121,480 research outputs found
Robust Computer Algebra, Theorem Proving, and Oracle AI
In the context of superintelligent AI systems, the term "oracle" has two
meanings. One refers to modular systems queried for domain-specific tasks.
Another usage, referring to a class of systems which may be useful for
addressing the value alignment and AI control problems, is a superintelligent
AI system that only answers questions. The aim of this manuscript is to survey
contemporary research problems related to oracles which align with long-term
research goals of AI safety. We examine existing question answering systems and
argue that their high degree of architectural heterogeneity makes them poor
candidates for rigorous analysis as oracles. On the other hand, we identify
computer algebra systems (CASs) as being primitive examples of domain-specific
oracles for mathematics and argue that efforts to integrate computer algebra
systems with theorem provers, systems which have largely been developed
independent of one another, provide a concrete set of problems related to the
notion of provable safety that has emerged in the AI safety community. We
review approaches to interfacing CASs with theorem provers, describe
well-defined architectural deficiencies that have been identified with CASs,
and suggest possible lines of research and practical software projects for
scientists interested in AI safety.Comment: 15 pages, 3 figure
Network algebra for synchronous dataflow
We develop an algebraic theory of synchronous dataflow networks. First, a
basic algebraic theory of networks, called BNA (Basic Network Algebra), is
introduced. This theory captures the basic algebraic properties of networks.
For synchronous dataflow networks, it is subsequently extended with additional
constants for the branching connections that occur between the cells of
synchronous dataflow networks and axioms for these additional constants. We
also give two models of the resulting theory, the one based on stream
transformers and the other based on processes as considered in process algebra.Comment: 24 page
A universe of processes and some of its guises
Our starting point is a particular `canvas' aimed to `draw' theories of
physics, which has symmetric monoidal categories as its mathematical backbone.
In this paper we consider the conceptual foundations for this canvas, and how
these can then be converted into mathematical structure. With very little
structural effort (i.e. in very abstract terms) and in a very short time span
the categorical quantum mechanics (CQM) research program has reproduced a
surprisingly large fragment of quantum theory. It also provides new insights
both in quantum foundations and in quantum information, and has even resulted
in automated reasoning software called `quantomatic' which exploits the
deductive power of CQM. In this paper we complement the available material by
not requiring prior knowledge of category theory, and by pointing at
connections to previous and current developments in the foundations of physics.
This research program is also in close synergy with developments elsewhere, for
example in representation theory, quantum algebra, knot theory, topological
quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World
through Mathematical Innovation", H. Halvorson, ed., Cambridge University
Press, forthcoming. (as usual, many pictures
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