Numerical simulations of Random Field Ising Model suggest that Parisi-Sourlas supersymmetry and dimensional reduction are present for spatial dimension d>d_c and are lost for d<d_c, where the critical dimension d_c is somewhere between 4 and 5. I will lecture about a recent theoretical framework, based on perturbative renormalization group, which predicts a mechanism for the loss of...
The solution of the dynamics of glasses at the mean-field level - for example in the limit of high dimension -- has a few surprises. The equations possess an emergent reparametrization invariance. The supersymmetry associated with thermal equilibrium is broken, but a new one arises ‘from nowhere’. These two intriguing mathematical features dominate the glassy phenomenology.
The mean field analysis of Ising spin glasses shows that at low temperature, these system display a non ergodic phase characterized by an exponential number of metastable states which is captured by the so called replica symmetry breaking (RSB) solution of the models.
However when this mean field theory picture is applied to finite dimensional systems, it runs into troubles. In these...
The mean field analysis of Ising spin glasses shows that at low temperature, these system display a non ergodic phase characterized by an exponential number of metastable states which is captured by the so called replica symmetry breaking (RSB) solution of the models.
However when this mean field theory picture is applied to finite dimensional systems, it runs into troubles. In these...
These lectures will cover two main topics relating to some computational aspects of mean-field spin glass Gibbs measures:
1- Optimization: Can we efficiently find ground state configurations whenever they exist?
I will introduce the framework of Incremental Approximate Message Passing and the associated optimal control problem. This will be used to compute near optimal ground state...
Numerical simulations of Random Field Ising Model suggest that Parisi-Sourlas supersymmetry and dimensional reduction are present for spatial dimension d>d_c and are lost for d<d_c, where the critical dimension d_c is somewhere between 4 and 5. I will lecture about a recent theoretical framework, based on perturbative renormalization group, which predicts a mechanism for the loss of...
The solution of the dynamics of glasses at the mean-field level - for example in the limit of high dimension -- has a few surprises. The equations possess an emergent reparametrization invariance. The supersymmetry associated with thermal equilibrium is broken, but a new one arises ‘from nowhere’. These two intriguing mathematical features dominate the glassy phenomenology.
The mean field analysis of Ising spin glasses shows that at low temperature, these system display a non ergodic phase characterized by an exponential number of metastable states which is captured by the so called replica symmetry breaking (RSB) solution of the models.
However when this mean field theory picture is applied to finite dimensional systems, it runs into troubles. In these...
The solution of the dynamics of glasses at the mean-field level - for example in the limit of high dimension -- has a few surprises. The equations possess an emergent reparametrization invariance. The supersymmetry associated with thermal equilibrium is broken, but a new one arises ‘from nowhere’. These two intriguing mathematical features dominate the glassy phenomenology.
These lectures will cover two main topics relating to some computational aspects of mean-field spin glass Gibbs measures:
1- Optimization: Can we efficiently find ground state configurations whenever they exist?
I will introduce the framework of Incremental Approximate Message Passing and the associated optimal control problem. This will be used to compute near optimal ground state...
Numerical simulations of Random Field Ising Model suggest that Parisi-Sourlas supersymmetry and dimensional reduction are present for spatial dimension d>d_c and are lost for d<d_c, where the critical dimension d_c is somewhere between 4 and 5. I will lecture about a recent theoretical framework, based on perturbative renormalization group, which predicts a mechanism for the loss of...
The mean field analysis of Ising spin glasses shows that at low temperature, these system display a non ergodic phase characterized by an exponential number of metastable states which is captured by the so called replica symmetry breaking (RSB) solution of the models.
However when this mean field theory picture is applied to finite dimensional systems, it runs into troubles. In these...
These lectures will cover two main topics relating to some computational aspects of mean-field spin glass Gibbs measures:
1- Optimization: Can we efficiently find ground state configurations whenever they exist?
I will introduce the framework of Incremental Approximate Message Passing and the associated optimal control problem. This will be used to compute near optimal ground state...
Numerical simulations of Random Field Ising Model suggest that Parisi-Sourlas supersymmetry and dimensional reduction are present for spatial dimension d>d_c and are lost for d<d_c, where the critical dimension d_c is somewhere between 4 and 5. I will lecture about a recent theoretical framework, based on perturbative renormalization group, which predicts a mechanism for the loss of...
These lectures will cover two main topics relating to some computational aspects of mean-field spin glass Gibbs measures:
1- Optimization: Can we efficiently find ground state configurations whenever they exist?
I will introduce the framework of Incremental Approximate Message Passing and the associated optimal control problem. This will be used to compute near optimal ground state...
The solution of the dynamics of glasses at the mean-field level - for example in the limit of high dimension -- has a few surprises. The equations possess an emergent reparametrization invariance. The supersymmetry associated with thermal equilibrium is broken, but a new one arises ‘from nowhere’. These two intriguing mathematical features dominate the glassy phenomenology.
The scope of these lectures will be to discuss the statistical physics approach to the phase diagram and landscape of machine learning problems focusing on the loss landscape of artificial neural networks. We will show how this analysis suggest new powerful training algorithms based on the role of wide flat minima of the corresponding cost functions.
