{
  "id": 334670,
  "title": " DART algorithm explained",
  "url": "/competitions/amex-default-prediction/discussion/334670",
  "author_name": "",
  "post_date": "2022-07-02T14:35:44.692171100Z",
  "votes": 132,
  "comment_count": 17,
  "views": 0,
  "content": "<h2>DART algorithm explained</h2>\n<p>In this competition the <code>DART: Dropouts meet Multiple Additive Regression Trees</code> [<a href=\"https://arxiv.org/pdf/1505.01866.pdf\" target=\"_blank\">paper</a>] algorithm had been used successfully by the top solutions to obtain high-performing LGBM models.</p>\n<p>But, what is it? and how can we use this knowledge to better tune the rest of LGBM's parameters?</p>\n<h3>The Multiple Additive Regression Trees (MART) algorithm</h3>\n<p>The basic idea behind GBM is to <strong>add weak learners and weigh them according to their performance</strong>. In this sense, all trees must be correlated, the earlier trees have a greater influence on the general trend of the function, so all trees are trained with the same information. <br>\nThis will likely cause that all trees are correlated, and are not enough to reduce bias and overfitting.</p>\n<p>To overcome this, the MART algorithm combines the trees learned so far and learns a new tree on top of them.<br>\nThis is done by constructing a multiple additive model, by adding trees one at a time. </p>\n<p>The main contribution of XGBoost (extreme gradient boosting) over the original MART is the addition of regularization terms.</p>\n<p>$$\\begin{align}<br>\nL(x,y,f) = \\sum_{i=1}^n \\ell(y_i, f(x_i)) + \\sum_{k=1}^K \\Omega(f_k)<br>\n\\end{align}$$</p>\n<p>where</p>\n<p>$$\\begin{align}<br>\nf(x) = \\sum_{k=1}^K f_k(x)<br>\n\\end{align}$$</p>\n<p>and the second sum is the regularization term <code>Ω</code> which in XGBoost's case is</p>\n<p>$$\\begin{align}<br>\n\\Omega(f) = \\gamma T + \\frac{1}{2} \\lambda \\sum_{j=1}^T w_j^2<br>\n\\end{align}$$</p>\n<p>This regularization is implemented in <code>xgboost</code> by:</p>\n<ul>\n<li><code>γ</code> being the <strong><code>min_split_loss</code></strong> parameter</li>\n<li><code>λ</code> being the <strong><code>reg_lambda</code></strong> parameter</li>\n<li><code>T</code> being the <strong><code>n_leaves</code></strong> - number of leaves in the tree</li>\n<li><code>w_j</code> being the value of the leaf</li>\n</ul>\n<h5>What is the GBM boosting procedure?</h5>\n<blockquote>\n  <p>Initialize the predicted output vector <code>F_0</code> to the constant <code>ŷ</code>.</p>\n  <p>At each step of the iteration, <code>m = 1, 2, 3, ..., M</code></p>\n  <ul>\n  <li>Train a regression tree, <code>h_m</code>, with the input data <code>(x_i, y_i, F_{m-1}(x_i))</code>, for <code>i = 1, 2, ..., n</code>.</li>\n  <li>Update the predicted output vector with the new tree's prediction <code>F_m(x) = F_{m-1}(x) + \\nu h_m(x)</code>, for <code>x = x_1, x_2, ..., x_n</code>.</li>\n  </ul>\n  <p>Output <code>F_M(x)</code> as the final predicted value.</p>\n</blockquote>\n<p>However, MART suffers from a problem of <strong>over-specialization</strong>: Trees added at later iterations tend to impact the prediction of only a few instances and make a negligible contribution towards the remaining instances.</p>\n<p><img src=\"https://i.ibb.co/Gk0Kyms/Selection-938.png\" alt=\"\"></p>\n<blockquote>\n  <p><strong>Figure (from the paper):</strong> </p>\n  <ul>\n  <li>The size of nodes is proportional to the percentage of the instances that reach this node. </li>\n  <li>The color gradient of leaves represents the range of values where green stands for the positive extreme, yellow for zero, and red for the negative extreme.</li>\n  </ul>\n  <p><strong>Shrinkage:</strong> A trick to overcome MART's problems by setting the contribution of each new tree to be reduced by a constant value - shrinkage factor. Out of scope for our review but it is on the figure.</p>\n</blockquote>\n<h3>The DART algorithm</h3>\n<h5>What is DART?</h5>\n<p>DART is a tree-based algorithm that uses dropout to regularize the model.<br>\nIt is an adaptation of the dropout algorithm used in Neural Networks to be used in GBM.<br>\nIn NN dropout randomly zeroes out activations of some nodes during training.</p>\n<p>So for GBMs: Each of the existing trees in the ensemble is dropped with a probability <code>p</code>.<br>\nDuring testing, this <code>p</code> is set to <code>0</code>, and all trees are used for prediction.</p>\n<h5>How does DART work?</h5>\n<ul>\n<li>At each iteration a new tree is added.</li>\n<li>If a tree <code>h_m</code> is selected:<ul>\n<li>the output prediction vector is updated as follows: <code>F_m(x) = F_{m-1}(x) + h_m(x)</code></li>\n<li><code>h_m</code> is set to <code>0</code> with probability <code>p</code>.</li></ul></li>\n</ul>\n<h5>What is the intuition behind it?</h5>\n<p>Using the dropout in GBM provides the model with the following properties:</p>\n<ul>\n<li>It helps to decorrelate the trees by making the updated <code>F_m(x)</code> dependent on some previously dropped trees.</li>\n<li>It reduces the bias of the trees by making them train on \"new\" instances.</li>\n</ul>\n<h5>How to use it?</h5>\n<p>To use DART in LGBM you need to set the following parameters:</p>\n<ul>\n<li><code>boosting_type</code> to <code>dart</code></li>\n<li><code>drop_rate</code> to the fraction of previous trees to drop during the dropout</li>\n<li><code>max_drop</code> to the max number of dropped trees during one boosting iteration</li>\n<li><code>skip_drop</code> probability of skipping the dropout procedure during a boosting iteration</li>\n<li><code>xgboost_dart_mode</code> for using xgboost dart mode, the difference is  not yet completely understood</li>\n<li><code>uniform_drop</code> for uniform dropout</li>\n<li><code>drop_seed</code> is the random seed when dropping trees</li>\n</ul>\n<h5>What about the rest of the parameters when using DART?</h5>\n<p>When using DART, the rest of the parameters that should be tuned are:</p>\n<ul>\n<li><code>max_depth</code> is one of the most important ones</li>\n<li><code>min_data_in_leaf</code> controls overfitting as higher values prevent a model from learning relations that might be highly specific to the particular sample selected for a tree.</li>\n<li><code>num_leaves</code> is usually used in the range <code>2^max_depth</code>.</li>\n<li><code>max_bin</code> is used to control over-fitting as larger bins reduce overfitting by smoothing the learning process.</li>\n<li><code>lambda_l1</code>, <code>lambda_l2</code> are the regularization terms for <code>L1</code> and <code>L2</code> which help to avoid overfitting.</li>\n<li><code>min_gain_to_split</code> controls the minimum loss reduction required to make a further partition on a leaf node of the tree.</li>\n<li><code>feature_fraction</code> controls the randomly selected fraction of features to be used for each tree.</li>\n<li><code>bagging_fraction</code> controls the randomly selected fraction of data (rows) to be used for each tree.</li>\n<li><code>learning_rate</code> is also very important</li>\n</ul>",
  "messages": [
    {
      "id": "1840760",
