diff --git a/doc/pub/BM/html/._BM-bs000.html b/doc/pub/BM/html/._BM-bs000.html index a52d8f786..dbed0cb69 100644 --- a/doc/pub/BM/html/._BM-bs000.html +++ b/doc/pub/BM/html/._BM-bs000.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -358,7 +343,7 @@ MathJax.Hub.Config({
    Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway

    -

    Nov 22, 2018

    +

    Nov 23, 2018


    @@ -382,7 +367,7 @@ MathJax.Hub.Config({

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    • diff --git a/doc/pub/BM/html/._BM-bs001.html b/doc/pub/BM/html/._BM-bs001.html index aa43ed314..f2659c400 100644 --- a/doc/pub/BM/html/._BM-bs001.html +++ b/doc/pub/BM/html/._BM-bs001.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -385,7 +370,7 @@ Some of the most common tasks are:
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    • diff --git a/doc/pub/BM/html/._BM-bs002.html b/doc/pub/BM/html/._BM-bs002.html index 63f1adab6..cb748fc57 100644 --- a/doc/pub/BM/html/._BM-bs002.html +++ b/doc/pub/BM/html/._BM-bs002.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -370,7 +355,7 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
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    • diff --git a/doc/pub/BM/html/._BM-bs003.html b/doc/pub/BM/html/._BM-bs003.html index 00a880588..77e3b3ed9 100644 --- a/doc/pub/BM/html/._BM-bs003.html +++ b/doc/pub/BM/html/._BM-bs003.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -342,6 +327,9 @@ MathJax.Hub.Config({

    An intermediate step, the Hopfield network and links to the Ising and Potts models

