{"id":3500,"date":"2023-08-31T11:12:59","date_gmt":"2023-08-31T11:12:59","guid":{"rendered":"https:\/\/neuraldesigner.com\/learning\/higgs\/"},"modified":"2026-08-06T08:48:06","modified_gmt":"2026-08-06T06:48:06","slug":"higgs","status":"publish","type":"learning","link":"https:\/\/www.neuraldesigner.com\/learning\/examples\/higgs\/","title":{"rendered":"Detect the Higgs boson"},"content":{"rendered":"<style>\n.nds{width:100vw;margin-left:calc(50% - 50vw);padding:22px 24px 14px;background:#eee;color:#1b2635;font-family:\"Outfit\",\"Roboto\",Arial,sans-serif}\n.nds *{box-sizing:border-box}.nds-wrap{width:min(100%,1200px);margin:0 auto}.nds a{text-decoration:none;color:#2d799f}\n.nds-executive{margin:0 0 34px;padding:32px;border-radius:20px;background:linear-gradient(135deg,#12354b,#245e80);color:#fff}.nds-executive h2{margin:0 0 12px;color:#fff;font-size:30px}.nds-executive 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12px;color:#12354b;font-size:20px}\n.nds-card pre{margin:22px auto;padding:20px 22px;max-width:760px;overflow-x:auto;border:1px solid #dce5eb;border-radius:14px;background:#f7fafc!important;color:#173246!important;font:13px\/1.55 Consolas,Menlo,monospace}\n.nds-card pre code{padding:0;background:transparent;color:inherit}\n.nds-centered-figure{width:min(780px,100%);margin:24px auto;padding:16px;border:1px solid #dce8ef;border-radius:15px;background:#f8fbfd}\n.nds-centered-figure img{width:100%;max-width:100%;margin:0 auto 12px}\n.nds-figure-full{grid-column:1\/-1;width:min(580px,100%);justify-self:center}\n.nds-flow{display:grid;grid-template-columns:repeat(5,minmax(0,1fr));gap:10px;margin:24px 0}\n.nds-flow div{position:relative;display:flex;min-height:92px;align-items:center;justify-content:center;padding:15px 12px;border-radius:13px;background:#12354b;color:#fff;text-align:center;font-weight:700}\n.nds-flow div:not(:last-child):after{content:\"\u2192\";position:absolute;right:-15px;top:50%;z-index:2;transform:translateY(-50%);color:#56a1c8;font-size:21px}\n.nds-metrics td:nth-child(2),.nds-confusion td{text-align:right;font-variant-numeric:tabular-nums}\n.nds-confusion tbody td:first-of-type{background:#e9f2f8!important;font-weight:700}\n@media(max-width:900px){.nds-flow{grid-template-columns:1fr 1fr}.nds-flow div:after{display:none}}\n@media(max-width:620px){.nds-flow{grid-template-columns:1fr}}\n<\/style>\n<div class=\"nds\" data-science-profile=\"physical-chemical\">\n<div class=\"nds-wrap\">\n<section class=\"nds-executive\">\n<h2>Separate simulated Higgs-signal events from background with a compact neural classifier<\/h2>\n<p>This reproducible benchmark maps 28 normalized event descriptors to a binary classification score. On 2,002 held-out simulated events, the model reaches an ROC AUC of 0.727. The result demonstrates multivariate event ranking; it is not evidence for a particle discovery or a production LHC analysis.<\/p>\n<div class=\"nds-kpis\">\n<div class=\"nds-kpi\"><strong>0.727<\/strong><span>testing ROC AUC<\/span><\/div>\n<div class=\"nds-kpi\"><strong>0.709\u20130.745<\/strong><span>95% AUC confidence interval<\/span><\/div>\n<div class=\"nds-kpi\"><strong>10,012<\/strong><span>simulated events in this subset<\/span><\/div>\n<div class=\"nds-kpi\"><strong>2,002<\/strong><span>independent testing events<\/span><\/div>\n<\/div>\n<div class=\"nds-actions\"><a href=\"#6-validation\">Review the validation<\/a><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-scientific-benchmark-2026.csv\">Download the data<\/a><\/div>\n<\/section>\n<ul class=\"nds-toc\">\n<li><a href=\"#1-scientific-objective\">Scientific objective<\/a><\/li>\n<li><a href=\"#2-data-provenance\">Data and provenance<\/a><\/li>\n<li><a href=\"#3-model\">Model<\/a><\/li>\n<li><a