Extensional Collapse Situations I: non-termination and unrecoverable errors

We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined form a lattice when ordered by the extensional collapse situation relation, introduced in order to compare models with respect to the amount of "intensional information" that they provide on computation. The proofs are carried out by exhibiting suitable applied {\lambda}-calculi, and by exploiting the fundamental lemma of logical relations

Non uniform (hyper/multi)coherence spaces

In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly) stable function, at arrow types. In (hyper)coherence semantics, the argument of a (strongly) stable functional is always a (strongly) stable function. As a consequence, comparatively to the relational semantics, where there is no edge relation, some vertices are missing. Recovering these vertices is essential for the purpose of reconstructing proofs/terms from their interpretations. It shall also be useful for the comparison with other semantics, like game semantics. In [BE01], Bucciarelli and Ehrhard introduced a so called non uniform coherence space semantics where no vertex is missing. By constructing the co-free exponential we set a new version of this last semantics, together with non uniform versions of hypercoherences and multicoherences, a new semantics where an edge is a finite multiset. Thanks to the co-free construction, these non uniform semantics are deterministic in the sense that the intersection of a clique and of an anti-clique contains at most one vertex, a result of interaction, and extensionally collapse onto the corresponding uniform semantics.Comment: 32 page

Sparse Estimation with the Swept Approximated Message-Passing Algorithm

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contexts that do not exactly match its assumptions. We propose a new approach to stabilizing AMP in these contexts by applying AMP updates to individual coefficients rather than in parallel. Our results show that this change to the AMP iteration can provide theoretically expected, but hitherto unobtainable, performance for problems on which the standard AMP iteration diverges. Additionally, we find that the computational costs of this swept coefficient update scheme is not unduly burdensome, allowing it to be applied efficiently to signals of large dimensionality.Comment: 11 pages, 3 figures, implementation available at https://github.com/eric-tramel/SwAMP-Dem