    +

    +More material on Hopfield networks will come here +

    @@ -361,7 +349,7 @@ MathJax.Hub.Config({

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    • diff --git a/doc/pub/BM/html/._BM-bs004.html b/doc/pub/BM/html/._BM-bs004.html index a521d9b3e..6c41955ac 100644 --- a/doc/pub/BM/html/._BM-bs004.html +++ b/doc/pub/BM/html/._BM-bs004.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -375,7 +360,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/BM/html/._BM-bs005.html b/doc/pub/BM/html/._BM-bs005.html index c3115e6c2..715e21166 100644 --- a/doc/pub/BM/html/._BM-bs005.html +++ b/doc/pub/BM/html/._BM-bs005.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -381,7 +366,7 @@ its most likely state at a given temperature of the surroundings.
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    • diff --git a/doc/pub/BM/html/._BM-bs006.html b/doc/pub/BM/html/._BM-bs006.html index bc1c06a89..2ecaa2033 100644 --- a/doc/pub/BM/html/._BM-bs006.html +++ b/doc/pub/BM/html/._BM-bs006.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -378,7 +363,7 @@ the interpretation of random walks and Markov processes.
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    • diff --git a/doc/pub/BM/html/._BM-bs007.html b/doc/pub/BM/html/._BM-bs007.html index 19eefb3d9..64523edda 100644 --- a/doc/pub/BM/html/._BM-bs007.html +++ b/doc/pub/BM/html/._BM-bs007.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -383,7 +368,7 @@ This sequence of steps forms a chain.
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    • diff --git a/doc/pub/BM/html/._BM-bs008.html b/doc/pub/BM/html/._BM-bs008.html index 39322e62e..0c272f456 100644 --- a/doc/pub/BM/html/._BM-bs008.html +++ b/doc/pub/BM/html/._BM-bs008.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -372,7 +357,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/BM/html/._BM-bs009.html b/doc/pub/BM/html/._BM-bs009.html index f1d1bc5c9..bd394572d 100644 --- a/doc/pub/BM/html/._BM-bs009.html +++ b/doc/pub/BM/html/._BM-bs009.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -386,7 +371,7 @@ The list of applications is endless.
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    • diff --git a/doc/pub/BM/html/._BM-bs010.html b/doc/pub/BM/html/._BM-bs010.html index 4dddfbe7b..2311d6067 100644 --- a/doc/pub/BM/html/._BM-bs010.html +++ b/doc/pub/BM/html/._BM-bs010.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -387,7 +372,7 @@ We can regard the discretized PDF as a vector.
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    • diff --git a/doc/pub/BM/html/._BM-bs011.html b/doc/pub/BM/html/._BM-bs011.html index 2c55d9468..f7453fcb8 100644 --- a/doc/pub/BM/html/._BM-bs011.html +++ b/doc/pub/BM/html/._BM-bs011.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -401,7 +386,7 @@ PDF with equal probability of jumping left or right.
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    • diff --git a/doc/pub/BM/html/._BM-bs012.html b/doc/pub/BM/html/._BM-bs012.html index e3f774d43..09dc2b2fe 100644 --- a/doc/pub/BM/html/._BM-bs012.html +++ b/doc/pub/BM/html/._BM-bs012.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -398,7 +383,7 @@ not necessarily equal zero.
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    • diff --git a/doc/pub/BM/html/._BM-bs013.html b/doc/pub/BM/html/._BM-bs013.html index 17666de22..1bc6d8446 100644 --- a/doc/pub/BM/html/._BM-bs013.html +++ b/doc/pub/BM/html/._BM-bs013.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -406,7 +391,7 @@ $$
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs014.html b/doc/pub/BM/html/._BM-bs014.html index a1ea70e81..2ea9085a8 100644 --- a/doc/pub/BM/html/._BM-bs014.html +++ b/doc/pub/BM/html/._BM-bs014.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -399,7 +384,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs015.html b/doc/pub/BM/html/._BM-bs015.html index 54ea65c0d..ed39a7cff 100644 --- a/doc/pub/BM/html/._BM-bs015.html +++ b/doc/pub/BM/html/._BM-bs015.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -396,7 +381,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs016.html b/doc/pub/BM/html/._BM-bs016.html index 40dd46c7f..b5bd1531d 100644 --- a/doc/pub/BM/html/._BM-bs016.html +++ b/doc/pub/BM/html/._BM-bs016.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -395,7 +380,7 @@ Note that the vector \( \hat{w} \) is always normalized to \( 1 \).
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    • diff --git a/doc/pub/BM/html/._BM-bs017.html b/doc/pub/BM/html/._BM-bs017.html index 5ef120149..6243f8bc9 100644 --- a/doc/pub/BM/html/._BM-bs017.html +++ b/doc/pub/BM/html/._BM-bs017.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -410,7 +395,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs018.html b/doc/pub/BM/html/._BM-bs018.html index fc2247a1d..9c44716b4 100644 --- a/doc/pub/BM/html/._BM-bs018.html +++ b/doc/pub/BM/html/._BM-bs018.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -407,7 +392,7 @@ time steps. After twelve iterations we have reached the exact value with six le
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    • diff --git a/doc/pub/BM/html/._BM-bs019.html b/doc/pub/BM/html/._BM-bs019.html index 00def40df..0e658e359 100644 --- a/doc/pub/BM/html/._BM-bs019.html +++ b/doc/pub/BM/html/._BM-bs019.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -388,7 +373,7 @@ transition probability matrix.
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    • diff --git a/doc/pub/BM/html/._BM-bs020.html b/doc/pub/BM/html/._BM-bs020.html index bf7523dcc..fe4a63987 100644 --- a/doc/pub/BM/html/._BM-bs020.html +++ b/doc/pub/BM/html/._BM-bs020.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -403,7 +388,7 @@ If we assume that \( \lambda_0 \) is the largest eigenvector we see that in the
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    • diff --git a/doc/pub/BM/html/._BM-bs021.html b/doc/pub/BM/html/._BM-bs021.html index bb1a569a8..05086e4fe 100644 --- a/doc/pub/BM/html/._BM-bs021.html +++ b/doc/pub/BM/html/._BM-bs021.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -409,7 +394,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs022.html b/doc/pub/BM/html/._BM-bs022.html index bbb8fdc94..a8bdbf06a 100644 --- a/doc/pub/BM/html/._BM-bs022.html +++ b/doc/pub/BM/html/._BM-bs022.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -400,7 +385,7 @@ Here we have written the previous matrix \( W_{ij}=W(j\rightarrow i) \).
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    • diff --git a/doc/pub/BM/html/._BM-bs023.html b/doc/pub/BM/html/._BM-bs023.html index e05290d61..4e87fccd2 100644 --- a/doc/pub/BM/html/._BM-bs023.html +++ b/doc/pub/BM/html/._BM-bs023.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -399,7 +384,7 @@ we have reached the most likely state of the system, the so-called steady state