href=\"#4-training\">Training<\/a><\/li>\n<li><a href=\"#5-selection\">Selection<\/a><\/li>\n<li><a href=\"#6-validation\">Validation<\/a><\/li>\n<li><a href=\"#7-inference\">Inference<\/a><\/li>\n<li><a href=\"#8-validity\">Validity<\/a><\/li>\n<\/ul>\n<section id=\"1-scientific-objective\" class=\"nds-card\">\n<h2>1. Scientific objective<\/h2>\n<p>The task is binary classification of simulated proton\u2013proton collision events: rank a benchmark signal process above a simulated top-quark background using reconstructed kinematic and derived mass features. The useful output is a discriminant score for downstream statistical analysis, not a stand-alone statement that an individual event contains a Higgs boson.<\/p>\n<div class=\"nds-value-grid\">\n<article class=\"nds-value\">\n<h3>Event prioritization<\/h3>\n<p>Rank simulated events so analysts can define signal-enriched and control regions.<\/p>\n<\/article>\n<article class=\"nds-value\">\n<h3>Operating-point studies<\/h3>\n<p>Compare signal efficiency with background rejection before selecting an analysis threshold.<\/p>\n<\/article>\n<article class=\"nds-value\">\n<h3>Reproducible benchmark<\/h3>\n<p>Inspect the complete preprocessing, network, split and exported inference implementation.<\/p>\n<\/article>\n<\/div>\n<div class=\"nds-audience\"><span>High-energy physics analysts<\/span><span>Scientific ML researchers<\/span><span>Detector data specialists<\/span><span>Research software engineers<\/span><\/div>\n<div class=\"nds-note\"><strong>Scope.<\/strong> This page reproduces a small educational subset of the HIGGS machine-learning benchmark. A real collider analysis additionally requires detector calibration, event weights, control regions, nuisance parameters, systematic uncertainties and a statistical significance calculation.<\/div>\n<\/section>\n<section id=\"2-data-provenance\" class=\"nds-card\">\n<h2>2. Data and provenance<\/h2>\n<p>The original UCI HIGGS data set contains 11 million Monte Carlo events. This example uses <strong>10,012 rows<\/strong>: 6,008 for training, 2,002 for model selection and 2,002 for testing. The benchmark signal and background were generated with MadGraph5, showered with PYTHIA and passed through the DELPHES fast detector simulation, as documented in the original study.<\/p>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Feature group<\/th>\n<th>Count<\/th>\n<th>Contents<\/th>\n<th>Representation here<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Lepton kinematics<\/th>\n<td>3<\/td>\n<td>pT, pseudorapidity \u03b7 and azimuth \u03c6<\/td>\n<td>Normalized benchmark values<\/td>\n<\/tr>\n<tr>\n<th>Missing transverse energy<\/th>\n<td>2<\/td>\n<td>Magnitude and azimuth \u03c6<\/td>\n<td>Normalized benchmark values<\/td>\n<\/tr>\n<tr>\n<th>Four leading jets<\/th>\n<td>16<\/td>\n<td>pT, \u03b7, \u03c6 and b-tag discriminant per jet<\/td>\n<td>Normalized benchmark values<\/td>\n<\/tr>\n<tr>\n<th>Derived mass features<\/th>\n<td>7<\/td>\n<td>M_jj, M_jjj, M_lv, M_jlv, M_bb, M_wbb and M_wwbb<\/td>\n<td>Normalized benchmark values<\/td>\n<\/tr>\n<tr>\n<th>Target<\/th>\n<td>1<\/td>\n<td>Event = 1 for signal; Event = 0 for background<\/td>\n<td>Binary label<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Subset<\/th>\n<th>Events<\/th>\n<th>Purpose<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Training<\/th>\n<td>6,008<\/td>\n<td>Fit network parameters<\/td>\n<\/tr>\n<tr>\n<th>Selection<\/th>\n<td>2,002<\/td>\n<td>Monitor generalization and stopping<\/td>\n<\/tr>\n<tr>\n<th>Testing<\/th>\n<td>2,002<\/td>\n<td>Final performance estimates<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-figure-grid\">\n<figure><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-event-distribution-2026.png\" alt=\"Pie chart showing 52.9 percent signal and 47.1 percent background events\"><figcaption>The educational subset is nearly balanced: 52.9% signal and 47.1% background. This balance is a benchmark design choice, not the class prevalence in recorded collider data.