3,213 research outputs found
What caused what? A quantitative account of actual causation using dynamical causal networks
Actual causation is concerned with the question "what caused what?" Consider
a transition between two states within a system of interacting elements, such
as an artificial neural network, or a biological brain circuit. Which
combination of synapses caused the neuron to fire? Which image features caused
the classifier to misinterpret the picture? Even detailed knowledge of the
system's causal network, its elements, their states, connectivity, and dynamics
does not automatically provide a straightforward answer to the "what caused
what?" question. Counterfactual accounts of actual causation based on graphical
models, paired with system interventions, have demonstrated initial success in
addressing specific problem cases in line with intuitive causal judgments.
Here, we start from a set of basic requirements for causation (realization,
composition, information, integration, and exclusion) and develop a rigorous,
quantitative account of actual causation that is generally applicable to
discrete dynamical systems. We present a formal framework to evaluate these
causal requirements that is based on system interventions and partitions, and
considers all counterfactuals of a state transition. This framework is used to
provide a complete causal account of the transition by identifying and
quantifying the strength of all actual causes and effects linking the two
consecutive system states. Finally, we examine several exemplary cases and
paradoxes of causation and show that they can be illuminated by the proposed
framework for quantifying actual causation.Comment: 43 pages, 16 figures, supplementary discussion, supplementary
methods, supplementary proof
Synthesising Graphical Theories
In recent years, diagrammatic languages have been shown to be a powerful and
expressive tool for reasoning about physical, logical, and semantic processes
represented as morphisms in a monoidal category. In particular, categorical
quantum mechanics, or "Quantum Picturalism", aims to turn concrete features of
quantum theory into abstract structural properties, expressed in the form of
diagrammatic identities. One way we search for these properties is to start
with a concrete model (e.g. a set of linear maps or finite relations) and start
composing generators into diagrams and looking for graphical identities.
Naively, we could automate this procedure by enumerating all diagrams up to a
given size and check for equalities, but this is intractable in practice
because it produces far too many equations. Luckily, many of these identities
are not primitive, but rather derivable from simpler ones. In 2010, Johansson,
Dixon, and Bundy developed a technique called conjecture synthesis for
automatically generating conjectured term equations to feed into an inductive
theorem prover. In this extended abstract, we adapt this technique to
diagrammatic theories, expressed as graph rewrite systems, and demonstrate its
application by synthesising a graphical theory for studying entangled quantum
states.Comment: 10 pages, 22 figures. Shortened and one theorem adde
Limits of Preprocessing
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a
complexity theoretic assumption, none of the considered problems can be reduced
by polynomial-time preprocessing to a problem kernel whose size is polynomial
in a structural problem parameter of the input, such as induced width or
backdoor size. Our results provide a firm theoretical boundary for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: This is a slightly longer version of a paper that appeared in the
proceedings of AAAI 201
A Biologically Informed Hylomorphism
Although contemporary metaphysics has recently undergone a neo-Aristotelian revival wherein dispositions, or capacities are now commonplace in empirically grounded ontologies, being routinely utilised in theories of causality and modality, a central Aristotelian concept has yet to be given serious attention – the doctrine of hylomorphism. The reason for this is clear: while the Aristotelian ontological distinction between actuality and potentiality has proven to be a fruitful conceptual framework with which to model the operation of the natural world, the distinction between form and matter has yet to similarly earn its keep. In this chapter, I offer a first step toward showing that the hylomorphic framework is up to that task. To do so, I return to the birthplace of that doctrine - the biological realm. Utilising recent advances in developmental biology, I argue that the hylomorphic framework is an empirically adequate and conceptually rich explanatory schema with which to model the nature of organism
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