MCMC with strings and branes: The suburban algorithm (Extended Version)

Heckman, Jonathan J.; Bernstein, Jeffrey; Vigoda, Ben

doi:10.1142/s0217751x17501330

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…This is related to the broader question of how well a low energy observer can ever hope to reconstruct a given UV completion, see, e.g.,[14,[40][41][42][43][44] as well as[45][46][47][48][49][50][51][52].…”

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confidence: 99%

Disorder Averaging and its UV (Dis)Contents

Heckman,

Turner,

2021

Preprint

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We present a stringy realization of quantum field theory ensembles in D ≤ 4 spacetime dimensions, thus realizing a disorder averaging over coupling constants. When each member of the ensemble is a conformal field theory with a standard semi-classical holographic dual of the same radius, the resulting bulk can be interpreted as a single asymptotically Anti-de Sitter space geometry with a distribution of boundary components joined by wormhole configurations, as dictated by the Hartle-Hawking wave function. This provides a UV completion of a recent proposal by Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed Swampland constraints of McNamara and Vafa. This is possible because our construction is really an approximation that breaks down both at short distances, but also at low energies for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to various claims in the literature that holographic and effective field theory considerations can be reliably developed without reference to any UV completion.

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confidence: 99%

Disorder Averaging and its UV (Dis)Contents

Heckman,

Turner,

2021

Preprint

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“…The second order expansion in θ i of the KL divergence then yields the Fisher information metric which forms the basis for information geometry [9,10]. (See [11][12][13][14][15][16][17][18][19][20][21][22] for contemporary appearances of the information metric in statistical inference and its relevance to quantum field theory and string theory. )…”

Section: Introductionmentioning

confidence: 99%

On the Dynamics of Inference and Learning

Berman¹,

Heckman²,

Klinger³

2022

Preprint

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Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of Bayes' theorem. We present a treatment of this Bayesian updating process as a continuous dynamical system. Statistical inference is then governed by a first order differential equation describing a trajectory or flow in the information geometry determined by a parametric family of models. We solve this equation for some simple models and show that when the Cramér-Rao bound is saturated the learning rate is governed by a simple 1/T power-law, with T a time-like variable denoting the quantity of data. The presence of hidden variables can be incorporated in this setting, leading to an additional driving term in the resulting flow equation. We illustrate this with both analytic and numerical examples based on Gaussians and Gaussian Random Processes and inference of the coupling constant in the 1D Ising model. Finally we compare the qualitative behaviour exhibited by Bayesian flows to the training of various neural networks on benchmarked data sets such as MNIST and CIFAR10 and show how that for networks exhibiting small final losses the simple power-law is also satisfied.

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“…On general grounds, one might ask to what extent a set of IR observables can serve to constrain the content of some candidate UV completion (see e.g. [5][6][7][8][9][10] as well as [11][12][13][14][15][16][17]). This issue is also of general interest in trying to understand the extent to which information is lost in passing from short to long distance scales.…”

Section: Introductionmentioning

confidence: 99%

Misanthropic Entropy and Renormalization as a Communication Channel

Fowler,

Heckman

2021

Preprint

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A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining / decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the "misanthropic entropy"-the mutual information obtained from decimating neighborsencodes the extent to which information is lost in marginalizing over / tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.

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MCMC with strings and branes: The suburban algorithm (Extended Version)

Cited by 5 publications

References 26 publications

Disorder Averaging and its UV (Dis)Contents

Disorder Averaging and its UV (Dis)Contents

On the Dynamics of Inference and Learning

Misanthropic Entropy and Renormalization as a Communication Channel

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