{"id":6247,"date":"2026-04-16T09:06:15","date_gmt":"2026-04-16T14:06:15","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=6247"},"modified":"2026-04-16T09:46:11","modified_gmt":"2026-04-16T14:46:11","slug":"impact-of-target-variable-ranges-on-model-performance","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/impact-of-target-variable-ranges-on-model-performance-6247\/","title":{"rendered":"Impact of Target Variable Ranges on Model Performance"},"content":{"rendered":"<style>.kadence-column6247_2cb227-32 > .kt-inside-inner-col,.kadence-column6247_2cb227-32 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6247_2cb227-32 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6247_2cb227-32 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6247_2cb227-32 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6247_2cb227-32 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6247_2cb227-32{position:relative;}@media all and (max-width: 1024px){.kadence-column6247_2cb227-32 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6247_2cb227-32 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6247_2cb227-32\"><div class=\"kt-inside-inner-col\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"572\" src=\"https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-1024x572.png\" alt=\"\" class=\"wp-image-6248\" style=\"width:800px\" srcset=\"https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-1024x572.png 1024w, https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-300x167.png 300w, https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-768x429.png 768w, https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-1536x857.png 1536w, https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-2048x1143.png 2048w, https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-128x72.png 128w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">1. Analysis of Small Positive Ranges (0 to 0.2)<\/h3>\n\n\n<style>.kadence-column6247_5f62f5-5a > .kt-inside-inner-col{padding-right:var(--global-kb-spacing-xl, 4rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6247_5f62f5-5a > .kt-inside-inner-col,.kadence-column6247_5f62f5-5a > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6247_5f62f5-5a > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6247_5f62f5-5a > .kt-inside-inner-col{flex-direction:column;}.kadence-column6247_5f62f5-5a > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6247_5f62f5-5a > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6247_5f62f5-5a{position:relative;}@media all and (max-width: 1024px){.kadence-column6247_5f62f5-5a > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6247_5f62f5-5a > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6247_5f62f5-5a\"><div class=\"kt-inside-inner-col\">\n<p class=\"wp-block-paragraph\">While a target range of 0 to 0.2 is mathematically valid, it presents several practical challenges in model training and optimization.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.1 Training Speed and Convergence Issues<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Small Loss:<\/strong> Since the discrepancy between the predicted and actual values is minimal, the resulting output of the <strong>Loss Function<\/strong> is also very small.<\/li>\n\n\n\n<li><strong>Small Gradient (Gradient Vanishing):<\/strong> When the loss value is small, the <strong>gradient<\/strong> of the loss with respect to the <strong>weights ($W$)<\/strong> becomes significantly diminished.<\/li>\n\n\n\n<li><strong>Slow Weight Update:<\/strong> Weights are updated according to the formula $W = W &#8211; (\\eta \\times \\text{Gradient})$. If the gradient is too small, the weight updates become negligible.<\/li>\n\n\n\n<li><strong>Slow Convergence:<\/strong> The speed at which weights approach the <strong>minimum (optimal point)<\/strong> slows down drastically, leading to excessively long training times or the model failing to reach an optimized state.<\/li>\n\n\n\n<li><strong>Solution:<\/strong> Apply <strong>Min-Max Scaling<\/strong> to expand the range to [0, 1] during training, then perform an <strong>Inverse Transform<\/strong> (multiply by 0.2) for the final prediction.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">1.2 Loss Function Sensitivity<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>MSE (Mean Squared Error):<\/strong> Since errors are squared, an error of 0.1 becomes 0.01. Small loss values might trigger early stopping prematurely, as the model &#8220;perceives&#8221; it has already converged.<\/li>\n\n\n\n<li><strong>MAE (Mean Absolute Error):<\/strong> In small-scale data, MAE often provides a more intuitive representation of the physical error than MSE.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">1.3 Compatibility with Activation Functions<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sigmoid:<\/strong> While the output range [0, 1] covers 0.2, the model may fail to utilize the non-linear characteristics of the function if values are concentrated in a narrow band.<\/li>\n\n\n\n<li><strong>ReLU\/Linear:<\/strong> In regression, a Linear output is standard. However, logic to prevent negative outputs may be necessary if the target is strictly positive.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">2. Analysis of Negative Ranges (-1 to 0)<\/h3>\n\n\n<style>.kadence-column6247_e958ae-47 > .kt-inside-inner-col{padding-right:var(--global-kb-spacing-xl, 4rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6247_e958ae-47 > .kt-inside-inner-col,.kadence-column6247_e958ae-47 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6247_e958ae-47 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6247_e958ae-47 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6247_e958ae-47 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6247_e958ae-47 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6247_e958ae-47{position:relative;}@media all and (max-width: 1024px){.kadence-column6247_e958ae-47 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6247_e958ae-47 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6247_e958ae-47\"><div class=\"kt-inside-inner-col\">\n<p class=\"wp-block-paragraph\">Targeting a range of -1 to 0 introduces unique constraints, particularly for regression models.