      "postDate": "07/02/2022 14:35:44",
      "content": "<h2>DART algorithm explained</h2>\n<p>In this competition the <code>DART: Dropouts meet Multiple Additive Regression Trees</code> [<a href=\"https://arxiv.org/pdf/1505.01866.pdf\" target=\"_blank\">paper</a>] algorithm had been used successfully by the top solutions to obtain high-performing LGBM models.</p>\n<p>But, what is it? and how can we use this knowledge to better tune the rest of LGBM's parameters?</p>\n<h3>The Multiple Additive Regression Trees (MART) algorithm</h3>\n<p>The basic idea behind GBM is to <strong>add weak learners and weigh them according to their performance</strong>. In this sense, all trees must be correlated, the earlier trees have a greater influence on the general trend of the function, so all trees are trained with the same information. <br>\nThis will likely cause that all trees are correlated, and are not enough to reduce bias and overfitting.</p>\n<p>To overcome this, the MART algorithm combines the trees learned so far and learns a new tree on top of them.<br>\nThis is done by constructing a multiple additive model, by adding trees one at a time. </p>\n<p>The main contribution of XGBoost (extreme gradient boosting) over the original MART is the addition of regularization terms.</p>\n<p>$$\\begin{align}<br>\nL(x,y,f) = \\sum_{i=1}^n \\ell(y_i, f(x_i)) + \\sum_{k=1}^K \\Omega(f_k)<br>\n\\end{align}$$</p>\n<p>where</p>\n<p>$$\\begin{align}<br>\nf(x) = \\sum_{k=1}^K f_k(x)<br>\n\\end{align}$$</p>\n<p>and the second sum is the regularization term <code>Ω</code> which in XGBoost's case is</p>\n<p>$$\\begin{align}<br>\n\\Omega(f) = \\gamma T + \\frac{1}{2} \\lambda \\sum_{j=1}^T w_j^2<br>\n\\end{align}$$</p>\n<p>This regularization is implemented in <code>xgboost</code> by:</p>\n<ul>\n<li><code>γ</code> being the <strong><code>min_split_loss</code></strong> parameter</li>\n<li><code>λ</code> being the <strong><code>reg_lambda</code></strong> parameter</li>\n<li><code>T</code> being the <strong><code>n_leaves</code></strong> - number of leaves in the tree</li>\n<li><code>w_j</code> being the value of the leaf</li>\n</ul>\n<h5>What is the GBM boosting procedure?</h5>\n<blockquote>\n  <p>Initialize the predicted output vector <code>F_0</code> to the constant <code>ŷ</code>.</p>\n  <p>At each step of the iteration, <code>m = 1, 2, 3, ..., M</code></p>\n  <ul>\n  <li>Train a regression tree, <code>h_m</code>, with the input data <code>(x_i, y_i, F_{m-1}(x_i))</code>, for <code>i = 1, 2, ..., n</code>.</li>\n  <li>Update the predicted output vector with the new tree's prediction <code>F_m(x) = F_{m-1}(x) + \\nu h_m(x)</code>, for <code>x = x_1, x_2, ..., x_n</code>.</li>\n  </ul>\n  <p>Output <code>F_M(x)</code> as the final predicted value.</p>\n</blockquote>\n<p>However, MART suffers from a problem of <strong>over-specialization</strong>: Trees added at later iterations tend to impact the prediction of only a few instances and make a negligible contribution towards the remaining instances.</p>\n<p><img src=\"https://i.ibb.co/Gk0Kyms/Selection-938.png\" alt=\"\"></p>\n<blockquote>\n  <p><strong>Figure (from the paper):</strong> </p>\n  <ul>\n  <li>The size of nodes is proportional to the percentage of the instances that reach this node. </li>\n  <li>The color gradient of leaves represents the range of values where green stands for the positive extreme, yellow for zero, and red for the negative extreme.</li>\n  </ul>\n  <p><strong>Shrinkage:</strong> A trick to overcome MART's problems by setting the contribution of each new tree to be reduced by a constant value - shrinkage factor. Out of scope for our review but it is on the figure.</p>\n</blockquote>\n<h3>The DART algorithm</h3>\n<h5>What is DART?</h5>\n<p>DART is a tree-based algorithm that uses dropout to regularize the model.<br>\nIt is an adaptation of the dropout algorithm used in Neural Networks to be used in GBM.<br>\nIn NN dropout randomly zeroes out activations of some nodes during training.</p>\n<p>So for GBMs: Each of the existing trees in the ensemble is dropped with a probability <code>p</code>.<br>\nDuring testing, this <code>p</code> is set to <code>0</code>, and all trees are used for prediction.</p>\n<h5>How does DART work?</h5>\n<ul>\n<li>At each iteration a new tree is added.</li>\n<li>If a tree <code>h_m</code> is selected:<ul>\n<li>the output prediction vector is updated as follows: <code>F_m(x) = F_{m-1}(x) + h_m(x)</code></li>\n<li><code>h_m</code> is set to <code>0</code> with probability <code>p</code>.</li></ul></li>\n</ul>\n<h5>What is the intuition behind it?</h5>\n<p>Using the dropout in GBM provides the model with the following properties:</p>\n<ul>\n<li>It helps to decorrelate the trees by making the updated <code>F_m(x)</code> dependent on some previously dropped trees.</li>\n<li>It reduces the bias of the trees by making them train on \"new\" instances.</li>\n</ul>\n<h5>How to use it?</h5>\n<p>To use DART in LGBM you need to set the following parameters:</p>\n<ul>\n<li><code>boosting_type</code> to <code>dart</code></li>\n<li><code>drop_rate</code> to the fraction of previous trees to drop during the dropout</li>\n<li><code>max_drop</code> to the max number of dropped trees during one boosting iteration</li>\n<li><code>skip_drop</code> probability of skipping the dropout procedure during a boosting iteration</li>\n<li><code>xgboost_dart_mode</code> for using xgboost dart mode, the difference is  not yet completely understood</li>\n<li><code>uniform_drop</code> for uniform dropout</li>\n<li><code>drop_seed</code> is the random seed when dropping trees</li>\n</ul>\n<h5>What about the rest of the parameters when using DART?</h5>\n<p>When using DART, the rest of the parameters that should be tuned are:</p>\n<ul>\n<li><code>max_depth</code> is one of the most important ones</li>\n<li><code>min_data_in_leaf</code> controls overfitting as higher values prevent a model from learning relations that might be highly specific to the particular sample selected for a tree.</li>\n<li><code>num_leaves</code> is usually used in the range <code>2^max_depth</code>.</li>\n<li><code>max_bin</code> is used to control over-fitting as larger bins reduce overfitting by smoothing the learning process.</li>\n<li><code>lambda_l1</code>, <code>lambda_l2</code> are the regularization terms for <code>L1</code> and <code>L2</code> which help to avoid overfitting.</li>\n<li><code>min_gain_to_split</code> controls the minimum loss reduction required to make a further partition on a leaf node of the tree.</li>\n<li><code>feature_fraction</code> controls the randomly selected fraction of features to be used for each tree.</li>\n<li><code>bagging_fraction</code> controls the randomly selected fraction of data (rows) to be used for each tree.</li>\n<li><code>learning_rate</code> is also very important</li>\n</ul>",