<\/figcaption><\/figure>\n<figure><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-event-correlations-2026.png\" alt=\"Horizontal bars of univariate correlations between HIGGS inputs and the event label\"><figcaption>The strongest single Pearson coefficient is only 0.156. These univariate associations are descriptive; they are neither causal effects nor multivariate feature importance.<\/figcaption><\/figure>\n<\/div>\n<div class=\"nds-note nds-note--provenance\"><strong>Provenance and units.<\/strong> The physical variables originate from a Monte Carlo simulation chain rather than experimental collision records. The released HIGGS features are normalized, so the numbers in this CSV must not be labelled or interpreted directly as raw GeV measurements. The downloadable CSV and model schema also correct three legacy column-name errors: <code>jet_2_b_tag<\/code>, <code>jet_3_pT<\/code> and <code>jet_4_phi<\/code>.<\/div>\n<\/section>\n<section id=\"3-model\" class=\"nds-card\">\n<h2>3. Model<\/h2>\n<p>The network receives the 28 continuous descriptors through a mean-and-standard-deviation scaling layer. One dense hidden layer contains three tanh neurons, followed by a single sigmoid output named <code>Event<\/code>.<\/p>\n<p>The sigmoid value is a <strong>classification score<\/strong>. No probability-calibration analysis is available in this project, so the value should not be reported as a calibrated probability that an event is signal.<\/p>\n<figure class=\"nds-architecture-figure\"><img decoding=\"async\" class=\"nds-architecture\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-network-architecture-2026.png\" alt=\"Neural network graph with 28 scaled event inputs, three hidden tanh neurons and one sigmoid Event output\"><figcaption>Final compact 28\u20133\u20131 architecture exported by Neural Designer.<\/figcaption><\/figure>\n<\/section>\n<section id=\"4-training\" class=\"nds-card\">\n<h2>4. Training strategy<\/h2>\n<p>The project minimizes a weighted squared error with no regularization. Class weights are 0.9445 for signal and 1.0624 for background, compensating for the small class imbalance. The Quasi-Newton optimizer stops after 221 epochs when the selection error has exceeded its improvement allowance.<\/p>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Training result<\/th>\n<th>Value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Final training error<\/th>\n<td>0.786<\/td>\n<\/tr>\n<tr>\n<th>Final selection error<\/th>\n<td>0.848<\/td>\n<\/tr>\n<tr>\n<th>Epochs completed<\/th>\n<td>221<\/td>\n<\/tr>\n<tr>\n<th>Stopping condition<\/th>\n<td>Maximum selection-error increases<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<figure class=\"nds-centered-figure\"><img decoding=\"async\" class=\"nds-chart-wide\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-training-history-2026.png\" alt=\"Quasi-Newton training and selection weighted-squared-error history over 221 epochs\"><figcaption>The separation between training and selection error is visible and should be monitored when comparing future architectures.<\/figcaption><\/figure>\n<\/section>\n<section id=\"5-selection\" class=\"nds-card\">\n<h2>5. Model selection and baseline<\/h2>\n<p>The project contains configurations for growing-input and growing-neuron searches, but no completed selection sweep is stored in the regenerated output. The three-neuron architecture is therefore reported as the <strong>final compact baseline<\/strong>, not as a demonstrated optimum.