相关论文: Black holes and the loss landscape in machine lear…

The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning…

The Bekenstein-Hawking entropy for certain BPS-saturated black holes in string theory has recently been derived by counting internal black hole microstates at weak coupling. We argue that the black hole microstate can be measured by…

The statistical mechanics of black holes arbitrarily far from extremality is modeled by a gas of weakly interacting strings. As an effective low energy description of black holes the model provides a number of highly non-trivial consistency…

The classical Bekenstein entropy of a black hole is argued to arise from configurations of strings with ends which are frozen on the horizon. Quantum corrections to this entropy are probably finite unlike the case in quantum field theory.…

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the…

The coupling of a string to gravity allows for Schwarzschild black holes whose entropy to area relation is $S=(A/4)(1-4\mu)$, where $\mu$ is the string tension. This departure from the A/4 universality results from a string instanton…

One of the major concerns for neural network training is that the non-convexity of the associated loss functions may cause bad landscape. The recent success of neural networks suggests that their loss landscape is not too bad, but what…

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than their area…

In string theory, black holes can be made from brane systems that are partially delocalized in string theory's extra dimensions. It is expected that they correspond to an ensemble of pure, horizonless microstates sourced by localized…

Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or…

This thesis is devoted to trying to find a microscopic quantum description of black holes. We consider black holes in string theory which is a quantum theory of gravity. We find that the ``area law'' black hole entropy for extremal and…

We consider corrections to the entropy of a black hole from an $O(N)$ invariant linear $\s$-model. We obtain the entropy from a $1/N$ expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to…

For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of…

We review the arguments that fundamental string states are in one to one correspondence with black hole states. We demonstrate the power of the assumption by showing that it implies that the statistical entropy of a wide class of nonextreme…

Traditional landscape analysis of deep neural networks aims to show that no sub-optimal local minima exist in some appropriate sense. From this, one may be tempted to conclude that descent algorithms which escape saddle points will reach a…

I review some recent work (done in collaboration with G. Veneziano) which clarifies the existence of a correspondence between self-gravitating fundamental string states and Schwarzschild black holes. The main result is a detailed…

Training a neural network requires navigating a high-dimensional, non-convex loss surface to find parameters that minimize this loss. In many ways, it is surprising that optimizers such as stochastic gradient descent and ADAM can reliably…

We discuss whether black hole entropy counts short or long range microstates in quantum gravity. In brick wall and induced gravity models the entropy arises due to short distance correlations across the event horizon cut off at the Planck…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

This thesis investigates two main topics concerning black holes in extensions of general relativity inspired by string theory. First, the structure of the equations of motion underlying black hole solutions is considered, in theories of…