      "rawMarkdown": "## DART algorithm explained\n\nIn this competition the `DART: Dropouts meet Multiple Additive Regression Trees` [[paper](https://arxiv.org/pdf/1505.01866.pdf)] algorithm had been used successfully by the top solutions to obtain high-performing LGBM models.\n\nBut, what is it? and how can we use this knowledge to better tune the rest of LGBM's parameters?\n\n### The Multiple Additive Regression Trees (MART) algorithm\n\nThe basic idea behind GBM is to **add weak learners and weigh them according to their performance**. In this sense, all trees must be correlated, the earlier trees have a greater influence on the general trend of the function, so all trees are trained with the same information. \nThis will likely cause that all trees are correlated, and are not enough to reduce bias and overfitting.\n\nTo overcome this, the MART algorithm combines the trees learned so far and learns a new tree on top of them.\nThis is done by constructing a multiple additive model, by adding trees one at a time. \n\nThe main contribution of XGBoost (extreme gradient boosting) over the original MART is the addition of regularization terms.\n\n$$\\begin{align}\nL(x,y,f) = \\sum_{i=1}^n \\ell(y_i, f(x_i)) + \\sum_{k=1}^K \\Omega(f_k)\n\\end{align}$$\n\nwhere\n\n$$\\begin{align}\nf(x) = \\sum_{k=1}^K f_k(x)\n\\end{align}$$\n\nand the second sum is the regularization term `Ω` which in XGBoost's case is\n\n$$\\begin{align}\n\\Omega(f) = \\gamma T + \\frac{1}{2} \\lambda \\sum_{j=1}^T w_j^2\n\\end{align}$$\n\nThis regularization is implemented in `xgboost` by:\n\n- `γ` being the **`min_split_loss`** parameter\n- `λ` being the **`reg_lambda`** parameter\n- `T` being the **`n_leaves`** - number of leaves in the tree\n- `w_j` being the value of the leaf\n\n##### What is the GBM boosting procedure?\n\n> Initialize the predicted output vector `F_0` to the constant `ŷ`.\n\n> At each step of the iteration, `m = 1, 2, 3, ..., M`\n- Train a regression tree, `h_m`, with the input data `(x_i, y_i, F_{m-1}(x_i))`, for `i = 1, 2, ..., n`.\n- Update the predicted output vector with the new tree's prediction `F_m(x) = F_{m-1}(x) + \\nu h_m(x)`, for `x = x_1, x_2, ..., x_n`.\n\n> Output `F_M(x)` as the final predicted value.\n\nHowever, MART suffers from a problem of **over-specialization**: Trees added at later iterations tend to impact the prediction of only a few instances and make a negligible contribution towards the remaining instances.\n\n![](https://i.ibb.co/Gk0Kyms/Selection-938.png)\n\n> **Figure (from the paper):** \n- The size of nodes is proportional to the percentage of the instances that reach this node. \n- The color gradient of leaves represents the range of values where green stands for the positive extreme, yellow for zero, and red for the negative extreme.\n\n> **Shrinkage:** A trick to overcome MART's problems by setting the contribution of each new tree to be reduced by a constant value - shrinkage factor. Out of scope for our review but it is on the figure.\n\n### The DART algorithm\n\n##### What is DART?\n\nDART is a tree-based algorithm that uses dropout to regularize the model.\nIt is an adaptation of the dropout algorithm used in Neural Networks to be used in GBM.\nIn NN dropout randomly zeroes out activations of some nodes during training.\n\nSo for GBMs: Each of the existing trees in the ensemble is dropped with a probability `p`.\nDuring testing, this `p` is set to `0`, and all trees are used for prediction.\n\n##### How does DART work?\n\n- At each iteration a new tree is added.\n- If a tree `h_m` is selected:\n    - the output prediction vector is updated as follows: `F_m(x) = F_{m-1}(x) + h_m(x)`\n    - `h_m` is set to `0` with probability `p`.\n\n##### What is the intuition behind it?\n\nUsing the dropout in GBM provides the model with the following properties:\n\n- It helps to decorrelate the trees by making the updated `F_m(x)` dependent on some previously dropped trees.\n- It reduces the bias of the trees by making them train on \"new\" instances.\n\n##### How to use it?\n\nTo use DART in LGBM you need to set the following parameters:\n\n- `boosting_type` to `dart`\n- `drop_rate` to the fraction of previous trees to drop during the dropout\n- `max_drop` to the max number of dropped trees during one boosting iteration\n- `skip_drop` probability of skipping the dropout procedure during a boosting iteration\n- `xgboost_dart_mode` for using xgboost dart mode, the difference is  not yet completely understood\n- `uniform_drop` for uniform dropout\n- `drop_seed` is the random seed when dropping trees\n\n##### What about the rest of the parameters when using DART?\n\nWhen using DART, the rest of the parameters that should be tuned are:\n\n- `max_depth` is one of the most important ones\n- `min_data_in_leaf` controls overfitting as higher values prevent a model from learning relations that might be highly specific to the particular sample selected for a tree.\n- `num_leaves` is usually used in the range `2^max_depth`.\n- `max_bin` is used to control over-fitting as larger bins reduce overfitting by smoothing the learning process.\n- `lambda_l1`, `lambda_l2` are the regularization terms for `L1` and `L2` which help to avoid overfitting.\n- `min_gain_to_split` controls the minimum loss reduction required to make a further partition on a leaf node of the tree.\n- `feature_fraction` controls the randomly selected fraction of features to be used for each tree.\n- `bagging_fraction` controls the randomly selected fraction of data (rows) to be used for each tree.\n- `learning_rate` is also very important",
      "votes": null
    },
    {
      "id": "1842072",
      "postDate": "07/03/2022 17:22:30",
      "content": "<p>This is incredible. I learn so much from you haha.</p>\n<p><a href=\"https://www.kaggle.com/thedevastator\" target=\"_blank\">@thedevastator</a> - you’re crushing it lately! Keep up the wonderful posts!</p>",
      "rawMarkdown": "This is incredible. I learn so much from you haha.\n\n@thedevastator - you’re crushing it lately! Keep up the wonderful posts!",
      "votes": null
    },
    {
      "id": "1842632",
      "postDate": "07/04/2022 06:54:48",
      "content": "<p>Great work! Thanks for sharing!</p>",
      "rawMarkdown": "Great work! Thanks for sharing!",
      "votes": null
    },
    {
      "id": "1842858",
      "postDate": "07/04/2022 10:52:01",
      "content": "<p>Nice, it is really interesting!</p>",
      "rawMarkdown": "Nice, it is really interesting!",
      "votes": null
    },
    {
      "id": "1843336",
      "postDate": "07/04/2022 17:59:59",
      "content": "<p>thank you so much</p>",
      "rawMarkdown": "thank you so much",
      "votes": null
    },
    {
      "id": "1844140",
      "postDate": "07/05/2022 11:24:03",
      "content": "<p>This is very interesting! Thank you!</p>",
      "rawMarkdown": "This is very interesting! Thank you!",
      "votes": null
    },
    {
      "id": "1845162",
      "postDate": "07/06/2022 05:41:10",
      "content": "<p>This is great! Thanks for sharing!</p>",
      "rawMarkdown": "This is great! Thanks for sharing!",
      "votes": null
    },
    {
      "id": "1845196",
      "postDate": "07/06/2022 06:07:07",
      "content": "<p>Very interesting article</p>",
      "rawMarkdown": "Very interesting article",
      "votes": null