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    • diff --git a/doc/pub/BM/html/._BM-bs024.html b/doc/pub/BM/html/._BM-bs024.html index 6d0103fc6..ac72c7617 100644 --- a/doc/pub/BM/html/._BM-bs024.html +++ b/doc/pub/BM/html/._BM-bs024.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -383,7 +368,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs025.html b/doc/pub/BM/html/._BM-bs025.html index 4521502e4..077b42ce7 100644 --- a/doc/pub/BM/html/._BM-bs025.html +++ b/doc/pub/BM/html/._BM-bs025.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -391,7 +376,7 @@ The algorithm can then be expressed as
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    • diff --git a/doc/pub/BM/html/._BM-bs026.html b/doc/pub/BM/html/._BM-bs026.html index f96c01e1f..4ed860462 100644 --- a/doc/pub/BM/html/._BM-bs026.html +++ b/doc/pub/BM/html/._BM-bs026.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -384,7 +369,7 @@ to the probability of being in a state \( j \) and performing a transition to th
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    • -
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs027.html b/doc/pub/BM/html/._BM-bs027.html index ca79c8a57..058a5a102 100644 --- a/doc/pub/BM/html/._BM-bs027.html +++ b/doc/pub/BM/html/._BM-bs027.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -388,7 +373,7 @@ $$
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs028.html b/doc/pub/BM/html/._BM-bs028.html index 95a1952bc..a6d322bef 100644 --- a/doc/pub/BM/html/._BM-bs028.html +++ b/doc/pub/BM/html/._BM-bs028.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -398,7 +383,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs029.html b/doc/pub/BM/html/._BM-bs029.html index 8b833ca9d..25082292b 100644 --- a/doc/pub/BM/html/._BM-bs029.html +++ b/doc/pub/BM/html/._BM-bs029.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -396,7 +381,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs030.html b/doc/pub/BM/html/._BM-bs030.html index 2bdac7d26..9a243e1e1 100644 --- a/doc/pub/BM/html/._BM-bs030.html +++ b/doc/pub/BM/html/._BM-bs030.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -406,7 +391,7 @@ which is nothing but the standard equation for a Markov chain when the steady st
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    • diff --git a/doc/pub/BM/html/._BM-bs031.html b/doc/pub/BM/html/._BM-bs031.html index 600461b04..0c0c37a83 100644 --- a/doc/pub/BM/html/._BM-bs031.html +++ b/doc/pub/BM/html/._BM-bs031.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -400,7 +385,7 @@ $$
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs032.html b/doc/pub/BM/html/._BM-bs032.html index 8db7d4494..ae5f78164 100644 --- a/doc/pub/BM/html/._BM-bs032.html +++ b/doc/pub/BM/html/._BM-bs032.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -384,7 +369,7 @@ $$
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs033.html b/doc/pub/BM/html/._BM-bs033.html index 04b6adc92..987e4b240 100644 --- a/doc/pub/BM/html/._BM-bs033.html +++ b/doc/pub/BM/html/._BM-bs033.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -399,7 +384,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs034.html b/doc/pub/BM/html/._BM-bs034.html index 8e99ac8ae..aa6f36fdd 100644 --- a/doc/pub/BM/html/._BM-bs034.html +++ b/doc/pub/BM/html/._BM-bs034.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -401,7 +386,7 @@ we never need to evaluate the partition function \( Z \).
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    • diff --git a/doc/pub/BM/html/._BM-bs035.html b/doc/pub/BM/html/._BM-bs035.html index 8741dc5ac..9acf0f427 100644 --- a/doc/pub/BM/html/._BM-bs035.html +++ b/doc/pub/BM/html/._BM-bs035.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -394,7 +379,7 @@ $$
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    • +
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    • diff --git a/doc/pub/BM/html/._BM-bs036.html b/doc/pub/BM/html/._BM-bs036.html index 7e061f6c2..965c8a38b 100644 --- a/doc/pub/BM/html/._BM-bs036.html +++ b/doc/pub/BM/html/._BM-bs036.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -389,7 +374,7 @@ one place to another in space, we 'jump' from one microstate to another.
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    • diff --git a/doc/pub/BM/html/._BM-bs037.html b/doc/pub/BM/html/._BM-bs037.html index e376bf4d3..527a3640c 100644 --- a/doc/pub/BM/html/._BM-bs037.html +++ b/doc/pub/BM/html/._BM-bs037.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -397,7 +382,7 @@ the transition probability \( T(i\rightarrow j) \) is symmetric, implying that \
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    • diff --git a/doc/pub/BM/html/._BM-bs038.html b/doc/pub/BM/html/._BM-bs038.html index d2e88ac13..a4dfc60e9 100644 --- a/doc/pub/BM/html/._BM-bs038.html +++ b/doc/pub/BM/html/._BM-bs038.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -391,7 +376,7 @@ Our desired energy is \( E_0 \).
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    • diff --git a/doc/pub/BM/html/._BM-bs039.html b/doc/pub/BM/html/._BM-bs039.html index b2952a9eb..3071bdf95 100644 --- a/doc/pub/BM/html/._BM-bs039.html +++ b/doc/pub/BM/html/._BM-bs039.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -390,7 +375,7 @@ we simulate long enough it should be included in our computation of an expectati
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    • diff --git a/doc/pub/BM/html/._BM-bs040.html b/doc/pub/BM/html/._BM-bs040.html index ff0d73885..29e3f2d41 100644 --- a/doc/pub/BM/html/._BM-bs040.html +++ b/doc/pub/BM/html/._BM-bs040.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -389,7 +374,7 @@ to this constraint.
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    • diff --git a/doc/pub/BM/html/._BM-bs041.html b/doc/pub/BM/html/._BM-bs041.html index 5b811f344..ef84a92c5 100644 --- a/doc/pub/BM/html/._BM-bs041.html +++ b/doc/pub/BM/html/._BM-bs041.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -388,7 +373,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs042.html b/doc/pub/BM/html/._BM-bs042.html index bf53a297b..4d92af66f 100644 --- a/doc/pub/BM/html/._BM-bs042.html +++ b/doc/pub/BM/html/._BM-bs042.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -392,7 +377,7 @@ If the ratio is smaller than a given random number we accept the move to a highe
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    • diff --git a/doc/pub/BM/html/._BM-bs043.html b/doc/pub/BM/html/._BM-bs043.html index 94e181eaf..8242f312c 100644 --- a/doc/pub/BM/html/._BM-bs043.html +++ b/doc/pub/BM/html/._BM-bs043.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -386,7 +371,7 @@ fewer accepted moves.
