Learning to Find Proofs and Theorems by Learning to Refine Search Strategies: The Case of Loop Invariant Synthesis

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies

Language-based Abstractions for Dynamical Systems

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366

Statistical Theory of Parity Nonconservation in Compound Nuclei

We present the first application of statistical spectroscopy to study the root-mean-square value of the parity nonconserving (PNC) interaction matrix element M determined experimentally by scattering longitudinally polarized neutrons from compound nuclei. Our effective PNC interaction consists of a standard two-body meson-exchange piece and a doorway term to account for spin-flip excitations. Strength functions are calculated using realistic single-particle energies and a residual strong interaction adjusted to fit the experimental density of states for the targets, ^{238} U for A\sim 230 and ^{104,105,106,108} Pd for A\sim 100. Using the standard Desplanques, Donoghue, and Holstein estimates of the weak PNC meson-nucleon coupling constants, we find that M is about a factor of 3 smaller than the experimental value for ^{238} U and about a factor of 1.7 smaller for Pd. The significance of this result for refining the empirical determination of the weak coupling constants is discussed.Comment: Latex file, no Fig

Conformal Gravity: Dark Matter and Dark Energy

This short review examines recent progress in understanding dark matter, dark energy, and galactic halos using theory that departs minimally from standard particle physics and cosmology. Strict conformal symmetry (local Weyl scaling covariance), postulated for all elementary massless fields, retains standard fermion and gauge boson theory but modifies Einstein-Hilbert general relativity and the Higgs scalar field model, with no new physical fields. Subgalactic phenomenology is retained. Without invoking dark matter, conformal gravity and a conformal Higgs model fit empirical data on galactic rotational velocities, galactic halos, and Hubble expansion including dark energy.Comment: 9 pp in revtex format. References added with minor text revision

Solving the 3D Ising Model with the Conformal Bootstrap

We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and OPE coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.Comment: 32 pages, 11 figures; v2: refs added, small changes in Section 5.3, Fig. 7 replaced; v3: ref added, fits redone in Section 5.