    },
    {
      "id": "1845352",
      "postDate": "07/06/2022 08:46:59",
      "content": "<p>Thank you, for sharing this knowledge!!!</p>",
      "rawMarkdown": "Thank you, for sharing this knowledge!!!",
      "votes": null
    },
    {
      "id": "1845390",
      "postDate": "07/06/2022 09:35:36",
      "content": "<p>Thanks for the explanation !</p>",
      "rawMarkdown": "Thanks for the explanation !",
      "votes": null
    },
    {
      "id": "1846927",
      "postDate": "07/07/2022 13:28:38",
      "content": "<p>Thank you for that !!</p>",
      "rawMarkdown": "Thank you for that !!",
      "votes": null
    },
    {
      "id": "1847492",
      "postDate": "07/08/2022 00:56:52",
      "content": "<p>Thanks this is a great piece of literature and reference will bookmark this 4 DART .. </p>",
      "rawMarkdown": "Thanks this is a great piece of literature and reference will bookmark this 4 DART ..",
      "votes": null
    },
    {
      "id": "1851007",
      "postDate": "07/11/2022 01:15:29",
      "content": "<p>Thank you for sharing! and good teaching</p>",
      "rawMarkdown": "Thank you for sharing! and good teaching",
      "votes": null
    },
    {
      "id": "1868338",
      "postDate": "07/23/2022 23:20:43",
      "content": "<p>Thanks for sharing <a href=\"https://www.kaggle.com/thedevastator\" target=\"_blank\">@thedevastator</a> </p>",
      "rawMarkdown": "Thanks for sharing @thedevastator",
      "votes": null
    },
    {
      "id": "1885114",
      "postDate": "08/04/2022 22:27:32",
      "content": "<p>Thanks so much! I currently diving into DART. Two questions:</p>\n<p>Why is DART SOO much lower? :)</p>\n<p>Which DART implementation would you recommend? xgboost or lgbm?</p>",
      "rawMarkdown": "Thanks so much! I currently diving into DART. Two questions:\n\nWhy is DART SOO much lower? :)\n\nWhich DART implementation would you recommend? xgboost or lgbm?",
      "votes": null
    },
    {
      "id": "1885115",
      "postDate": "08/04/2022 22:31:14",
      "content": "<p>Thank you for the explanation!</p>",
      "rawMarkdown": "Thank you for the explanation!",
      "votes": null
    },
    {
      "id": "1917306",
      "postDate": "08/28/2022 16:05:03",
      "content": "<p>it is really interesting!</p>",
      "rawMarkdown": "it is really interesting!",
      "votes": null
    },
    {
      "id": "3380733",
      "postDate": "12/22/2025 23:00:30",
      "content": "<p>What do you think of a 3 trillion-fold improved algorithm for the micro-model universe</p>\n<p><a href=\"https://www.kaggle.com/code/shuiquan/super-algorithm\" target=\"_blank\">https://www.kaggle.com/code/shuiquan/super-algorithm</a></p>\n<p>=== zsfsynthesizedadaptive_fused: full-model demo (integrated all modules) === injmult=3.0, couplingmult=3.0, lowerthreshold=False, highnoise=False Sample fused params: { \"xi\": 0.01800219087086863, \"lambda\": 0.12026826260974306, \"injectionamp\": 0.08886804312825797, \"etaamp\": 3.0529081490799215e-05, \"mixgain\": 10.0, \"kappa\": 0.001, \"diffusionnu\": 0.002961 } step 0: phi=1.179487e-01, trit=0, injadapt=2.154114e-02 step 50: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 step 199: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 final phi: 1.1496 final tritstate: 1</p>\n<p>lambda set to 0.121 phi biased +0.1 -&gt; 1.000000e-01 Reached trit=1 at step 2 trigger success: injected energy=1.200000e-01 J, curvature change=2.483487e-44 m^-1 after trigger zs: {'phi': 0.7372094356394613, 'tritstate': 1, 'entropy': 0.0004, 'energy': 0.12000000000000001, 'curvature': 2.4834871703044647e-44}</p>\n<p>carbon synthesis result: {'strengthGPa': 11.2, 'fusedtrit': 0, 'fused': {'tritstate': 0, 'xi': 0.021, 'entropy': 0.0}, 'carbonzs': {'xi': 0.021, 'lambda': 0.121, 'entropy': 0.0, 'tritstate': 1}}</p>\n<p>TRIT distribution (-1/0/1): [0. 0.002 0.998]</p>\n<p>=== Fused ZSF-Microcosm Model Comparison Test === { \"seed\": 20251204, \"inj_mult\": 3.0, \"grid_Nx\": 128, \"T_total\": 0.01, \"nruns\": 10 } Simulation finished: failed=False, runtime=1.444s, final_trit=0</p>\n<p>evolved seed=20251204: mean_err=1.132e-01, max_err=3.530e+00, drift=-5.610e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.444s Simulation finished: failed=False, runtime=1.205s, final_trit=0</p>\n<p>evolved seed=20251205: mean_err=1.180e-01, max_err=3.482e+00, drift=-1.176e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.205s Simulation finished: failed=False, runtime=1.059s, final_trit=0</p>\n<p>evolved seed=20251206: mean_err=1.185e-01, max_err=3.474e+00, drift=-8.117e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.059s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>evolved seed=20251207: mean_err=1.196e-01, max_err=3.471e+00, drift=-1.669e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.057s, final_trit=0</p>\n<p>evolved seed=20251208: mean_err=1.183e-01, max_err=3.476e+00, drift=-8.856e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s Simulation finished: failed=False, runtime=1.053s, final_trit=0</p>\n<p>evolved seed=20251209: mean_err=1.196e-01, max_err=3.472e+00, drift=-1.244e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>evolved seed=20251210: mean_err=1.199e-01, max_err=3.483e+00, drift=-1.537e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>evolved seed=20251211: mean_err=1.188e-01, max_err=3.491e+00, drift=-5.470e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>evolved seed=20251212: mean_err=1.183e-01, max_err=3.477e+00, drift=-9.080e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.053s, final_trit=0</p>\n<p>evolved seed=20251213: mean_err=1.197e-01, max_err=3.482e+00, drift=-1.465e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.048s, final_trit=0</p>\n<p>original seed=20251204: mean_err=4.487e+11, max_err=2.302e+13, drift=3.312e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>original seed=20251205: mean_err=3.569e+11, max_err=2.018e+13, drift=2.857e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.087s, final_trit=0</p>\n<p>original seed=20251206: mean_err=3.708e+11, max_err=2.519e+13, drift=2.339e+03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.087s Simulation finished: failed=False, runtime=1.050s, final_trit=0</p>\n<p>original seed=20251207: mean_err=4.649e+11, max_err=2.309e+13, drift=3.844e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.050s Simulation finished: failed=False, runtime=1.064s, final_trit=0</p>\n<p>original seed=20251208: mean_err=5.190e+11, max_err=2.571e+13, drift=3.911e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.064s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>original seed=20251209: mean_err=3.767e+11, max_err=1.972e+13, drift=3.689e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.048s, final_trit=0</p>\n<p>original seed=20251210: mean_err=4.430e+11, max_err=2.344e+13, drift=3.669e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.066s, final_trit=0</p>\n<p>original seed=20251211: mean_err=3.513e+11, max_err=2.034e+13, drift=2.720e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.066s Simulation finished: failed=False, runtime=1.068s, final_trit=0</p>\n<p>original seed=20251212: mean_err=2.586e+11, max_err=1.679e+13, drift=4.730e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.068s Simulation finished: failed=False, runtime=1.057s, final_trit=0</p>\n<p>original seed=20251213: mean_err=3.614e+11, max_err=1.972e+13, drift=2.625e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s</p>\n<p>==================================================</p>\n<p>Fused Comparison Summary (Evolved vs Original)\nMean Energy Error: 1.184e-01 ± 1.952e-03 vs 3.951e+11 ± 7.413e+10 Energy Drift: -1.080e-02 ± 3.990e-03 vs 3.159e+04 ± 1.211e+04 Trit Active Rate: 0.00 vs 0.00 Final Carbon Strength (GPa): 11.20 vs 11.20 NaN Failures: 0/10 vs 0/10 Avg Runtime (s): 1.108 vs 1.059</p>\n<p>Energy Error Improvement Factor: 3337523027298.930x</p>\n<p>=== Simulation Completed === Result saved to: ./fused_result.json</p>\n<p>[Program finished]</p>",