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    • diff --git a/doc/pub/BM/html/._BM-bs044.html b/doc/pub/BM/html/._BM-bs044.html index 056e5f29f..fad0f4148 100644 --- a/doc/pub/BM/html/._BM-bs044.html +++ b/doc/pub/BM/html/._BM-bs044.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -395,7 +380,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs045.html b/doc/pub/BM/html/._BM-bs045.html index 1335e12d1..274d4f3df 100644 --- a/doc/pub/BM/html/._BM-bs045.html +++ b/doc/pub/BM/html/._BM-bs045.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -371,7 +356,7 @@ More text to come.
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    • diff --git a/doc/pub/BM/html/._BM-bs046.html b/doc/pub/BM/html/._BM-bs046.html index 81f85937e..182334f5a 100644 --- a/doc/pub/BM/html/._BM-bs046.html +++ b/doc/pub/BM/html/._BM-bs046.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -382,7 +367,7 @@ Why use a generative model rather than the more well known discriminative deep n
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    • diff --git a/doc/pub/BM/html/._BM-bs047.html b/doc/pub/BM/html/._BM-bs047.html index 718b4f084..4e43a466b 100644 --- a/doc/pub/BM/html/._BM-bs047.html +++ b/doc/pub/BM/html/._BM-bs047.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -376,7 +361,7 @@ History: The RBM was developed by amongst others Geoffrey Hinton, called by some
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    • diff --git a/doc/pub/BM/html/._BM-bs048.html b/doc/pub/BM/html/._BM-bs048.html index 272040ee3..c25206634 100644 --- a/doc/pub/BM/html/._BM-bs048.html +++ b/doc/pub/BM/html/._BM-bs048.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -371,7 +356,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/BM/html/._BM-bs049.html b/doc/pub/BM/html/._BM-bs049.html index 1fd5ef036..f01e332e8 100644 --- a/doc/pub/BM/html/._BM-bs049.html +++ b/doc/pub/BM/html/._BM-bs049.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -375,7 +360,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/BM/html/._BM-bs050.html b/doc/pub/BM/html/._BM-bs050.html index 1ad96bea4..797909147 100644 --- a/doc/pub/BM/html/._BM-bs050.html +++ b/doc/pub/BM/html/._BM-bs050.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -387,7 +372,7 @@ Examples of this trick being employed in physics:
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    • diff --git a/doc/pub/BM/html/._BM-bs051.html b/doc/pub/BM/html/._BM-bs051.html index 8615571f7..1217b8bef 100644 --- a/doc/pub/BM/html/._BM-bs051.html +++ b/doc/pub/BM/html/._BM-bs051.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -385,7 +370,7 @@ It is common to ignore \( T_0 \) by setting it to one.
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    • diff --git a/doc/pub/BM/html/._BM-bs052.html b/doc/pub/BM/html/._BM-bs052.html index 578419a56..3c998c9d7 100644 --- a/doc/pub/BM/html/._BM-bs052.html +++ b/doc/pub/BM/html/._BM-bs052.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -376,7 +361,7 @@ adjusting the energy function to best fit our problem.
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    • diff --git a/doc/pub/BM/html/._BM-bs053.html b/doc/pub/BM/html/._BM-bs053.html index 3c105a3a3..450ae601e 100644 --- a/doc/pub/BM/html/._BM-bs053.html +++ b/doc/pub/BM/html/._BM-bs053.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -403,7 +388,7 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs054.html b/doc/pub/BM/html/._BM-bs054.html index a54ff6dd4..6560a5359 100644 --- a/doc/pub/BM/html/._BM-bs054.html +++ b/doc/pub/BM/html/._BM-bs054.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -380,8 +365,6 @@ Other types of units include:
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    • diff --git a/doc/pub/BM/html/._BM-bs055.html b/doc/pub/BM/html/._BM-bs055.html index 8abe9babd..dde2da421 100644 --- a/doc/pub/BM/html/._BM-bs055.html +++ b/doc/pub/BM/html/._BM-bs055.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -386,9 +371,6 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs056.html b/doc/pub/BM/html/._BM-bs056.html index 5b16a20b0..1577b29ad 100644 --- a/doc/pub/BM/html/._BM-bs056.html +++ b/doc/pub/BM/html/._BM-bs056.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -382,10 +367,6 @@ where we recognize the logistic sigmoid function \( \sigma (x) = 1/(1+exp(-x)) \
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    • diff --git a/doc/pub/BM/html/._BM-bs057.html b/doc/pub/BM/html/._BM-bs057.html index 4df0fc73c..76edbecd6 100644 --- a/doc/pub/BM/html/._BM-bs057.html +++ b/doc/pub/BM/html/._BM-bs057.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -375,11 +360,6 @@ while the visible units now follow a normal distribution, we see the hidden unit
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    • diff --git a/doc/pub/BM/html/._BM-bs058.html b/doc/pub/BM/html/._BM-bs058.html index d52acd9ea..5a3283a64 100644 --- a/doc/pub/BM/html/._BM-bs058.html +++ b/doc/pub/BM/html/._BM-bs058.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -378,12 +363,6 @@ Our cost function is the negative log-likelihood, \( \mathcal{C}(\{ \theta_i \})
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    • diff --git a/doc/pub/BM/html/._BM-bs059.html b/doc/pub/BM/html/._BM-bs059.html index 5680f32bb..d820433ab 100644 --- a/doc/pub/BM/html/._BM-bs059.html +++ b/doc/pub/BM/html/._BM-bs059.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -400,13 +385,6 @@ $$
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    • diff --git a/doc/pub/BM/html/._BM-bs060.html b/doc/pub/BM/html/._BM-bs060.html index 3aada1952..b9fd3b967 100644 --- a/doc/pub/BM/html/._BM-bs060.html +++ b/doc/pub/BM/html/._BM-bs060.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -380,12 +365,6 @@ To get the expecation values with respect to the data, we set the visib
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    • diff --git a/doc/pub/BM/html/._BM-bs061.html b/doc/pub/BM/html/._BM-bs061.html index 0401a220d..102c6c1e1 100644 --- a/doc/pub/BM/html/._BM-bs061.html +++ b/doc/pub/BM/html/._BM-bs061.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -363,12 +348,6 @@ To get the expectation values with respect to the model, we use Gibbs s
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    • diff --git a/doc/pub/BM/html/._BM-bs062.html b/doc/pub/BM/html/._BM-bs062.html index cd58d837d..2322c9e79 100644 --- a/doc/pub/BM/html/._BM-bs062.html +++ b/doc/pub/BM/html/._BM-bs062.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -340,7 +325,7 @@ MathJax.Hub.Config({ -