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.1 Constraints on Loss Functions<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inapplicability of MAPE:<\/strong> MAPE cannot be calculated because the denominator (target) includes zero or negative values, leading to division by zero or distorted results.<\/li>\n\n\n\n<li><strong>Inapplicability of Log-based Loss:<\/strong> Metrics like RMSLE are undefined for non-positive targets.<\/li>\n\n\n\n<li><strong>Solution:<\/strong> Utilize <strong>MSE<\/strong> or <strong>MAE<\/strong> as the primary loss functions.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.2 Activation Function Mismatch<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sigmoid\/Softmax:<\/strong> Cannot be used as their output range is [0, 1].<\/li>\n\n\n\n<li><strong>ReLU:<\/strong> Cannot be used in the output layer as it zeros out all negative values.<\/li>\n\n\n\n<li><strong>Solution:<\/strong> Use a <strong>Linear<\/strong> output layer or <strong>Tanh<\/strong> (range: -1 to 1) if boundary constraints are required.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.3 Physical Interpretation and Challenges<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">In semiconductor FDC data, negative targets often represent <strong>deltas from a baseline<\/strong> or <strong>log-transformed values<\/strong>. These require careful handling to maintain physical meaning.<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">3. Practical Recommendations (Semiconductor VM\/FDC Context)<\/h3>\n\n\n<style>.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col{padding-right:var(--global-kb-spacing-xl, 4rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col,.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col{flex-direction:column;}.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6247_2fcb2a-e8{position:relative;}@media all and (max-width: 1024px){.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6247_2fcb2a-e8 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6247_2fcb2a-e8\"><div class=\"kt-inside-inner-col\">\n<p class=\"wp-block-paragraph\">For high-precision tasks such as thickness prediction or fault detection:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mandatory Scaling:<\/strong> Always use scaling (Min-Max or Standardization) internally. Learning the difference between 0.1 and 0.2 is numerically more stable for a model than learning the difference between 0.001 and 0.002.<\/li>\n\n\n\n<li><strong>Precision Verification:<\/strong> Ensure the use of <code>float32<\/code> or higher. Minimal value fluctuations can be lost due to precision limitations in lower-bit formats.<\/li>\n\n\n\n<li><strong>Monitor Relative Error:<\/strong> Alongside absolute loss, track <strong>MAPE<\/strong> (for positive ranges) or relative percentage errors to ensure predictions meet actual process specifications.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-theme-palette-13-color\">4. Summary: Does the Target Range Matter?<\/mark><\/h3>\n\n\n<style>.kadence-column6247_6afd51-5e > .kt-inside-inner-col{padding-right:var(--global-kb-spacing-xl, 4rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kadence-column6247_6afd51-5e > .kt-inside-inner-col,.kadence-column6247_6afd51-5e > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column6247_6afd51-5e > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column6247_6afd51-5e > .kt-inside-inner-col{flex-direction:column;}.kadence-column6247_6afd51-5e > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column6247_6afd51-5e > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column6247_6afd51-5e{position:relative;}@media all and (max-width: 1024px){.kadence-column6247_6afd51-5e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column6247_6afd51-5e > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column kadence-column6247_6afd51-5e\"><div class=\"kt-inside-inner-col\">\n<ul class=\"wp-block-list\">\n<li><strong>Theoretically:<\/strong> <strong>No.<\/strong> (The computer treats them as mere numerical values.)<\/li>\n\n\n\n<li><strong>Convergence Speed:<\/strong> <strong>Yes.<\/strong> (Small gradients may result in sluggish learning.)<\/li>\n\n\n\n<li><strong>Evaluation Metrics:<\/strong> <strong>Yes.<\/strong> (Calculating relative errors becomes difficult or skewed.)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<div style='text-align:center' class='yasr-auto-insert-overall'><\/div><div style='text-align:center' class='yasr-auto-insert-visitor'><\/div>","protected":false},"excerpt":{"rendered":"<p>1. Analysis of Small Positive Ranges (0 to 0.2) While a target range of 0 to 0.2 is mathematically valid, it presents several practical challenges in model training and optimization. 1.1 Training Speed and Convergence Issues 1.2 Loss Function Sensitivity 1.3 Compatibility with Activation Functions 2. Analysis of Negative Ranges (-1 to 0) Targeting a&#8230;<\/p>\n","protected":false},"author":4,"featured_media":6248,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","fifu_image_url":"","fifu_image_alt":"","iawp_total_views":0,"footnotes":""},"categories":[56,373],"tags":[],"class_list":["post-6247","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-science-slug","category-feature-engineering-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":0,"sum_votes":0},"jetpack_featured_media_url":"https:\/\/ykim.synology.me\/wordpress\/wp-content\/uploads\/2026\/04\/9x9-grid-red-chairs-in-an-infinite-white-void-scaled.png","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/comments?post=6247"}],"version-history":[{"count":5,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6247\/revisions"}],"predecessor-version":[{"id":6254,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/6247\/revisions\/6254"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media\/6248"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=6247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=6247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=6247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}