      "rawMarkdown": "What do you think of a 3 trillion-fold improved algorithm for the micro-model universe\n\nhttps://www.kaggle.com/code/shuiquan/super-algorithm\n\n=== zsfsynthesizedadaptive_fused: full-model demo (integrated all modules) === injmult=3.0, couplingmult=3.0, lowerthreshold=False, highnoise=False Sample fused params: { \"xi\": 0.01800219087086863, \"lambda\": 0.12026826260974306, \"injectionamp\": 0.08886804312825797, \"etaamp\": 3.0529081490799215e-05, \"mixgain\": 10.0, \"kappa\": 0.001, \"diffusionnu\": 0.002961 } step 0: phi=1.179487e-01, trit=0, injadapt=2.154114e-02 step 50: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 step 199: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 final phi: 1.1496 final tritstate: 1\n\nlambda set to 0.121 phi biased +0.1 -> 1.000000e-01 Reached trit=1 at step 2 trigger success: injected energy=1.200000e-01 J, curvature change=2.483487e-44 m^-1 after trigger zs: {'phi': 0.7372094356394613, 'tritstate': 1, 'entropy': 0.0004, 'energy': 0.12000000000000001, 'curvature': 2.4834871703044647e-44}\n\ncarbon synthesis result: {'strengthGPa': 11.2, 'fusedtrit': 0, 'fused': {'tritstate': 0, 'xi': 0.021, 'entropy': 0.0}, 'carbonzs': {'xi': 0.021, 'lambda': 0.121, 'entropy': 0.0, 'tritstate': 1}}\n\nTRIT distribution (-1/0/1): [0. 0.002 0.998]\n\n=== Fused ZSF-Microcosm Model Comparison Test === { \"seed\": 20251204, \"inj_mult\": 3.0, \"grid_Nx\": 128, \"T_total\": 0.01, \"nruns\": 10 } Simulation finished: failed=False, runtime=1.444s, final_trit=0\n\nevolved seed=20251204: mean_err=1.132e-01, max_err=3.530e+00, drift=-5.610e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.444s Simulation finished: failed=False, runtime=1.205s, final_trit=0\n\nevolved seed=20251205: mean_err=1.180e-01, max_err=3.482e+00, drift=-1.176e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.205s Simulation finished: failed=False, runtime=1.059s, final_trit=0\n\nevolved seed=20251206: mean_err=1.185e-01, max_err=3.474e+00, drift=-8.117e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.059s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\nevolved seed=20251207: mean_err=1.196e-01, max_err=3.471e+00, drift=-1.669e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.057s, final_trit=0\n\nevolved seed=20251208: mean_err=1.183e-01, max_err=3.476e+00, drift=-8.856e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s Simulation finished: failed=False, runtime=1.053s, final_trit=0\n\nevolved seed=20251209: mean_err=1.196e-01, max_err=3.472e+00, drift=-1.244e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\nevolved seed=20251210: mean_err=1.199e-01, max_err=3.483e+00, drift=-1.537e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\nevolved seed=20251211: mean_err=1.188e-01, max_err=3.491e+00, drift=-5.470e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\nevolved seed=20251212: mean_err=1.183e-01, max_err=3.477e+00, drift=-9.080e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.053s, final_trit=0\n\nevolved seed=20251213: mean_err=1.197e-01, max_err=3.482e+00, drift=-1.465e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.048s, final_trit=0\n\noriginal seed=20251204: mean_err=4.487e+11, max_err=2.302e+13, drift=3.312e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\noriginal seed=20251205: mean_err=3.569e+11, max_err=2.018e+13, drift=2.857e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.087s, final_trit=0\n\noriginal seed=20251206: mean_err=3.708e+11, max_err=2.519e+13, drift=2.339e+03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.087s Simulation finished: failed=False, runtime=1.050s, final_trit=0\n\noriginal seed=20251207: mean_err=4.649e+11, max_err=2.309e+13, drift=3.844e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.050s Simulation finished: failed=False, runtime=1.064s, final_trit=0\n\noriginal seed=20251208: mean_err=5.190e+11, max_err=2.571e+13, drift=3.911e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.064s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\noriginal seed=20251209: mean_err=3.767e+11, max_err=1.972e+13, drift=3.689e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.048s, final_trit=0\n\noriginal seed=20251210: mean_err=4.430e+11, max_err=2.344e+13, drift=3.669e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.066s, final_trit=0\n\noriginal seed=20251211: mean_err=3.513e+11, max_err=2.034e+13, drift=2.720e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.066s Simulation finished: failed=False, runtime=1.068s, final_trit=0\n\noriginal seed=20251212: mean_err=2.586e+11, max_err=1.679e+13, drift=4.730e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.068s Simulation finished: failed=False, runtime=1.057s, final_trit=0\n\noriginal seed=20251213: mean_err=3.614e+11, max_err=1.972e+13, drift=2.625e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s\n\n==================================================\n\nFused Comparison Summary (Evolved vs Original)\nMean Energy Error: 1.184e-01 ± 1.952e-03 vs 3.951e+11 ± 7.413e+10 Energy Drift: -1.080e-02 ± 3.990e-03 vs 3.159e+04 ± 1.211e+04 Trit Active Rate: 0.00 vs 0.00 Final Carbon Strength (GPa): 11.20 vs 11.20 NaN Failures: 0/10 vs 0/10 Avg Runtime (s): 1.108 vs 1.059\n\nEnergy Error Improvement Factor: 3337523027298.930x\n\n=== Simulation Completed === Result saved to: ./fused_result.json\n\n[Program finished]",
      "votes": null
    }
  ],
  "comments": [
    {
      "id": 1842072,
      "author_name": "dschettler8845",
      "author_url": "",
      "post_date": "07/03/2022 17:22:30",
      "content": "<p>This is incredible. I learn so much from you haha.</p>\n<p><a href=\"https://www.kaggle.com/thedevastator\" target=\"_blank\">@thedevastator</a> - you’re crushing it lately! Keep up the wonderful posts!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1842632,
      "author_name": "mohammadrahmati",
      "author_url": "",
      "post_date": "07/04/2022 06:54:48",
      "content": "<p>Great work! Thanks for sharing!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1842858,
      "author_name": "paulojunqueira",
      "author_url": "",
      "post_date": "07/04/2022 10:52:01",