    RBMs for the quantum many body problem

    +

    Recent examples: RBMs for the quantum many body problem

    The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research. @@ -378,12 +363,6 @@ Some of their motivation included

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    • diff --git a/doc/pub/BM/html/._BM-bs063.html b/doc/pub/BM/html/._BM-bs063.html index 26a6ddee6..064423b3e 100644 --- a/doc/pub/BM/html/._BM-bs063.html +++ b/doc/pub/BM/html/._BM-bs063.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -346,6 +331,7 @@ MathJax.Hub.Config({ Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.

    +

    diff --git a/doc/pub/BM/html/BM-bs.html b/doc/pub/BM/html/BM-bs.html index a52d8f786..dbed0cb69 100644 --- a/doc/pub/BM/html/BM-bs.html +++ b/doc/pub/BM/html/BM-bs.html @@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -317,14 +308,8 @@ MathJax.Hub.Config({
  • Optimization / Training
  • More on RBMs
  • Which sampling to use
    • -
  • RBMs for the quantum many body problem
    • +
  • Recent examples: RBMs for the quantum many body problem
  • Choose the right RBM
    • -
  • Representing the wave function
    • -
  • Choose the cost function
    • -
  • Running the codes
    • -
  • Energy as function of iterations, \( N=2 \) electrons
    • -
  • Energy as function of iterations, \( N=6 \) electrons
    • -
  • Conclusions and where do we stand
    • @@ -358,7 +343,7 @@ MathJax.Hub.Config({
    Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway

    -

    Nov 22, 2018

    +

    Nov 23, 2018


    @@ -382,7 +367,7 @@ MathJax.Hub.Config({

  • 9
  • 10
  • ...
    • -
  • 70
    • +
  • 64
  • »
    • diff --git a/doc/pub/BM/html/BM-reveal.html b/doc/pub/BM/html/BM-reveal.html index 05f0caff7..703656134 100644 --- a/doc/pub/BM/html/BM-reveal.html +++ b/doc/pub/BM/html/BM-reveal.html @@ -147,7 +147,7 @@ MathJax.Hub.Config({
    Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway

     
    -

    Nov 22, 2018

    +

    Nov 23, 2018


    @@ -207,6 +207,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa

    An intermediate step, the Hopfield network and links to the Ising and Potts models

    + +

    +More material on Hopfield networks will come here

    @@ -1820,7 +1823,7 @@ To get the expectation values with respect to the model, we use Gibbs s
    -

    RBMs for the quantum many body problem

    +

    Recent examples: RBMs for the quantum many body problem

    The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research. @@ -1851,134 +1854,6 @@ Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems

    -
    -

    Representing the wave function

    -The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \) -

     
    -$$ -\begin{align} - F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}. -\tag{27} -\end{align} -$$ -

     
    - -To find the marginal distribution of \( \boldsymbol{x} \) we set: -

     
    -$$ -\begin{align} - F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h}) -\tag{28}\\ - &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. -\tag{29} -\end{align} -$$ -

     
    - -Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS) -

     
    -$$ -\begin{align} - \Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) -\tag{30}\\ - &= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})} -\tag{31}\\ - &= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} -\tag{32}\\ - &= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}). -\tag{33}\\ -\tag{34} -\end{align} -$$ -

     
    -

    - - -
    -

    Choose the cost function

    -Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is -

     
    -$$ -\begin{align} - G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i} - = 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ), -\tag{35} -\end{align} -$$ -

     
    - -where the local energy is given by -

     
    -$$ -\begin{align} - E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi. -\tag{36} -\end{align} -$$ -

     
    -

    - - -
    -

    Running the codes

    -
    - -

    -You can find the codes for the simple two-electron case at the Github repository https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src. Python codes to come, only c++ as of now. - -