<\/p>\n<div class=\"nds-note nds-note--warning\"><strong>Professional baseline still required.<\/strong> Before interpreting gains scientifically, compare the same split and metrics with at least logistic regression and a gradient-boosted tree, then repeat across several seeds or cross-validation folds.<\/div>\n<\/section>\n<section id=\"6-validation\" class=\"nds-card\">\n<h2>6. Scientific validation<\/h2>\n<p>All headline metrics below come from the untouched 2,002-event testing subset. The ROC analysis reports an AUC of 0.727 with a 95% confidence interval from 0.709 to 0.745.<\/p>\n<div class=\"nds-table-scroll\">\n<table class=\"nds-metrics\">\n<thead>\n<tr>\n<th>Testing metric<\/th>\n<th>Value<\/th>\n<th>Interpretation<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>ROC AUC<\/th>\n<td>0.727<\/td>\n<td>Moderate ranking discrimination<\/td>\n<\/tr>\n<tr>\n<th>Accuracy at threshold 0.50<\/th>\n<td>67.5%<\/td>\n<td>1,352 of 2,002 events classified correctly<\/td>\n<\/tr>\n<tr>\n<th>Precision at threshold 0.50<\/th>\n<td>71.5%<\/td>\n<td>Signal fraction among predicted-positive events<\/td>\n<\/tr>\n<tr>\n<th>Signal efficiency at threshold 0.50<\/th>\n<td>66.7%<\/td>\n<td>724 of 1,086 simulated signal events retained<\/td>\n<\/tr>\n<tr>\n<th>Background rejection at threshold 0.50<\/th>\n<td>68.6%<\/td>\n<td>628 of 916 simulated background events rejected<\/td>\n<\/tr>\n<tr>\n<th>F1 score at threshold 0.50<\/th>\n<td>69.0%<\/td>\n<td>Balance of precision and signal efficiency<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3>Confusion matrix at the default 0.50 threshold<\/h3>\n<div class=\"nds-table-scroll\">\n<table class=\"nds-confusion\">\n<thead>\n<tr>\n<th>Actual \/ predicted<\/th>\n<th>Signal<\/th>\n<th>Background<\/th>\n<th>Total<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Signal<\/th>\n<td>724<\/td>\n<td>362<\/td>\n<td>1,086<\/td>\n<\/tr>\n<tr>\n<th>Background<\/th>\n<td>288<\/td>\n<td>628<\/td>\n<td>916<\/td>\n<\/tr>\n<tr>\n<th>Total<\/th>\n<td>1,012<\/td>\n<td>990<\/td>\n<td>2,002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-figure-grid\">\n<figure class=\"nds-figure-full\"><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-roc-2026.png\" alt=\"ROC curve for the HIGGS testing subset with area under the curve 0.727\"><figcaption>At the ROC tool&#8217;s balanced operating point, threshold 0.49 gives 67.9% signal efficiency and 67.7% background rejection. The confusion matrix uses the default 0.50 threshold, so its percentages differ slightly.<\/figcaption><\/figure>\n<\/div>\n<div class=\"nds-note\"><strong>Scientific interpretation.<\/strong> The model ranks signal above background better than chance, but the overlap is substantial. The AUC and threshold metrics characterize this simulated benchmark only; they do not establish discovery significance, expected limits or performance on recorded data.<\/div>\n<\/section>\n<section id=\"7-inference\" class=\"nds-card\">\n<h2>7. Inference and reproducibility<\/h2>\n<p>A credible inference workflow validates the 28-feature schema, applies the exported preprocessing and model, stores the score alongside the event identifier and model version, and lets the physics analysis define score regions. The score is one input to a statistical procedure, never the final scientific conclusion.<\/p>\n<div class=\"nds-flow\">\n<div>Reconstructed event features<\/div>\n<div>Schema and range checks<\/div>\n<div>Neural classification score<\/div>\n<div>Signal and control regions<\/div>\n<div>Statistical analysis with systematics<\/div>\n<\/div>\n<div class=\"nds-note\"><strong>Operating-point example.