Extensional and Intensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that these extensional and intensional representations are equivalent, by showing how to construct the unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may-testing and must-testing denotational semantics for sequential functional languages with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may-testing and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped {\lambda}-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract.

SEMANTIC BORROWING FOR GENERALIZED ZERO-SHOT LEARNING

<p>Generalized zero-shot learning (GZSL) is one of the most realistic problems, but also one of the most challenging problems due to the partiality of the classifier to supervised classes. Instance-borrowing methods and synthesizing methods solve this problem to some extent with the help of testing semantics, but therefore neither can be used under the class-inductive instance-inductive (CIII) training setting where testing data are not available, and the latter require the training process of a classifier after generating examples. In contrast, a novel method called Semantic Borrowing for improving GZSL methods with compatibility metric learning under CIII is proposed in this paper. It borrows similar semantics in the training set, so that the classifier can model the relationship between the semantics of zero-shot and supervised classes more accurately during training. In practice, the information of semantics of unseen or unknown classes would not be available for training while this approach does NOT need any information of semantics of unseen or unknown classes. The experimental results on representative GZSL benchmark datasets show that it can reduce the partiality of the classifier to supervised classes and improve the performance of generalized zero-shot classification.</p>

SEMANTIC BORROWING FOR GENERALIZED ZERO-SHOT LEARNING

<p>Generalized zero-shot learning (GZSL) is one of the most realistic problems, but also one of the most challenging problems due to the partiality of the classifier to supervised classes. Instance-borrowing methods and synthesizing methods solve this problem to some extent with the help of testing semantics, but therefore neither can be used under the class-inductive instance-inductive (CIII) training setting where testing data are not available, and the latter require the training process of a classifier after generating examples. In contrast, a novel method called Semantic Borrowing for improving GZSL methods with compatibility metric learning under CIII is proposed in this paper. It borrows similar semantics in the training set, so that the classifier can model the relationship between the semantics of zero-shot and supervised classes more accurately during training. In practice, the information of semantics of unseen or unknown classes would not be available for training while this approach does NOT need any information of semantics of unseen or unknown classes. The experimental results on representative GZSL benchmark datasets show that it can reduce the partiality of the classifier to supervised classes and improve the performance of generalized zero-shot classification.</p>

Order algebras: a quantitative model of interaction

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and non-interleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of non-determinism as linear combinations is the same.