32K views · 235 reactions | The Universal Approximation Theorem states that a feedforward neural network with a single hidden layer, using a non-linear activation function, can approximate any continuous function on a compact, given enough neurons. | Visual Math+ | Facebook
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Definition of universal approximator
Definition of universal approximator
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aishima on Instagram‎: "‌ قضیه تقریب جهانی (Universal Approximation Theorem) نشون می‌ده که یک شبکه عصبی با فقط یک لایه مخفی و فعال‌سازی مناسب (مثل سیگموید یا ReLU) می‌تونه هر تابع پیوسته‌ای رو با دقت دلخواه تقریب بزنه. اما این تضمین درباره‌ی اندازه‌ی شبکه حرفی نمی‌زنه. برای توابع پیچیده، شبکه‌های کم‌عمق به پهنایی نمایی نیاز دارن، در حالی‌که شبکه‌های عمیق همون توابع رو با عمق بیشتر و پارامترهای بسیار کمتر نمایش می‌دن. حالا چرا شبکه‌های عمیق (deep networks) بهترن؟ چون با اضافه کردن لایه‌ها، پیچیدگ
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