<\/strong> If an exploratory study prioritizes a balanced compromise, the ROC tool suggests a threshold of 0.49, retaining 67.9% of simulated signal while rejecting 67.7% of simulated background. A real analysis would optimize a physics objective such as expected significance or exclusion sensitivity and include event weights and nuisance parameters.<\/div>\n<h3>Reproduce the calculation<\/h3>\n<p>The Python package contains the corrected 28-input export, an explicit ordered schema and a README. The Neural Designer project preserves the split, trained parameters and regenerated analysis. The repaired Python export was executed over all 2,002 testing events and reproduced the Neural Designer confusion matrix exactly, with AUC 0.727335.<\/p>\n<pre><code>from model import NeuralNetwork\n\nmodel = NeuralNetwork()\nscore = model.calculate_outputs(event_features)[0]<\/code><\/pre>\n<div class=\"nds-downloads\"><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-python-model-2026-v2.zip\">Download Python model (ZIP)<\/a><br \/>\n<a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-neural-designer-project-2026-v2.zip\">Download Neural Designer project (ZIP)<\/a><br \/>\n<a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/higgs-scientific-benchmark-2026.csv\">Download corrected data (CSV)<\/a><\/div>\n<\/section>\n<section id=\"8-validity\" class=\"nds-card\">\n<h2>8. Validity, uncertainty and limitations<\/h2>\n<ul>\n<li><strong>Simulation-to-data transfer is untested.<\/strong> MadGraph5, PYTHIA and DELPHES cannot represent every detector and modelling uncertainty present in recorded data.<\/li>\n<li><strong>This is a small educational subset.<\/strong> It does not use the canonical large-scale HIGGS benchmark split, and results can vary with the sampled rows and random partition.<\/li>\n<li><strong>Thresholds are analysis-dependent.<\/strong> Class balance and equal-error operation do not encode the background rates, event weights or costs of a collider analysis.<\/li>\n<li><strong>Calibration is absent.<\/strong> The sigmoid score has not been checked with reliability curves, Brier score or calibration on independent data.<\/li>\n<li><strong>Architecture optimality is unproven.<\/strong> No stored completed model-selection sweep or classical baseline comparison supports the final three-neuron choice.<\/li>\n<li><strong>Uncertainty is incomplete.<\/strong> The AUC confidence interval covers test-sample uncertainty only; systematic uncertainties, nuisance parameters and analysis significance are outside this example.<\/li>\n<\/ul>\n<\/section>\n<section id=\"references\" class=\"nds-card\">\n<h2>References<\/h2>\n<ul>\n<li><a href=\"https:\/\/archive.ics.uci.edu\/dataset\/280\/higgs\">UCI Machine Learning Repository: HIGGS data set<\/a> (DOI: <a href=\"https:\/\/doi.org\/10.24432\/C5V312\">10.24432\/C5V312<\/a>; CC BY 4.0).<\/li>\n<li>P. Baldi, P. Sadowski and D. Whiteson, <a href=\"https:\/\/www.nature.com\/articles\/ncomms5308\">Searching for exotic particles in high-energy physics with deep learning<\/a>, Nature Communications 5, 4308 (2014).<\/li>\n<li><a href=\"https:\/\/home.cern\/science\/physics\/higgs-boson\">CERN: The Higgs boson<\/a>, including the 4 July 2012 discovery announcement.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<\/div>\n","protected":false},"author":13,"featured_media":2185,"template":"","categories":[29],"tags":[],"class_list":["post-3500","learning","type-learning","status-publish","has-post-thumbnail","hentry","category-examples"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Detect the Higgs boson<\/title>\n<meta name=\"description\" content=\"This example contains simulated data, provided by the ATLAS experiment at CERN, that physicists use to optimize the analysis of the Higgs Boson.\" \/>\n<meta name=\"robots\" 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