      "content": "<p>Nice, it is really interesting!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1843336,
      "author_name": "ltrahul",
      "author_url": "",
      "post_date": "07/04/2022 17:59:59",
      "content": "<p>thank you so much</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1844140,
      "author_name": "dhruvkulgod",
      "author_url": "",
      "post_date": "07/05/2022 11:24:03",
      "content": "<p>This is very interesting! Thank you!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1845162,
      "author_name": "hanmoli",
      "author_url": "",
      "post_date": "07/06/2022 05:41:10",
      "content": "<p>This is great! Thanks for sharing!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1845196,
      "author_name": "truefyre",
      "author_url": "",
      "post_date": "07/06/2022 06:07:07",
      "content": "<p>Very interesting article</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1845352,
      "author_name": "zhytnykoleksandr",
      "author_url": "",
      "post_date": "07/06/2022 08:46:59",
      "content": "<p>Thank you, for sharing this knowledge!!!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1845390,
      "author_name": "hugogabrielidis",
      "author_url": "",
      "post_date": "07/06/2022 09:35:36",
      "content": "<p>Thanks for the explanation !</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1846927,
      "author_name": "robirobii",
      "author_url": "",
      "post_date": "07/07/2022 13:28:38",
      "content": "<p>Thank you for that !!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1847492,
      "author_name": "gauravbrills",
      "author_url": "",
      "post_date": "07/08/2022 00:56:52",
      "content": "<p>Thanks this is a great piece of literature and reference will bookmark this 4 DART .. </p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1851007,
      "author_name": "arti1117",
      "author_url": "",
      "post_date": "07/11/2022 01:15:29",
      "content": "<p>Thank you for sharing! and good teaching</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1868338,
      "author_name": "cv13j0",
      "author_url": "",
      "post_date": "07/23/2022 23:20:43",
      "content": "<p>Thanks for sharing <a href=\"https://www.kaggle.com/thedevastator\" target=\"_blank\">@thedevastator</a> </p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1885114,
      "author_name": "gzguevara",
      "author_url": "",
      "post_date": "08/04/2022 22:27:32",
      "content": "<p>Thanks so much! I currently diving into DART. Two questions:</p>\n<p>Why is DART SOO much lower? :)</p>\n<p>Which DART implementation would you recommend? xgboost or lgbm?</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1885115,
      "author_name": "bellapisani",
      "author_url": "",
      "post_date": "08/04/2022 22:31:14",
      "content": "<p>Thank you for the explanation!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 1917306,
      "author_name": "gazu468",
      "author_url": "",
      "post_date": "08/28/2022 16:05:03",
      "content": "<p>it is really interesting!</p>",
      "votes": null,
      "replies": []
    },
    {
      "id": 3380733,
      "author_name": "shuiquan",
      "author_url": "",
      "post_date": "12/22/2025 23:00:30",
      "content": "<p>What do you think of a 3 trillion-fold improved algorithm for the micro-model universe</p>\n<p><a href=\"https://www.kaggle.com/code/shuiquan/super-algorithm\" target=\"_blank\">https://www.kaggle.com/code/shuiquan/super-algorithm</a></p>\n<p>=== zsfsynthesizedadaptive_fused: full-model demo (integrated all modules) === injmult=3.0, couplingmult=3.0, lowerthreshold=False, highnoise=False Sample fused params: { \"xi\": 0.01800219087086863, \"lambda\": 0.12026826260974306, \"injectionamp\": 0.08886804312825797, \"etaamp\": 3.0529081490799215e-05, \"mixgain\": 10.0, \"kappa\": 0.001, \"diffusionnu\": 0.002961 } step 0: phi=1.179487e-01, trit=0, injadapt=2.154114e-02 step 50: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 step 199: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 final phi: 1.1496 final tritstate: 1</p>\n<p>lambda set to 0.121 phi biased +0.1 -&gt; 1.000000e-01 Reached trit=1 at step 2 trigger success: injected energy=1.200000e-01 J, curvature change=2.483487e-44 m^-1 after trigger zs: {'phi': 0.7372094356394613, 'tritstate': 1, 'entropy': 0.0004, 'energy': 0.12000000000000001, 'curvature': 2.4834871703044647e-44}</p>\n<p>carbon synthesis result: {'strengthGPa': 11.2, 'fusedtrit': 0, 'fused': {'tritstate': 0, 'xi': 0.021, 'entropy': 0.0}, 'carbonzs': {'xi': 0.021, 'lambda': 0.121, 'entropy': 0.0, 'tritstate': 1}}</p>\n<p>TRIT distribution (-1/0/1): [0. 0.002 0.998]</p>\n<p>=== Fused ZSF-Microcosm Model Comparison Test === { \"seed\": 20251204, \"inj_mult\": 3.0, \"grid_Nx\": 128, \"T_total\": 0.01, \"nruns\": 10 } Simulation finished: failed=False, runtime=1.444s, final_trit=0</p>\n<p>evolved seed=20251204: mean_err=1.132e-01, max_err=3.530e+00, drift=-5.610e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.444s Simulation finished: failed=False, runtime=1.205s, final_trit=0</p>\n<p>evolved seed=20251205: mean_err=1.180e-01, max_err=3.482e+00, drift=-1.176e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.205s Simulation finished: failed=False, runtime=1.059s, final_trit=0</p>\n<p>evolved seed=20251206: mean_err=1.185e-01, max_err=3.474e+00, drift=-8.117e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.059s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>evolved seed=20251207: mean_err=1.196e-01, max_err=3.471e+00, drift=-1.669e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.057s, final_trit=0</p>\n<p>evolved seed=20251208: mean_err=1.183e-01, max_err=3.476e+00, drift=-8.856e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s Simulation finished: failed=False, runtime=1.053s, final_trit=0</p>\n<p>evolved seed=20251209: mean_err=1.196e-01, max_err=3.472e+00, drift=-1.244e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>evolved seed=20251210: mean_err=1.199e-01, max_err=3.483e+00, drift=-1.537e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>evolved seed=20251211: mean_err=1.188e-01, max_err=3.491e+00, drift=-5.470e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>evolved seed=20251212: mean_err=1.183e-01, max_err=3.477e+00, drift=-9.080e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.053s, final_trit=0</p>\n<p>evolved seed=20251213: mean_err=1.197e-01, max_err=3.482e+00, drift=-1.465e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.048s, final_trit=0</p>\n<p>original seed=20251204: mean_err=4.487e+11, max_err=2.302e+13, drift=3.312e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.054s, final_trit=0</p>\n<p>original seed=20251205: mean_err=3.569e+11, max_err=2.018e+13, drift=2.857e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.087s, final_trit=0</p>\n<p>original seed=20251206: mean_err=3.708e+11, max_err=2.519e+13, drift=2.339e+03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.087s Simulation finished: failed=False, runtime=1.050s, final_trit=0</p>\n<p>original