    -The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines. - -

    -The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below. - - -

    -
    - - -
    -

    Energy as function of iterations, \( N=2 \) electrons

    -
    - -

    -



    -
    -
    - - -
    -

    Energy as function of iterations, \( N=6 \) electrons

    -
    - -

    -



    -
    -
    - - -
    -

    Conclusions and where do we stand

    -
    - - -
    -
    - - diff --git a/doc/pub/BM/html/BM-solarized.html b/doc/pub/BM/html/BM-solarized.html index f1a1778ca..836b5e915 100644 --- a/doc/pub/BM/html/BM-solarized.html +++ b/doc/pub/BM/html/BM-solarized.html @@ -225,20 +225,11 @@ div { text-align: justify; text-justify: inter-word; } ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -279,7 +270,7 @@ MathJax.Hub.Config({
    Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway

    -

    Nov 22, 2018

    +

    Nov 23, 2018












    @@ -331,6 +322,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa

    An intermediate step, the Hopfield network and links to the Ising and Potts models

    +

    +More material on Hopfield networks will come here +











    @@ -1880,7 +1874,7 @@ To get the expectation values with respect to the model, we use Gibbs s











    -

    RBMs for the quantum many body problem

    +

    Recent examples: RBMs for the quantum many body problem

    The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research. @@ -1909,131 +1903,6 @@ Some of their motivation included

    Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice. -

    -









    - -

    Representing the wave function

    -The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \) -$$ -\begin{align} - F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}. -\label{_auto25} -\end{align} -$$ - -To find the marginal distribution of \( \boldsymbol{x} \) we set: -$$ -\begin{align} - F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h}) -\label{_auto26}\\ - &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. -\label{_auto27} -\end{align} -$$ - -Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS) -$$ -\begin{align} - \Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) -\label{_auto28}\\ - &= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})} -\label{_auto29}\\ - &= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} -\label{_auto30}\\ - &= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}). -\label{_auto31}\\ -\label{_auto32} -\end{align} -$$ - -

    -









    - -

    Choose the cost function

    -Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is -$$ -\begin{align} - G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i} - = 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ), -\label{_auto33} -\end{align} -$$ - -where the local energy is given by -$$ -\begin{align} - E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi. -\label{_auto34} -\end{align} -$$ - -

    -









    - -

    Running the codes

    -
    - -

    -You can find the codes for the simple two-electron case at the Github repository https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src. Python codes to come, only c++ as of now. - -

    -The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines. - -

    -The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below. - - -

    - - -

    -









    - -

    Energy as function of iterations, \( N=2 \) electrons

    -
    - -

    -



    -
    - - -

    -









    - -

    Energy as function of iterations, \( N=6 \) electrons

    -
    - -

    -



    -
    - - -

    -









    - -

    Conclusions and where do we stand

    -
    - -

    - -

    -
    - -

    diff --git a/doc/pub/BM/html/BM.html b/doc/pub/BM/html/BM.html index 7c0452875..2598a9fd6 100644 --- a/doc/pub/BM/html/BM.html +++ b/doc/pub/BM/html/BM.html @@ -230,20 +230,11 @@ div { text-align: justify; text-justify: inter-word; } ('Optimization / Training', 2, None, '___sec58'), ('More on RBMs', 2, None, '___sec59'), ('Which sampling to use', 2, None, '___sec60'), - ('RBMs for the quantum many body problem', 2, None, '___sec61'), - ('Choose the right RBM', 2, None, '___sec62'), - ('Representing the wave function', 2, None, '___sec63'), - ('Choose the cost function', 2, None, '___sec64'), - ('Running the codes', 2, None, '___sec65'), - ('Energy as function of iterations, $N=2$ electrons', + ('Recent examples: RBMs for the quantum many body problem', 2, None, - '___sec66'), - ('Energy as function of iterations, $N=6$ electrons', - 2, - None, - '___sec67'), - ('Conclusions and where do we stand', 2, None, '___sec68')]} + '___sec61'), + ('Choose the right RBM', 2, None, '___sec62')]} end of tocinfo --> @@ -284,7 +275,7 @@ MathJax.Hub.Config({

    Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway

    -

    Nov 22, 2018

    +

    Nov 23, 2018












    @@ -336,6 +327,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa

    An intermediate step, the Hopfield network and links to the Ising and Potts models

    +

    +More material on Hopfield networks will come here +











    @@ -1885,7 +1879,7 @@ To get the expectation values with respect to the model, we use Gibbs s











    -

    RBMs for the quantum many body problem

    +

    Recent examples: RBMs for the quantum many body problem

    The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research. @@ -1914,131 +1908,6 @@ Some of their motivation included

    Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice. -

    -









    - -

    Representing the wave function

    -The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \) -$$ -\begin{align} - F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}. -\label{_auto25} -\end{align} -$$ - -To find the marginal distribution of \( \boldsymbol{x} \) we set: -$$ -\begin{align} - F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h}) -\label{_auto26}\\ - &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. -\label{_auto27} -\end{align} -$$ - -Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS) -$$ -\begin{align} - \Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) -\label{_auto28}\\ - &= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})} -\label{_auto29}\\ - &= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} -\label{_auto30}\\ - &= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}). -\label{_auto31}\\ -\label{_auto32} -\end{align} -$$ - -

    -









    - -

    Choose the cost function

    -Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is -$$ -\begin{align} - G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i} - = 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ), -\label{_auto33} -\end{align} -$$ - -where the local energy is given by -$$ -\begin{align} - E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi. -\label{_auto34} -\end{align} -$$ - -

