared across all classes and explore k-nea...

This work introduces a model that can recognize objects in images even if no training data is available for the objects. The only necessary knowledge about the unseen categories comes from unsupervised large text corpora. In our zero-shot framework distributional information in language can be seen as spanning a semantic basis for understanding what objects look like. Most previous zero-shot le...