seed=20251207: mean_err=4.649e+11, max_err=2.309e+13, drift=3.844e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.050s Simulation finished: failed=False, runtime=1.064s, final_trit=0</p>\n<p>original seed=20251208: mean_err=5.190e+11, max_err=2.571e+13, drift=3.911e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.064s Simulation finished: failed=False, runtime=1.051s, final_trit=0</p>\n<p>original seed=20251209: mean_err=3.767e+11, max_err=1.972e+13, drift=3.689e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.048s, final_trit=0</p>\n<p>original seed=20251210: mean_err=4.430e+11, max_err=2.344e+13, drift=3.669e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.066s, final_trit=0</p>\n<p>original seed=20251211: mean_err=3.513e+11, max_err=2.034e+13, drift=2.720e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.066s Simulation finished: failed=False, runtime=1.068s, final_trit=0</p>\n<p>original seed=20251212: mean_err=2.586e+11, max_err=1.679e+13, drift=4.730e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.068s Simulation finished: failed=False, runtime=1.057s, final_trit=0</p>\n<p>original seed=20251213: mean_err=3.614e+11, max_err=1.972e+13, drift=2.625e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s</p>\n<p>==================================================</p>\n<p>Fused Comparison Summary (Evolved vs Original)\nMean Energy Error: 1.184e-01 ± 1.952e-03 vs 3.951e+11 ± 7.413e+10 Energy Drift: -1.080e-02 ± 3.990e-03 vs 3.159e+04 ± 1.211e+04 Trit Active Rate: 0.00 vs 0.00 Final Carbon Strength (GPa): 11.20 vs 11.20 NaN Failures: 0/10 vs 0/10 Avg Runtime (s): 1.108 vs 1.059</p>\n<p>Energy Error Improvement Factor: 3337523027298.930x</p>\n<p>=== Simulation Completed === Result saved to: ./fused_result.json</p>\n<p>[Program finished]</p>",
      "votes": null,
      "replies": []
    }
  ],
  "raw_markdown_by_id": {
    "1840760": "## DART algorithm explained\n\nIn this competition the `DART: Dropouts meet Multiple Additive Regression Trees` [[paper](https://arxiv.org/pdf/1505.01866.pdf)] algorithm had been used successfully by the top solutions to obtain high-performing LGBM models.\n\nBut, what is it? and how can we use this knowledge to better tune the rest of LGBM's parameters?\n\n### The Multiple Additive Regression Trees (MART) algorithm\n\nThe basic idea behind GBM is to **add weak learners and weigh them according to their performance**. In this sense, all trees must be correlated, the earlier trees have a greater influence on the general trend of the function, so all trees are trained with the same information. \nThis will likely cause that all trees are correlated, and are not enough to reduce bias and overfitting.\n\nTo overcome this, the MART algorithm combines the trees learned so far and learns a new tree on top of them.\nThis is done by constructing a multiple additive model, by adding trees one at a time. \n\nThe main contribution of XGBoost (extreme gradient boosting) over the original MART is the addition of regularization terms.\n\n$$\\begin{align}\nL(x,y,f) = \\sum_{i=1}^n \\ell(y_i, f(x_i)) + \\sum_{k=1}^K \\Omega(f_k)\n\\end{align}$$\n\nwhere\n\n$$\\begin{align}\nf(x) = \\sum_{k=1}^K f_k(x)\n\\end{align}$$\n\nand the second sum is the regularization term `Ω` which in XGBoost's case is\n\n$$\\begin{align}\n\\Omega(f) = \\gamma T + \\frac{1}{2} \\lambda \\sum_{j=1}^T w_j^2\n\\end{align}$$\n\nThis regularization is implemented in `xgboost` by:\n\n- `γ` being the **`min_split_loss`** parameter\n- `λ` being the **`reg_lambda`** parameter\n- `T` being the **`n_leaves`** - number of leaves in the tree\n- `w_j` being the value of the leaf\n\n##### What is the GBM boosting procedure?\n\n> Initialize the predicted output vector `F_0` to the constant `ŷ`.\n\n> At each step of the iteration, `m = 1, 2, 3, ..., M`\n- Train a regression tree, `h_m`, with the input data `(x_i, y_i, F_{m-1}(x_i))`, for `i = 1, 2, ..., n`.\n- Update the predicted output vector with the new tree's prediction `F_m(x) = F_{m-1}(x) + \\nu h_m(x)`, for `x = x_1, x_2, ..., x_n`.\n\n> Output `F_M(x)` as the final predicted value.\n\nHowever, MART suffers from a problem of **over-specialization**: Trees added at later iterations tend to impact the prediction of only a few instances and make a negligible contribution towards the remaining instances.\n\n![](https://i.ibb.co/Gk0Kyms/Selection-938.png)\n\n> **Figure (from the paper):** \n- The size of nodes is proportional to the percentage of the instances that reach this node. \n- The color gradient of leaves represents the range of values where green stands for the positive extreme, yellow for zero, and red for the negative extreme.\n\n> **Shrinkage:** A trick to overcome MART's problems by setting the contribution of each new tree to be reduced by a constant value - shrinkage factor. Out of scope for our review but it is on the figure.\n\n### The DART algorithm\n\n##### What is DART?\n\nDART is a tree-based algorithm that uses dropout to regularize the model.\nIt is an adaptation of the dropout algorithm used in Neural Networks to be used in GBM.\nIn NN dropout randomly zeroes out activations of some nodes during training.\n\nSo for GBMs: Each of the existing trees in the ensemble is dropped with a probability `p`.\nDuring testing, this `p` is set to `0`, and all trees are used for prediction.\n\n##### How does DART work?\n\n- At each iteration a new tree is added.\n- If a tree `h_m` is selected:\n    - the output prediction vector is updated as follows: `F_m(x) = F_{m-1}(x) + h_m(x)`\n    - `h_m` is set to `0` with probability `p`.\n\n##### What is the intuition behind it?\n\nUsing the dropout in GBM provides the model with the following properties:\n\n- It helps to decorrelate the trees by making the updated `F_m(x)` dependent on some previously dropped trees.\n- It reduces the bias of the trees by making them train on \"new\" instances.\n\n##### How to use it?\n\nTo use DART in LGBM you need to set the following parameters:\n\n- `boosting_type` to `dart`\n- `drop_rate` to the fraction of previous trees to drop during the dropout\n- `max_drop` to the max number of dropped trees during one boosting iteration\n- `skip_drop` probability of skipping the dropout procedure during a boosting iteration\n- `xgboost_dart_mode` for using xgboost dart mode, the difference is  not yet completely understood\n- `uniform_drop` for uniform dropout\n- `drop_seed` is the random seed when dropping trees\n\n##### What about the rest of the parameters when using DART?\n\nWhen using DART, the rest of the parameters that should be tuned are:\n\n- `max_depth` is one of the most important ones\n- `min_data_in_leaf` controls overfitting as higher values prevent a model from learning relations that might be highly specific to the particular sample selected for a tree.\n- `num_leaves` is usually used in the range `2^max_depth`.\n- `max_bin` is used to control over-fitting as larger bins reduce overfitting by smoothing the learning process.\n- `lambda_l1`, `lambda_l2` are the regularization terms for `L1` and `L2` which help to avoid overfitting.\n- `min_gain_to_split` controls the minimum loss reduction required to make a further partition on a leaf node of the tree.\n- `feature_fraction` controls the randomly selected fraction of features to be used for each tree.\n- `bagging_fraction` controls the randomly selected fraction of data (rows) to be used for each tree.\n- `learning_rate` is also very important",