    -









    - -

    Running the codes

    -
    - -

    -You can find the codes for the simple two-electron case at the Github repository https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src. Python codes to come, only c++ as of now. - -

    -The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines. - -

    -The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below. - - -

    - - -

    -









    - -

    Energy as function of iterations, \( N=2 \) electrons

    -
    - -

    -



    -
    - - -

    -









    - -

    Energy as function of iterations, \( N=6 \) electrons

    -
    - -

    -



    -
    - - -

    -









    - -

    Conclusions and where do we stand

    -
    - -

    - -

    -
    - -

    diff --git a/doc/pub/BM/ipynb/BM.ipynb b/doc/pub/BM/ipynb/BM.ipynb index 46edca5b7..b04e34ce3 100644 --- a/doc/pub/BM/ipynb/BM.ipynb +++ b/doc/pub/BM/ipynb/BM.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway\n", "\n", - "Date: **Nov 22, 2018**\n", + "Date: **Nov 23, 2018**\n", "\n", "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -54,6 +54,8 @@ "\n", "## An intermediate step, the Hopfield network and links to the Ising and Potts models\n", "\n", + "More material on Hopfield networks will come here\n", + "\n", "## A brief review on Markov Chains, Metropolis and Gibbs sampling\n", "\n", "\n", @@ -2036,7 +2038,7 @@ "\n", "To get the expectation values with respect to the *model*, we use Gibbs sampling. We can either initialize the $\\boldsymbol{x}$ randomly or with a training sample. While we ideally want a large number of Gibbs iterations $n\\rightarrow n$, one might decide to truncate it earlier for efficiency. Doing this while having intialized $\\boldsymbol{x}$ with a training data vector is referred to as contrastive divergence (CD), because one is then closer to approximating the gradient of this function than the negative log-likelihood. The contrastive divergence function is the difference between two Kullback-Leibler divergences (also called relative entropy), which measure how one probability distribution diverges from a second, expected probability distribution (in this case the estimated one from the ground truth one).\n", "\n", - "## RBMs for the quantum many body problem\n", + "## Recent examples: RBMs for the quantum many body problem\n", "\n", "The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.\n", "\n", @@ -2059,251 +2061,7 @@ "\n", "## Choose the right RBM\n", "\n", - "Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.\n", - "\n", - "## Representing the wave function\n", - "The wavefunction should be a probability amplitude depending on $\\boldsymbol{x}$. The RBM model is given by the joint distribution of $\\boldsymbol{x}$ and $\\boldsymbol{h}$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\tF_{rbm}(\\mathbf{x},\\mathbf{h}) = \\frac{1}{Z} e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})}.\n", - "\\label{_auto25} \\tag{27}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To find the marginal distribution of $\\boldsymbol{x}$ we set:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\tF_{rbm}(\\mathbf{x}) = \\sum_\\mathbf{h} F_{rbm}(\\mathbf{x}, \\mathbf{h}) \n", - "\\label{_auto26} \\tag{28}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\t\t\t\t= \\frac{1}{Z}\\sum_\\mathbf{h} e^{-E(\\mathbf{x}, \\mathbf{h})}.\n", - "\\label{_auto27} \\tag{29}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\t\\Psi (\\mathbf{X}) = F_{rbm}(\\mathbf{x}) \n", - "\\label{_auto28} \\tag{30}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\t= \\frac{1}{Z}\\sum_{\\boldsymbol{h}} e^{-E(\\mathbf{x}, \\mathbf{h})} \n", - "\\label{_auto29} \\tag{31}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\t= \\frac{1}{Z} \\sum_{\\{h_j\\}} e^{-\\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma^2} + \\sum_j^N b_j h_j + \\sum_{i,j}^{M,N} \\frac{x_i w_{ij} h_j}{\\sigma^2}} \n", - "\\label{_auto30} \\tag{32}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\t= \\frac{1}{Z} e^{-\\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma^2}} \\prod_j^N (1 + e^{b_j + \\sum_i^M \\frac{x_i w_{ij}}{\\sigma^2}}). \n", - "\\label{_auto31} \\tag{33}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\\label{_auto32} \\tag{34}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Choose the cost function\n", - "Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\tG_i = \\frac{\\partial \\langle E_L \\rangle}{\\partial \\theta_i}\n", - "\t= 2(\\langle E_L \\frac{1}{\\Psi}\\frac{\\partial \\Psi}{\\partial \\theta_i} \\rangle - \\langle E_L \\rangle \\langle \\frac{1}{\\Psi}\\frac{\\partial \\Psi}{\\partial \\theta_i} \\rangle ),\n", - "\\label{_auto33} \\tag{35}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the local energy is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
    \n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\tE_L = \\frac{1}{\\Psi} \\hat{\\mathbf{H}} \\Psi.\n", - "\\label{_auto34} \\tag{36}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Running the codes\n", - "You can find the codes for the simple two-electron case at the Github repository . Python codes to come, only c++ as of now. \n", - "\n", - "The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor $\\exp{(r_{ij})}$ and the reduced Boltzmann machines. \n", - "\n", - "The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used $14$ hidden nodes in the calculations below.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Energy as function of iterations, $N=2$ electrons\n", - "\n", - "\n", - "\n", - "