The scope of these lectures will be to discuss the statistical physics approach to the phase diagram and landscape of machine learning problems focusing on the loss landscape of artificial neural networks. We will show how this analysis suggest new powerful training algorithms based on the role of wide flat minima of the corresponding cost functions.
The scope of these lectures is to discuss the statistical physics approach to high dimensional inference and learning. In these problems one seeks for a particular configuration of some variables (the signal) which is hidden in a rough energy landscape of spurious non-informative minima. We will focus on two aspects of these problems: on the one hand we will show how statistical physics...
The scope of these lectures is to discuss the statistical physics approach to high dimensional inference and learning. In these problems one seeks for a particular configuration of some variables (the signal) which is hidden in a rough energy landscape of spurious non-informative minima. We will focus on two aspects of these problems: on the one hand we will show how statistical physics...
Disordered models on Bethe lattices, i.e., the random d-regular graph, emerge naturally both in the context of the mean field treatment of spin glasses as well as in computer science where they arise as generic random instances of constraint satisfaction problems (CSPs).
Their analysis has been performed in the physics literature through the non-rigorous cavity method technique developed in...
The energy landscape of mean field spin glasses displays a large (exponential in the dimension of the problem) number of minima and saddles. The geometrical properties of such random functions in high dimensions are of fundamental importance to understand the behavior of local algorithms that try to find optima in such landscapes (for example gradient descent).
The aim of these lectures we...
The scope of these lectures is to discuss the statistical physics approach to high dimensional inference and learning. In these problems one seeks for a particular configuration of some variables (the signal) which is hidden in a rough energy landscape of spurious non-informative minima. We will focus on two aspects of these problems: on the one hand we will show how statistical physics...
The scope of these lectures is to discuss the statistical physics approach to high dimensional inference and learning. In these problems one seeks for a particular configuration of some variables (the signal) which is hidden in a rough energy landscape of spurious non-informative minima. We will focus on two aspects of these problems: on the one hand we will show how statistical physics...
Spin glasses at low temperature, display a non-ergodic phase characterized by an exponential number of pure states. The properties of the corresponding Gibbs measure have been characterized through the heuristic replica method culminated in the celebrated Parisi formula for low temperature spin glasses. The scope of these lectures will be to describe and analyze rigorously the properties of...
Disordered models on Bethe lattices, i.e., the random d-regular graph, emerge naturally both in the context of the mean field treatment of spin glasses as well as in computer science where they arise as generic random instances of constraint satisfaction problems (CSPs).
Their analysis has been performed in the physics literature through the non-rigorous cavity method technique developed in...
The energy landscape of mean field spin glasses displays a large (exponential in the dimension of the problem) number of minima and saddles. The geometrical properties of such random functions in high dimensions are of fundamental importance to understand the behavior of local algorithms that try to find optima in such landscapes (for example gradient descent).
The aim of these lectures we...
Spin glasses at low temperature, display a non-ergodic phase characterized by an exponential number of pure states. The properties of the corresponding Gibbs measure have been characterized through the heuristic replica method culminated in the celebrated Parisi formula for low temperature spin glasses. The scope of these lectures will be to describe and analyze rigorously the properties of...
Spin glasses at low temperature, display a non-ergodic phase characterized by an exponential number of pure states. The properties of the corresponding Gibbs measure have been characterized through the heuristic replica method culminated in the celebrated Parisi formula for low temperature spin glasses. The scope of these lectures will be to describe and analyze rigorously the properties of...
The energy landscape of mean field spin glasses displays a large (exponential in the dimension of the problem) number of minima and saddles. The geometrical properties of such random functions in high dimensions are of fundamental importance to understand the behavior of local algorithms that try to find optima in such landscapes (for example gradient descent).
The aim of these lectures we...
Disordered models on Bethe lattices, i.e., the random d-regular graph, emerge naturally both in the context of the mean field treatment of spin glasses as well as in computer science where they arise as generic random instances of constraint satisfaction problems (CSPs).
Their analysis has been performed in the physics literature through the non-rigorous cavity method technique developed in...
The energy landscape of mean field spin glasses displays a large (exponential in the dimension of the problem) number of minima and saddles. The geometrical properties of such random functions in high dimensions are of fundamental importance to understand the behavior of local algorithms that try to find optima in such landscapes (for example gradient descent).
The aim of these lectures we...
Spin glasses at low temperature, display a non-ergodic phase characterized by an exponential number of pure states. The properties of the corresponding Gibbs measure have been characterized through the heuristic replica method culminated in the celebrated Parisi formula for low temperature spin glasses. The scope of these lectures will be to describe and analyze rigorously the properties of...
Disordered models on Bethe lattices, i.e., the random d-regular graph, emerge naturally both in the context of the mean field treatment of spin glasses as well as in computer science where they arise as generic random instances of constraint satisfaction problems (CSPs).
Their analysis has been performed in the physics literature through the non-rigorous cavity method technique developed in...
