66,074 research outputs found
Statistical mechanics of spatial evolutionary games
We discuss the long-run behavior of stochastic dynamics of many interacting
players in spatial evolutionary games. In particular, we investigate the effect
of the number of players and the noise level on the stochastic stability of
Nash equilibria. We discuss similarities and differences between systems of
interacting players maximizing their individual payoffs and particles
minimizing their interaction energy. We use concepts and techniques of
statistical mechanics to study game-theoretic models. In order to obtain
results in the case of the so-called potential games, we analyze the
thermodynamic limit of the appropriate models of interacting particles.Comment: 19 pages, to appear in J. Phys.
On the logical structure of Bell theorems without inequalities
Bell theorems show how to experimentally falsify local realism. Conclusive
falsification is highly desirable as it would provide support for the most
profoundly counterintuitive feature of quantum theory - nonlocality. Despite
the preponderance of evidence for quantum mechanics, practical limits on
detector efficiency and the difficulty of coordinating space-like separated
measurements have provided loopholes for a classical worldview; these loopholes
have never been simultaneously closed. A number of new experiments have
recently been proposed to close both loopholes at once. We show some of these
novel designs fail in the most basic way, by not ruling out local hidden
variable models, and we provide an explicit classical model to demonstrate
this. They share a common flaw, which reveals a basic misunderstanding of how
nonlocality proofs work. Given the time and resources now being devoted to such
experiments, theoretical clarity is essential. Our explanation is presented in
terms of simple logic and should serve to correct misconceptions and avoid
future mistakes. We also show a nonlocality proof involving four participants
which has interesting theoretical properties.Comment: 8 pages, text clarified, explicit LHV model provided for flawed
nonlocality tes
Differentiable Game Mechanics
Deep learning is built on the foundational guarantee that gradient descent on
an objective function converges to local minima. Unfortunately, this guarantee
fails in settings, such as generative adversarial nets, that exhibit multiple
interacting losses. The behavior of gradient-based methods in games is not well
understood -- and is becoming increasingly important as adversarial and
multi-objective architectures proliferate. In this paper, we develop new tools
to understand and control the dynamics in n-player differentiable games.
The key result is to decompose the game Jacobian into two components. The
first, symmetric component, is related to potential games, which reduce to
gradient descent on an implicit function. The second, antisymmetric component,
relates to Hamiltonian games, a new class of games that obey a conservation law
akin to conservation laws in classical mechanical systems. The decomposition
motivates Symplectic Gradient Adjustment (SGA), a new algorithm for finding
stable fixed points in differentiable games. Basic experiments show SGA is
competitive with recently proposed algorithms for finding stable fixed points
in GANs -- while at the same time being applicable to, and having guarantees
in, much more general cases.Comment: JMLR 2019, journal version of arXiv:1802.0564
Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
Characterizing quantum correlations in terms of information-theoretic
principles is a popular chapter of quantum foundations. Traditionally, the
principles adopted for this scope have been expressed in terms of conditional
probability distributions, specifying the probability that a black box produces
a certain output upon receiving a certain input. This framework is known as
"device-independent". Another major chapter of quantum foundations is the
information-theoretic characterization of quantum theory, with its sets of
states and measurements, and with its allowed dynamics. The different
frameworks adopted for this scope are known under the umbrella term "general
probabilistic theories". With only a few exceptions, the two programmes on
characterizing quantum correlations and characterizing quantum theory have so
far proceeded on separate tracks, each one developing its own methods and its
own agenda. This paper aims at bridging the gap, by comparing the two
frameworks and illustrating how the two programmes can benefit each other.Comment: 61 pages, no figures, published versio
Graphical Methods in Device-Independent Quantum Cryptography
We introduce a framework for graphical security proofs in device-independent
quantum cryptography using the methods of categorical quantum mechanics. We are
optimistic that this approach will make some of the highly complex proofs in
quantum cryptography more accessible, facilitate the discovery of new proofs,
and enable automated proof verification. As an example of our framework, we
reprove a previous result from device-independent quantum cryptography: any
linear randomness expansion protocol can be converted into an unbounded
randomness expansion protocol. We give a graphical proof of this result, and
implement part of it in the Globular proof assistant.Comment: Publishable version. Diagrams have been polished, minor revisions to
the text, and an appendix added with supplementary proof
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