    \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Energy as function of iterations, $N=6$ electrons\n", - "\n", - "\n", - "\n", - "

    \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Conclusions and where do we stand\n", - "* A simple extension of the work of [G. Carleo and M. Troyer, Science **355**, Issue 6325, pp. 602-606 (2017)](http://science.sciencemag.org/content/355/6325/602) gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for $N=6$ and $N=12$ electrons.\n", - "\n", - "* Minimization problem can be tricky.\n", - "\n", - "* Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.\n", - "\n", - "* To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.\n", - "\n", - "* Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?\n", - "\n", - " a. Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?\n", - "\n", - " b. Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).\n", - "\n", - " c. Test this for multi-fermion systems and compare with other many-body methods.\n", - "\n", - "\n", - "* Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?" + "Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice." ] } ], diff --git a/doc/pub/BM/ipynb/ipynb-BM-src.tar.gz b/doc/pub/BM/ipynb/ipynb-BM-src.tar.gz index 51117e2f1..245e47f51 100644 Binary files a/doc/pub/BM/ipynb/ipynb-BM-src.tar.gz and b/doc/pub/BM/ipynb/ipynb-BM-src.tar.gz differ diff --git a/doc/pub/BM/pdf/BM-minted.pdf b/doc/pub/BM/pdf/BM-minted.pdf index 16b285ccc..6187f8a5a 100644 Binary files a/doc/pub/BM/pdf/BM-minted.pdf and b/doc/pub/BM/pdf/BM-minted.pdf differ diff --git a/doc/src/BoltzmannMachines/BM.do.txt b/doc/src/BoltzmannMachines/BM.do.txt index f538baab2..0c4750e82 100644 --- a/doc/src/BoltzmannMachines/BM.do.txt +++ b/doc/src/BoltzmannMachines/BM.do.txt @@ -43,6 +43,8 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa !split ===== An intermediate step, the Hopfield network and links to the Ising and Potts models ===== +More material on Hopfield networks will come here + !split ===== A brief review on Markov Chains, Metropolis and Gibbs sampling ===== @@ -1184,7 +1186,7 @@ To get the expecation values with respect to the *data*, we set the visible unit To get the expectation values with respect to the *model*, we use Gibbs sampling. We can either initialize the $\bm{x}$ randomly or with a training sample. While we ideally want a large number of Gibbs iterations $n\rightarrow n$, one might decide to truncate it earlier for efficiency. Doing this while having intialized $\bm{x}$ with a training data vector is referred to as contrastive divergence (CD), because one is then closer to approximating the gradient of this function than the negative log-likelihood. The contrastive divergence function is the difference between two Kullback-Leibler divergences (also called relative entropy), which measure how one probability distribution diverges from a second, expected probability distribution (in this case the estimated one from the ground truth one). !split -===== RBMs for the quantum many body problem ===== +===== Recent examples: RBMs for the quantum many body problem ===== The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research. @@ -1203,90 +1205,5 @@ Some of their motivation included Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice. -!split -===== Representing the wave function ===== -The wavefunction should be a probability amplitude depending on $\bm{x}$. The RBM model is given by the joint distribution of $\bm{x}$ and $\bm{h}$ -!bt -\begin{align} - F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}. -\end{align} -!et -To find the marginal distribution of $\bm{x}$ we set: -!bt -\begin{align} - F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h}) \\ - &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. -\end{align} -!et -Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS) -!bt -\begin{align} - \Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) \\ - &= \frac{1}{Z}\sum_{\bm{h}} e^{-E(\mathbf{x}, \mathbf{h})} \\ - &= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} \\ - &= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}). \\ -\end{align} -!et - -!split -===== Choose the cost function ===== -Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is -!bt -\begin{align} - G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i} - = 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ), -\end{align} -!et -where the local energy is given by -!bt -\begin{align} - E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi. -\end{align} -!et - - -!split -===== Running the codes ===== -!bblock -You can find the codes for the simple two-electron case at the Github repository URL:"https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src". Python codes to come, only c++ as of now. - -The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor $\exp{(r_{ij})}$ and the reduced Boltzmann machines. - -The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used $14$ hidden nodes in the calculations below. - -!eblock - - - - -!split -===== Energy as function of iterations, $N=2$ electrons ===== -!bblock -FIGURE: [figures/figN2.pdf, width=700 frac=0.9] -!eblock - - -!split -===== Energy as function of iterations, $N=6$ electrons ===== -!bblock -FIGURE: [figures/figN6.pdf, width=700 frac=0.9] -!eblock - - - -!split -===== Conclusions and where do we stand ===== -!bblock -* A simple extension of the work of "G. Carleo and M. Troyer, Science _355_, Issue 6325, pp. 602-606 (2017)":"http://science.sciencemag.org/content/355/6325/602" gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for $N=6$ and $N=12$ electrons. -* Minimization problem can be tricky. -* Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant. -* To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case. -* Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function? - o Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function? - o Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor). - o Test this for multi-fermion systems and compare with other many-body methods. -* Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories? - -!eblock