    "1842072": "This is incredible. I learn so much from you haha.\n\n@thedevastator - you’re crushing it lately! Keep up the wonderful posts!",
    "1842632": "Great work! Thanks for sharing!",
    "1842858": "Nice, it is really interesting!",
    "1843336": "thank you so much",
    "1844140": "This is very interesting! Thank you!",
    "1845162": "This is great! Thanks for sharing!",
    "1845196": "Very interesting article",
    "1845352": "Thank you, for sharing this knowledge!!!",
    "1845390": "Thanks for the explanation !",
    "1846927": "Thank you for that !!",
    "1847492": "Thanks this is a great piece of literature and reference will bookmark this 4 DART ..",
    "1851007": "Thank you for sharing! and good teaching",
    "1868338": "Thanks for sharing @thedevastator",
    "1885114": "Thanks so much! I currently diving into DART. Two questions:\n\nWhy is DART SOO much lower? :)\n\nWhich DART implementation would you recommend? xgboost or lgbm?",
    "1885115": "Thank you for the explanation!",
    "1917306": "it is really interesting!",
    "3380733": "What do you think of a 3 trillion-fold improved algorithm for the micro-model universe\n\nhttps://www.kaggle.com/code/shuiquan/super-algorithm\n\n=== zsfsynthesizedadaptive_fused: full-model demo (integrated all modules) === injmult=3.0, couplingmult=3.0, lowerthreshold=False, highnoise=False Sample fused params: { \"xi\": 0.01800219087086863, \"lambda\": 0.12026826260974306, \"injectionamp\": 0.08886804312825797, \"etaamp\": 3.0529081490799215e-05, \"mixgain\": 10.0, \"kappa\": 0.001, \"diffusionnu\": 0.002961 } step 0: phi=1.179487e-01, trit=0, injadapt=2.154114e-02 step 50: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 step 199: phi=1.149600e+00, trit=1, injadapt=4.900000e-02 final phi: 1.1496 final tritstate: 1\n\nlambda set to 0.121 phi biased +0.1 -> 1.000000e-01 Reached trit=1 at step 2 trigger success: injected energy=1.200000e-01 J, curvature change=2.483487e-44 m^-1 after trigger zs: {'phi': 0.7372094356394613, 'tritstate': 1, 'entropy': 0.0004, 'energy': 0.12000000000000001, 'curvature': 2.4834871703044647e-44}\n\ncarbon synthesis result: {'strengthGPa': 11.2, 'fusedtrit': 0, 'fused': {'tritstate': 0, 'xi': 0.021, 'entropy': 0.0}, 'carbonzs': {'xi': 0.021, 'lambda': 0.121, 'entropy': 0.0, 'tritstate': 1}}\n\nTRIT distribution (-1/0/1): [0. 0.002 0.998]\n\n=== Fused ZSF-Microcosm Model Comparison Test === { \"seed\": 20251204, \"inj_mult\": 3.0, \"grid_Nx\": 128, \"T_total\": 0.01, \"nruns\": 10 } Simulation finished: failed=False, runtime=1.444s, final_trit=0\n\nevolved seed=20251204: mean_err=1.132e-01, max_err=3.530e+00, drift=-5.610e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.444s Simulation finished: failed=False, runtime=1.205s, final_trit=0\n\nevolved seed=20251205: mean_err=1.180e-01, max_err=3.482e+00, drift=-1.176e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.205s Simulation finished: failed=False, runtime=1.059s, final_trit=0\n\nevolved seed=20251206: mean_err=1.185e-01, max_err=3.474e+00, drift=-8.117e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.059s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\nevolved seed=20251207: mean_err=1.196e-01, max_err=3.471e+00, drift=-1.669e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.057s, final_trit=0\n\nevolved seed=20251208: mean_err=1.183e-01, max_err=3.476e+00, drift=-8.856e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s Simulation finished: failed=False, runtime=1.053s, final_trit=0\n\nevolved seed=20251209: mean_err=1.196e-01, max_err=3.472e+00, drift=-1.244e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\nevolved seed=20251210: mean_err=1.199e-01, max_err=3.483e+00, drift=-1.537e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\nevolved seed=20251211: mean_err=1.188e-01, max_err=3.491e+00, drift=-5.470e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\nevolved seed=20251212: mean_err=1.183e-01, max_err=3.477e+00, drift=-9.080e-03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.053s, final_trit=0\n\nevolved seed=20251213: mean_err=1.197e-01, max_err=3.482e+00, drift=-1.465e-02 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.053s Simulation finished: failed=False, runtime=1.048s, final_trit=0\n\noriginal seed=20251204: mean_err=4.487e+11, max_err=2.302e+13, drift=3.312e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.054s, final_trit=0\n\noriginal seed=20251205: mean_err=3.569e+11, max_err=2.018e+13, drift=2.857e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.054s Simulation finished: failed=False, runtime=1.087s, final_trit=0\n\noriginal seed=20251206: mean_err=3.708e+11, max_err=2.519e+13, drift=2.339e+03 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.087s Simulation finished: failed=False, runtime=1.050s, final_trit=0\n\noriginal seed=20251207: mean_err=4.649e+11, max_err=2.309e+13, drift=3.844e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.050s Simulation finished: failed=False, runtime=1.064s, final_trit=0\n\noriginal seed=20251208: mean_err=5.190e+11, max_err=2.571e+13, drift=3.911e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.064s Simulation finished: failed=False, runtime=1.051s, final_trit=0\n\noriginal seed=20251209: mean_err=3.767e+11, max_err=1.972e+13, drift=3.689e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.051s Simulation finished: failed=False, runtime=1.048s, final_trit=0\n\noriginal seed=20251210: mean_err=4.430e+11, max_err=2.344e+13, drift=3.669e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.048s Simulation finished: failed=False, runtime=1.066s, final_trit=0\n\noriginal seed=20251211: mean_err=3.513e+11, max_err=2.034e+13, drift=2.720e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.066s Simulation finished: failed=False, runtime=1.068s, final_trit=0\n\noriginal seed=20251212: mean_err=2.586e+11, max_err=1.679e+13, drift=4.730e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.068s Simulation finished: failed=False, runtime=1.057s, final_trit=0\n\noriginal seed=20251213: mean_err=3.614e+11, max_err=1.972e+13, drift=2.625e+04 trit_active_rate=0.00, final_carbon_strength=11.20GPa nan=False, time=1.057s\n\n==================================================\n\nFused Comparison Summary (Evolved vs Original)\nMean Energy Error: 1.184e-01 ± 1.952e-03 vs 3.951e+11 ± 7.413e+10 Energy Drift: -1.080e-02 ± 3.990e-03 vs 3.159e+04 ± 1.211e+04 Trit Active Rate: 0.00 vs 0.00 Final Carbon Strength (GPa): 11.20 vs 11.20 NaN Failures: 0/10 vs 0/10 Avg Runtime (s): 1.108 vs 1.059\n\nEnergy Error Improvement Factor: 3337523027298.930x\n\n=== Simulation Completed === Result saved to: ./fused_result.json\n\n[Program finished]"
  },
  "source": "meta"
}